Hearing Harmony: Toward a Tonal Theory for the Rock Era

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Acknowledgments Sometimes the chords got to be an obsessionВ .В .В . —John Lennon While a few of the ideas in this book began to take shape well before my formal training in music theory, my written work on this topic started with a paper on the harmony of Radiohead I wrote as a doctoral student at Columbia University, a paper that eventually led to my dissertation “Listening to Rock Harmony” (2007). Although the current monograph is a new project, written from scratch, it is indeed based on my doctoral work, and so I must begin by acknowledging the efforts and insights of my Columbia theory mentors—Joseph Dubiel, Ellie Hisama, David Cohen, Fred Lerdahl, the late Jonathan Kramer—all of whom embodied a terrifically and terrifyingly high standard of precision in writing style and argumentation to which I have only ever been able to aspire. For helping make the dream of this book a reality, I am in the debt of Christopher Hebert at the University of Michigan Press, who saw in my dissertation the potential for a book well before I did, and of the Tracking Pop series editors Lori Burns, John Covach, Jocelyn Neal, and Albin Zak, who, with Chris, deftly guided the manuscript through the gauntlet of peer review. After Chris left the press for greener pastures, Mary Francis handled the reins with great skill, and with Kevin Rennells steered the monograph toward completion. Drew Bryan did an admirable job copyediting this dense work. I am also very grateful to Sergio LasuГ©n for his careful reading of an early version of the manuscript and for his painstaking improvements of many of my transcriptions. While not exactly duplicating any of my previously published articles, this text does present some ideas and examples that have already appeared in “Between Rock and a Harmony Place” (Popular Music Worlds, Popular Music Histories: Proceedings of the Biennial Conference of the International Association for the Study of Popular Music, 2009, 83–91), “Transformation in Rock Harmony: An Explanatory Strategy” (Gamut 2, no. 1, 2009, 1–44), “Rockin’ Out: Expressive Modulation in Verse-Chorus Form” (Music Theory Online 17, no. 3, 2011), and “Definitions of вЂChord’ in the Teaching of Tonal Harmony” (Dutch Journal of Music Theory 18, no. 2, 91–106). Page x → Walter Everett, whose own work displays an awe-inspiring knowledge of the popular repertory and covers every major issue relevant to the serious study of pitch in this music, has been my primary model as a scholar of popular music, as well as a fountain of encouragement and friendly criticism. Allan Moore, Ken Stephenson, and Philip Tagg, through their own pioneering monographs on popular music, have also greatly influenced my work; Allan and Ken personally have been supportive of my own career, for which I am ever grateful. My Rutgers colleagues and friends Rufus Hallmark and Nancy Rao have been, and remain, tremendous sources of wisdom and encouragement in matters musical and professional. Joshua Walden, over many years, has provided much-needed levity and skepticism within the all-too-serious and self-satisfied confines of the scholarly world. Anton Vishio graciously offered his time and talents in helping me prepare for the horror show that is the academic job market. Upon acquiring gainful employment at the Mason Gross School of the Arts, Rutgers, I was fortunate to receive a semester’s sabbatical in the fall of 2010, during which time I wrote a significant chunk of this text. Additionally, funds from the Rutgers Chancellor’s Scholar program directly supported this project. I am also honored to acknowledge the following people for their various contributions, large and small, direct and indirect, in their roles as teachers, mentors, colleagues, editors, hosts, and sources of inspiration: Robert Aldridge, Wayne Alpern, Joseph Auner, David Carson Berry, Nicole Biamonte, Giorgio Biancorosso, David Neal Brown, Guy Capuzzo, Jennifer Conner, Trevor de Clercq, Daniel DiPaolo, David Easley, Andrew Flory, Matthew Gelbart, Louis Giannetti, Perry Goldstein, Marion Guck, William Guerin, Daniel Harrison, Eduardo Herrera, Dave Headlam, Kevin Holm-Hudson, Patricia Howland, Brian Kane, Steven Kemper, Andrew Kirkman, the late Steve

Larson, Judith Lochhead, Yonatan Malin, Henry Martin, Nancy Murphy, Scott Murphy, Richard Nelson, Drew Nobile, Shaugn O’Donnell, Brad Osborn, Steven Rings, Frank Samarotto, Janna Saslaw, Jonathan Sauceda, John Shepard, Elaine Sisman, Daniel Sonenberg, Mark Spicer, George Stauffer, Anna Stephan-Robinson, the late Steven Strunk, David Temperley, Peter Winkler, Robert Zierolf, Ricardo Zohn-Muldoon, and my students at the University of Cincinnati, Stony Brook University, Barnard Pre-College, Columbia University, and Rutgers University. I wish to thank my father, Thomas Doll, for encouraging me in everything I ever wanted to do, and my mother, Debra Clark, for making me try all the things I didn’t want to do. Lastly, my deepest gratitude goes to Zoe Browder Doll and little Rosemary, who had to endure my daily insanity while I wrote this book.

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Introduction Between Rock and a Harmony Place In 1990, at the age of thirteen, I bought a newly published book by William J. Dowlding entitled Beatlesongs. By this point, I was already a great fan of the Fab Four, and I was looking to find out everything there was to know about them. Reading this book opened my eyes to a great many things, not only to many details of the Beatles’ biography, but also, and much more importantly, to several aspects of the band’s music. Chief among these musical insights was a statement by John Lennon, a brief quotation from one of his last major interviews: [“If I Fell” is] my first attempt at a ballad proper. That was the precursor to “In My Life.” It has the same chord sequences as “In My Life”: D and B minor and E minor, those kind of things [sic]. (Dowlding 1989, 69) It is now difficult for me to convey just how perplexing and intriguing I found this quote when I first read it. At the time, I had no real background in music theory, and I did not understand how the songs “In My Life” (1965) and “If I Fell” (1964) could in any way be considered musically “the same,” even via some magical, abstract things called “chord sequences.” My curiosity was piqued; I set out immediately to learn as much as I could about chords. The following text represents the culmination of my studies to date. Hearing Harmony is, to my knowledge, the first academic monograph devoted entirely to chords in the popular sphere. Yet it is no mere inventory of progressions (Lennon’s “sequences”) or survey of standard chordal theory; rather, it offers an original philosophical-psychological harmonic theory, a large set of rigorously defined and interrelated concepts that facilitate, and are facilitated by, open-minded, self-reflective listening. Readers are invited to fetishize aurality itself, in an attempt to put into words some of the multilayered experiences available to us when we sit down, tune in, and think Page 2 →about what we hear. (And sometimes, about what we don’t hear.) For all its ultimate complexity, the theory to be presented rests on a relatively simple premise: the more informed and attentive our listening, the richer our experience, a sentiment often expressed about Western classical music (eighteenth- and nineteenth-century European concert music) but too frequently absent in academic studies of popular repertories. Indeed, there is an old saying that all popular music is “just the same three chords.” There is no denying that the harmony of popular music can often be frustratingly, or gratifyingly, austere and repetitive.1 But for listeners whose sights are set higher, on richer and more varied encounters, this repertory will not disappoint. Hearing Harmony engages the extremes of this experiential spectrum, from single-chord blues, through fourchord pop, to the harmonic intricacies of prog. Popular-music harmonic practice is so astoundingly diverse, in fact, that any attempt to verbalize it—even an entire monograph devoted exclusively to it—is destined to come up short. Yet the rewards for trying are abundant. Not only does close study of popular music allow us to bask in its veritable kaleidoscope of harmonic colors, it also can facilitate the discovery of important reasons why we find certain songs so thrilling, so moving, or so evocative of a particular time, place, or community. Moreover, given that this repertory has increasingly become a defining feature of global popular culture and an integral part of our personal and communal identities, an understanding of how we perceive this music brings us closer, in a certain way, to an understanding of how we perceive each other in relation to ourselves. This book focuses on the harmonic practice of North American and British popular music of what I call the “rock era”: roughly 1950 to the present. This period of popular music contains within it a wide range of different styles, and readers might naturally wonder just how we can hope to say anything meaningful about them all.2 To be sure, many of these styles could support their own individual harmonic theories, as scholars of heavy metal have amply shown.3 Nevertheless, there are great benefits to a large-scale approach: our global view will allow us to see the numerous harmonic similarities (as well as some of the dissimilarities) across all these styles,

and will enable us to formulate a substantial theory that is generalized enough to accommodate songs and artists that do not clearly reside in one camp or another (stylistic promiscuity being one of the rock era’s defining characteristics). The title of this book reflects this all-inclusive attitude toward the harmonic practice of this overwhelmingly massive repertory: to hear harmony is not simply to listen to chords, but to hear agreement in the artistic voices of distinct, and even seemingly disparate, musical traditions. While somewhat arbitrary, 1950 is a nice round date that fulfills the Page 3 →important role of separating popular music of the rock era from that of the jazz era. This separation is an oversimplification, of course: jazz thrived well into the 1960s and continues to maintain a notable, if more limited, presence to this day; and rhythm’n’blues, a style located squarely within the rock era, has been around at least since the 1940s (known then as “race music”); on the other side, the actual term “rock” (as opposed to “rock and roll” or “rock’n’roll”) did not gain prominence until the mid-1960s. Still, the culture of popular music as a whole changed drastically with the arrival of rhythm’n’blues and rock’n’roll around the middle of the century, a change the likes of which, in my opinion, we have not seen since with any new style of music (although the strongest contender so far would undeniably be hip hop, even as it samples earlier rock-era tracks). Additionally, and more importantly, the harmonic language of the jazz era strikes me as fundamentally different from that of the rock era overall, at least with regard to favored sonorities—jazz-era seventh chords versus rock-era triads and power chords. (And so, while “rock” will serve primarily as a chronological designation, it still will also convey information about style at a very broad level.) Jazz-era songs will not be considered in this book beyond those that influenced later music, and jazz-styled songs that were recorded during the rock era will likewise not receive much attention unless they are stylistic hybrids (such as jazz-rock fusion) or recorded by performers known principally as rock musicians. The larger question of defining “popular music, ” of which rock and jazz are types, will be answered here by considerations of style and transmission specific to the era. While there are significant exceptions, rock-era popular music comprises songs (as opposed to purely instrumental works) that are characterized by both a high degree of harmonic repetition and the use of recordings as the chief mode of musical distribution. Certain musical traditions, including film music and musical theater, do not fit neatly within or without “rock-era popular music”; a few examples in these areas that are indeed germane to the topic of rock-era harmony will be discussed. But why use the term “rock” specifically to account for an entire era? To some skeptical readers, the use of “rock” in this manner might seem ethically or even morally suspect, perhaps representing a kind of musictheoretical imperialism that redefines diverse cultural forms in accordance with the personal tastes of the author, a white, heterosexual, American male. Indeed, the term “rock” in many other contexts refers to an individual style of late twentieth-century popular music, one that includes artists such as the Rolling Stones, Joan Jett, and Lenny Kravitz, but not their contemporaries Menudo, Rihanna, or John Denver. By putting all these dissimilar artists into one basket, this book does open itself up to these kinds of criticisms. Like all Page 4 →broad labels, “rock” has its advantages and disadvantages, but in my opinion it just is too rhetorically convenient not to use. “Popular music,” “vernacular music, “commercial music”; these phrases are both unwieldy and nebulous. “Rock,” by contrast, is only one word, one syllable, and valid as a noun and an adjective. The only other viable term that shares all these virtues is “pop,” but “pop” dates back at least to the middle of the nineteenth century, denoting styles that are well outside the repertory in question, whereas “rock” is tied specifically to the second half of the twentieth century onward (just as “jazz” is attached to the twentieth century’s first half). Using “rock” to denote the diverse assortment of post1950 British-American popular music is at least as reasonable as using the time-honored rubric “romantic” to group Chopin’s brief, intimate French nocturnes together with Wagner’s monumental, bombastic German Ring-cycle operas, and likewise just as reasonable as using “baroque” for both Monteverdi’s proto-operatic Italian L’Orfeo and Bach’s solo-contrapuntal German cello suites. “Rock” may not be a perfect label, but it is perfectly practical. Its succinctness will be taken full advantage of hereafter, by my dropping the “era” and thus referring to the entire repertory simply as rock. The examples of rock that lie ahead thus represent the work of a vast number of culturally, ethnically, geographically, temporally, and sonically distinct artists. In preparation for this monograph, I have listened to tens

of thousands of songs, deliberately seeking out styles and musicians I previously did not know. Not every relevant style, let alone every major artist, can be represented here with an example, but I include as many as are feasible. Readers will encounter several hundred unique recordings from punk, funk, folk, surf, soul, grunge, disco, emo, country, reggae, and new wave, among many others. The primary criterion for the inclusion of certain songs over others is their relevance to the points at hand; a secondary criterion is the degree to which they provide stylistic diversity; a tertiary criterion is the degree to which they provide personal diversity. Such aspirations of representation aside, this book’s concentration on commercially successful recordings from the past seven decades also has the unfortunate side effect of reflecting the repertory’s absolute dominance by white and black male musicians; the industry’s historical paucity of female musicians, as well as musicians of other races and ethnicities, inevitably infects the following pages. I must also acknowledge my own musical biases: a scholar can never fully suppress his or her personal preferences (or perhaps even recognize all these preferences), so I must ask for readers’ indulgence concerning the overabundance of British Invasion and nineties alternative tracks, along with any other surplus representatives. Needless to say, just because one song or style happens to be Page 5 →mentioned does not necessarily mean I think it is more aesthetically valuable than any other, and just because another song or style remains unmentioned does not mean it is unmentionable. It should also go without saying that by discussing harmony in this wide assortment of styles I am in no way implying that harmony is equally important in understanding each one. For those styles in which harmony plays less of an interesting role in the overall aesthetic, the concepts developed in this book will be less applicable. This strategy does, then, end up favoring styles for which harmony is central, but this inevitable outcome should not encourage us to ignore chords in any style. I strongly believe that the study of a given musical style should not be limited to a vantage point that highlights the style’s most significant features as determined by insiders (what we might call the “insiders only” rule); on the contrary, outside perspectives should always be welcome, to the extent that any sort of separation of emic (insider) from etic (outsider) approaches is desirable or even possible. I personally have great difficulty accepting a simplistic divide between the hearings of insiders and those of outsiders; as a professional music theorist reared exclusively on rock music, I would seem to be both inside and outside simultaneously. No doubt, there are people who consider themselves part of certain groups and not others, but an evaluation of the applicability, not to mention the validity, of certain hearings that is based on these kinds of divisions marginalizes the hearings of anyone who does not fit neatly into one of the two camps with regard to any particular body of music, wherever we decide boundaries could be usefully drawn. This line of thinking leads to the tricky question of how the proposed theory relates to the average fan or to the musicians themselves who wrote, recorded, and continue to perform this music. There is a short answer and a long answer to this question. The short answer is that there is no real relation at all, or at least that this relation is not of immediate concern. This book does not attempt to summarize an average hearing (whatever we may define that to mean) nor try to discover or articulate authorial intentions. The goal of Hearing Harmony is selfish: it is to attain the richest possible listening experience for ourselves. The word “hearing” in the book’s title, even when taken in its less grandiose sense, specifies an activity beyond mere listening. It is a form of focused aural attention empowered by our training and bounded only by the limits of our musical imagination. The long answer to the question is that the relation is quite complicated. I stand firmly by the belief that we as listeners hear chords—we experience their presence—whether we know it or not. We respond to their inherent acoustical properties, to their juxtaposition with melody and rhythm and timbre and Page 6 →lyrics, to their relationships with chords we have heard in the past or will hear in the future or that we will never hear and can only imagine. Lay audiences may not call them “chords,” and they may not be able to isolate portions of the auditory signal as harmonic versus timbral versus anything else. Still, an ability to understand a language does not require conscious knowledge of its grammar; an appreciation of a film is not predicated on one’s awareness of its editing techniques or mise-en-scГЁne. Rather, linguistic and artistic conventions are absorbed by lay audiences subconsciously. This “implicit learning” (as it is often called in psychology) is no less applicable to listeners of rock.4 To be sure, listening experiences can differ widely, but generally speaking, to experience rock music is, on some level, to perceive harmony. Yet it is equally true that the kind of analytical listening I am promoting in this book “seems to reorder the

prominence of aspects of aesthetic experience” (as Mark DeBellis has put it) and can sometimes feel “more like alertly following a train of thought than like appreciating the qualities of something” (as Joseph Dubiel has observed).5 The act of hearing harmony (in the present, technical sense) partially dictates which musical objects and effects are foregrounded and which are backgrounded. A full discussion of all the numerous ways rock music affects its listeners would necessarily give considerable weight to rhythm and timbre and overall groove (of which harmony is surely a part); by concentrating on pitch versus nonpitch elements, I do not imply any position concerning the relative prominence of, say, harmony over rhythm across all possible listening experiences (just as I do not insinuate that harmony is equally significant in all styles). There are various kinds of experiences any single listener can undertake, which is the reason why the long answer to the question of relevancy is so long: for average fans and rock musicians, the proposed theory is as relevant as they care for it to be. If our stated objective is the richest possible experience of harmony, then it is important that we not be restricted by considerations of whether other people would approve of our results.6 Indeed, it is almost guaranteed that many other people would not, if only because of the great demands the present undertaking makes on our ears and minds. Effortless simplicity, so the conventional thinking goes, is the cornerstone of that most virtuous of virtues: expressive authenticity. “Music is such a beautiful innocent thing for me,” Sir Paul McCartney has said, “that I don’t want it ever to smack of homework, that would ruin it all.”7 There is certainly nothing wrong with letting the sounds pour out of us, or wash over us. But these tactics will not gain us access to all the subtleties the music has to offer. If we want to acquire as many different kinds of listening options as we can—so that we can pick and choose which ones we care to engage with at any given point—then we must put in some real work. Page 7 →But it will take more than sheer effort to convert the abstract goal of maximizing experiential options into a concrete strategy for dealing with actual music. It will also require some difficult decisions. Consider the issue of which musical standards should be brought to bear on this repertory. Most readers of this book, even those whose interests lie primarily in rock, will have some background in the harmony of prerock traditions, to wit, Western classical music and, probably to a lesser degree, jazz. This background cannot help but make a major impact on the development of our ideas about rock, even if we are also fluent in rock as listeners, performers, and songwriters. The question is: To what extent do we want to address someone hearing, say, Bon Iver as relating to Beethoven? If we wish to let the rock chordal practice “speak for itself,” then our classical education puts us in an unenviable starting position: between rock and a harmony place. Many scholars (see the bibliography) have tried to come to terms with rock harmony in original ways that avoid forcing upon it any theoretical models that are conceptually inappropriate, especially those models that would treat the music simply as a watered-down version of the Western classical repertory. The degree of variation in these scholars’ approaches is quite striking, particularly with regard to their views on the proper relationship between classical tonal and rock tonal theory. (This is a separate issue from the historical relationship between classical tonal and rock tonal practice.) My own viewpoint is that theories of classical and rock harmony can relate in multiple ways, depending on the purposes to which those theories are put. Those purposes, however, should be made absolutely clear from the start: in this text, the goal is to derive a tonal theory out of rock, as opposed to using classical tonal theory as a jumping-off point into rock. To be sure, there is no theory of rock harmony in existence that abstains completely from using some inherited concepts (including some from classical tonal theory) as a point of departure; “harmony” itself is an inherited construct, not to mention other terms found in this text such as “scale, ” “triad,” “pitch,” “note,” and even “music.” Inherited theory, once it is learned, can never be erased entirely, so we are talking purely about matters of degree here.8 Simply put, Hearing Harmony attempts to minimize its reliance on inherited theory as much as is practical. While this text will engage relevant theoretical scholarship, it will also scrutinize and rework several conventional, basic theoretical concepts, including some that are regularly used by the rock community, most notably “key” and “mode.” This book will even pursue a few ideas that will turn out to be untenable, all in the interest of exploring the complete range of our theoretical potentialities. A combination of inherited, reimagined, and newly formulated concepts and terms will work in unison to give the fullest possible sense of what rock harmony can sound Page 8 →like when heard. (For this reason, readers are encouraged not to skip ahead to later chapters without devoting some time to the more basic, earlier concepts, even those readers well conversant in Western classical theory.) One more technical term that we cannot get very far without, and which I thus must immediately define, is

“harmony.” In rock parlance, “harmony” typically denotes backing vocal parts that feature different pitches from the lead melody. It also can serve as a synonym for “chord,” referring to an actual multitone sonority (or arpeggiated sonority) played by keyboardists and guitarists or, more commonly, to an abstracted representation of the notes of such a sonority. For a classical musician, “harmony” additionally denotes the succession of many such abstractions of groups of notes, a kind of melody of chords. This last meaning, which in rock parlance is usually referred to as “the chords” or “the changes,” is how the term has been used so far in this introduction, and it will be the principal way it will be meant throughout this book. That said, I will also use “harmony” to indicate a specific sonority or abstraction itself, because I will need to refer to these specifics and abstractions so often that relying solely on the word “chord” would render the prose unbearably monotonous. Context will render their meanings clear. And when I do refer to individual “chords” (“harmonies,” “sonorities”), I will not limit myself to the notes in the instrumental accompaniment; all notes in a musical texture, including those of the lead and backing vocals, can participate in the articulation of a chord. This means that composite sonorities made up of individual lines are potentially just as much chords as are those played in their entirety by a single instrument (but more on this in the coming chapters). The chapters ahead concentrate on four major aural qualities of rock harmony: function, schema, transformation, and ambiguity. (All qualities to be discussed are defined in Appendix A.) These chordal qualities—or harmonic effects—result from the interaction of certain kinds of chords within certain kinds of melodic, rhythmic, textural, timbral, and extramusical contexts. Such interaction determines, for instance, whether a chordal riff is tonally centered or tonally ambiguous, whether it sounds aggressive or playful or sad, whether it seems to evoke an earlier song using a similar series of chords, and so on. Bringing to light the precise aural mechanics of chords as they operate within their assorted contexts, in order to allow us the choice of focusing our aural attention on these mechanics, is the main task at hand. Some brief explanation of the word “effect” is in order, as it will inhabit nearly every page of this monograph. By “effect,” and its synonym “quality,” I simply mean the experiential impression of a sonic object. Simpler than the philosophical term “quale” (plural: “qualia”), “effect” comes most directly from that giant of tonal theory Heinrich Schenker,9 although hopefully without Page 9 →any substantial conceptual baggage to carry. This book’s persistent reference to “effects” as compared to its relative downplaying of harmonic “objects” (or “structures”) is intended to keep the focus at all times on the listening experience itself, as well as to facilitate engagement with multiple, and even contradictory, interpretations of presumably fixed aural stimuli, whether these differing interpretations be between different listeners’ experiences or contained within a given individual’s own complex encounters with the music. This said, the fundamental distinction between “effects” and “qualities” on the one hand and “objects” and “structures” on the other will itself be reevaluated throughout the book, in the interest of fully exploring all the possible things one might consider part of the actual experience of hearing harmony. Methodologically, the book’s content emerges out of a combination of two distinct types of activities: in-themoment, focused listening; and slow, meticulous analysis of a structural and historical kind. The latter strategy would seem to need little justification in a scholarly setting, but the former is a potential minefield. The focused listening comprises my, the author’s, own personal aural introspection, informed by nearly forty years of engagement with the repertory as a keyboardist, guitarist, songwriter, and most recently scholar and pedagogue. Keeping in mind this individualized basis for the analytical claims is important, especially in light of two aspects of the language to be used in this book, aspects that might cloud this personal core. The first is that I will write about music doing various things. These supposed actions are of course metaphorical; as listeners, we effortlessly project agency onto the audio signal. Projections of this sort, along with other occasional, colorful descriptions of recordings, will help liven up the otherwise monotonous character inherent to music-theory prose. But it is imperative that readers remain cognizant of the fact that the music never does but rather simply is, lest we lapse into thinking we as listeners are merely witnesses to, and not vital participants in, our experiences. Excessive musical agency can encroach on the room we make for ourselves in our experiential stories; readers make choices that affect their hearings and that cannot be reassigned to the audio signal. (This threat will be diminished somewhat by the consistent use of the terms “effect” and “quality,” another of their benefits.)

The second aspect is that this book will, once past this introduction, refer to the listening subject as the authorial “we.” “I” would be a more literally correct word, because the author can really only speak for himself, and indeed there will be times when the author necessarily must make this distinction. But there are compelling reasons to avoid “I” and “my” overall. For one thing, “I” is easily confused with Roman numeral I, which will become an omnipresent symbol starting in chapter 2. For another, the plural pronouns will Page 10 →(I hope) sound more inclusive and inviting and less lecture-like, especially to those readers without an extensive background in the challenging technical vocabulary of Western music theory. A potential downside to using “we” and “our” is that the author might be perceived as trying to homogenize all his readers in an attempt to pre-empt any differing opinions. Nothing could be further from the truth; the intention here is that “we” and “our” be understood to indicate shared ownership, that this theory is not just the author’s but also the reader’s. The reader is, after all, a collaborative participant in any and every theory’s acceptance and dissemination. Furthermore, any author would be foolish to think readers will embrace every facet of a theory of this size; I fully expect my audience to take what they like, discard the rest, and improve upon it all. But there is another, more fundamental problem at hand: only an individual person knows what she hears and how she hears it, and even this self-knowledge can be faulty. Even though our aural experiences derive from a mix of objective and subjective forces, the latter are subjective in the extreme, meaning they belong solely to individual subjects. We can talk to one another about our experiences, and we can make guesses about other people’s experiences based on so-called hard evidence (whether gathered via ethnography or scientific experimentation), but all this is a very different thing from having access to the experiences themselves. This impenetrable barrier not only prevents the author from knowing what his readers are truly hearing, it also prevents the author from being able to fully understand (let alone articulate) his own experiences, because even the raw data of the author’s hearings must be construed by the author himself through the filter of a rational framework to get them down on paper (or screen). And this is not even to get into the very real issue of any individual person being able to hear a song in different ways at different times (this issue will, however, emerge in the following chapters). We descend swiftly down a rabbit hole of unsolvable philosophical problems when we try to be precise about how any one person’s experiences and how they can relate to any other’s. As Friedrich Nietzsche famously wrote, “Rational thought is [itself] interpretation according to a scheme that we cannot throw off.”10 But still, even if our attempts at communicating with each other about our experiences represent an endeavor ultimately doomed to fail, one can find value in the attempts. Despite any discrepancies between our hearings, I trust most of my interpretive claims will at least resonate with readers, and I am hopeful this text will be successful in conveying some of the richness—and perhaps even some of the pleasure—of listening to rock harmony in a serious, educated, open-minded, self-reflective way. So long as we argue in good faith, disagreement can only bring us closer to the truth. Page 11 →

Hearing with Our Eyes, Reading with Our Ears Rock is a recorded art. Live performance is also, of course, an important part of its tradition, but ever since the stunning studio work of the Beach Boys’ Pet Sounds and the Beatles’ Revolver, both released in the summer of 1966, rock musicians have become increasingly oriented toward making recordings, many of these featuring remarkably complex textures created through the use of highly sophisticated audio-signal processing, multitrack mixing, and mastering techniques, often close to impossible to reproduce in their entirety live on stage. This distinguishes rock from essentially every other repertory that came before it (notwithstanding electronic classical music). For music scholars, rock’s recorded format alleviates a major problem inherent in the analysis of Western classical music, namely the imagining of an aural object (sound) from a written one (score), realizing the music with one’s own hypothetical details of phrasing, tone, and textural balance that can then go on to influence the claims made about (for instance) tonal structure. When engaging a rock recording, by contrast, we are dealing directly with a sonic object; no hypotheticals need come between us and the music. And yet rock’s ontology also creates various problems for a study of this kind. Among the more mundane issues is bibliographic style. Many of the recordings to be discussed were originally released as single 45s during

the 1950s and 1960s, but a listing of the original distribution information would not likely help readers in obtaining the recordings for the purposes of listening to harmony, not when one can simply stream or download digital copies from Internet sources (often for free). Accordingly, the recordings cited in this book will be identified only by title, performer name(s), and, for comparative purposes, the year the recording was originally released (which is not necessarily the year the performance was recorded). When referring to a musical agent other than the music itself, I will generally refer to the recording artist as the only one doing things in the music, unless there is some other major figure worth identifying (whether in composing, performing, mixing, etc.); this rhetorical tactic may appear to tacitly endorse a naive notion of headliner auteurism, but there is simply no room in this text to consistently account for the teams of individuals and larger social machinery that enabled, controlled, and facilitated the production, distribution, and consumption of the hundreds of rock recordings to be cited. Furthermore, the terms “recording,” “track,” “performance,” and “song” will in general be treated synonymously, except in those cases in which their different shades of meaning must remain distinct, as when engaging transformational harmonic effects that rely on the comparison of two different recorded performances of the same song (chapter 5). Page 12 →Now on to the hard stuff. The chief difficulty in talking about harmony in recorded rock songs is figuring out precisely which pitches we hear. Transcription is a long, laborious process, fraught with guesswork and destined to contain errors. We can employ computers for help, but the aid they can currently offer us is limited. Moreover, if we want to know the pitches of a recording, we are technically required to ask (or study) a real person, because pitch is not actually a physical property of a sound but rather a human response to, among other things, a sound wave’s frequency. To further explore this point, consider the power chord, a combination of pitches that are generally understood to cohere as a chordal root and (perfect) fifth. Occasionally, such bare intervals are straightforward with regard to their note content, as are the alternating piano power chords that open the Police’s 1983 “King of Pain” (B5 and A5). More commonly, power chords are distorted, as when played on an electric guitar through an overdriven amplifier. In these cases, additional pitches come into focus, ones that the guitarist is not “playing” in the traditional sense. Truth be told, most tones we hear in our daily life are complex tones: they are really sonorities unto themselves, comprising multiple pitches of varying loudness; the single note we identify as the pitch of these sonorities is called the “fundamental” of the entire complex tone. But with the distorted power chord, the additional notes can become so loud that it is problematic, from a listener-based perspective, to simply ignore them. When a power chord is voiced as a perfect fifth, the overtone at the major tenth (an octave plus a major third) above the root-bass will often begin to assert itself as a (purely tuned) chordal third.11 In the 1993 riot-grrrl track “Rebel Girl” by Bikini Kill, the initial power chord that chugs along throughout the song’s opening can easily give the impression of including a faint chordal major third. Do we include the third in our inventory of pitches or relegate it to the fuzzy realm of timbre? Can we hear the third? Do “mere” acoustical or psychoacoustical phenomena such as overtones and combination tones constitute part of our hearing, and if they do, should they carry the same weight as other tones? There are no obvious answers to these questions, and there is no one rule that will cover all cases of unclear pitch. Many invisible judgment calls will be made in the following pages, and no doubt there will be examples for which the reader does not hear all the pitches notated or hears some notes the author has ignored. (For what it is worth, power chords will be treated as two-note sonorities unless the chordal third is so prominent that it more or less demands acknowledgment, or else the chordal major third is part of the vocal line or instrumental solo, making the issue moot.) There will also undoubtedly be some outright transcription errors (transcription is too difficult to do perfectly several hundred times in a row), although every Page 13 →effort has been taken to minimize such lapses. If (or when) the reader comes upon a transcription that is in some way faulty, I can only ask that she entertain the theoretical argument being made and regard the specific musical example as a hypothetical case. Musical examples will be presented in the form of descriptive prose, snippets from song lyrics, and various types of musical notation, including letter names, numerals, and occasional staff notation. In order to make sure recordings are readily available to readers, the discussion will stick mainly to mainstream commercial artists. For best results, readers should listen using headphones (not earbuds) or a decent speaker system, so that all the sonic details of the tracks can become readily apparent; internal laptop speakers should be avoided at all costs, since

they tend to obliterate the bass line, an often crucial element in hearing harmony. Recordings not tuned exactly to A=440 hertz will be transcribed to the closest equal-tempered pitches, up or down; occasionally chords will be transposed up or down by full intervals (semitone and larger) to allow easy comparison with other examples, but it will always be made clear when this occurs. Sectional names (intro, verse, chorus, etc.) rather than track minutes and seconds will be cited, because digital timings can vary from source to source; the definitions of the traditional categories of intro, verse, pre-chorus, chorus, bridge, and coda are given in Appendix A, though it is appropriate to point out here that the author considers sectional terms to be descriptions of sectional effects, the qualities of cohesion and rhetorical purpose projected by specific portions of a song.12

Mapping the Terrain Hearing Harmony is aimed primarily at music academics: professional music theorists, ethnomusicologists, historical musicologists, and their students. Old and new terminology, however, will be presented at a pace appropriate to a broader readership (particularly in the first two chapters), to embrace (it is hoped) not only inquisitive nonacademic musicians but also the sizeable community of popular-music scholars who are not trained in advanced music theory, scholars in fields such as psychology, media studies, American studies, and literature. Because the anticipated readership for this text will largely be North American and British, most of this book’s examples have English lyrics; it makes sense to use familiar songs—or at least familiar-sounding songs—to illustrate unfamiliar theory. (That said, popular music around the world has, over the past several decades, taken on the sonic features of British-American music, a process sociologist Motti Regev (2013) calls global “pop-rockization,”Page 14 → and so the claims of this book apply well to other geographical and linguistic areas.) Literacy in musical staff notation will certainly aid in comprehension of the material, particularly with the scale-degree details in chapters 1 and 2. But musical notation itself, in all its various forms, is a topic that the book examines carefully. Thus an initial inability to read notes on a staff should not keep readers from being able to relate to much of the material, so long as they already have some basic knowledge of traditional Western music theory, as one might get from piano or guitar lessons or from a class in theory rudiments. While this text will interrogate many fundamental theoretical concepts, there will not be occasion to question every possible idea; many will be treated simply as philosophical primitives that will not receive definition or redefinition. (This will be true, for instance, of diatonic scales, although plenty will be said about the role of such scales in hearing harmony.) Readers who desire a crash course in these theory rudiments should consult texts such as Walter Everett’s 2009 Foundations of Rock or Philip Tagg’s 2009 Everyday Tonality. There are six large chapters. The first two deal principally with the venerable notion of harmonic function, which will here designate a category of aural effects describing, first and foremost, a chord’s relative stability or instability; function will also describe chordal qualities of departing from a prior chord, of resolving (or temporarily resolving) a prior chord, of predicting progression to another chord, of softening the strengths of a prior chord, and of delaying the arrival of a predicted chord. Chapter 1 concentrates on two main functional effects—tonic and pre-tonic effects—and additionally on the effect of tonal center. Abandonment of the conventional notion of key is advocated. Pre-tonic function is divided according to the distinct qualities of different anticipated scale-degree motions in an unconventional manner (and with unconventional scale-degree notation using up and down arrows), allowing for novel definitions of three types of pre-tonic effects—dominant, subdominant, and mediant—which further yield the subtype effects of lead dominant, rogue dominant, upper subdominant, and lower subdominant. The notion of a diatonic-pentatonic pre-tonic hybrid is posited, as is the notion of a scalar effect. The mounting tension between theoretical disinterest and analytical advocacy is also examined. Chapter 2 continues the exploration of function by theorizing other predictive effects, most notably pre-pretonic effects, which open up discussion of functional chains: chord progressions featuring interlocking functions. The conventional term “secondary dominant” is discarded in favor of the adjectives “hyper,” “hypo, ” and “medial,” which describe the relative scale-degree motions that are anticipated by any predictive chord. Having developed an Page 15 →extremely detailed functional nomenclature by this point, the chapter turns to streamlining the labeling system by admitting Greek letters as placeholders for chords according to their

position relative to their resolving tonic, with alpha being tonic, beta being pre-tonic, gamma being pre-pretonic, and so on. A Roman numeric labeling system is then introduced, one that is based exclusively on chordal roots and carefully molded to reflect the relative commonness of chords in the rock repertory. Numerals are eventually theorized as another kind of aural effect, one more or less distinct from harmonic function. A discussion of harmonic levels and functional strength leads to the idea of chordal identity as an effect in itself and thus also to the ideas of root effects, letter effects, and entity effects, among others. A host of new functions is then introduced—softening, delaying, post-tonic, anchoring, pre-anchoring, post-anchoring, passing, and neighboring—as is the idea of a harmonic effect being projected by chordal progressions as well as by individual chords and pitch classes. A discussion of some philosophical and methodological problems with the notion of prediction rounds out the presentation of the function theory. The next two chapters together explore schematic effects, which entail an evocation of a familiar stereotypical harmonic pattern identified either as a numeric series (i.e., as root motions) or as some other scale-degree motion. After distinguishing between harmonic progressions, chains, phrases, loops, and cadences, chapter 3 posits common phrasings for eleven two-chord and twelve three-chord schemas, and then introduces the notion of a slot schema, which is defined by its number of distinct harmonic entities, not necessarily numerals. Twenty-one fourslot schemas are explored theoretically and historically, several of these being given special names to due to their prominence in the repertory. Chapter 4 begins by discussing nine schemas of various size that are prone to project pentatonic effects, before proceeding to a special class of fourteen largely chromatic “meta-schemas,” each of which allows multiple different numeric (root) incarnations. Ten extended (lengthy) schemas are then examined, making for a grand total of seventy-seven distinct harmonic schemas in a wide assortment of different phrasings. The historical development of a few significant schemas is also traced. Chapters 3 and 4 are by far the densest chapters in terms of sheer information; they cite roughly six hundred songs, mostly in the form of textual description (rather than tables).13 The reader is advised to engage these two chapters slowly, in small doses at a time (as one would a reference book), and in consultation with a reliable, comprehensive collection of recordings. Transformational effects, the topic of the next and shortest chapter, are those aural qualities of change that accompany certain chords and chord progressions.Page 16 → Such qualities involve the alteration of either a real or imaginary previous harmonic state, a state termed a “transformee.” Chapter 5 postulates five distinct kinds of transformees—norms, precedents, bases, wholes, and fragments—all of which are defined in accordance to the order in which we hear the harmonic change, regardless of the order in which the chords came into the world. (A progression from 2000 might be heard as transforming one from 1950, if we learn them in reverse-chronological order.) Several types and subtypes of transformational effects are then formulated: transposition, modulation, reorientation, breaking-out, pumping-up, reordering, rotation, reversal, subtraction, addition, and substitution. Chordal substitution, due to its complicated nature, is given especially close consideration; four subtypes of substitution are offered: coloristic, numeric, functional, and hierarchical. The sixth and final chapter turns to ambiguous effects. Harmonic ambiguity is differentiated from mere harmonic multivalence, the former defined as always entailing multiple harmonic hierarchies that are outright contradictory. This kind of contradiction is determined to surround only the harmonic effects of center, schema, scale, and function—and no other harmonic effects identified in previous chapters—a determination that leads to an inventory of all the assorted musical factors that can contribute to a sense of center, schema, scale, and function and thus also possibly to a sense of centric, schematic, scalar, and functional ambiguity. The more experientially complex qualities of center and function are discussed in great detail, within a systematic comparison of the very similar chordal riffs of Warren Zevon’s “Werewolves of London” and Lynyrd Skynyrd’s “Sweet Home Alabama” (and a few other tracks as well). From there, chapter 6 identifies assorted brands of centric, schematic, scalar, and functional ambiguity in various settings, from simple two-chord loops to entire songs wherein nearly every sonority is a convincing tonic. The conventional wisdom that modal and pentatonic progressions are inherently ambiguous is thoroughly scrutinized and ultimately dismissed. Although not as consistently dense as the chapters on schemas, chapter 6 does have some sections that are fully packed with examples; as before, the reader is encouraged here to engage these passages at a relaxed pace. In the brief conclusion, I address the highly personal, and hence all-important, issue of musical expression by

laying out different forms of expressive harmonic effects. Such effects involve the music’s conveying some sort of meaning that extends beyond the notes themselves, be it as universal as an emotion or as specific as an event in a story. Expressive effects differ in this way from functional, schematic, transformational, and ambiguous effects: while all five of these represent ways of hearing meaning in music, only expressive effects communicate something outside of music.

Page 17 →

Chapter 1 Tonic and Pre-tonic Chordal Identity The thrashing riffs of angry punk songs, the quiet accompaniments of lyrical pop ballads, the shimmering atmospheres of electronic dance mixes—all of these forms of musical expression depend on the sonic interaction of sonorities that musicians call “chords.” Our first order of business is to establish a reliable way of identifying these chords. Let us start by examining Radiohead’s “Lucky,” a song that appeared on the 1995 Bosnian War charity collection The Help Album and later on Radiohead’s celebrated 1997 OK Computer. After an atmospheric introduction, the track alternates between two main sections: a verse and a chorus. The first chorus is initiated by the lyrics “Pull me out of the air crash,” with the word “out” marking the true starting point of the new section. We know there is a new section for several reasons: the mood and texture change, the melody changes, and, most significantly to our objective here, the chords change. There are several ways we could identify these chords; one easy way, which any rocker worth her salt would definitely know, is using letter notation. See Example 1.1, which uses letter notation to depict the chords in the chorus.1 The vertical lines indicate the end of one bar and the beginning of another, as gauged against the backbeat and phrasing.2 (Other rhythmic syncopations not relevant to a particular theoretical point have been reduced out for ease of reading.) What does this notation tell us? First and foremost, there are nine distinct chords. (The AM–Em pair is stated three times. And even though the chorus really ends with the B7, the final Em is included here for reasons to be discussed shortly.) The first entity, AM, is a set of three pitch classes: the chordal root A, the chordal third Cв™Ї, and the chordal fifth E. These are classes of pitch (or “chromas” as psychologists call them), not pitches themselves; they are abstracted from any specific registral (octave) placement and are likewise not specified as to timbre or textural arrangement. (As pitch classes, then, the Cв™Їs sung by Thom Yorke are equivalent to the higher Cв™Їs wrenched out of Page 18 →Jonny Greenwood’s electric guitar.) The one aspect of the chord’s voicing—the chord’s registral placement of its pitches—that this notation does denote is the primary bass note, A. (“Bass” here means “lowest note,” not “bass guitar.”) Had the same set of pitch classes A, Cв™Ї, and E, been supported in the lowest voice/instrument not by the root, A, but by, say, an E, the chord would have been written as “AM/E” in compliance with standard “slash” notation.3 Our letter notation thus identifies the harmonies according to total pitch-class content and to the lowest pitch class sounded. “Em” indicates pitch classes E, G, and B, with bass note E. “B7” signifies bass note B, plus pitch classes Dв™Ї, Fв™Ї, and A. “C7” denotes E, G, and Bв™-built on C.4 See Appendix B for a key to this style of letter notation. Example 18.1. Radiohead, “Lucky” (from chorus) As much information as this notation provides, there is plenty more about the harmony that remains to be said. We have not yet even begun to link the chords to one another—they are still, at the moment, isolated entities. And what about the musical effects generated by their deployment in this particular series, in this chord progression? Surely we do not want to ignore, for instance, the feelings of tension and relaxation created by the oscillation back and forth between AM and Em: to what would we attribute this dramatic effect? Perhaps the drama results simply from an alternation between two chords that are different, different in their pitch-class contents (A and Cв™Ї versus G and B), their bass notes (A versus E), and their arrangements of pitch-class intervals (major triad versus minor triad).5 Yet the AM and Em harmonies are not just distinct, they are related dynamically: the former would seem to convey an impulse to relax into the latter. This effect lies beyond the inventory of pitch classes and intervals. This effect is qualitative. A similar quality attaches to the remaining chords, but most especially to the B7. At the moment this chord comes, the instruments and voices fade away, and we clench in anticipation of a resolution to Em. Thom Yorke seems perfectly aware of the effect: at this precise moment, he fittingly sings

“We are [C7] standin’ on the [B7] edge.”6 (With this example, as with every example in this book, readers are asked to at least imagine hearing the song this way, even if their natural inclination is different. Disagreements between hearings will begin to be addressed at the end of this chapter.) Page 19 →One useful way to describe these qualities of tension and relaxation is by invoking the metaphor of stability. AM and B7 give the impression of being unstable, of requiring resolution. This quality is quenched each time with the arrival of Em, which acts as a kind of anchor. AM and B7 are dependent; Em is foundational. There is a hierarchy at work here, one that speaks to the chords’ relative degrees of stability (“hierarchy” in the everyday sense of a ranking). This is to say, from a stability standpoint, AM and B7 are auxiliary and are subordinate to Em; Em is self-sufficient and is superordinate to AM and B7. This is not to say that AM and B7 are any less important musically; rather, subordination and superordination here are nothing more than ways to describe the impressionistic qualities of the chords. Indeed, if Radiohead were to present us with one long, drawnout Em sonority, sans subordinates, the song would certainly be stable, but it would also be harmonically static and possibly quite boring. (Many rock songs, especially electronic dance tracks, do in fact offer only stable harmony for long periods of time; we could call these protracted chords catatonics.) In contrast, “Lucky” ebbs and flows with each passing chord. Even the brief C7 harmony, despite not leading directly to Em, projects a feeling of instability; this chord relaxes into the relatively more stable B7, itself resolving to Em, thereby creating a sequential increase in stability, a kind of hierarchical chain propelling us into the ensuing verse. (Such chains will be explored more in chapter 2.) In describing the qualities of such hierarchically related chords, musicians use words such as “tonic,” “dominant,” and “subdominant” (or “pre-dominant,” or “dominant preparation”). Unlike letter designations, these terms do not indicate precise pitch classes or certain intervallic structures. On the other hand, they do speak to a salient type of relationship between our chords, to the roles the chords play in creating a sense of musical motion. These labels can in fact serve as markers of harmonic identification itself, in lieu of letter notation. In Example 1.1, for instance, we could just as well have written “tonic” instead of “Em” and “dominant” rather than “B7.” We will wait to fully explore this alternative method of identifying chords, along with another one based on Roman numerals, in chapter 2. For present purposes, it is best simply to take this alternative method of chordal identification as a given and turn our full attention to the use of these hierarchically based labels as descriptions of harmonic effects. The general category of chordal qualities in question here shall go by the name function, an old term that requires careful and extensive explanation.7 The first step in this explanation will be to differentiate harmonic function from a related but distinct musical effect, tonal center. Page 20 →

Tonal Center and Tonic Function Functional effects are symbionts with the effect of tonal center, which is to say that our hearing the former automatically entails our hearing the latter as well. (The reverse is not always true, as we shall soon see.) Both kinds of effects deal primarily in stability and instability, though of different sorts: center pertains to pitch classes, while function pertains to chords. Tonal center, or simply center, describes orientation toward a single, moststable pitch class to which all other pitch classes are subordinate. The centric effect is akin to bodily orientation; just as we only ever face a single direction in the real world, so too do our ears tend to concentrate on one fixed position in pitch-class space. (This analogy cannot be pushed too far, however, because unlike bodily orientation in physical phase, centric orientation is not so easily controlled by the subject. The objective constraints on our centric orientations, and the potential for disorientation—i.e., centric ambiguity—will be explored in chapter 6.) In “Lucky,” the pitch class that sounds most stable is E. All other pitch classes can be heard as away from E. Thus, E projects a centric effect; E is center. (“Center” will denote not just the effect but also the centric pitch class itself.) It is not a coincidence that, among the song’s chords, Em is the most stable: with its bass note serving as center, Em is the harmony by which the other chords navigate their terrain. The chordal equivalent to the pitch-class effect of center is the effect of tonic function; the Em triads in “Lucky” are all tonic-functioning (though not necessarily exclusively tonic-functioning, another thought to hold on to for now).

Like so many musical terms, “tonic” carries more than one meaning. For the sake of clarity, we will use it to denote a type of functional effect that involves a harmony stable enough to preclude any sense of requiring resolution because of its inclusion of the centric pitch class. Tonic effect often manifests itself as an alleviation of prior harmonic instability (as when Radiohead’s tonic Em chord relaxes the tension of the B7); however, tonic-functioning chords also typically appear at the beginnings of tunes, where they serve not as a resolution of past subordinates but rather as a sturdy jumping-off point for future harmonic exploration (the first clear chord in “Lucky” is a tonic Em triad). In the presence of other non-tonic chords, a tonic-functioning harmony is by definition hierarchically superordinate. (In chapter 2, we will further generalize tonic function as a specific kind of “anchoring function.”) Although a tonic will never really resolve to another chord, there certainly exists the possibility that one tonic could move to an even more stable one, and vice versa. (But once a chord reaches a certain threshold of aural stability, it will presumably project tonic function to some degree, no matter what else happens.) Page 21 →By distinguishing between tonic and center, we abandon a traditional way of talking about tonic, namely, the idea of the tonic. There is no the tonic in the current theory, there are only individual chords that project tonic function. The tonic is an abstract representative of a group of sonorities or single pitches, an idea worth abandoning because such abstractions do not always adequately represent their constituents. There are two big reasons why this is so. The first is that functions are ultimately determined by specific musical contexts, not by any unalterable fate of their pitch-class content or intervallic relationship to tonal center. The Em triads in “Lucky,” for instance, do not automatically function as tonics (even if they tend to); indeed, once we become familiar with the how the chorus goes, the third Em triad will likely begin to take on an additional function, one of preparation for the C7, though this extra function will probably never become as strong as the triad’s initial tonic effect. The repertory is replete with songs in which the same chords, in terms of letter notation, display different functions, though we will need to lay out more of the theory before we can properly engage such examples. Suffice it to say for now, we avoid a particular conceptual problem—what we might call the many-functions-to-one-chord problem—by confining tonic function (and harmonic function more generally) to the realm of particular chords. The second reason why the tonic is an idea worth avoiding is what we will call the many-chords-to-one-functionproblem, which is well-illustrated by the harmonies of another alt-rock track, Puddle of Mudd’s “Blurry” (2001). Even with an unwavering center of E (actually Eв™-, but our transposing it up a semitone will make life much simpler as this early point in the text), this track blurs any sense that there is a single, abstract tonic sonority at work. “Blurry” continually repeats a progression of three chords: one on C, then one on D, and then a resolving chord on E. The only change in this pattern occurs in this final spot, which sometimes offers EM, sometimes Em, and other times EM(m) (“M(m)” or “m(M)” meaning “major and minor, ” indicating E, G, Gв™Ї, B). Which one of these is the tonic? If we separate center from tonic, the question becomes moot; the E-chords are tonics, and center is E. For those readers already conversant with Western classical music theory, the notion of “key” probably comes to mind here. Key fuses a tonal center to a primary diatonic (heptatonic, seven-note) scale,8 resulting in descriptions such as “E major” or “E minor.” Such descriptions work fine for some songs but not for others. In “Blurry,” for instance, Puddle of Mudd freely mixes notes from the E natural-minor (aeolian) scale (E, Fв™Ї, G, A, B, C, D) with the Gв™Ї from the E major (ionian) scale. (The natural-minor and aeolian scales are intervallically identical, as are the major and ionian scales. We will not use the term “mode” except in special circumstances.) In cases with more Page 22 →than one prominent scale, the classical concept of “mixture” or “borrowing” can be invoked, which entails a primary key being inflected by foreign notes derived from a different key. In “Blurry,” the best designation of key would be “E minor borrowing from E major,” because Gв™Ї (which is in major but not minor) is heard less often than the C, D, and G-natural (which are in minor but not major). Fair enough. The problem is that this kind of resistance to key exhibited by “Blurry” is no isolated phenomenon; mixture will need to be invoked constantly, and oftentimes we will face difficulties in designating one scale as primary and the other as secondary. Another issue facing the concept of mixture, and facing “key” more generally, is that rock music makes regular use of mixolydian (e.g., on E: E, Fв™Ї, Gв™Ї, A, B, Cв™Ї, D) and dorian (e.g., on E: E, Fв™Ї, G, A, B, Cв™Ї, D)

scales, which would seem to demand a mixture/borrowing explanation because neither scale falls neatly within the traditional categories of major or minor keys. At the very least, the prominence of mixolydian and dorian would appear to compel our expanding the conventional scalar limits of “key.” But there is still yet another problem with “key”: in many strands of Western classical theory, the identification of a key hinges on the appearance of a particular kind of harmonic progression we will identify later as a V–I cadence. This chordal motion is nowhere to be found in “Blurry.” (A possible version would have been B7–Em, like we had in “Lucky.” The D-E chordal motions in “Blurry” are similar in certain ways to this V–I cadence, but it is specifically the B7–Em type of motion that is typically associated with “key.”) This progression is in fact absent from a large chunk of the rock repertory as a whole. (IV–I, rather than V–I, would seem to be the foremost progression in confirming or establishing a tonal center in rock.) In response to these assorted problems with key, we could lift the requirement of a V–I cadence, add mixolydian and dorian to the list of acceptable scales, and deploy mixture/borrowing explanations for all further problematic songs even when no single primary scale is forthcoming. We could, but we needn’t. “Center” and “tonic” are perfectly suited to describing the effects in question; “key” is essentially extraneous to the discussion. For those readers unwilling to abandon “key” all together, however, we could justify keeping the term based on its ability to differentiate between songs that conform to older ideas of tonality and songs that do not (but such differentiation will not be a focus in this book.)9 In relying solely on center and tonic, and making them distinct phenomena, we set up an easy method for describing the harmonic effects of songs that are scarce on tonic-functioning chords. For example, in Betty Everett’s classic 1964 cover of “It’s in His Kiss (The Shoop Shoop Song)” (originally recorded by Merry Clayton in 1963), a center of D is established from the very start, despite Page 23 →a paucity of tonic stability. The first tonic chord, DM, arrives only at the onset of the refrain, when we are finally notified (after having asked repeatedly as to the location of proof of his love) that “if you [DM] wanna knowВ .В .В . it’s in his kiss.” Here, it is the very divorce of pitch-class orientation (center) from local harmonic stability (tonic function) that makes the arrival of DM so special, that makes the text-music relation so cleverly crafted. An even more extreme center-without-tonic case is BjГ¶rk’s “Hyper-Ballad” (1995). This song offers clues of a center on Bв™-(to be discussed later) despite an unaccommodating electric bass line that is poignantly unable, or unwilling, to sink below C or rise above A, never reaching the promised Bв™-: in the verses (“We live on a mountain”), the bass descends from Eв™-to D to C, but then simply repeats this same descent over and over; in the choruses (“I go through a list”), the bass is more active, going up (Eв™-–F–G) then back down (G–F–Eв™-) then up almost to Bв™-(Eв™-–F–G–A) before simply repeating the same struggle. By denying us strong statements of a Bв™-tonic chord (but providing weak ones, which also will be explained later), “Hyper-Ballad” evades the predictability of an ordinary ballad in favor of the passionate agitation of a hyper one. Even though strong Bв™-tonics are in short supply, BjГ¶rk’s Bв™-tonal center is clear: our understanding of tonic function as an effect of particular harmonies, and as distinct from the orientating effect projected by individual pitch classes, helps us to keep our harmonic direction even when there are no strong tonics in sight.10 But given that “Hyper-Ballad” withholds a strong tonic-functioning chord on Bв™-, how do we know at all that a Bв™-chord would, were it present, likely function as tonic? Following from our earlier argument, a chord built on—that has as its chordal root—the centric pitch class would not necessarily be a tonic here, just as the Em chords in “Lucky” were not all tonics simply by virtue of their pitch-class uniformity. It is true that if BjГ¶rk had provided a resounding Bв™-chord at the end of the chorus of “Hyper-Ballad,” that triad would not function as a tonic necessarily. The odds are, however, that it indeed would, because any sonority that features the tonal center as its root is more or less defaulted to tonic function and will function otherwise only in certain kinds of musical settings. (Some such settings will be discussed in the next chapter.) This claim is not a rationalization, but rather an experiential observation concerning the typical behavior of chords built on the centric pitch class: there is something special about the placement of tonal center at the root of a chord that makes tonic function almost—although not quite—inevitable. It is perfectly reasonable, then, when listening to BjГ¶rk’s song, for our ears to crave a chord on Bв™-, because, given the centric orientation on Bв™-, such a

chord is the strongest candidate for supplying tonic stability. Page 24 →Of course, in order to anticipate the arrival of a harmony built on the centric pitch class, we must first know where the tonal center is. Pitch-class orientation is a fairly automatic reaction to any rock song, but we have so far avoided the question of how this orientation comes about. We mentioned that in “Hyper-Ballad” there are “clues of a center on Bв™-”; these include a scale and a chord outlined by the strings and vocals. The scale, which includes every pitch heard in the entire song, is that of Bв™--major (Bв™-, C, D, Eв™-, F, G, A), though it would be more accurate to call this simply a “pitch-class set” rather than a scale per se, since in this context the center Bв™-is itself being indicated by the set, not the other way around. (That is, at this point, we could just as well label the set C dorian, or D phrygian, or Eв™-lydian, etc.) This set of notes does not point toward a center of Bв™-in particular, but it does assist in weeding out certain other pitch classes as possibilities, such as Cв™Ї and Gв™Ї, by virtue of their absence. (It is difficult, although not impossible, for a pitch class to create the effect of center when it never appears.) More important in producing the effect of center in “HyperBallad” are the string tones and vocal line, which sketch some kinds of Bв™-chord. The soft strings, which can be heard at various times but most obviously in the opening seconds of the track, sustain a sonority of Bв™-, F, and C—a Bв™-2 (otherwise known as a “Bв™-sus2”). BjГ¶rk’s vocal line reinforces this sonority by emphasizing Bв™-and F over the rest of its pitches, especially at the ends of the verses, where she leaps down from Bв™-down through F to land on the Bв™-below (G embellishes the line): “a [Bв™-] way [F] to [G] start [F] the [F–Bв™-] day.” These moments are the closest we get to an explicit statement of a Bв™-tonic and are probably the prime reason why our ears will gravitate toward Bв™-: a Bв™-chord seems to hover quietly somewhere in the background, exerting a significant influence yet revealing itself only obliquely. With the help of these sorts of musical features, centric and functional effects bootstrap each other into existence. (Chapter 6 will offer a more detailed and systematic investigation into the ways center and function are established.) We might infer from the foregoing discussion that the establishment of center is wrapped up entirely in the promise—if not quite the actual appearance—of a tonic-functioning chord. It is true that tonic and center are inextricably linked, yet there are other harmonic functions that participate just as actively in creating, and that are just as heavily influenced by, center. Indeed, any “promise” of tonic is necessarily made by non-tonic chords; thus these other harmonies can also contribute to determinations of center by predicting resolution to a center-containing chord. The question now is: how does one harmony predict another? Page 25 →

Pre-Tonic Function: Dominant and Subdominant Consider again the chorus from Radiohead’s “Lucky” (Example 1.1). The B7 chord seeks the stability of a tonic-functioning sonority: it exhibits pre-tonic function. The function is “pre” not in the sense of “preceding” but of “predicting”; the function is not a summary rationalization of how the music happened to turn out (in which case B7 would be a pre-tonic only after resolving to Em) as much as it is an anticipatory impression of which notes might follow (although we will finesse this point momentarily). This effect of anticipation is rooted in the instability of these chords relative to the steadiness of Em and of other potential tonic harmonies; or, put in hierarchical terms, pre-tonic function involves the effect of subordination to an expected, immediately ensuing tonic. Thus, B7 is a pre-tonic because it sounds as though resolution to tonic is right behind it, regardless of whether this prediction turn out to be correct. There are certainly situations wherein pre-tonics lead us astray: the last chorus of “Lucky,” for instance, stops short of resolving to a tonic at the end of the song. Radiohead instead leaves us “standin’ on the edge,” with an open-ended B7 that is as unstable as any of the B7s before it but that here predicts resolution to a tonic we never get. This example demonstrates that pre-tonic function, like tonic function, is the effect of a single, particular chord; it is (almost) immaterial what the function of the next chord is, or whether there is a next chord. Indeed, once we have heard the song once, we know there is no next chord, yet the predictive effect can endure. The parenthetical “almost” above might raise a red flag. Does the answer to a predictive function bear on the prediction or not? A prediction is a prediction, no matter the result; a pre-tonic materializes (is heard) before

the arrival of any other chord that could possibly refute it. Thus, the final B7 in “Lucky” would seem safe in its pre-tonic role. Yet once we have heard the entire track, or at least one pass of a given section, we will know, assuming we were paying enough attention, when and where the unstable sonorities will resolve. This knowledge cannot help but color the qualities we hear projected by the unstable chords upon future listenings, even if those future listenings merely involve hearing a section being repeated later in the track. In the choruses to “Lucky, ” once we know the AM triads are consistently followed by stable Em triads, each AM will undoubtedly be heard as projecting pre-tonic function. But upon first hearing the track, a listener may or may not have that impression; she might, understandably, expect AM to move to some sort of B chord, understandably because chorus sections in many other songs often do begin with such a move before resolving to a tonic. This kind of potentialPage 26 → discrepancy between hearings is part and parcel of predictive listening in particular and of experiential-based music theory in general; accordingly, this issue will crop up repeatedly throughout this book. Without delving too deeply here into this quagmire, we can simply acknowledge for now that not every possible hearing can be articulated in every case (for lack of space), and so in the interest of moving forward, this book will tend to focus on those hearings that are likely to stay with a listener after obtaining at least a modicum of familiarity with the music. We will thus describe the AM triads in the chorus of “Lucky” as primarily pretonics, because they resolve that way repeatedly throughout the song. However, Radiohead’s final B7 is likewise a pre-tonic despite its unanswered prediction, because its brethren (all the other B7s in the song) do resolve to Em, and because the suggestive line “standin’ on the edge” haunts us until the track’s very last moment (the chord’s instability does not dissipate with repeated hearings). It should be noted that “pre-tonic” is not a conventional expression; more typically, musicians use terms such as “dominant function” and “subdominant function” to denote the effects of non-tonic sonorities. “Dominant” and “subdominant” are convenient terms, but their meanings are not fixed. In order to exploit these terms’ usefulness, we will need to take great care in defining them. (And eventually, in chapter 2, we will explore additional, alternative names for them.) Dominant function is so named because of its association with those harmonies built on the fifth spot of the ascending major and minor diatonic scales, on the “dominant scale degree.” (“Dominant” is actually a bit of a misnomer, since the governing, dominating scale degree is actually the first scale degree, and the ruling harmonic function is called “tonic.” But swapping the terms “dominant” and “tonic” would have disastrous consequences for this theory’s comprehensibility.) Earlier we remarked that the B7 chords in the choruses to Radiohead’s “Lucky” would traditionally be called “dominants”; this is so because scale degree 5 (B in relation to E) is the root of these chords. “Dominant” as a scale degree and as a function are historically linked, yet if we are thinking of dominant function as a category of pre-tonic function and not as a label indicating the scale degree of the chordal root, we should label a chord a “dominant” if, and only if, its effect is one of anticipating another more stable sonority that contains the centric pitch class: scale degree 1. This is to say, not every harmony built on 5 necessarily functions as a dominant, only those that predict resolution to a tonic. (A root of 5 is not even a requisite for dominant function, as we shall soon see.) Radiohead’s AM triads also predict resolution to a tonic, but they are not built on 5; in fact, they do not feature 5 at all. Tradition would have us call Page 27 →them “subdominants” because they are built on the so-called subdominant scale degree, 4. (There is another tradition of using “subdominant” to indicate a predominant function; in this book, “pre-dominant” will indicate a function altogether different, to be discussed in chapter 2.) The term “subdominant” means both “the scale degree immediately below the dominant” and “the dominant below the center.” The first meaning is self-explanatory (one step below 5); the second meaning derives from the fact that in a major or minor scale, 4 is a perfect fifth below 1 (e.g., A below E), just as 5 is a perfect fifth above 1. (Scale-degree numbers, by convention, are always arranged in ascending order up the musical staff, or in descending order down. We can thus also measure 4 as a fourth above 1, and 5 a fourth below.) The implication of the traditional dominant-subdominant split is that pre-tonics with scale degrees in common are more perceptually similar to each other than they are to other pre-tonics with fewer or no shared scale degrees. So, for instance, in the verse to Radiohead’s Lucky,” the Bm triads that anticipate resolution to tonic Em triads (“I’m on a [Bm] roll this time [tonic Em].В .В . my luck [Bm]

could change [tonic Em]”) sound less like the chorus’s AM triads and more like the B7s. We can label all three of them “pre-tonics,” yet we can further specify that Bm and B7 are dominants while AM is a subdominant.11 There are many other chords in the repertory that predict resolution to tonic but that are not built on 5 or 4. In the Toadies’ “Possum Kingdom” (1994), as the second chorus drives into the bridge by using a DM/Fв™Ї triad that anticipates the arrival of a tonic E power chord, or “E5” (“so [DM/Fв™Ї] help me, Je- [E5] sus”). (A “power chord” comprises a chordal root and fifth, with no third.) The aural quality of this pretonic DM/Fв™Ї is strikingly similar to that of the pre-tonic Bm in the verse to “Lucky.” The similarity here is in large part due to the chords’ sharing two of each of their three pitch classes, Fв™Ї and D; thus the chords are also alike in terms of scale-degree content (both feature 2 and 7), despite DM/F♯’s withholding of scale degree 5. Example 1.2a illustrates this correspondence using staff notation,12 with scale degrees arbitrarily assigned to pitches that lie neatly on a treble clef. (The arbitrariness resides in the fact that scale degrees, like pitch classes, are unfettered by registral placement and could be depicted in any octave.13 Additionally, there are scales other than natural minor that would work just as well here, so the precise pitch classes indicated in the example merely represent choices among other possibilities.) The sonic resemblance between the Bm and DM/Fв™Ї is so strong that we are justified in grouping these two harmonies into the same class of pre-tonic. Since we called Radiohead’s Bm and B7 chords “dominants,” the Toadies’ DM /Fв™Ї triad would by extension also be a dominant. But as we just noted, the Toadies’ chord is not built on 5, the so-called dominant Page 28 →scale degree; 5 does not appear anywhere in the chord, and the sonority moreover does feature 4, a detail that might push us toward calling the harmony a “subdominant.” There is a dilemma emerging: we can either abandon the conviction that the Toadies’ DM/Fв™Ї and Radiohead’s Bm are, because of their aural similarity, worthy of occupying the same functional category, or we can declare that dominant function should not be predicated on the presence of 5. In keeping with this book’s favoring of experiential qualities over a priori rationalizations, we should stand strong and declare that the DM/Fв™Ї, Bm, and B7 are all “dominants.” The scale degrees that all three of these harmonies do share are 2 and 7, the latter in two versions: the “leading tone” (one semitone below center, as B7’s Dв™Ї is to E) and the “subtonic” (two semitones below center, as Bm’s and DM/F♯’s D is to E). We can therefore gauge dominant function not by scale degree 5, but rather by 2 and 7 (although even this refinement will be further nuanced later on).14 Example 1.2b depicts the scale degrees of Radiohead’s dominant-functioning B7. It is counterintuitive to detach dominant function from the dominant scale degree. In Western classical theory, chordal roots are usually treated as absolutely fundamental (to some degree) in explaining movement between harmonies, and in some traditions only certain types of intervallic motions between successive roots are considered worthy of being called “harmonic” at all. (These intervals are often limited to ascending fourths /descending fifths, descending thirds/ascending sixths, and ascending seconds/descending sevenths.) And yet our separation of functional name from scale-degree name is hardly a novel idea: diminished leading-tone chords (that is, diminished chords whose root is the leading tone), which are common in Western classical music though much rarer in rock, are traditionally considered to be dominant in function despite their lack of scale degree 5. So in actual fact there is nothing too radical about a dominant without 5 (even if a common justification for 5-less dominants is that the 5 is implicit instead of explicit). More unusual is the idea we are about to engage, which is that subdominant function likewise be disconnected from 4.15 Consider the Smashing Pumpkins’ “Spaceboy” (1993), which offers two different pre-tonic harmonies that merit subdominant status: CM7 at the end of the first verse and Em at the end of the first chorus. In relation to center G, CM7 is built on 4, Em on 6; see Example 1.3a. These two chords are very similar; in fact, in terms of scale-degree content, the only difference between them is that the latter leaves out 4. Upon further admitting to the similarity of these chords’ functional effects,16 we can deduce that subdominant function should not be delimited by the presence of the subdominant scale degree. Our remaining scale-degree choices here are 1, 3, and 6; in “Spaceboy,” G, Page 29 →B, and E respectively. 3 should be left out, since it was not part of the AM chords previously identified as subdominants in the choruses of “Lucky” (an AM triad on center E would be equivalent to a CM triad with no chordal seventh (B, or 3) on center G). 1 also should be excluded, considering

cases such as the sung portions of Pink Floyd’s “Wish You Were Here” (1975); in this song, tonic GM is repeatedly anticipated by pre-tonic Am (Example 1.3b): this chord features no 1, yet its 6 strongly aligns the chord with the subdominants of “Lucky” and “Spaceboy.” The slink downward from 6 to 5 (E to D) in David Gilmour’s electric guitar, as Am melts into GM during the first verse, is especially relevant here. All things considered, as far as its scale degrees go, subdominant function really is all about 6.17 Example 29.1. Dominant function 1.2a. Dominants DM/Fв™Ї (“Possum Kingdom”) and Bm (“Lucky”) as scale degrees 1.2b. Dominant B7 (“Lucky”) as scale degrees This extended discussion of scale degrees might strike some readers as beside the point. Indeed, our reason for theorizing a pre-tonic function is not to provide an (incomplete) inventory of a sonority’s notes; it is to put a name to the aural effect of one sonority predicting resolution to another. To clarify: we grouped Radiohead’s B7 and Bm with the Toadies’ DM/Fв™Ї, and grouped The Pumpkins’ CM with Floyd’s Am, not simply because they overlap in their scale-degree contents, but because they exhibit similar sonic qualities. We are attributing those sonic qualities to their scale-degree contents, although the usefulness of specifying pre-tonic function as either “dominant” or “subdominant” really has to do less with the pre-tonic’s scale degrees themselves than with the anticipated motions from these scale degrees to those Page 30 →of the predicted resolution. This kind of motion can be thought of as a sort of metaphorical voice leading, wherein the chordal voices—the scale degrees of the predicting and predicted sonorities—imply abstract melodic lines in an imaginary scale-degree space. (This idea is not as academic as it may at first seem. When backing vocalists improvise “harmony” to a melodic line, they must intuit how the part of a chord they are currently singing will lead to a part of the next chord; this is similar to the kind of voice leading we are positing here.) Pre-tonic harmonies project the desire to move from their own scale-degree voices to those of the forecasted tonic, and these expected motions correspond to pre-tonics’ distinctive qualities.18 The Toadies’ DM/Fв™Ї triad intimates that its 2 and 7 (Fв™Ї and D) will close in on 1 (E), as depicted in Example 1.4a; the flavor of these expected movements is markedly different from that of the 6–5 (E–D) resolution promised by Pink Floyd, Example 1.4b. Dominants and subdominants are thus distinguished from one another not simply because they feature dissimilar scale degrees, but because there is a qualitative difference in their anticipated voice leading, in their projected scale-degree motions to tonic. The dominant/subdominant distinction traces the difference in chords’ predictive effects. Example 30.1. Subdominant function 1.3a. Subdominants CM7 and Em in scale degrees (“Spaceboy”) 1.3b. Subdominant Am in scale degrees (“Wish You Were Here”) In unhinging dominant function from 5 and subdominant function from 4, we might very well wonder if we should unhinge tonic function from the so-called tonic scale degree, 1. The answer must be an unequivocal no, since this entire venture is predicated on locating tonic function with 1. There is, however, one small complication to address. As will become clear in the next Page 32 →section, every scale degree has more than one version. (See Appendix C.) There is a в™Ї1 that appears with some frequency in the repertory, a scale degree that sounds like natural 1 but a semitone higher. (The sharp sign here simply indicates “raised by a semitone,” not necessarily an actual sharp note. The same logic goes for the word “natural.” If natural 1 is Bв™-, then в™Ї1 is B-natural.) The question then becomes: is tonic function ever an effect of chords containing в™Ї1 but not 1? And for that matter, can dominants and subdominants predict tonics with a в™Ї1 instead of 1? The short answers to both questions is no: tonic function is dependent on, and only on, the natural version of 1; only 1 can be tonal center. When we hear, say, a dominant resolving to a chord with в™Ї1 but not 1, we are not hearing any tonic function: the resolving chord is not final, merely temporary. Slightly longer answers to these questions will arrive near the end of chapter 2, in the form of discussion of temporary resolutions and other related effects. Page 31 → Example 1.4. Dominant and subdominant scale-degree motions 1.4a. Dominant function in “Possum Kingdom” 1.4b. Subdominant function in “Wish You Were Here” 1.4c. Combined dominant and subdominant function in “I Want You (She’s So Heavy)” 1.4d. Dominant function in “Glad All Over” 1.4e. Subdominant function in “One”

To summarize so far: we have encountered examples of two types of pre-tonics—dominants and subdominants—that we identified in terms of scale-degree content, 2 and 7 for the former and 6 for the latter (although we will finesse the definition of dominants later in this chapter). It is worth acknowledging explicitly that this division between dominants and subdominants entails a fair amount of theoretical choice, one might even say whimsy. Take, as a possible counterexample, Lauryn Hill’s hip-hop rendition of “Can’t Take My Eyes Off of You” (1998), the verses of which conclude with a tonic EM triad (with center E) predicted by an Fв™Їm chord: “You’re just too [Fв™Їm] good to be true. Can’t keep my [EM] eyes off of you.” Hill’s pre-tonic Fв™Їm shares two pitch classes and scale degrees with both Radiohead’s B7 and the Toadies’ DM/Fв™Ї (Fв™Ї and A, 2 and 4).19 The anticipated voice-leading motions offered by these two shared notes presumably match in degree of aural similarity those offered by the two shared notes common to the DM/Fв™Ї and Radiohead’s Bm (D and Fв™Ї). This is to say, Fв™Їm could have been called, under a different theorization, a dominant rather than the subdominant it is under the current nomenclature (because of its chordal fifth 6, Cв™Ї). This discrepancy reflects the undeniable truth that there are multiple ways of hearing similarity, and thus multiple ways of using similarity as a basis for categorizing pre-tonic effects.20 Without negating the possibility or even potential usefulness of an alternative pre-tonic division, we will continue with the current categories, if only because the whole point of specifying kinds of pre-tonics according to anticipated voice-leading motions between scale degrees has been to give readers the opportunity to see and employ the familiar terms “dominant” and “subdominant” while making sure they do some useful work for us. If we so choose, we need not use these expressions; we can always resort to the Page 33 →more general classification of “pre-tonic” to describe a given functional effect, if that will suffice for our purposes. Readers at this point may wonder whether a single chord can function as both dominant and subdominant. The short answer to this question is yes, although such chords are relatively uncommon compared to their more singleminded pre-tonic siblings. One such poly-functional pre-tonic is the E7(m9) in the Beatles’ “I Want You (She’s So Heavy)” (1969), Example 1.4c. This chord promises resolution to a tonic Am by way of dominant motions—Gв™Ї to A (leading tone 7 to 1) and B to A (2 to 1)—and a subdominant motion F to E (an aeolian 6 to 5). John Lennon’s highly dissonant minor-ninth chord thus can be said to project “dominant-subdominant” function. This functional multivalency is not a failure on the part of either the theory or our hearing; it is simply a reflection of our willingness to recognize the potential richness of the harmony. (Indeed, functional multivalency at the level of major types—tonic, pre-tonic, etc.—is a normal feature of harmony, a point to be addressed in more detail in chapter 6.) It bears repeating that dominant and subdominant functions are qualities of predictions only; the resolutions need not be actualized, merely anticipated. Thus, even though the E7(m9) chord in “I Want You” resolves correctly just once in all of its four appearances (at the end of the first verse, when it relaxes into a tonic Am), it is no less a dominant-subdominant in those other instances when it goes somewhere else. At the same time, when dealing with any kind of pre-tonic chord, we obviously need to have a good idea as to the scale-degree makeup of the expected tonic: we must know which of the expected tonic’s scale degrees we are potentially traveling toward if we are to categorize pre-tonics according to their projected scale-degree motions. Often, as seen in the examples above, the 7 and 2 of a dominant predict resolution to center 1 (the latter being a requirement for tonic function), while the 6 of a subdominant anticipates 5 (5 typically being the chordal fifth of a tonic-functioning sonority). Yet other possibilities exist. On the dominant side, 2 can occasionally lean more toward 3 than 1; this motion is characteristic of augmented triads built on 5, such as the A+ sonority leading out of the first bridge of the Dave Clark Five’s “Glad All Over” (1963), Example 1.4d (“it’s by your side I will [A5] stay, I’ll [A+] stay. Our love will [DM] last now”). This dominant-functioning harmony sounds as though its chordal fifth (2) has been raised by a semitone—to Eв™Ї from the E in the previous A5—creating an intense desire to continue ascending to the predicted tonic chord’s third, Fв™Ї (3).21 On the subdominant side, 6 can gesticulate toward 1: such is the case with the opening rhythm-guitar riff to Metallica’s ominous “One” (1988), Example 1.4e. Page 34 →

Dominant and Subdominant Subtypes

Recognizing that the scale degrees of dominants and subdominants have more than one option with regard to anticipated resolution, and that these different anticipated resolutions correspond to somewhat different predictive qualities of the scale degrees’ encompassing chords, we might see a way to subdivide dominant and subdominant functions into subtler categories. But creating pre-tonic subtypes according to anticipated voiceleading resolutions turns out not to be very practical. Consider that whenever we encounter a dominant, we are likely to hear scale degree 2 forecasting 3 or 5, in addition to anticipating 1. (Uncommon cases such as the augmented triad in “Glad All Over,” wherein 2 gravitates exclusively toward 3, constitute exceptions that effectively prove this rule.)22 In the rapped verses to Eminem’s “We Made You” (2009), Example 1.5a, we repeatedly hear dominant DM/Fв™Ї resolve to tonic Gm at the end of each iteration of the looped progression (“You’re ready to tackle [DM/Fв™Ї] any task there is at hand. How does it feel? [Gm] Is it fantastic? Is it grand?”): the piano’s recurring 2–3 (A–Bв™-) gesture never quite extinguishes the potential of 2’s pull downward to 1 (G). In a comparable manner, a subdominant’s 6 often predicts resolution to both 5 and 1. In Example 1.5b, from the verses of Roxy Music’s “Love is the Drug” (1975), the disco bass line leads us from the 6 root of subdominant FM to the 1 root of Am, yet in Bryan Ferry’s backing vocal line, 6 (F) anticipates 5 (E): “Ain’t [Dm] no big thing to [FM] wait for the [Am] bell to ring.”23 Calling Eminem’s DM/Fв™Ї a “dominant” and Roxy Music’s FM a “subdominant” is sufficiently specific; we need not worry about splitting our descriptions of these commonplace predictions between all-purpose dominant and subdominant subtypes based solely on the multiplicity of locations to which the scale degrees might lead us. There are even cases where the voice-leading anticipation includes stasis. Returning to the Toadies’ DM /Fв™Ї in “Possum Kingdom” (Example 1.4a), we can now admit a slight trick in our earlier discussion of this dominant predicting resolution to tonic E5 at the end of the second chorus: in all statements of the song’s chorus except the second one, the resolution of DM/Fв™Ї is to E7, which, unlike E5, includes 7 (D), one of the two scale degrees that defined the DM/Fв™Ї as a dominant in the first place (the other was 2, Fв™Ї). This is to say, if we hear DM/Fв™Ї as a dominant predicting resolution not to E5 but to E7, then it is quite likely we are hearing the dominant’s 7 anticipate resolution not only to the tonic’s 1 but also its 7; that latter motion is indeed still a resolution, because of the surrounding harmonic context (the stability brought on by the new root 1), but this static line—an “oblique” motion in classical Page 35 →contrapuntal terms—points up just how many different compelling ways there can be to aurally link a pre-tonic to its predicted end. Subdominants are no different; see Example 1.5c. The famous tonic GM6 that ends the Beatles’ “She Loves You” (1963), for instance, is predicted by a CM triad, of which the chordal third E (the subdominant-defining scale degree 6) is sappily sustained in George Harrison’s vocal harmony (E becomes the 6 of GM6, on the final “yeah! ”), while John Lennon’s vocal E resolves down to D (5) and Paul McCartney’s vocal E resolves up to G (1). Multiple paths indeed! Example 35.1. Multiple predicted points of scale-degree resolution 1.5a. Dominant function in “We Made You” 1.5b. Subdominant function in “Love Is the Drug” 1.5c. Subdominant function in “She Loves You” It should be clear at this point that subdividing dominants and subdominants according to the vast number of possible voice-leading anticipations between the scale degrees of a pre-tonic and its predicted tonic is a daunting, if not foolhardy, proposition (especially as we begin to consider predicted tonics containing more and more notes, not just power chords and triads). We are better off coming to terms with the reality that the qualitative differences between, say, subdominants whose scale degree 6 anticipates only 5, Page 36 →versus subdominants whose 6 anticipates only 1, versus subdominants whose 6 anticipates 1, 5, and 6, and so on, are differences that our functional labels cannot reasonably be asked to address. A subdominant is a subdominant, whether its 6 predicts 5, or 1, or 6, or 3, or any other scale degree thought to be featured in the predicted tonic, or any combination thereof; ditto for a dominant and its 2 and 7. Of course, we may insist on locating very precisely the expected scale-degree destinations of the notes of some individual chord in a particular song, but it makes sense to refrain from devising a general distinction along these lines, because any given harmony will usually, as a matter of course, predict multiple points of resolution contained within any one resolving chord.24

While we cannot easily subdivide dominant and subdominant functions by appealing to differences in scale degrees’ predicted points of resolution, we can further refine dominant and subdominant categories by invoking a fixed point of reference, say, tonal center. By classifying pre-tonics based on the semitonal interval between tonal center and their relevant scale degrees, we can add another layer of specificity to our pre-tonic descriptors. Consider scale degree 6, which usually comes in one of two distinct flavors: nine semitones above 1 (or three below), which we will hereafter designate with a superscript up arrow as књ›6 (Cв™Ї in relation to E); and eight semitones above 1 (or four below), which we will designate with a superscript down arrow as књњ6 (C in relation to E). Example 1.6 lists all commonly occurring scale degrees with appropriate titles. (These are reproduced in Appendix C.) Referring to the former as “upper” and the latter as “lower,” we could accordingly differentiate between upper-subdominant function and lower-subdominant function, based on which version of 6 the pre-tonic contains. Some readers might wonder whether “major” and “minor” would be better terms to use here, but those words could easily be mistaken as indicators of the type of chord rather than the type of 6: with center E, a subdominant CM is better labeled a lower subdominant, rather than not a minor subdominant. Likewise, the more traditional binary of “sharp” versus “flat” is best avoided altogether here because there is no natural 6 (unraised or unlowered). This said, we still can refer to “6” without an up or down arrow to signify the scale degree in general, to include both upper and lower forms; this goes for every scale degree with no natural form. (When needed, additional arrows can be added, akin to additional sharps and flats: књ›књ›6, књњкњњ6, and so on.) The distinction between upper and lower subtypes of subdominants offers us a way to be more specific about what we are hearing, to articulate a fundamental qualitative difference between commonly occurring harmonic qualities. Such specificity is in no way compulsory since we always maintain Page 37 →control over how detailed we wish our analytical depictions to be. There are many situations in which it will pay to be less particular, but other cases will benefit from our being more detailed, including especially those songs offering both kinds of subdominants set in opposition to each other, as heard in Carl Perkins’ 1955 “Honey Don’t.” In the verse, tonic EM chords are predicted by a brash lower subdominant CM triad, creating a stark contrast between the implied major scale of the major tonic (with its Gв™Ї) and the implied minor scale of the lower subdominant (with its C: “Well [EM] how come you say you will when you won’t, ya [CM] tell me you do, baby, when you don’t? [EM]”) This contrast carries over to a deeper level when we compare the subdominant of the verse with that of the chorus: in the latter section, the tonic chords are anticipated by a tamer upper subdominant A7 chord. The palpable difference between these two separate pre-tonics contributes to the song’s distinctive sound (along with oscillating effects of the competing scales); the upper/lowersubdominant distinction gives voice to this sonic dichotomy (as will the notion of scalar effects in later in this chapter). Example 1.6. Commonly occurring scale degrees sharp/upper: в™Ї1 в™Ї2 књ›3 в™Ї4 в™Ї5 књ›6 књ›7 natural: flat/lower:

1

2 — 4 в™-2 књњ3

5 — — в™-5 књњ6 књњ7

In a similar way, we could differentiate between dominants featuring different versions of 7 or 2, measured in terms of the scale degrees’ semitonal relations to 1. Like 6, 7 commonly appears in two separate forms, the upper књ›7 (the leading tone: eleven semitones above 1, or one below) and the lower књњ7 (the subtonic: ten semitones above 1, or two below), and we noted earlier, during the discussion of “Lucky” and “Possum Kingdom” (Examples 1.1 and 1.2), that both are possible markers of dominant function. 2 comes in three forms, sharp в™Ї2 (three semitones above 1), natural 2 (two semitones above 1, the most prevalent version), and flat в™-2 (one semitone above 1). (“Sharp,” “natural,” and “flat” in this context do not necessarily pertain to letter notation, just semitonal distance from the version of the scale degree appearing in one of the four commonly occurring diatonic scales in rock—ionian (major), dorian, mixolydian, and aeolian (natural minor). E.g., with center E, в™Ї2 is Fв™Їв™Ї, natural 2 is Fв™Ї, and в™-2 is F.) But the middle version—natural—is the only one regularly featured by dominant-functioning sonorities (exceptions to this

fact are truly exceptional), so it makes sense to assume natural 2 when devising our general dominant subtypes. In other words, the most effective way to subdivide dominant function is in accordance solely with the kind of 7 involved. We will therefore speak of just two general kinds of dominants, Page 38 →those featuring the leading tone—which we will dub lead dominants—and those featuring the subtonic—which we will call rogue dominants. Both kinds were present in Radiohead’s “Lucky”: tonic Em was predicted by lead dominant B7 in the chorus and by rogue dominant Bm in the verse. The terms “lead” and “rogue” require some explanation, especially since we have already used “upper” and “lower” to subdivide subdominant function. Why not “upper dominant” and “lower dominant”? First of all, it would be awkward to have “lower” in the function’s description when one of its defining scale degrees is not в™-2 but natural 2 (even though 2 does not factor into the functional distinction itself). Second of all, and more significantly, “upper” and “lower” would not convey the affective difference—the difference in expressive meaning—that normally obtains between these dominant subtypes. “Lead” implies not just the leading tone but a quality of organized direction. “Rogue” implies a sense of relative independence, one that reflects an aural quality of resistance in comparison to the conformity indicative of most of their lead brethren. (This is relative. The rogue’s comparatively independent air nuances its more fundamental subservience to its predicted tonic.) Note that there is an opposition implied in these names: lead versus rogue. It is important to recognize that this opposition is observable within the rock repertory itself; it is not, as might be suspected by some readers, contingent on our comparing rock harmony (with its numerous rogues) with Western classical harmony (with its favoring of leads), even if the lead/rogue opposition could also be used for such a comparison. As mentioned in the introduction, there are all sorts of interesting ways in which these two repertories can be shown to relate, and there are close readings of many individual rock songs that may benefit from such an interpretive backdrop. But lead and rogue dominants normally operate as part of an expressive dialectic that is intra-repertory, independent of any larger, potential inter-repertory assessments. The typical competing expressive effects lead and rogue dominants project are directly relevant to our current discussion of semitonal intervals. As music-cognition scholarship has suggested, the leading tone is generally heard as more strongly attracted to 1 than is the subtonic, because the former is conceptually closer: one pitchclass semitone versus two.25 Of course, we just made a big deal about a pre-tonic’s scale degrees being free to anticipate any or all notes of a tonic in a particular context, but in the bulk of cases, 1 is a tonic’s strongest gravitational force. This relative proximity endows many—perhaps a majority of—lead dominants with a hyperloyal quality in regard to tonic prediction, one met by the rogues with a subtonic smirk. (These effects are made all the more palpable when juxtaposed within the same song, as they are in “Lucky.”) In this way, the normal expressive qualities of lead and Page 39 →rogue dominants mirror their 7s’ quantitatively distinct semitonal distances to tonal center. Quality and quantity in this regard are generally aligned. Although we have already implied that scale degree 2 is not a good feature to use for differentiating between subtypes of dominants, it should be said that when a dominant contains a 2 that is not natural—to wit, в™Ї2 and в™-2—the sound is definitely affected.26 We have already encountered an exceptional dominant with a в™Ї2, the augmented triad in the Dave Clark Five’s “Glad All Over” (Example 1.4d). Another relatively uncommon в™Ї2-containing dominant is the major triad built on the leading tone; Example 1.7a offers a specimen from the repeated Eв™-M–EM–FM hook from the opening of the Jimi Hendrix Experience’s “The Wind Cries Mary” (1967), with the EM functioning as a lead dominant of tonic FM (E is књ›7 and Gв™Ї is в™Ї2, resolving to 1 F). More unusual are pre-tonics pairing the leading tone with в™-2, but they do happen occasionally in jazz-rock contexts such as the Casinos’ 1967 cover of “Then You Can Tell Me Goodbye.” In Example 1.7b, the track’s brassy opening chord, Bв™-7(в™Ї9) (with Bв™-root serving as в™-2, and chordal seventh Aв™-doubling as Gв™Ї to serve as књ›7) collapses into tonic AM7 (A being 1), exemplifying a jazz phenomenon known as “tritone substitution,” to be discussed in chapter 5.27 Rarest is the coupling of the в™-2 and the subtonic, as seen in Example 1.7c. This rogue dominant FM7(6) (F is в™-2, and chordal major sixth D is књњ7, anticipating 1 E) is heard at the end of the chorus to Nick Drake’s 1972 “Parasite,” with Drake’s vocal line supplying the roguish D on the word “this”: “[FM7(6)]

for I am the parasite of this [EM] town.” If we so chose, we could devise functional subcategories for all of these relatively atypical chords; however, we will not bother doing so here. Instead we will opt to refer to each simply as a lead or rogue dominant, but with a peculiar shading.28

Pre-Tonic Function: Mediant versus Dominant Lead- and rogue-dominant function, together with upper- and lower-subdominant function, will serve us well as significant subtypes of tonic prediction. But there is still one more kind of pre-tonic function we should consider employing: mediant function. While not quite as conventional as the dominant or the subdominant, the mediant as a class of harmonic function is not without precedent; indeed, Hugo Riemann himself (coiner of harmonic “function”) proposed the possibility in 1917, and others have followed his example.29 Just as the other pretonic titles originally derive from those for the fifth and fourth scale degrees, “mediant” is named after 3, which mediates between 1 and 5 by roughly splitting the distance between them. We will use Page 40 →the term “mediant” precisely because 3 is essential to the harmonic predictive quality to be identified. There is an upper књ›3 (four semitones above 1; Gв™Ї above center E), and a lower књњ3 (three semitones above 1; G above center E). We hear књ›3 in the choruses to Lady Antebellum’s “Need You Now” (2009), Example 1.8a, wherein tonic-functioning EM alternates with mediant-functioning Gв™Їm (It’s a [EM] quarter after oneВ .В .В . and I [Gв™Їm] need you now. [EM] Said I wouldn’t callВ .В .В .”): the mediant’s књ›7 (Dв™Ї) and upper књ›3 (Gв™Ї, four semitones above 1, E) guide us toward tonic resolution in a manner similar to that of a dominant’s 7 and 2. But there is a significant difference between the potential resolutions of a dominant’s 2 and those of a mediant’s 3, in that only the former scale degree can possibly resolve directly by step to tonal center. In contrast,Page 41 → Antebellum’s root Gв™Ї књ›3 anticipates resolution by leap to 1, and additionally anticipates resolution to itself in the form of the chordal third of the tonic EM (also Gв™Ї). The predictive quality of the Gв™Їm triads is similar to that of a dominant (they even include 5, B, the root of many dominant-functioning chords), but the difference in voice leading creates enough of a distinction to warrant our creating a new functional designation of “mediant.” Example 40.1. Unusual dominants 1.7a. в™Ї2 and књ›7, “The Wind Cries Mary” 1.7b. в™-2 and књ›7, “Then You Can Tell Me Goodbye” 1.7c. в™-2 and књњ7, “Parasite” Appendix D summarizes all the functional classes we have so far discussed (and some we have yet to define). There, mediant functions hold a position equal to that of dominants and subdominants. Given this arrangement, we could potentially divide mediant function into subtypes, so as to match its two pre-tonic counterparts; however, an attempt at such division will have unforeseen repercussions, as will become clear shortly. The most obvious way to do this would be put pre-tonics with књ›3 and књ›7 in one camp, like the Gв™Їm from “Need You Now,” and those with књњ3 and књњ7 in another,30 like the pre-tonic GM triad in the repeating Em–GM guitar riff to Nirvana’s Unplugged performance of “About a Girl” (1994), Example 1.8b. (The chords in this live version actually sound as Eв™-m and Gв™-M, the guitars being tuned down a semitone from the original studio performance.) We might be tempted to label Antebellum’s chord an “upper mediant” and Nirvana’s a “lower mediant,” but there is another significant predictive quality to Nirvana’s GM triad that “lower mediant” does not adequately address. Instead, we will call Antebellum’s simply a mediant (књ›3 and књ›7) and Nirvana’s a new sort of rogue dominant (књњ3 and књњ7). This decision requires considerable explanation. Compare the pre-tonic GM in “About a Girl” to the rogue dominant DM/Fв™Ї that we encountered in the Toadies’ “Possum Kingdom”; see Example 1.8c. The peculiar connection between these harmonies lies in their bass voices: the Toadies’ 2 and Nirvana’s књњ3 both sound as though are right next to 1, and predict resolution directly to 1 by step. This stepwise quality was not an effect of the mediant in “Need You Now,” probably because Antebellum’s 3 was in its upper form, as opposed to Nirvana’s lower version, which is a semitone closer to 1. (Again, semitonal distance plays a role in the aural effect.) It is as though Nirvana’s књњ3 is not really a књњ3, or not just a књњ3. In fact, the root of this GM triad can be heard as a second scale degree in the E minor pentatonic scale (E, G, A, B, D), established clearly in Kurt Cobain’s

vocal line: “[B] I [D] need [E] an [G] ea- [A] -sy [G] friend”; see Example 1.8d.31 This G–E gesture thus represents not just a leap in a diatonic (seven-note) scale but also a step in a pentatonic (five-note) scale. Even though Nirvana’s harmony could be called a “lower (diatonic) mediant,” its effect as a pentatonic pretonic is actually far more potent that its mediant effect (although not necessarily more potent than its diatonic effect in toto, as will be explained in a moment). This Page 42 →reality holds true for most pre-tonics with књњ3 and књњ7, and consequently we will not divide mediant function into any sort of discrete subtypes; rather, all mediants will contain књ›3 and књ›7. (In the unlikely event we were faced with a purely diatonic-sounding pretonic with књњ3 and књњ7, it would be advisable not to call it a “mediant” and instead settle for the simpler “pre-tonic.”) Example 42.1. Mediant and pentatonic scale-degree motions 1.8a. Mediant function in “Need You Now” 1.8b. “About a Girl” on center E (transposed from center Eв™-) 1.8c. Rogue-dominant function in “Possum Kingdom” 1.8d. E minor pentatonic scale degrees in “About a Girl” Nirvana’s GM could actually be conceptualized as purely pentatonic, since it fits perfectly, as does its predicted resolution Em, into the E minor pentatonic scale. Yet pure pentatonicism is fairly rare in rock music; indeed, even in “About a Girl,” Nirvana breaks free of its pentatonic asceticism in its very next section (“I’ll take advantage whileВ .В .В .”). Pentatonicism in rock Page 43 →is typically blended with diatonicism, and so when encountering pentatonic harmony, we will be prone—assuming some basic familiarity with the repertory—to hearing these chords as diatonic-pentatonic hybrids. Since Nirvana’s pre-tonic GM is so strongly reminiscent of the Toadies’ pre-tonic DM/F♯—both sharing the rogue-defining diatonic књњ7 (D)—it makes sense to apply the same functional designation for both: rogue dominant. This decision requires that we modify our previous definition of dominant function, which assumed diatonic scale degrees 7 and 2. This is not as big a deal as it may sound: in our original definition, we made an implicit rule that a dominant normally (although again not always or exclusively) anticipates stepwise resolution to 1 from both below (7) and above (2), which we can now reformulate more generally as stepwise scale-degree anticipations toward the center from below and above, including not just diatonic but also pentatonic steps (while still allowing, of course, for additional or alternative anticipations in any specific song). To call Nirvana’s GM triad a “rogue dominant,” then, is to acknowledge its diatonicism and its pentatonicism: it is a rogue because its D pushes stepwise diatonically (as књ›7) upward to E; it is a dominant because its D and G respectively push stepwise pentatonically upward and downward to E. Consequently, pre-tonics featuring књ›7 and књ›3 will be labeled “mediants”; pre-tonics featuring књњ7 and књњ3 will be branded “rogue dominants.” The introduction of the pentatonic scale into the functional equation may cause us to wonder about other prevalent kinds of pentatonic pre-tonics, maybe even purely pentatonic pre-tonics, with no diatonic tints. It turns out that this is not really the case, at least not at any generalizable level. To see why, we must recognize that pentatonic scales in rock are nearly always either minor or major (E minor pentatonic: E, G, A, B, D; E major pentatonic: E, Fв™Ї, Gв™Ї, B, Cв™Ї). (Other types of pentatonic scales are possible but uncommon; we shall discuss this point fully in chapter 6.) Since these major and minor scales can be thought of as different configurations of the same notes, and since we can transpose them (move them all by the same pitch-class interval) to fit exactly onto the black keys of the piano (Fв™Ї, Gв™Ї, Aв™Ї, Cв™Ї, Dв™Ї or Gв™-, Aв™-, Bв™-, Dв™-, Eв™-), we can refer to them collectively as representing black-key pentatonicism (even though six of these scales—Em, Dm, Am, GM, FM, and CM—would not actually involve any black keys on a piano); or, alternatively, we can call it openstring pentatonicism, based on the standard tuning of a six-string guitar (E, A, D, G, B, E, although, again, all other transpositions are covered as well). In black-key/open-string scales, few possibilities exist for the two most common sonority-types in the repertory, the power chord and the triad: there are only four of the former and two of the latter (in the E minor pentatonic scale, for instance, these are E5, G5, A5, D5, EM and GM). Consequently, Page 44 →when pentatonicism seems to be at work in the harmony, it usually mingles freely with diatonicism. The GM–Em progression in “About a Girl” is actually not exceptional in this regard, because in the song’s very next section Nirvana breaks free of its pentatonic bindings to explore unmistakably diatonic spaces, and by the end of the chorus is throwing in the E major pentatonic scale for good measure: “[B] But I

[Cв™Ї] can’t [E] see [Gв™Ї] you [Fв™Ї] e- [E] -very [G (minor pentatonic)] ni- [E] -ght free.” So it is entirely reasonable for us to hear Nirvana’s GM triads as part of a larger scalar wash, to hear them as dominant-pentatonic pre-tonic hybrids. This goes for pentatonic-based pre-tonics in general: diatonicism is hardly ever far enough away to allow pentatonic harmony to project a pure version of itself.32 We might refer to this as rock’s “diatonic default,” something pentatonicism and chromaticism must overcome in order to assert themselves. As for the possibility of other diatonic-pentatonic pre-tonics, we should at least consider the scenario of two chords a semitone away where the lower chord is a tonic and the higher chord is a pre-tonic, effectively the functional reverse of Nirvana’s progression. Such a case presents itself in the repeating FM–Dm progression from the fast sections of the Isley Brothers’ iconic 1959 “Shout” ([FM] Shout! Kick my heels up and [Dm] shout! .В .В . ”). The pentatonic scale in question here is not minor but F major (F, G, A, C, D, into which both FM and Dm fit), and in this context Dm could hypothetically be understood as a kind of pentatonic mediant: the chordal root D could anticipate resolution up a major pentatonic step to tonal center F (just as a mediant’s књ›7 would do diatonically), and the chordal fifth A could anticipate resolution down two steps to tonal center F, as well as remaining static through FM’s chordal third (just like a mediant’s књ›3). However, there is too much scalar fog here to get a very strong sense of pentatonicism; the vocal lines occasionally stray from the major pentatonic scale (“[A] Don’t [G] for- [F] -get [Eв™-minor pentatonic] to [F] say”), and the bass motion between the two chords is never cleanly pentatonic, never simply D–F or F–D; rather, this space is always filled in with a passing diatonic E and also often with a chromatic (nonpentatonic, nondiatonic) Dв™Ї/Eв™-. This is the crux of the matter: hearing pentatonicism at all typically requires some clear, concrete statement of the scale’s distinctive three-semitone step, actual three-semitone distances between temporally adjacent pitches and not merely abstract motions between pitch-classes or scale degrees devoid of registral placement or rhythmic proximity. Black-key/open-string scales are aurally defined not by their total number of notes but by the kinds of steps they entail, especially the three-semitone step, on which they have a monopoly and which thus distinguishes them utterly from diatonic scales. Absent any real threesemitone motions, or faced with only a Page 45 →few that are far between, we will have little reason to hear anything other than diatonic-based harmony. The Isley Brothers’ Dm, therefore, to the extent we hear it as a pre-tonic, is best termed a (diatonic) upper subdominant (its root D being књ›6). This is true in general for these kinds of major-pentatonic progressions; the Isley Brothers’ sort, with a pre-tonic rooted three semitones below tonal center, is usually not particularly pentatonic sounding, while Nirvana’s sort, with a pre-tonic rooted three semitones above center, normally is pentatonic-sounding (although not just pentatonic-sounding). And with this, we have exhausted any potentially fruitful discussion of hypothetical pentatonic pre-tonics. It is necessary at this point to stop and recognize an emerging idea, that of the scalar effect. Whenever we hear a passage projecting a particular stepwise space with a ruling tonal center, we are hearing a scalar effect, of which the four most widespread types are pentatonic effects, diatonic effects, chromatic effects, and blue-note effects. When describing pentatonic effects, we will assume black-key/open-string pentatonicism unless otherwise stated, and we can further specify pentatonic major or pentatonic minor effects. The quality of pentatonicism is tied, as already stated, to the three-semitone step, but of course the interval of three semitones is present as a leap in diatonic scales, so the interval’s role as a pentatonic step or diatonic leap is shaped in large part by what else is going on around it (like the diatonic and chromatic fills in the fast sections of “Shout” or the purely pentatonic vocal line in the verses of “About a Girl”). Diatonic effects will entail white-key diatonicism, meaning adherence to one of the seven jazz modes (all of which can be transposed to fit exactly onto the white keys of a piano, even though the majority of these scales would actually involve at least one black key); thus we can comment on ionian (major) effects, dorian effects, mixolydian effects, and aeolian (natural minor) effects, and also, if warranted, the rarer effects of phrygian, lydian, and locrian. Shifting diatonic effects are one way to explain the battle between upper and lower subdominants we encountered earlier in Carl Perkins’ “Honey Don’t.”33 Chromatic effects are easy to find but a little trickier to define, if only because of the multitude of meanings the term “chromaticism” takes among musicians. In this book, chromaticism will not constitute an incursion by a new scale (the so-called “chromatic scale”) but rather merely a semitonal motion that temporarily takes us out of—or, alternatively, that transforms—a prevailing diatonic or pentatonic

scale.34 Likewise, there will be no appeals made to any sort of ostensible “blues scale,” but blue-note effects will be defined as those qualities projected when certain notes in pentatonic scales (particularly књњ3,књ›3, 5, књњ6, књ›6, and књњ7) are performed out of tune.35 All these scalar effects, save for blue-note effects, will figure Page 46 →prominently throughout this book. (For consideration of space, issues of tuning—including blue-note effects—will largely be ignored.) To sum up our entire discussion of pre-tonics, and to demonstrate the power and the limitations of our classification scheme, let us look at one final example, the Mamas and the Papas’ autobiographical and fatshaming “Creeque Alley” (1967). Each verse concludes with a clear prediction of and resolution to a tonic B7 chord, with B as 1, led by pre-tonic D7 (“and no one’s gettin’ [D7] fat ’cept Mama [B7] Cass”). The power of our system is apparent from the numerous different ways we can account for the functional effects of this pre-tonic. Example 1.9a interprets D7 as a rogue dominant split between diatonic and pentatonic scales: the roguish chordal fifth A keeps static as well as resolves up to center by diatonic step and resolves down to Fв™Ї (B7’s chordal fifth) by minor pentatonic step in the Mamas’ vocal harmony (“[A]’cept [A] Ma- [A] -ma [Fв™Ї] Cass”); the chordal root D hops down to tonal center B by pentatonic step in the bottom range of the guitar and in the Papas’ B minor pentatonic main vocal descent (“[Fв™Ї]’cept [E] Ma- [D] -ma [B] Cass”). However, if we interpret D7’s root not as D but as Cв™Їв™Ї pushing upward to Dв™Ї, then we might call the D7 a purely diatonic rogue dominant, since the root is now в™Ї2 resolving up by semitone and this interval is unavailable in a black-key/open-string space; see Example 1.9b. (We rejected a similar kind of analysis during our exploration of “About a Girl” because by labeling a note as “♯2” we are implying that its gravitational pull is specifically upward by semitone; in “Creeque Alley,” we are indeed primed for a possible semitonal resolution up to Dв™Ї because we hear this note for long stretches of time throughout the track, as the chordal third of each of the tonic-functioning B7s.) Even if we ignored the pre-tonic’s root altogether, we could still identify the sonority as a rogue dominant (if of an unusual kind) because of its chordal seventh, C, which, as в™-2, thrusts downward hard to 1; see Example 1.9c. One term—rogue dominant—covers all three of these different interpretations, but our ability to articulate the assorted aural aspects of this single harmony is testament to the classification scheme’s descriptive capacity. The scheme’s primary limitations are implied here by its not deciding automatically which of these three interpretations is the best or most obvious. Our pre-tonic types and subtypes do not make these kinds of decisions for us; they merely put a name to an effect. It is worth emphasizing here yet again that our pre-tonic descriptors describe functional effects—aural qualities—and so our application of these terms should ultimately be dictated not by any automated inventorying of scale degrees but rather by what we hear. Individual idiosyncrasies aside, we listeners will likely not be able to escape the influence of the minor pentatonicism in the various lines. The initial interpretation,Page 47 → then, Example 1.9a, will probably be the strongest of the three different rogue-dominant qualities, and accordingly we can say that the chord is first and foremost a split-scale rogue dominant, projecting both pentatonic and diatonic voice-leading anticipations. The other two rogue-dominant interpretations are not wrong, merely secondary. The main point is that these interpretations can be articulated, and through that articulation we may find it easier to hear the corresponding aural qualities, thus potentially adding another element to our experiential options. Example 47.1. D7–B7 progression in “Creeque Alley” 1.9a. Mixed diatonic-pentatonic rogue dominant 1.9b. Rogue dominant with в™Ї2 and књњ7 1.9c. Rogue dominant with в™-2 and књњ7 But more needs to be said here about the issue of choice as it applies to the nature of the theory we are building. Already in this first chapter, there is a tension starting to build between descriptive and prescriptive language, between reporting what can happen versus dictating what should happen.36 The actual technical vocabulary we have so far developed is about as clearly descriptive as one finds in the field of music theory; there is nothing in the theory’s letter that would suggest any one particular analysis of a given song is preferable. Indeed, there would seem to be something in the theory’s spirit Page 48 →that would suggest there is not a preferable one. (On another note, the theory is also not even especially explanatory at this point: it has focused mostly on the what as opposed to the why. This will become less and less true as the book progresses, although only to the extent that

such explanations will have a descriptive purpose.) And yet much of the analytical prose we have offered might insinuate another, contradictory position, as numerous other possible hearings are being argued against, downplayed, and for the most part utterly ignored. In fact, we have already made an explicit concession that we will be primarily addressing hearings that assume a basic familiarity with the particulars of the chords in question. Any new experience-relevant theory is guaranteed, at the very least, to conceptualize and label experiences in ways that differ from past or current ways, an act that would seem necessarily to involve prescription, if only in that such new conceptualization and labeling will emphasize those particular experiential matters over others. The theory here is thus no different from any other in this regard. More pressing is the question that if, according to the introduction, the purported goal of this book is “the richest possible experience of harmony”—hearing, in our technical sense—then how could this goal not require readers to engage the music in new ways? Would this not certainly involve prescribing new experiences? Would this lengthy book even be worth writing or reading if it did not have something new to prescribe? The best way to address these concerns is to recognize that while the theory we are painstakingly assembling will indeed allow descriptions of any and all hearings, in that it deliberately does not mandate which chords are analyzed in which ways, the analyses on which we are focused are specifically rich hearings. In other words, the theory embraces innumerable potential interpretations, but our use of the theory here is for much narrower purposes, purposes that entail favoring certain hearings over others. The justification given for constructing the framework—that it can lead to experiential enrichment—is essentially separable from the framework itself, which, once assembled, can serve to facilitate access to and verbalization of hearings as naive as a child’s or as seasoned as can be imagined, and everything in between. But to get there, we must first complete construction. Predictive qualities, chord-scale relationships, the interplay of center and tonic function, functional multivalence, chordal identity in general—these are all important topics of which this first chapter has merely scratched the surface. The many categorical distinctions posited so far represent only the first stage of production in an ongoing project, and as we continue to broaden our scope to engage more complex musical passages, it will become clear just how many different aural experiences still wait to be faced. Without a doubt, the fruits of our labors have only just begun to bud.

Page 49 →

Chapter 2 Chains, Numerals, and Levels Chained Functions The functional effects of tonic, dominant, subdominant, and mediant apply to a great number of harmonies in rock. Yet the qualities of (in)stability and prediction that constitute these pre-tonic functions surround many other sonorities that are not covered by these categories. Examples of such sonorities have already cropped up. In studying the chorus of Radiohead’s “Lucky,” for instance, we noted a series of three chords—C7, B7, and Em—that propelled us into the ensuing verse; see Example 2.1a. The highly unstable C7 pushed toward the relative stability of B7, and B7 itself drove toward the greater stability and resolution of Em. We eventually put precise names to the functional effects of the latter two chords: B7 pre-tonic (specifically, lead dominant) and Em tonic. Yet we gave no more attention to the initial C7. Following the taxonomical logic used so far, we can now call Radiohead’s C7 a kind of pre-pretonic (or gamma as we will later call it). Pre-pretonics are longrange predictors: by definition, they anticipate motion not just to one chord but to a succession of two. The first chord being predicted is itself a predictor, a pre-tonic, which, were it to arrive, would then anticipate its own harmonic resolution. When a pre-pretonic is fully accurate in its prediction, it creates a chain of functions, a series of three or more harmonies that are functionally interlocked. The C7–B7–Em progression in “Lucky” is a particular kind of functional chain that continuously moves toward an increasingly stable state of harmony. Yet unlike pretonic harmonies, which by definition project anticipation of relaxation toward a more stable state (i.e., a tonic), pre-pretonic harmonies more frequently entail a sense of greater stability than the chords they predict, building up the tension that peaks with a pre-tonic, as heard in the opening verse of Garth Brooks’ “The Dance” (1989): “[tonic GM] Lookin’ back on the [pre-pretonic CM] memory of the [dominant DM] dance we shared beneath the [tonic GM] stars above.” Thus pre-pretonics may or may not predictPage 50 → greater stability, but they do always predict another chord that is less stable than the tonic it promises. Example 50.2. Pre-pretonic (gamma) function 2.1a. Hyper pre-dominant (“Lucky”) 2.1b. Hyper presubdominant (“Itchycoo Park”) 2.1c. Hypo pre-mediant (“Anarchy in the UK”) Having previously divided pre-tonic function into dominant, subdominant, and mediant, it makes sense to break down pre-pretonic function into various subtypes as well. The most efficient course of action here is to add “pre-” to our existing pre-tonic categories, which produces pre-dominant (which applies to Radiohead’s C7 and Garth Brooks’ CM), pre-subdominant, and pre-mediant functions. Only the first of these is a recognized category in traditional harmonic theory, but that fact alone will not stop us from using the other two. Indeed, chords predicting a subdominant are ubiquitous in rock, and chords predicting a mediant, while actually quite rare, at least warrant acknowledgment, if only to round out the system. In the pre-choruses of the Small Faces’ druggy “Itchycoo Park” (1967), the defiant statement “I got high” is emphasized by a quick guitar and organ gesture made up of pre-subdominantPage 51 → GM/A falling to subdominant DM, which then resolves to tonic AM (supported by tonal center A). See Example 2.1b. In the verses of 1976’s “Anarchy in the UK,” the Sex Pistols sit on a tonic CM chord (C is center) that is punctuated every two bars by Steve Jones’ slashing guitar riff, which features pre-mediant FM thrusting downward to mediant Em, itself collapsing onto tonic CM (“I am an anti- [FM] -christ [Em] [CM]”). See Example 2.1c. Pre-dominant, pre-subdominant, and pre-mediant will be helpful terms as we continue to engage other types of functional chains and different kinds of harmonic progressions more generally. We might wish to partition these three categories even further to allow at least for the possibility of more precise designations, in a manner parallel to our earlier partitioning of dominant, subdominant, and mediant. To be exactly parallel, we should adopt the strategy of listening to anticipated scale-degree resolutions as they relate not to the tonic but rather to the

immediately expected chord: to the pre-tonic. The easiest way of doing this is to assume that the anticipated pretonic is built on a temporary, hypothetical 1, and that the preceding pre-pretonic is akin to a temporary, hypothetical dominant, subdominant, or mediant. In the case of “Lucky,” the B7 makes its root pitch class the pretend tonal center, so the C7 is a kind of reoriented lead dominant, with its C as в™-2 (instead of књњ6) and its Bв™-(Aв™Ї) as књ›7 (instead of в™-5/в™Ї4). There are some conventional terms that require discussion at this juncture: “secondary dominant,” “applied dominant,” and “artificial dominant.” In classical theory, these interchangeable terms are used to explain, among other things, chords that do not conform to a progression’s prevailing major or minor diatonic scale (assuming these is one).1 The simplest such progressions involve a major triad built on 2, which drives toward a major triad on 5, which then resolves to a tonic on 1. This sort of motion occurs in innumerable old-style bridge sections, such as that heard in Hank Williams’ “Hey Good Lookin’” (1951). Williams’ song also happens to loop this same chord progression throughout the verses: “[pre-dominant DM] How’s about cookin’ [dominant G7] somethin’ up with [tonic CM] me.” The scale being altered in Williams’ song would be C major, which fits all the chords except for DM (because of its third, Fв™Ї). DM would hence be a foreign, chromatic element, requiring some kind of special explanation; the notion of secondary/applied/artificial dominants provides such an explanation by creating an analogy between the triads GM–CM on the one hand and DM–GM on the other.2 And yet from our own perspective, such an explanation is unnecessary because we already know that rock songs frequently do not adhere to a single scale, even within the same section (this was one of our motivations for putting aside the traditional concept of key in chapter 1). Therefore, in the interest of avoiding Page 52 →the connotation of scalar alteration that clings to them, we will refrain altogether from using the expressions “secondary/applied/artificial dominant.” While we could easily substitute some other word for, while still maintaining the notion of, secondary/applied /artificial dominant, it would be more consistent with our previous work to outline another set of adjectives that could differentiate between the voice-leading anticipations of different sorts of pre-dominants, pre-subdominants, and pre-mediants. To this end, we will employ the adjectives hyper for dominant-like voice leading, hypo for subdominant-like, and medial for mediant-like. The first two terms appropriately reflect the typical strengths of their respective pre-pretonics: dominant motion is characteristically more forceful, more driven than is subdominant motion (although we will finesse this distinction later on); “medial” should not be taken to indicate greater pre-tonic strength than “hypo,” merely that it echoes a pre-tonic mediant’s scaledegree anticipations. “Hyper,” “hypo,” and “medial,” in combination with our three categories of pre-pretonics, result in the nine functional names listed in Example 2.2a. For the purpose of having a comprehensive theory, these labels serve a role, but they are obviously too cumbersome to use all the time, and we need not feel compelled to use them if less specific designations will do.3 (At any rate, even more labeling options, and simpler ones at that, will become available shortly.) Each one of these ostensibly detailed categories itself represents numerous possible scale-degree motions that would require many pages to discuss and a long cluttered table to illustrate. (Think of the large number of different anticipated voice leadings we discussed in chapter 1 in the context of predicting tonics and then multiple that by the number of different potential roots for pre-tonics in terms of upper/sharp, natural, and lower/flat scale degrees; i.e., multiply by eleven.) For these reasons, we will forgo exploring these labels further. Instead, let it suffice that we can now say, as shown in Examples 2.1a–c, that the C7 in “Lucky” is a hyper predominant since its C (temporary в™-2) and Bв™-(Aв™Ї) (temporary књ›7) anticipate dominant B7’s root B (temporary 1); the GM/A in “Itchycoo Park” is a hypo pre-subdominant since its B (temporary књ›6) anticipates subdominant DM’s root D (temporary 1); and the FM in “Anarchy in the UK” is a hypo pre-mediant since its C (temporary књњ6) anticipates Em’s root E (temporary 1). (For simplicity’s sake, we will take as a given the potential for alternative and multiple scale-degree voice-leading anticipations that might arise between pre-pretonics and pre-tonics, reflecting the similarly complex anticipations between pretonics and tonics. All hyper, hypo, and medial relations will be measured simply to the referential scale degree 1, which in these cases is not the true centric 1.) If we wanted to be even more detailed, we could add “lead” and “rogue” to Page 53 →our hyper

pre-pretonics and “upper” and “lower” to our hypo pre-pretonics, creating a layered nomenclature that itself begins to mimic the functional chains of chords often created with these functions. For that matter, we can move beyond the whole category of pre-pretonics to the next notch up on the chain, to pre-prepretonic function, and apply all these terms to that notch’s subtypes. And from there we could move to prepreprepretonic function, ad infinitum. While this route would be obstructed by many terminological tongue twisters, there are countless songs that would be candidates for such extra-long functional terms. Indeed, there are several lengthy harmonic progressions that have become standardized to the point now of being wholly predictable, and pre-preprepretonic function (and beyond) could be well said to apply to these longer (“extended”) harmonic schemas (which we will discuss in chapter 4). Nevertheless, in order to avoid being stuck with tediously named subtypes of pre-prepretonic function, we could simply apply “pre-” to our main pre-pretonic names, resulting in: pre-predominant, pre-presubdominant, and pre-premediant. The last of these is not especially useful because of its rarity, but the first two apply to innumerable cases. In the choruses to Coolio’s 1995 “Gangsta’s Paradise,” singer L.V. belts out the refrain over a repeating progression that starts with a pre-predominant: “[pre-predominant Aв™-M] We’ve been spending [pre-dominant Bв™-4] most our lives living [dominant GM] in the gangsta’s [tonic Cm/Eв™-] paradise.” (Coolio’s progression arrives as a reworked Page 54 →sample from Stevie Wonder’s 1976 “Pastime Paradise.”) In Weezer’s 1994 “Say It Ain’t So,” the loop begins on a pre-presubdominant: “[prepresubdominant Cm7] Somebody’s [pre-subdominant GM] Heiney is [subdominant Aв™-M] crowdin’ my [tonic Eв™-M] icebox.” Example 53.2. Labeling options 2.2a. Voice-leading subtypes of pre-pretonics hyper pre-dominant = dominant of a dominant hypo pre-dominant = subdominant of a dominant medial pre-dominant = mediant of a dominant hyper pre-subdominant = dominant of a subdominant hypo pre-subdominant = subdominant of a subdominant medial pre-subdominant = mediant of a subdominant hyper pre-mediant hypo pre-mediant medial pre-mediant

= dominant of a mediant = subdominant of a mediant = mediant of a mediant

2.2b. Greek-letter functions Yet even the terms “pre-predominant” and “pre-presubdominant” are too awkward to use all the time. It would be prudent to create an even simpler alternative nomenclature for pre-prepretonic functions and up. We will rely on position in a chain. If we count a tonic-functioning chord as being in first position of a functional chain and work backward, pre-tonic would be in second, pre-pretonic would be in third, and pre-prepretonic would be in fourth. Rather than using Arabic-numeric designations,4 we will avail ourselves of the letters of the Greek alphabet, symbols that are widely known and in plentiful supply (and which in fact can also be used as numerals, although true Greek numerals work in a slightly different way). If we named tonic the alpha function, pre-tonic would be beta function, pre-pretonic would be gamma function, pre-prepretonic would be delta function, pre-preprepretonic would be epsilon function; see Example 2.2b. We could keep going through the alphabet, but we would almost never need these other functional labels; functional chains are in reality not usually longer than five chords total (i.e., through epsilon). And since there is no reason to discard perfectly good terms such as “tonic,” “dominant,” and “pre-dominant” (especially after we have spent so much time redefining them), the most useful Greek names will be for fourth and fifth positions: delta and epsilon. So the harmonic functions in “Gangsta’s Paradise” would be delta, then pre-dominant, then dominant, then tonic; and in “Say It Ain’t So” they would be delta, then pre-subdominant, then subdominant, then tonic. In the chorus to Queen’s epochal 1977 “We Are the Champions,” after familiarizing ourselves with the progression to the point of hearing a tonic or predictive effect for each chord, the functions go up to epsilon (“[tonic FM] We are the [epsilon Am] champions, my [delta Dm] friends, [pre-dominant Bв™-M]

[dominant CM] andВ .В .В .”). The Greek labels specify only how many chords we are away from the predicted tonic; they trade specificity for simplicity. But all the “pre-” terms will remain at our disposal for whenever we choose to be more detailed; alternatively, it is possible to use a hybrid system, to create, for example, “hyper epsilon Am” (i.e., hyper pre-preprepretonic Am). In developing “hyper,” “hypo,” and “medial” as descriptors of voice-leading anticipations, we have also opened up a new labeling system for the pre-tonic functions theorized in chapter 1. A dominant can rightly be called a hyper pre-tonic (or hyper beta), a subdominant a hypo pre-tonic (or hypo beta), and a mediant a medial pre-tonic (or medial beta). We might want to Page 55 →go even further and recast the slanted binary of dominant vs. subdominant as one of “hyperdominant” versus “hypodominant,” but these would result in some comically unruly labels down the line; we will thus keep the slightly problematic “dominant” and “subdominant” where they were and accept that this binary is slightly biased in favor of the former (with its lack of a qualifying prefix).5 See Appendix D for a summary of predictive functions through epsilon, using various labels.

Numerals One labeling system that we have so far carefully avoided but that will help us immensely is Roman numeric notation. Roman numerals have been in use in classical tonal theory for more than two hundred years, yet rock musicians on the whole have not adopted them, preferring instead to identify chords in terms of letter notation. This reluctance of rock musicians is not by itself a sufficient reason to preclude the use of these numerals in the current theory. As with all inherited tools, however, numerals must be adopted with care; we should make absolutely sure that they perform the tasks we wish them to carry out and that they do not create more problems than they solve. Having defined our functional system, we are now in a position to devote close attention to this form of notation. Although it will take us some time to explore this system in detail, Roman numerals will prove incredibly handy, allowing us to indicate functional chains with speed and accuracy. Roman numeric notation—which we will hereafter call simply “numeric notation”—often uses major and natural minor versions of the diatonic scale as the basis for the numerals given to harmonies. The placement of a chord’s root within the scale determines the particular numeral, with the Arabic number becoming a Roman one; hence a chord built on 5 is designated “V.” This conventional method is fairly straightforward so long as a progression uses only one of these diatonic scales. Unfortunately, we know rock cannot be relied on to do this. If a passage centered on E freely mixes ionian (major) and aeolian (natural minor) diatonic scales, not to mention pentatonic, how do we know whether the symbol “III” signifies a chord on G or a chord on Gв™Ї? How are we to determine which scale will serve as the basis for that passage’s numerals? The simplest solution would be to use a single scale for all songs.6 Music theorists often take this route, and they usually choose as their all-purpose standard the ionian scale. In this method, harmonies built on the aeolian, lower versions of scale degrees књњ3, књњ6, and књњ7 are prefixed with a flat to indicatePage 56 → the alteration of the underlying major, natural-sign, scale degrees. Thus, with tonal center E, “III” would indicate a chord on Gв™Ї, and “в™-III” would denote a chord on G. This solution is convenient, but from a purely theoretical perspective it is arbitrary. We could just as easily make the natural-minor (aeolian) scale our standard, in which case, with center E, “III” would have a root of G and “♯III” would signify a sonority built on Gв™Ї. But the real problem here is not arbitrariness; it is the false generalization implied by using a single scale to measure all songs. The falsity is inherent in the explanatory method itself: all chord-supporting scale degrees we encounter in the repertory are evaluated according to—and, if they do not correspond, are conceptualized as variants of—the arbitrarily chosen standard. To call a chord on Gв™Ї a “III” and a chord on G a “в™-III” is to suggest that the latter is understood, in some way, as representing a lower version of the former, or at least as deriving from a scale-degree source that itself is altered. But aeolian harmonies are not less common variants—or any kind of variants—of ionian harmonies, certainly not at any generalizable level. (A particular song might suggest such a relationship, but that is a different story.) If we wish for our nomenclature to correlate consistently with our hearing, we should not accept this approach to numeric notation.

An alternative taxonomy more closely aligned with rock practice is presented in Example 2.3a (and in Appendix C). This system works on the principle of assigning sharps, flats, large up arrows, and large down arrows as prefixes to numerals according roughly to the commonness of those chords in the overall rock repertory.7 Supporting this system is the general belief that relatively uncommon musical structures can be meaningfully heard in terms of structures that are more widely used (assuming a fair degree of familiarity with the relevant repertory.)8 These numerals correspond to our scale-degree notation in terms of the prefixes (also in Appendix C), although в™Ї2 and в™Ї5 do not appear here as roots of chords because these chords are uncommon (unlike the scale degrees themselves, which are perfectly ordinary). Four numerals—I, II, IV, and V—have no prefix; these chords are shared among the four most common diatonic scales in the repertory at large: ionian, dorian, mixolydian, and aeolian. (Common scales with their diatonic numerals also are given in Appendix C.) These natural numerals can be modified up or down with sharps or flats, just like their corresponding scale degrees. (And just like the flats and sharps for scale degrees, the flats and sharps here indicate only the semitonal relationship to the natural version, and do not necessarily mean that the letter notation of the roots will contain a flat or sharp.) Only four sharp/flat numerals are regularly seen in rock—♯I, в™-II, в™ЇIV, Page 57 →and в™-V—the first two being different interpretations of a single chord (and which we will sometimes write as в™ЇI), ditto for the last two (в™ЇIV/в™-V); these chords are quite less common than their natural counterparts. III, VI, and VII, like scale degrees 3, 6, and 7, have no natural version, and so up and down arrows are used instead of sharps and flats. Sonorities built on an ionian scale would be written I, II, ↑III, IV, V, ↑VI, ↑VII; on an aeolian scale they would be I, II, ↓III, IV, V, ↓VI, ↓VII. (There is no reason this numeric system could not be used also for Western classical music, since chordal commonness in that repertory is roughly the same as in rock. Indeed, it might relieve some notational difficulties when dealing with different versions of VI and VII in minor keys.) The designations in Example 2.3a will cover most harmonies in the rock repertory, but, as we shall soon see, other possibilities exist. Example 57.2. Numeric notation 2.3a. Commonly occurring numerals 2.3b. Chordal roots with center E 2.3c. Stone Temple Pilots, “Big Bang Baby” (from verse) Example 2.3b illustrates the precise pitch classes that correspond to the roots of numerals when the tonal center is E; notice that the entire twelve-tone pitch-class set is covered from E through Dв™Ї. Example 2.3c features several of these chordal roots as they appear in the first half of the repeated four-bar guitar riff in the verses of Stone Temple Pilots’ “Big Bang Baby” (1996): in just two bars, we get I, ↓III, ↑III, IV, в™-V, V, ↓VI, ↑VI, and ↓VII. The highly chromatic nature of STP’s progression actually invites multiple interpretations of a few of the harmonies. The Bв™-5 в™-V, for instance, might be heard instead or Page 58 →additionally as an Aв™Ї5 в™ЇIV; neither letter nor numeric notation itself chooses between these two interpretations for us; that choice is the listener’s. Likewise, the Cв™Ї5 ↑VI might be heard as a Dв™-5 ↓↓VII (an interpretation favored by the officially published sheet music for the song). Even though ↓↓VII does not even appear in the chart of Example 2.3a, there is nothing stopping us from using it; we can freely extend this group of common numerals by adding as many arrows, sharps, and flats as are warranted on any numeral we wish. The only versions this system does not support are natural forms for III, VI, and VII; every other possibility is at our disposal. Despite its flexibility, this numeric system is fundamentally diatonic in nature. This means that pentatonic and chromatic scalar effects will not always be faithfully represented. Take STP’s initial three-semitone move from E to G, I to ↓III; this motion appears to leap over some diatonic version of F (в™-II, II, or в™ЇII), but this is easily understood simply as an E minor pentatonic step. Similarity, the one chromatic stop in the riff’s otherwise-pentatonic first five chords—lying between G5 ↓III and A5 IV—is necessarily written as a different version of the chord from which it departs: as Gв™Ї5 ↑III. (We do have the option of notating this chromatic departure as an Aв™-5 в™-IV, but this label exhibits the same problem in relation to A5 IV.) No matter the scale spoken, all harmonic information is translated into white-key language. As philosophically objectionable as this sounds, translation of this sort is really unavoidable. There is no one notational system that will show chromatic, diatonic, and pentatonic steps all as steps, and it is not practical to constantly switch back and forth between differently sized systems. In a way, though, using a diatonically based numeric system is in tune with our

assertion in the previous chapter that diatonicism is everywhere in rock. If there is one rock scala franca, it is the white-key diatonic scale (which serves already as the basis for our scale degrees, letter names, and staff notation). Care should be taken, however, that we do not allow our diatonic-based notation to cloud the possibility of hearing, say, pentatonic three-semitone steps (as opposed to diatonic three-semitone leaps), lest we miss out on some potentially important hearings. Our newly minted numeric notation is devised with the overall rock repertory in mind; it does not discriminate based on stylistic categories such as hard rock, country, and hip hop. This is an important point because some styles are, to a certain extent, harmonically defined by their regular use of numerals otherwise understood as rare, such as heavy metal’s heavy use of в™ЇI/в™-II and в™ЇIV/в™-V. Our flat/sharp notation fails to accurately represent relative commonness at the level of this musical style. In truth, no single notational system can reflect the details of every level of musical categorization, and Page 59 →since this book’s focus is on the big picture—on the harmony of the rock era—we must accept here a more distant, less nuanced view of the matter. All this said, our notation is not really that misleading: styles frequently using their own set of chords are defined in great part by their divergence from a larger repertory. This contrast helps to make these styles distinctive and unconventional. Indeed, listening to metal or other ostensibly subversive styles without also hearing mainstream music in the background would be to miss just how the musical subversion works. Even within individual songs this contrast is often apparent. In Marilyn Manson’s 1996 industrial-metal “The Beautiful People,” в™ЇIV/в™-V in the signature guitar riff (I–♯IV–I–♯IV–I) is juxtaposed with the bridge’s persistent, pedal-tone natural 5 and plain IV and V (“There’s no time to discriminate”), conveying not only a general stylistic subversion but also a particular lyrical theme: the social disparity between the “weak ones” and the pitiless “beautiful people.” To an extent, then, Manson’s harmonic subversion is apparent even without recourse to a broader rock standard, since even within the song we can clearly hear the disparity between the narrator’s symbolic harmonic idiom contrasted with that of oppressive, conformist mainstream. Some readers will no doubt be thrown by the exclusive employment here of capital numerals. Today’s North American musicians most often use a system employing both upper case (for augmented and major triads) and lower case (for minor and diminished triads). Rock music, however, sometimes offers sonorities containing both a chordal major and minor third; sometimes a sonority’s third is present only as an overtone (per the discussion of power chords in the introduction) and is therefore not self-evidently part of the chord; sometimes we will want to use one symbol to stand for a chord that is major in one iteration, minor in a later iteration, and a power chord in yet a later iteration (think back to the discussion in chapter 1 of the various tonic chords in the song “Blurry”; each of these is “I”). These and other situations call for all-purpose, upper-case numerals that do not specify or default to a particular kind of sonority.9 In circumstances where we want to be more specific about a harmony’s constituent tones, we can augment these root-only numerals with traditional triadic notation: e.g., I5, IM, Im, I+, Im7, I6, I4, I9, IM(m9), and so forth; see Appendix B for the equivalents of these chords in letter notation. (In chapter 4, we will add superscripts to the mix—e.g., “I5, IM, I+, IM7, etc.—indicating one specific note in addition to the root without precluding other possibilities.) For now, we just need to remember that when we use numerals by themselves, we are not specifying any particular kind of sonority, merely a chordal root. “V” and “V7,” for instance, are very different: “V” denotes one specific note (5) while allowing for any number of others (up Page 60 →to twelve total), while “V7” identifies exactly four notes (5, књ›7, 2, 4). (To get 5, књ›7, 4, we write “VM.”) The lack of specificity afforded by lone numerals will keep us from getting mired in the minutiae of letter notation and overly specific numeric notation when our attention should be elsewhere.

Numerals versus Functions One distinct advantage numerals have over letters is their closer relationship with functions. In chapter 1, we worked hard to classify differing pre-tonic qualities according to anticipated scale-degree resolutions, an action that effectively resulted in making certain scale degrees into markers for particular functional effects. In addition, for tonic function, we identified 1 as the essential scale degree. Since numerals represent nothing more than the

scale degrees of chordal roots, it stands to reason that a chord’s potential function(s) might be knowable from its numeral. In a few cases, this is definitely true: I is always a potential tonic, since we know for sure it includes 1; ↑VI and ↓VI are always potential subdominants, as they are built on the subdominant-defining књ›6 and књњ6. These are potential functions, not actual functions. As an aural quality, function is not knowable in the abstract; it must be assessed by ear in the context of a musical passage. Yet because numeric notation provides us with little direct information, we cannot with absolute certainty deduce all potential functions from numerals. For instance, since “IV” indicates only a chordal root on 4 and does not assure the existence of a chordal third on књ›6 or књњ6, we cannot know for sure whether a IV can even potentially function as a subdominant. (Or, we might say a IV is a potential subdominant only potentially.) Likewise, the fact that numerals only guarantee the existence of one scale degree (the root) precludes us from confidently identifying potential dominants and mediants altogether, since these functions by definition require two scale degrees each. On the other hand, if we are willing to relinquish certainty in the interest of usefulness, we can go ahead and assume a chord to have particular scale degrees beyond that which is denoted unequivocally by its numeral, and act that would allow us to see potential functions that are commonly realized by chords built on certain scale degrees. Almost always safe to assume is the scale degree that would serve as a chord’s (perfect) fifth: rock harmony primarily comprises power chords, major triads, and minor triads, and all three of these types of harmonies contain chordal (perfect) fifths. The presence of a chordal third is a harder assumption to justify, because of the repertory-wide deployment of power chords. But even in cases where Page 61 →the scale degrees required for a particular functional effect are not present, our own musical imaginations can add them. For example, in the Kinks’ “Tired of Waiting for You” (1965), the alternating chords outlined in the opening arpeggiated guitar riff (“[tonic G6 I] tired of [rogue dominant FM9 ↓VII] waitin’”) are thinned out later in the song (after the first bridge), when the texture becomes overwhelmed by G5 and F5 power chords. These F5s are just as much rogue dominants as their earlier FM9s even though they contain no chordal third 2 (A); whether we attribute the note’s absence to some kind of lyrical representation or simply a change in timbre, we are surely justified in imagining its contribution to the chord’s predictive and hierarchical effects. In other cases, even a single tone can create the effect of a harmonic function, as does the lone bass E (doubled at the octave) in the stop-time section (after the second chorus) in the middle of Jewel’s 1996 “Who Will Save Your Soul.” The bass’s lone 5 by itself is enough to convey V and, more importantly, to predict tonic resolution involving an imagined 2 and књ›7 or књњ7. In other words, Jewel’s single-tone V offers dominant function, whether rogue- or lead-dominant depends on whether we imagine the subtonic or the leading tone, although the former is more likely, given the Vm7 sonorities heard throughout the rest of the song. Musical contexts often suggest the presence of notes that are not truly there, whether those contexts are other parts of the song, earlier performances of the song, or, more generally, common harmonic schemas evoked by a series of sonorities or individual tones. (We will examine all these various types of contexts in due time.) Even a chordal root can be imagined, as likely happens when we listen to the opening verses of Prince and the Revolution’s 1984 “When Doves Cry”: the leading tone Gв™Ї at the end of the unharmonized line “of [G] you and I engaged in a [Gв™Ї] kiss” is easily heard as the chordal major third of a V, a sonority that gradually materializes over the course of the entire song. (Granted, Gв™Ї as the root of ↑VII would be another possibility, but since ↑VIIs are much less prevalent in the repertory and in this song, this possible hearing is much less obvious.) Imagined tones may seem to open up a can of worms, blurring the seemingly selfevident distinction between what we hear and what we wish we heard. The notion of imagined tones would appear to permit our claiming, among other things, that all dominant ↓VIIs and ↑VIIs and all subdominant ↑VIs and ↓VIs are really incomplete Vs and IVs respectively. (Such a claim would allow us to recapture traditional definitions of dominant and subdominant functions based on the presence of 5, although there are perhaps too many dominant ↓VIIs and ↑VIIs and subdominant ↑VIs and ↓VIs floating around the repertory to support hearing them all as inherently incomplete.) Dangers acknowledged, we must keep the division between real and imaginaryPage 62 → tones flexible if we are going to be honest about what we are actually experiencing when we listen; in reality, tones are all too easy to unknowingly imagine (ask any professional transcriber). Our taking into

(restrained) consideration the scale degrees that numerals connote, in addition to the actual scale degrees they denote, will enable us to use numerals as rough indicators of any of the functions we have theorized, even the ones involving two predicting notes. (And even if we were not to entertain imaginary tones, we could still use the more general “pre-” designations and Greek labels, which do not indicate anticipated scale-degree motions.) All this said, it would be ill-advised to attempt to make a large chart showing the potential functions of all numerically identified harmonies. Since there are innumerable scale-degree variations with regard to gammas (pre-pretonics) and up (deltas, epsilons, etc.), such a chart would be impractically dense. This fact might seem odd to those readers who already know that in many Western tonal-theory traditions, functions and numerals are often treated as though there were a one-to-one correspondence between them (a practice that traces back to Riemann’s using the names of 1, 4, and 5 as the labels for the basic functional categories themselves). Yet, this function-numeral synonymy is frequently suspended, even in classical theories: both V and ↑VII triads are customarily viewed as dominants, and II, в™-II, and IV triads as pre-dominants. In the current theory, functions and numerals are entirely distinct categories.10 The only real exceptions to this distinction are mediant and tonic function, which for all intents and purposes are wedded to ↑III and I respectively. The main, unspoken motivation for theorizing mediant function in the first place was to give a name to the pre-tonic quality of ↑III chords, so it is not surprising that no other numerals have any regular association with that function. Nevertheless, one could make the argument for extraordinary medial cases such as the main guitar riff to Sixpence None the Richer’s “Kiss Me” (1997): although the riff can be heard as a single I chord with a semitonal melody above it, we could also hear separate I chords—[Eв™-M] Kiss me [Eв™-M7] out of the bearded barley. [Eв™-7] Nightly, [Eв™-M7] besideВ .В .В .”—with the last Eв™-M7 I functioning as a mediant, complete with књ›3 (G) and књ›7 (D), resolving to the tonic Eв™-M I that starts the next iteration. (Alternatively, we could hear this mediant Eв™-M7 I as a mediant Gm/Eв™-↑III.) As for tonic function itself, I chords are the only real possibility, although so long as a chord contains 1, it is a potential tonic. There are indeed many cases of non-I chords resolving pre-tonic sonorities, at least in a temporary way, but to call these resolving non-I chords “tonics” is to drain the term of its viscerally descriptive power. A better approach is to theorize these non-I chords as projecting another Page 63 →kind of stable function. We will do this at the end of this chapter (in the section Anchoring Functions). Notwithstanding the exceptional cases of mediant and tonic, multiple numerals in general are capable of projecting any given function, and, likewise, multiple functions can be mapped onto every single numeral. For instance, with regard to the one-function-to-many-numerals claim, dominant function is expressed most often by V, ↓VII, ↓III, and ↑VII, all of which we encountered in chapter 1. Subdominant function is projected most often by IV, II, ↑VI, ↓VI, and в™-II, all of which we encountered in chapter 1 as well. And since all other hyper and hypo (and medial) functions behave like dominants and subdominants (and mediant ↑III) except for their allegiance to scale degrees beyond 1, we can envision some of the many assorted numerals that could communicate each of these other predictive functions by looking to the numerals we just cited as models. This is to say, for any gamma function (pre-pretonic) and up, we can transpose the previously mentioned numerals (V, ↓VII, ↓III, and ↑VII for dominant; IV, II, ↑VI, ↓VI, and в™-II for subdominant; ↑III for mediant) by the appropriate number of semitones to produce a fair number (although not absolutely all possibilities) of numerals that might likely function as hyper, hypo, and medial gammas respective to any other scale degree. For example, to generate numerals that might function as hyper pre-dominants to V, we first would find the predominant analogues to dominant V, ↓VII, IV, ↓III, and ↑VII: the analogue to V would be II (i.e., II is to V as V is to I), the analogue to ↓VII would be IV, the analogue to ↓III would be ↓VII, and the analogue to ↑VII would be в™ЇIV. As it turns out, all these hypothetical hyper pre-dominants do indeed occur in the repertory. We already heard hyper pre-dominant II in the form of the DM from Hank Williams’ “Hey Good Lookin’.” Hyper pre-dominant IV opens the looped IV–V–I–↑VI progression that runs throughout Coldplay’s 2008 “Viva la Vida.” ↓VII as hyper pre-dominant appears in the Ramones’ 1976 “Beat on the Brat” (“what can you lose? [↓VII] [V] What can you do?[I]”). в™ЇIV as hyper pre-dominant, usually projecting a chromatic effect because of its semitonal relation to surrounding IVs and Vs, is heard repeatedly in the bridge of the Dovells’ 1961 “Bristol Stomp”

(“[IV] .В .В . you’ll fall in love with me. [в™ЇIV] The [V] Bristol Stomp will [в™ЇIV] make you [V] mine, [в™ЇIV] all [V] mine”). All these hyper pre-dominants are specifically predicting dominant V; we could do a whole additional series each for dominant ↓VII, dominant ↓III, and ↑VII, not to mention в™-II and other less common dominant possibilities. (We previously heard a hyper pre-dominant of V that was a pre-dominant analogue to dominant в™-II: the C7 ↓VI resolving to B7 V in Radiohead’s “Lucky.” ↓VI is actually an incredibly common pre-dominant.) Yet the point has been made clear: Page 64 →gamma functions and up are even more numerically promiscuous than their pre-tonic counterparts. Flipping around now to the many-functions-to-one-numeral claim, we could cite numerous significant examples, but there are two specific numerals that will inevitably be on the minds of skeptical readers: V and I. Although V typically functions as a dominant, it can on occasion function more as a predictor of subdominant IV, as a hypo pre-subdominant: in The Who’s “Baba O’Riley” (1971), the electro-minimalist opening inspired by namesake composer Terry Riley is foiled by Pete Townshend’s crashing I–V–IV(–I) piano chords, of which the fleeting V falls not to I but to IV. V also occasionally functions simultaneously as a dominant and a subdominant when it contains a 6 along with a 2 (or књњ3) and 7, as witnessed in the previous chapter with the Beatles’ E7(m9) V (with књ›7 as its third, 2 as its fifth, and књњ6 as its ninth) from “I Want You (She’s So Heavy)” (Example 1.4c). Relevant here as well is the jazzy dominant-subdominant V11(-3) (“-3” meaning “no third”), heard in its characteristically thirdless form as the opening B11(-3) sonority of Wings’ “With a Little Luck” (1978); see Example 2.4a. The chordal ninth is књ›6 (Cв™Ї), the chordal fifth is scale degree 2 (Fв™Ї), and the chordal third—which we must imagine if we are to hear true dominant function—would be either књ›7 or књњ7 (Dв™Ї or D). The V11(-3) is a tricky chord; it is often identified as a IV major triad over a bass 5 (IVM/5, here AM/B), even though the V11(-3)’s chordal fifth, scale degree 2 (B), is usually quite strong, and even when it is not strong the bass 5 normally features 2 as a noticeable overtone.11 (There would be no such scale degree 2 in a IVM/5.) The functional multivalency of the Beatles’ and Wings’ individual Vs exemplify the more general point here regarding the multiplicity of numerals’ functional potential. A V can function in more than one way: it is not necessarily a dominant, and not necessarily just a dominant. As for I chords, we know they are defaulted to tonic function. Yet a I can instead serve as an unstable predictor of other functions, most notably IV and V. When manifesting itself as a major-minor seventh chord (7), I often sets up a move to IV, functioning as a pre-subdominant or pre-predominant (depending on the nature of the IV); the pre-predominant version happens in Elvis’s 1956 recording of “Love Me” as F9 (which contains F7 within it: “Treat me like a [FM I] fool, treat me mean and [F9 I] cruel, but [Bв™-M IV] love me [V]”). As a predictor of dominant D7 V, GM I appears at the end of the second verse, leading into the bridge, of Paul Simon’s 1975 “Still Crazy after All These Years”; see Example 2.4b. Readers already accustomed to classical numeric notation might balk at using the label “I” for a non-tonic chord, preferring instead “V/IV” (“V of IV”) for Elvis’s F9 and perhaps even “IV/V” (“IV of V”) for Simon’s GM (or Page 65 →more typically “cadential 64” for the latter, as we shall discuss in a moment). Numeral-of-numeral labels represent a venerable technique of chordal identification, and they parallel our own hyper/hypo method of classifying gammas (and up), which are measured always in reference to some particular predicted numeral: Elvis’s F9 I, for instance, is “hyper” specifically in relation to IV, and in this sense is as much a pre-IV as it is a pre-predominant. There is nothing wrong with calling Elvis’s chord a “V/IV,” except that numeral-of-numeral notation is closely associated with the concept of secondary/applied/artificial dominants (which we have already declined to use), and additionally it conflates numerals and functions by trying to convey functional information (predictive and possibly hierarchical effects) through the numeric notation. For these reasons, we will avoid these designations. I will always be I, whether it functions as tonic, or as pre-dominant, or as pre-predominant, or as anything else; the same is true of all other numerals. Strict fidelity to our basic numeric nomenclature will pay off when dealing with an individual harmony that functions in multiple, contradictory ways (a phenomenon to be explored in depth in chapter 6). Pre-numeral notation such as “pre-IV” is not as problematic as numeral-of-numeral, since it is nonstandard (it has no accrued connotations) and since it uses the prefix “pre-” rather than a numeral to indicate the actual

function. Indeed, it has a certain advantage over pre-function labels in that its identification of the predicted chord Page 66 →according to the scale degree of its root does not require the predicted chord’s function (which we might not be able to guess). Nonetheless, we already have an abundance of labels at our disposal, so we will not need to adopt this additional notational style, except for a few particular situations in which it will be especially helpful. Example 65.2. Numerous functions for V and I 2.4a. Combined dominant and subdominant function (opening of “With a Little Luck”) 2.4b. Pre-dominant I? (“Still Crazy after All These Years”)

Harmonic Levels, Functional Strengths, and Identity as Effect It is all well and good to differentiate between numerals and functions in the abstract. But listening to real music often involves making simultaneous judgments about each; to hear a chordal root in a scale is frequently also to hear a function, and vice versa. Take for instance the non-tonic GM/D I we identified in “Still Crazy after All These Years.” This sonority is an example of a phenomenon known in the classical music world as a “cadential 64” (among other names).12 In certain brands of Western classical tonal theory—most notably Schenkerian theory—the cadential 64 is viewed not as a true chord in its own right but rather as the temporary result of two unstable nonchord tones (here G and B) above a root 5 (D), with the nonchord tones anticipating resolution to the chordal third and fifth (Fв™Ї and A) of the actual chord awaiting completion: dominant V.13 In this hearing, the chordal root and third of the I are not a root and third at all, and moreover the chord itself is not a I but a partially materialized V.14 This interpretation appropriately highlights the GM/D’s aural quality of dependence on the resolving dominant D7, as well as the clear trajectory toward to D upward from the в™Ї4 root of the preceding Cв™Їo7 в™ЇIV. But it says nothing about the GM/D’s functional potential as a tonic. This tonic potential is hard to ignore given that there are six spots in the song like this one (each of the song’s three verses has two titular refrains) and in half of those instances we get a GM triad with a bass note not of D but of the root G: in first verse the bass notes are D then G, and in the second and third verses they are G then D. These GM /G triads project stronger tonic effects than do the GM/D triads, but the chords’ interchangeability in these sections would seem to support our decision to use a single numeral (I) for both versions of theses GM triads and would support our hearing at least some tonic function emanating from the GM/D. What is at stake here is the recognition of two contradictory aspects of the GM/D: the tonic-functional potential of a triad with the tonal center as its root, versus the strong impression made by the bass note 5 in the context of a predicted dominant V. As a tonic, GM/D would be more stable than dominant V, but as a pre-dominant it is less stable, to the point where we might not Page 67 →even hear it cohere as a chord at all. In order to give voice to both sides of this sonority, we can make a distinction between harmonic levels: on one level, we hear GM/D as a pre-dominant I, followed by dominant D7 V; on another level, the GM/D functions as a pre-dominant to the D7; on yet another level, the GM/D evaporates entirely, leaving behind the dominant D7 V as the only harmonic entity (we will later speak of “entity effects”). Our differentiating between levels of aural focus on Simon’s GM/D is no academic exercise; it is an instance of how harmonic hearing always goes. Indeed, we have been silently employing such harmonic levels this whole time, throughout all the various examples we have explored since the opening chapter. Even in “Still Crazy, ” we unceremoniously interpreted Simon’s song as containing a D7 V after the GM/D I, even though at this point there is a B in the vocals (on “all”) and in the distant electric guitar; we ignored this B in favor of the following A, which we construed as the V’s chordal fifth. To include this B as a chord tone, we could reidentify the V as a D7(6)—D, Fв™Ї, A, B, C—or we might rearrange the notes to spell a Bm7(m9) ↑III—B, D, Fв™Ї, A, C. Or we might hear two chords, the first with B and the second with A, echoing our decision to keep GM/D I and D7 V separate on the next level. Whenever we hear rock music in terms of chords, we are necessarily making many interpretive choices: even in our simple acknowledgment of the existence of Simon’s indisputable dominant V, we must decide which tones are parts of the chord and which are not. This is one area in particular where veteran listeners’ experiences can vary widely amongst themselves, partly because it is subjectively based and partly because there is often not agreement over (or even explicit discussion of) the factors that go into these decisions.15

In determining when a new harmony has occurred and what pitch classes it comprises, we can employ several distinct aural criteria. These criteria are part of a messy intuitive process; nonetheless, for the purposes of discussion, these factors can be extracted and identified individually. One criterion is timbral and textural similarity/dissimilarity; generally speaking, it is harder to hear a note as a nonchord tone—as unstable with regard to the sounding chord—if it is sounded along with other tones by a polyphonic instrument such as a guitar or keyboard, whereas it is easier to separate pitches from a chord if they appear in individual vocal or other singleline parts. This is why Simon’s B was so easy to ignore: it was sonically separated from the primary polyphonic instrument playing in the texture, the keyboard.16 Another criterion is the harmonic pulse (otherwise known as “harmonic rhythm”): our sensing that a new harmony has arrived is largely dependent on the arrival point’s coinciding with our expectations about the rate of chordal change, expectations based on comparisons to Page 68 →what has happened so far in the song as well as to stylistic conventions.17 In “Still Crazy,” for the most part, the harmony changes once every slow beat (subdivided into threes), and so it is natural for us to expect two discrete chords on the two beats of “crazy after” and “all these.” The literal speed of the harmonic pulse also matters: the slower the harmonies change, the more likely we will accept dissonances as stable, which again supports hearing the GM/D as a its own chord. Another criterion is the degree of pitch-class change: if the note content shifts drastically, we doubtless will hear a new chord occurring, while a small change may indicate a mere nonchord tone or tones, especially if the bass of the current sonority persists as the bass of the next chordal candidate. Simon’s GM/D and D7 have the same bass note, a fact that supports our hearing the two sonorities fused together as one essential harmony. Small variations in chords that are repeated throughout a song also do not usually change our sense of what these chords are, although such changes must be evaluated on a case-by-case basis. Since Simon alternates the bass note of his GM triad between G and D, we might take these differences into account when determining their status as independent harmonies: that is, if we hear the GM triad with G in the bass as its own chord, then this fact might help push us into hearing GM/D as its own chord as well. One final criterion we often use in distinguishing between relatively stable chord tones and relatively unstable nonchord tones is acoustic dissonance. Musicians in fact frequently use “dissonant” as a metaphorical synonym for “unstable” when describing nonchord tones. If two simultaneous pitches create a dissonant interval, we are less likely to hear both of them operating as chord tones. The issue is how to define what counts as dissonant. Consonance and dissonance are areas along a continuum, not discrete categories, and where we as listeners draw the line between them is dictated in part by the harmonic conventions of individual musical styles, which of course change over time. The history of Western music can in fact be understood as exhibiting a gradual relaxation of attitudes toward dissonance; that is, Westerners’ definition of consonance has steadily broadened. This statement is even more true if we consider issues of tuning: today’s equally tempered perfect fifths, for instance, would almost certainly not have sounded very sweet to the ears of a Renaissance musician. As a dissonance-defining style, rock offers an abundance of sonorities that seem to stand on their own as chords, which is to say that rock musicians’ attitudes toward dissonance are incredibly permissive by previous standards. While the triad and the power chord are certainly the most prevalent types of chords in the overall repertory, many other structures are also standard, including seventh, ninth, and eleventh chords, 4-chords Page 69 →and 2-chords (or “sus4” and “sus2”), 6-chords (or “add6”) (see Appendix B), and to a lesser extent quartal chords (built entirely in consecutive fourths, a type of harmony mainly restricted to prog rock). In essence, any imaginable combination of notes can cohere as a chord, a fact that reveals acoustic dissonance to be a meaningful criterion for rock’s nonchord tones only when other musical factors point to possible instability.18 In one setting, a given dissonant sonority may sound like a stable set of chord tones (i.e., a pure chord), while in another setting that same dissonant sonority may sound like a nonchord tone (or multiple nonchord tones) plus a partially obscured chord. The final tonic I chord of Bobby Darin’s riveting interpretation of “Mack the Knife” (1959, based on the originally German-language song from Kurt Weill and Bertolt Brecht’s 1928 Threepenny Opera), is a drawn-out tonic I thirteenth chord with sharp eleventh, which sounds perfectly stable despite the scale degree в™Ї4 (the chordal sharp eleventh) that forms a tritone above the center-root. Yet the tonic thirteenth chord at the end of Les Paul and Mary Ford’s recording of the traditional song “The World Is Waiting for the Sunrise” (1951) is not nearly so stable-sounding; even with its harsh, brassy timbre, Weill’s chord is prepared by the many-noted chords immediately prior to it, while

Paul’s warmer multitracked guitar sonority cannot quite shake its lack of preparation.19 A terminological issue that we should address here concerns the “sus2” and “sus4,” or what we have been calling simply “2-chords” and “4-chords.”20 The “sus” in these terms is an abbreviation of “suspended,” meaning that the note in question (a major second or perfect fourth above the root) is a dissonant nonchord tone (against the root and/or fifth) that sounds unstable and seeks resolution to an actual chord tone (usually a chordal third, a diatonic step away).21 If a sonority is truly a 2-chord or 4-chord, then by definition its 2 or 4 cannot be a nonchord tone and thus is not being suspended. In other words, “sus2” and “sus4” are self-contradictory labels, hence our easy rejection of the “sus” part of the term. The final tonic I sonority of Joni Mitchell’s folksy “I Had a King” (1968) is a crystal-clear, open-string A2 chord that requires resolution no more than would a major or minor I.22 Yet self-coherent 2-chords and 4-chords may indeed be unstable at a different harmonic level. In Foreigner’s single-minded hit “Hot Blooded” (1978), the tonic G4 I chord that begins the guitar riff accompanying the refrain (“[G4] hot blood- [GM] ed”) can be thought of as its own harmony, but at the next level it will most certainly sound unstable against the subsequent GM; and since the only difference in notes between these two fast-moving sonorities is the dissonant fourth (C) versus the consonant third (B), these two chords will fuse into one—GM—with the C sounding as a nonharmonic tone.23 In recognizing that the pitch-class content of chords, and thus their Page 70 →numeric designations, are not selfevident but rather determined by a complex process of aural interpretation, we arrive at the idea that a chord’s numeric identity itself can be theorized as an aural effect, a numeric effect. From there, we could say the quality of a chord’s cohering around certain pitch classes with one as the root—a quality describable by a full letter designation—is a letter effect. Even the most fundamental forms of harmonic identity, that of a chord’s cohering around some root by itself (irrespective of what the other chord tones are), and that of a chord’s existence at all as its own entity, can be thought of as effects, as root effects and entity effects respectively.24 (The expression “entity effect” can also describe the coherence of multiple chords (two or more) into that other fundamental harmonic entity known as the “progression.”) We could go further and describe the effects of individual tones by themselves: pitch effects would be those projected when we hear a frequency as its own acoustical fundamental and not merely within the timbral envelope of another tone (i.e., as a weak overtone); pitch-class effects would be those projected by all individual tones whose frequencies differ only by octaves. Such notions appropriately highlight the absolutely foundational role that the listening subject, and thus too subjective interpretation, plays in our recognition of harmonic objects as objects. Entity effects and numeric effects in particular are helpful in explaining common discrepancies between different listeners’ interpretations of certain chords: a sonority such as the GM/D in “Still Crazy” projects both I and V identities simultaneously, at different levels. Similarly, major triads with a major sixth above the root—e.g., EM6—can often be understood alternatively as minor-minor seventh chords with their thirds in the bass (Cв™Їm7/E); this regularly happens when the chords are either: IV or II; I or ↑VI; ↓VI or IV; or ↓VII or V. A chord by itself, insofar as it manifests the relationships between individual pitches, represents on its own an entire harmonic level, while the relationship between that chord and another chord represents an altogether different harmonic level. The aural criteria we use to determine the relative (in)stability between individual tones in relation to a single chord, which we have just examined, are not quite the same as those we use between distinct harmonies (although there is some overlap). The chord-to-chord criteria are much more complex, and this complexity requires long and detailed discussion that must be postponed until chapter 6, at which point we will have all the necessary components of the current theory at our disposal. This said, it is appropriate here to acknowledge that once we move beyond nonchord tones, the effect of (in)stability by itself is inadequate to describe how the arrangement of harmonic levels is determined. We need the aid of the additional concept of functional strength. Page 71 →Let us consider a simple example, the Troggs’ “Wild Thing” (1966), with its repeating progression I–IV–V–IV(–I): “[I] Wild thing, [IV] [V] [IV] you make my [I] heart sing”; see Example 2.5. Levels are already in place if we accept the claim that the progression is indeed I–IV–V–IV(–I), because the guitars frequently fill in the spaces between these harmonies with

nonchord tones or sonorities that might even qualify as chords unto themselves. But levels are also helpful in describing the functional effects of the V–IV(–I) motion. The I is of course a tonic, and the preceding IV ambles toward it as a subdominant. The V predicts subdominant IV, but it also, much more strongly, predicts tonic I itself: the V is probably going to be more of a dominant and as such represents the most harmonically unstable moment in the entire progression, a tension built up beforehand by gamma pre-dominant IV. Our invoking harmonic levels is useful here because dominant effect, as we have defined it, involves prediction of immediate resolution to tonic, not merely eventual resolution. On one level, that of the full progression I–IV–V–IV(–I), the V is a pre-subdominant (gamma) to IV, but on a deeper level it is a dominant that correctly predicts direct resolution to tonic, as part of the shorter functional chain I–IV–V(–I). (The first IV will change functions as well, serving as a delta (pre-presubdominant) when we are hearing V as a presubdominant, but serving as a pre-dominant when V is a dominant.) And since the V is the focus of the middle part of the progression, being the chord that most obviously points us back to tonic, it would make sense to think of an even deeper level that features just I–V(–I), the hierarchical pairing of a tonic and pre-tonic. The deepest possible level would include only the harmony-defining tonic I, the point to which every other chord aspires to resolve. We thus have defined four distinct harmonic levels, each with its own progression: I–IV–V–IV(–I), I–IV–V(–I), I–V(–I), and finally just I. When comparing these progressions at different levels of “Wild Thing,” it becomes clear that we are not constructing a hierarchy of chords based simply on their stability, but rather one based on a combination of stability and functional strength. (We can also speak of centric strength—how strongly we feel a specific tonal center—which will be become important when we examine centric ambiguity in chapter 6.) The IVs are each more stable than the V, but it is the V that remains in effect the longest. It is the V’s strength of dominant function that establishes the chord so securely within the chordal hierarchy, a functional strength that overrides the chord’s quality of instability. The relative instability and strength of first IV versus those of the second IV are not palpably different, so the second level down could in fact be either I–IV–V(–I) or I–V–IV(–I), or we could simply dispense with this level altogether since it is really the I–V(–I) that constitutes the deepest motion (although the Troggs Page 72 →actually give us the shorter I–IV–V–I a few times in the song, most notably right before the final chorus, where the V is greatly drawn-out in order to prolong the harmonic tension). The point here is that the functional strength of the V as a dominant essentially eclipses the chord’s additional function as a pre-subdominant, and this same dominant–functional strength pushes the chord past the two IVs in terms of hierarchical rank, despite its being the single most unstable sonority in the progression. Example 72.2. Harmonic levels in “Wild Thing” tonic I – delta IV – pre-subdominant V – subdominant IV – tonic I tonic I – pre-dominant IV – dominant V – – tonic I tonic I – – dominant V – – tonic I tonic I –

– tonic I

This interpretation of the Troggs’ V–IV(–I) might at first seem strange, since it may appear to give too much weight to V and not enough to IV. Certainly we should not confuse the justifiable claim that the V operates at a deeper level than the IV with the unjustifiable claim that the IV is musically dispensable. The IV is of course an essential part of the sound and meaning of the song; after all, IV–I is the quintessential sound of rock harmony at large. As we noted in chapter 1, hierarchical superordination does not equate to aesthetic importance. Yet in the particular case of “Wild Thing,” the V’s drive toward one I is much stronger than the IV’s, and if we hear the V as a pre-tonic that resolves as predicted, we must conceive of it as moving directly to tonic on some level where the IV is absent. Supporting this interpretation is the fact that we actually hear a V–I motion—without an intervening IV—in two spots in the song, first in the instrumental introduction right before the singer comes in, the second when the extended instrumental V prepares the final iterations of the fadeout chorus. The overall sound changes at these two points, yet the harmonic progressions are clearly propped up by the same infrastructure. Hence the IV–I motion is an embellishment of, or is embedded within, the

V–I motion, and when the Troggs leave out the IV, the harmonic momentum sounds more or less undisturbed. By contrast, if the Troggs took out the V and left the IV, the motion would sound fundamentally different. The situation is nearly identical in Ritchie Valens’ 1958 “La Bamba”: we hear the same repeating I–IV–V–IV progression throughout, and occasionally the IV is dropped altogether (when the band drops out and Valens sings the titular refrain). When we do get the IV, it starts as the last note of an ascending majorminor seventh chord arpeggio of V (5–ꜛ7–2–4), as though the IV were merely part of the V (the chordal seventh, 4). We could say that Page 73 →Valens’ IV does not project a strong entity effect; in fact, not all listeners recognize it as its own chord.25 At any rate, the IV clearly does not operate on as deep a level as the V. Hearing the V–IV–I progression in “Wild Thing” and “La Bamba” is certainly not necessitated by any properties inherent to the numeric series itself. As we observed earlier in this chapter, the same V–IV–I series appears in the riff to The Who’s “Baba O’Riley,” and in that case the V functions more as a pre-subdominant, within a hierarchy that favors IV–I at a deeper level. These two distinct interpretations of the same numeric series serve to illustrate that functions and functional strengths—and therefore harmonic levels too—exist only in the context of actual pieces of music. Indeed, the same musical factors that determine harmonic function are the same ones that help determine strengths and levels (beyond chord tones versus nonchord tones), factors that we will spell out in chapter 6. The chaos of real music prevents us from forecasting with certainty just how harmonic levels will result in each and every case of numeric series. All this said, an abstract numeric series such as V–IV–I has a very limited number of hierarchical possibilities, and furthermore it often arrives in one of only a few typical musical settings. Thus while we cannot be certain about which functional effects any given progression will project simply based on its numerals, we usually can be fairly accurate in guessing a limited range of functional possibilities. Such generalizations about progressions’ functions, functional strengths, and harmonic levels will be offered throughout the next two chapters on schemas.

Additional Functions The V–IV–I progression is frequently termed a “retrogression” in Western classical tonal theory, because it appears to reverse the IV–V–I progression so fundamental to the classical style. While there is no reason to hear V–IV–I progressions in general as backwards versions of IV–V–I progressions—any more than there is to hear IV–V–I progressions in general as backwards V–IV–I progressions—there is still often something regressive about the functional effects of V–IV–I.26 For instance, in “Wild Thing” and “La Bamba,” V pushes to tonic I, but so does the IV, only with less punch; the IV does not just embellish the V, it subtly weakens the overall trajectory. Theorist Walter Everett has described this kind of function as softening, a term that conveys an aspect of the IV’s sound not captured by the mere label “subdominant” or by the evocation of harmonic levels.27 We will thus identify a softening function that can be defined as a pre-tonic effect weaker than another, immediatelyPage 74 → preceding pre-tonic effect. Softening thus involves at least two chords, the softener itself and the earlier chord whose function is softened. Softening function is absolutely predicated on the notion of harmonic levels: in order for the first, stronger pre-tonic to be softened, it needs to be present through its softening, and therefore the softener must exist on a different level from its stronger predecessor. With this in mind, we can think of a softening IV as prolonging the preceding V, as being an extension of it, which means that when we hear the IV, we are hearing subdominant and dominant functions simultaneously. Usually, softening function is projected by a subdominant heard in between a dominant and a tonic. IV is the most common softener, and it most often appears between V and I. ↓VII–I, the second most common dominant в†’ tonic motion, is much less likely to be softened by a IV, even though ↓VII–IV–I is an absolutely standard progression (and one we will talk about in depth in the next chapter). (A right arrow “→” will be used to indicate a progression from one functional name to another.) The IVs in these instances tend to be stronger pretonics than the ↓VIIs, and hence ↓VII is usually restricted to pre-subdominant status. In order for the IV in ↓VII–IV–I to project a softening effect, extenuating circumstances are usually required. In the choruses to George Harrison’s 1987 “When We Was Fab,” ↓VII–IV–I is preceded by ↓VII–I; the

rogue dominant в†’ tonic motion of the first progression naturally informs our hearing of the second, making the IV into an interposing softener: “[↓VII] Fab. Long time ago when we was [I] fab. [↓VII] Fab. [IV] Back when income tax was all [I] we had.” (Of course, hearing the song repeatedly will lessen the softening effect and result in the IV having greater pre-tonic strength.) The other main dominant в†’ tonic motion, ↓III–I, is not typically softened by IV; ↓III–IV–I, which is also a widespread progression, nearly always operates instead as a functional chain of pre-subdominant в†’ subdominant в†’ tonic. Other numerals that can project a softening subdominant effect include ↑VI and ↓VI. In the choruses of Creedence Clearwater Revival’s 1969 “Proud Mary,” we get the progression V–↑VI–I (“[V] Big wheel keep on turnin’. [↑VI] Proud Mary keep on burnin’. [I] Rollin’ .В .В .”), the subdominant ↑VI softening the V’s dominant effect en route to tonic I. ↓VI as a softener of dominant ↓VII, as part of the motion ↓VII–↓VI–I, appears in the riff heard throughout Cracker’s 1993 “Low”: [↓VII] Bein’ with you, [↓VI] girl, [I] is like bein’ low.” In these cases, the ↑VI and ↓VI both contain 1, and so they are possible tonics. Indeed, there is a tonic quality projected by both chords, although it is very weak compared to that of the impending Is, and does not really resolve the pre-tonic quality projected by the V and ↓VII. Sometimes, a subdominant that could possibly soften a preceding dominantPage 75 → instead delays the arrival of a tonic; this effect will be called delaying function. In the verses of “Can’t You Hear Me Knocking” (1971), the Rolling Stones use rogue dominant ↓VII to predict resolution to I (“[↓VII] Can’t you hear me knockin’, on your [I] window?”), but they follow up ↓VII–I with ↓VII–IV–I (“[↓VII] Can’t you hear me knockin’, on your [IV] door? [I]”). This subdominant IV affects the I, not the ↓VII, because the IV arrives when the I did previously, and none of the ↓VII’s time is taken away; tonic resolution is postponed by the delaying subdominant IV. In 1964’s “Can’t Buy Me Love, ” the Beatles use a subdominant IV in both a softening and delaying way: both dominant V and tonic I are cut short by an interposing IV as Paul McCartney sings the refrain at the end of the verses. The softening and delaying effects are so strong and distinct from one another that it sounds as though there are two IVs, one followed immediately by the other: “’Cause [V] I don’t care too [softening IV] much for money, but [delaying IV] money can’t buy me [I] love.” Delaying function is not restricted to subdominant IVs and tonic Is; it can be projected by any chord that delays the arrival of another, irrespective of the hierarchical relationship between the harmonies. Because of its lack of hierarchical requirements, it is of limited value as a functional category, but it is of value nonetheless, especially as an alternative to softening function. Delaying and softening function are both listed in Example 2.6, alongside six other additional kinds of functions left to identify. Related to both softening and delaying functions is the harmonic effect of departing, a quality of removal from some immediately preceding state of harmonic activity. This preceding activity can be nearly anything, but often it is specifically a strong tonic. The effect of departing from a tonic we will dub post-tonic function (a particular subtype of a larger category we will soon label “post-anchoring function”). Technically speaking, posttonic function of some magnitude is present each and every time we leave a tonic, yet in many of these instances the effect is so much weaker than other functional effects that it is not really worth pointing out. The weakest cases worth mentioning are loops of four chords that start on tonic I and move to a weakly functional second sonority that is a delta (predicting the initial tonic I at the start of the next iteration), a predictor of the third chord (which can be various things), and a post-tonic. In the choruses of Rihanna’s 2009 “Rude Boy,” we get the progression I–V–↓VI–IV, in which the V functions in exactly this way (“[I] Come on, rude boy. [V] Boy, can you get it up? [↓VI]”). Stronger post-tonics are those that project a departing effect that stems not just from their mere placement after a tonic but also from their presentation of scale degrees that exist outside a previously heard scale. ↓VII tends to be a strong post-tonic when it is used immediately after a passage clearly using the major diatonic Page 76 →scale, a scale that does not feature the subtonic root of ↓VII. We can hear this in the choruses to Nazareth’s 1975 cover of “Love Hurts” (“[IV] holds a lot [V] of rain. [IV] Love [I] hurts. [↓VII] OohВ .В .В .”).28 ↑III and II chords, when they have chordal major thirds, are also frequently heard as post-tonics departing from I major triads. In ↑III’s case, the в™Ї5 (the chordal major third) departs from the I’s natural 5 (its fifth), as heard in Peter and Gordon’s 1964 “A World without

Love”; appropriately, the harmonic departure appears at the word “away” in the first verse: “[I] Please lock me away [↑III].” (This kind of progression will loom large as the “stretch” in our discussion of meta-schemas in chapter 4.) As for II, its striking chordal third, в™Ї4, could be understood as a part of the lydian scale, but since lydian is extremely rare in the repertory (and thus we are not used to hearing it), we are more likely to understand the в™Ї4 as a departure from the I’s partial ionian or mixolydian scale (the only two common diatonic scales that fit a I major triad). A departing, post-tonic II major triad appears after I in each iteration of the repeating I–II–IV–I progression of the coda to Lou Reed’s 1972 “Satellite of Love” (note that the departing в™Ї4 is immediately snuffed out by the root of the ensuing IV, evoking a common chromatic line we will later brand the “slouch”). ↓VIs can also be strong post-tonics when they appear after a I major triad, because their књњ6 root and typical књњ3 chordal perfect fifth do not appear alongside the I’s књ›3 chordal third in any standard rock scale. Soundgarden repeatedly gives us such a post-tonic ↓VIM in the demented verses of their 1996 “Blow up the Outside World,” although this ↓VIM is also a pre-tonic predicting resolution back to I: “[IM] Nothing [↓VIM] seems to [IM] kill me.”29 Post-tonics are not the only chords that project a departing effect. We can depart from any chord, although the effect we are describing is specific to chords that are hierarchically subordinate to their immediate predecessors. For instance, it makes little sense to say that we hear a departure from a dominant V when we resolve to tonic I. Yet a departing quality could indeed follow a dominant V if the next chord is even less stable or functionally weaker than that V, especially if that less-stable chord were to imply a scale different from that of the V. This occurs in the Rembrandts’ 1994 “I’ll Be There for You” (the theme song for the television series Friends): in the chorus, we get a repeating I–IV–V progression with a doubly long V—just like riffs of “Wild Thing” and “La Bamba” without the softening IV—which gives way at the end of the section to a delaying, rogue dominant ↓VII (“[I] I’ll be [IV] there for you [V] ’cause you’re there for me [↓VII] too [I]”). While the ↓VII had been heard in the verses, the choruses’ I, IV, and V major triads conform completely to the ionian scale, the ↓VII’s arrival shifting us to a mixolydian or minor pentatonic scale (the latter only in the roots of IV–V–↓VII–I). The ↓VII is not a Page 77 →posttonic, but it is definitely a post-something (in addition to being a pre-tonic). Clearly, it would be helpful to have a category of harmonic function that applies to this role of the V. Example 2.6. Additional functions anchor = a chord that is hierarchically superordinate on some harmonic level pre-anchor = a chord that predicts a hierarchically superordinate chord; includes all pre-tonics post-anchor = a chord that departs from a hierarchically superordinate chord post-tonic = a post-anchor to a tonic passer = a chord that is a post-anchor to one chord and a pre-anchor to a predicted different chord softener = a passing pre-tonic that lessens the functional strength of a relatively stronger preceding pre-tonic neighbor = a chord that is a post-anchor to one chord and a pre-anchor to that same chord repeated delayer = a chord that delays the arrival of another chord Anchoring function, as we will call it, is the effect of hierarchical superordination that these departing chords (such as post-tonics) can be heard as leaving. This hierarchical superordination, as we discussed in the context of harmonic levels, results from a combination of stability and strength of function. Tonic function is a specific type of anchoring function, one whose superordination is founded primarily upon inclusion of the tonal center (usually as a chordal root). Post-tonic function is a specific type of post-anchoring function. The Rembrandts’ V is an anchor; their ↓VII is a post-anchor. Their I is also an anchor, and since the ↓VII predicts resolution to this

more stable chord, the ↓VII is also a pre-anchor to anchor I. Pre-anchoring function is the larger category subsuming pre-tonic function, but it applies equally to any effect of prediction of a hierarchically superordinate harmony. Anchoring, post-anchoring, and pre-anchoring effects are the functional equivalents to positions with the harmonic levels; it is possible to apply at least one of these three functional categories to any chord at any harmonic level, although we will save these functional labels for situations in which more specific functional labels are not appropriate. The final two functions we will identify in this chapter, and in the entire theory, are both examples of combinations of pre-anchoring and post-anchoring. The first function, passing function, describes the effect of a sonority that acts simultaneously as a post-anchor to one chord and a pre-anchor to a different chord. For instance, in all the I–IV–V progressions we encountered above, the pre-dominant IV is passing: it is a post-anchor to the Page 78 →anchoring (tonic) I, and pre-anchor to the anchoring (dominant) V. Likewise, the softening IV in the V–IV–I progressions of “Wild Thing” and “La Bamba” are also passing in function; a softening effect is in fact a particular kind of passing effect. (A delaying effect may or may not also be a passing effect, since delaying sonorities have no hierarchical requirements.) Passing function is somewhat of a redundant category, in that applies to many chords that are already well covered by other functional designations. Nevertheless, passing effects are real and common and deserve recognition as their own function. It is an especially salient effect when the pre-anchor/post-anchor is shorter than its anchors. In Electric Light Orchestra’s 1977 “Jungle,” every other, brief chord (V, ↑III, and IV) projects a passing effect between I and ↑VI (I–↑VI being the deeper harmonic motion): “I was [I] standing in the jungle, [passing ↑III] I was [↑VI] feelin’ all right [passing IV] [I] [passing V] [I].” While ELO’s IV is primarily a subdominant and their V is a dominant, their ↑III’s strongest function is the combined effect of its post-anchor and pre-anchor qualities, which is perfectly captured by the category of “passing.” Our last function is neighboring function, which differs from passing function only in the anchors involved: a passing chord departs from one anchor and anticipates landing on a different anchor, while a neighboring chord moves away and predicts motion back to the same anchor. Twice in each section of the rough-and-tumble instrumental “Rumble” (1958) by Link Wray and His Ray Men (sometimes Raymen or Wraymen), pretonic ↓VII serves as neighbor to the tonic I; the ↓VII both departs from and predicts I. (At other times, the ↓VII functions as passing chord between I and IV, IV and I, and V and I, as part of a twelve-bar blues pattern.) At the very start of “Rumble,” however, we get ↓VII by itself, without an initial I to depart from. In this one instance, the Ray Men’s ↓VII is technically not a neighbor, because it is technically not a post-anchor. Yet a listener already familiar with the track will no doubt hear that opening chord as projecting the same neighboring effect as all the others, and so we will call it an “incomplete neighbor,” meaning that its neighboring function is present only if we imagine the presence of another anchor. In this case, the imaginary anchor comes before the neighbor, but in other cases it comes after: The Strokes oscillate between I and IV in the verses of their 2001 “Is This It,” but they end the track on IV, an incomplete neighboring subdominant and pre-anchor to an imagined tonic I. Incompleteness is possible not only for neighboring functions but also for passing ones. In the choruses to “Mystify” (1987), INXS repeatedly move from tonic I to passing predominant ↓III to rogue dominant ↓VII and then back to tonic I (“Mysti- [I] -fy, [↓III] mystify [↓VII] me. Mysti- [I] -fy”), but in the final iteration they Page 79 →make it only to ↓III, whose passing (and preanchor, pre-dominant) effect is no less strong despite not being followed by an anchoring ↓VII. It should be mentioned that “passing chords” and “neighboring chords” are venerable classical terms. They are rooted, however, in an even older tradition that applied “passing” and “neighboring” not to harmonies but rather to individual notes, usually with specific requirements regarding stepwise lines (e.g, the D in C–D–E could be passing, and the D in C–D–C could be neighboring). The conception of passing and neighboring functions presented here carries with it absolutely no requirements regarding melodic lines or even note content. Since we have distinguished passing from neighboring function only on the basis of whether their anchors are the same or not, we need to define what qualifies two anchors as being “the same.” This is not an easy task. Even when we think chords are repeating, there are often changes in the arrangement of the chords’ pitch

classes in the musical texture, changes in the relative loudness of different notes of the chord, and even small changes in pitch-class content. If our standard for sameness were identicalness in every conceivable aspect, then neighboring function would not exist. Theoretically speaking, there needs to be a line drawn between neighboring and passing functions, but practically speaking, we only need to know such a line exists, not where it exists exactly. Whether two anchors sound similar enough to one another so as to qualify as “the same” is an issue best raised not in the abstract but in the context of a real passage of music. However, we can at least stipulate that neighboring function is limited to progressions involving two anchors that are of the same numeral and the same basic functional effect. If we are not sure whether the anchors are the same or not, we are not obligated to specify “neighboring” or “passing”; the chord can simply be a post-anchor and pre-anchor. Post-anchors (including post-tonics) are obviously counterparts to pre-anchors (and pre-tonics), yet an important difference between them is that the former are predicated on the presence of their anchors. Neighboring and passing—including softening—functions likewise are projected only when one at least one of the anchors is heard as well. Our theorization of post-anchoring, post-tonic, passing, and neighboring functions requires the existence of at least two chords, and in this way they can be thought of not just as individual chord effects but also chordal progression effects. Indeed, in cases where a post-anchor follows a fairly unstable chord, we may have no reason to hear the preceding anchor as an anchor in the first place until we get the ensuing chord (assuming we have not already heard the progression). In Prince’s 1980 “When You Were Mine,” the repeating I–V–IV–V riff featuresPage 80 → a motion from dominant V to neighbor IV back to dominant V, the first V being heard as an anchor only after the post-anchor IV casts an anchoring effect backward onto it. While it is certainly true that all functions emerge from a musical context, post-anchoring, passing, and neighboring functions are clearly of a different order. Our notion of functional effect, and of harmonic effect more generally, must be broad enough to encompass differently sized projecting entities: chords as well as chord progressions (both of which themselves have been defined as contingent upon entity effects). In the next two chapters, we will focus on another significant kind of progression-based effect, the schematic effect, in a wide range of musical settings. In this section we have spent most of our time on the chords that attach to anchors rather than on the anchors themselves. Anchoring function itself is extremely useful, particularly in describing the resolution of pre-tonics to non-I chords (a point we alluded to earlier in the chapter). Even if such resolving chords include 1 (as some chordal member other than the root), they are only very weak tonics at best, and so it is helpful to refrain from calling them tonics at all and simply refer to them as anchors. Common anchors with 1 include ↑VI with a chordal minor, ↓VI with a chordal major third, and IV with a chordal perfect fifth. All three of these anchors can be heard in the bridge to the faux-Beatles ballad “Look What You’ve Done” by the Australian band Jet (2003). Each verse features anchor ↑VI resolving V: “[I] Take my photo off the [V] wall if it just won’t sing [↑VI] for you.” The second chorus’s final line (“[IV] Oh, look what you’ve done [V] you’ve made aВ .В .В .”) resolves to anchor ↓VI at the start of the bridge (“fool [↓VI] ofВ .В .В .”). This ↓VI then moves to ↓VII, which then resolves twice to anchor IV (“fool [↓VI] of e[↓VII] -veryone [IV]”), before finally returning us back to the verse and to a much more stable tonic I. Such resolutions to non-I anchors are conventionally labeled “deceptive,” “interrupted,” or “false.” “Deceptive” is an excellent description of the motion when we expected some other chord instead, but it is problematic when applied to a song that we have already heard a million times, a song that can hardly be said to deceive us anymore.30 “Interrupted” is a good way to describe certain progressions with non-I anchors, but not all such motions; the ↑VI in the verses of Jet’s song, for instance, in way no interrupts the flow of the progression. “False” is more widely applicable than the first two terms, but it smacks of an improper and unnecessary value judgment. Instead, we will simply refer to non-tonic resolutions as temporary resolutions, since the resolving anchor in question is itself unstable enough to project a need to resolve eventually to a tonic I. This temporary-resolving effect is a specific type of delaying effect: a temporary-resolving chord is one that functions as Page 81 →an anchor to a pre-tonic but that functions at a deeper level as a delayer of a more strongly sought tonic I. As we wrap up these two chapters on harmonic function, it is appropriate to delve a bit deeper into the

problematic notion of harmonic prediction. In the introduction, we made the point that our attributing actions to music—to chords and their constituent parts—is merely a rhetorical contrivance, a contrivance especially conspicuous as such with regard to harmonic prediction: a person can predict; a chord cannot. Our aural expectations are shaped by our training, our attitudes (in this book, that would be hearing), and our familiarity with musical stylistic conventions and relevant particular precedents (such as earlier performances of a song, or even an earlier part of a repeating track). Most importantly, our expectations are molded by our prior experience with a particular track, which is to say that harmonic prediction is just as much about guessing what might happen as knowing exactly what does happen. A listener who is not already familiar with “Look What You’ve Done” will probably hear the Vs and ↓VII as dominants predicting tonic Is and will hear the ↑VI, ↓VI, and IV as temporary-resolving anchors and delayers of tonic Is. A listener who is familiar with the track will know that these chords actually go to ↑VI, ↓VI, and IV; she may still hear dominants and delayers based on broad stylistic conventions, but she also is likely to hear, more strongly, the Vs and ↓VII as predicting the non-I anchors ↑VI, ↓VI, and IV. In the former case, the resolutions are temporary; in the latter case, they are expected. Hearing multiple, distinct functional effects projected by a given chord or progression is simply part of the multifaceted experience of hearing harmony. With all the various functional categories now at our disposal, we are in a better position to be able to pinpoint and verbalize the assorted ways we as individual listeners can hear a single musical passage, although we do now face the problem of keeping track of which label applies to which hearing. For instance, Jet’s ↓VII is a hyper pre-tonic when we hear it predicting tonic I (which is delayed by IV), but that same ↓VII is a hypo pre-anchor when we hear it predicting the anchoring IV itself. This sort of dichotomy between virgin and veteran hearings of a progression points up the extent to which we as listeners determine what the music is allowed to sound like. But when discussing veteran hearings, are we really justified in using the term prediction at all? The “exposure effect,” as it is called in psychology, would seem to completely redefine harmonic prediction as harmonic progression in this context, with predictive effects constituting a mere illusion, a manifestation of our confusing hindsight for foresight.31 To a certain extent this is true: prediction necessarily begins to align with progression as Page 82 →we become more familiar with the latter. Yet they are probably never quite one and the same. Hearings are highly complex; residue of earlier ones seems to stick to newer ones, creating multilayered, subtly colored patchworks that might contain outright contradictions (some of which may include “ambiguous effects,” to be explored in chapter 6). When we try to verbalize a “hearing,” we are probably describing a kind of Frankenstein-like composite of pieces of distinct experiences from different moments in our lives. Even if pure prediction were to diminish immediately after an event, or become less reliant on knowledge of generic norms and more reliant on knowledge of a song’s particulars, the memory of earlier guesses can remain with us and thus can be experienced, in some sense and to some degree, again and again. In the absence of any real scientific evidence to the contrary, it would seem reasonable to continue to talk about prediction as an operative concept in veteran listening, and so we shall, even if the predictive effects change over time, multiply, or become selfcontradictory. The alternative would be to disregard prediction entirely; this would be a safer course of action, but also a less ambitious—and less compelling—one. By keeping prediction in the mix, we take on the responsibility to be self-aware and upfront about how and when our different kinds of hearings can clash. These first two chapters have discussed a great number of different functional effects. Traditional terms such as “tonic,” “dominant,” and “subdominant” have been scrutinized and precisely (re)defined, and a number of new expressions have been posited alongside them, particularly Greek letters for positions in relation to a tonic, and “hyper,” “hypo,” and “medial” for categories of voice-leading anticipations. We have proposed a modified numeric notation, made an argument for distinguishing between numerals and functions, and examined the role of functional strength in the formation of harmonic levels. Our discussion of the most abstract functional categories—anchoring, post-anchoring, pre-anchoring, softening, delaying, passing, neighboring, temporary-resolving—has completed our foundational work; we are now in the position to tackle the other major harmonic effects of the repertory. Of course, our treatment of harmonic function has not been so exhaustive and detailed that we have precluded the possibility of further expansion and refinement. By their very nature as discrete lexical categories, functional names can only ever capture certain aspects of the experiential continuum that is harmonic hearing. But the functional definitions we have laid out here will prove more than

adequate as a jumping off point for discussion of even more complex effects: those of schema, transformation, and ambiguity.

Page 83 →

Chapter 3 Short and Slot Schemas Two-Chord Loops and Cadences When we recognize a song’s chord progression as stereotypical, we can say the chords in question, taken together, project a schematic effect.1 “Schema” is a term from philosophy and psychology that is used by music scholars to describe mental representations of stock patterns; for us here, the term will carry two primary meanings. The first, broader one covers familiar harmonic formulas in general. The second one specifically denotes an archetypal numeric harmonic series, a model progression of chords identified according to their roots’ positions in relation to a diatonic scale.2 Technically speaking, schemas of either kind reside not in songs but in our minds; they are evoked by particular progressions in actual songs. It is possible for a single progression to evoke multiple schemas, and it is equally possible for a lengthy schema to be projected by just a few chords. All this said, for the sake of verbal convenience, we will also sometimes use the term “schema” as a rough synonym for “progression” (which itself has multiple meanings), to indicate series of chords within the music itself. This rhetorical tactic should be understood not as a result of intellectual laziness but rather as a reflection of our accepting the fluid nature between what the music is and what we hear the music as—and of our recognizing (as we have already stated) that every descriptive music theory is also always to some degree prescriptive. In lieu of theorizing different categories of schematic effects per se, we will concentrate on identifying the various incarnations of the individual schemas these effects entail. Numeric notation is the most efficient way of identifying schemas, because it enables us to compare progressions across songs with different tonal centers, and because it allows us to use one brief set of symbols for numerous progressions that may all differ slightly in their exact intervallic makeup. Most of the schemas we will study (aside from a small group we will call “meta-schemas”) will be identified solely by their constituent numerals; however, we as listeners are in no way barred from hearing more detailed Page 84 →schemas that involve specific types of sonorities: power chords, major triads, major-minor seventh chords, whatever. As we noted in chapter 2, we cannot say for sure what sort of function any given numeral might project without a concrete musical context. Nevertheless, series of numerals only have so many hierarchical possibilities, and this fact, combined with schemas’ stereotypical nature, allows us to guess with reasonable certainty what kinds of functions, functional strengths, and harmonic levels we are likely to encounter when we hear a certain schematic effect, given, as we have already assumed, some familiarity with how the music actually goes. Thus, in addition to focusing on the schemas themselves, we will devote considerable space in these two chapters to investigating the functional proclivities of all the schemas to be discussed (based on the author’s own experiences). Laying out the historical development of a few of the more important schemas will also be part of our mission. (These two chapters on schemas are thus dependent for their content on particular rock songs and styles in a way that the book’s theory as a whole is not. Consequently, engagement with different songs and styles would presumably result in a different list of schemas.) The seventy-seven schemas to be identified represent progressions so memorable that an avid listener will likely already have them stored in her memory. The memorability of these progressions usually results from their repeated employment throughout the repertory, although a few progressions are memorable simply because they are aurally arresting.3 While this text will not offer any formal explanation of exactly how or why a given listener is likely to be familiar with certain patterns and not others, it stands to reason that an inexperienced listener will have fewer schemas to draw on than an expert and thus will hear fewer schematic effects overall.

As for these two chapters’ casual claims about relative frequency of harmonic structures, they should be read in the same light as the soft assertions about commonness made in the preceding chapters, such as chapter 1’s classification of customary voice-leading motions and chapter 2’s determination of standard numerals. None of this text’s claims about commonness should be taken as reflecting anything more than an intuitive appraisal by a single researcher. True statistical “corpus studies” have recently begun to gain traction in the professional discipline of music theory, and this is a good thing (although there are some potential problems too). But statistical studies of musical materials are, arguably, most valuable when serving to refine or re-evaluate assessments made initially via the intuitions of veteran listeners, assessments such as those to be explored presently. In any event, the issue of whether our intuitions about commonness are correct is technically irrelevant in the current context because we are dealing here with schematic effects; Page 85 →what matters is that we experience a certain progression as common or conspicuous—as archetypal—regardless of how well our experiences correspond to the outside world. (That said, it is the author’s intention to paint as realistic a portrait of the repertory as he can.) The easiest way for a progression to become memorable, so as to potentially engender a schema, is to arrive set off from other chords. This means two things. First, a schema should have appeared, at some point, unadorned by other chords, which is to say that a schema normally manifests itself not exclusively as a deep-level structure but also, at least sometimes, as a series of chords that we can easily hear at the surface level (where the only ornaments are nonchord tones). Schematic effects are often projected at deeper levels, but these likely flow from earlier-encountered surface manifestations.4 Second, a schema typically will have comprised at some point its own discrete section of the harmonic surface, which we will call a harmonic phrase, lasting anywhere from a few beats to dozens of bars. A harmonic phrase is not the same thing as a progression or a functional chain. A progression (a more general term for any series of two or more chords adjacent on some harmonic level) or a chain (a progression specifically with three or more interlocking predictive functions) may or may not be contained entirely within a single harmonic phrase, and a progression or chain may only be part of a harmonic phrase. A harmonic phrase is also different from a melodic phrase; it is commonplace for several melodic phrases to occur during a single harmonic phrase, and the reverse is also possible. A harmonic phrasal effect is the quality of a series of chords adjacent on the harmonic surface cohering into a unit by virtue of a variety of factors, including melodic phrasing, harmonic functional effects, chordal repetition, small-scale meter, large-scale meter (so-called “hypermeter”), texture, timbre, lyrics, and even harmonic schemas themselves, the last of these indicating that there is a reciprocity of influence between harmonic schemas and harmonic phrases; a schematic effect can help create a phrasal effect, and a phrasal effect can help create a schematic effect (or contribute to a progression’s quality of familiarity that might eventually lead to its becoming a schema). The simplest harmonic phrases involve just one chord, such as a catatonic I (as we called it in the chapter 1), but we will reserve the term “schema” for series of two chords or more (i.e., for progressions). To simplify the upcoming discussion slightly, we will quantize standard schematic phrasings to the closest beat. Deciding when one harmonic phrase ends and another begins is not always straightforward, especially when the harmonic and melodic phrasing do not seem entirely aligned (which is often the case). Yet there are two standard settings in which harmonic phrases are clearly articulated: the loop and Page 86 →the cadence. Loops are harmonic phrases that end where they began, which is to say they repeat at least once unchanged, although they often recur for an entire section and sometimes for an entire song.5 A loop need not be a schema; any progression may be looped, but for the most part looped progressions in rock are instances of, or variations on, schemas. Two-chord looping schemas ordinarily feature tonic I for the first half of the phrase (typically a half a bar or one full bar), with the second half of the phrase (another half or full bar) offering a chord that functions as a neighbor resolving to the ensuing I in the next iteration, thus creating (once we can predict this resolution) a pre-tonicв†’tonic progression over two phrases. Less common is a motion of pre-tonicв†’tonic within the loop itself. Another possibility is tonicв†’pretonicв†’tonic all within a single loop, usually with the ending tonic held twice as long as the other chords. The neighboring pre-tonic can be anything, but subdominant IV, with a real or imagined chordal third as scale degree 6, fulfills this role more often than any other chord. In fact, I followed by IV is not just rock’s most common two-chord loop but the repertory’s most common progression in general. Such a phrase should be called “I–IV”; on the other hand, since the IV typically depends on the repeated I to resolve its instability, we will identify the general schema as , with less-than and greater-than

brackets, understanding that this designation covers every possible phrasing of these two looping chords. (This includes rotation but not permutation: ergo, stands for x–y–z, y–z–x, and z–x–y, but not x–z–y, y–x–z, or z–y–x). is projected by everything from the deliberately tedious organ riffs of “96 Tears” by ? and The Mysterians (1966), to the playful acoustic-guitar riff in the verses of “Blister in the Sun” by Violent Femmes (1983), to the electroacoustic dance riff of Maroon 5’s “Moves like Jagger” (2011); each of these examples features a I–IV loop. Its less common retrograde, IV–I, repeats in the choruses of the Beatles’ 1968 “Helter Skelter” (“[IV] Helter skelter. [I] Helter skelter”) and throughout the entirety of Missy “Misdemeanor” Elliot’s 1999 “Hot Boyz” (“[IV] What’s your name? .В .В .В [I] You’re a hot boy”). Carole King’s “It’s Too Late” (1971) offers both orderings: I–IV on A in its verses (“[I, A] Stayed in bed all mornin’ just to [IV] pass the time”), and IV–I on F in its choruses (“And it’s [IV] too late, baby, now [I, F] it’s too late”). The least common arrangement of a loop is I–IV–I, heard in Buddy Holly’s opening guitar riff to the Crickets’ 1957 “Not Fade Away.” The second most widespread two-chord schematic loop is probably . Typically functioning as tonic I and dominant ↓VII (with a real or imagined 2 as a chordal major third, a requirement for it to function as a dominant), most often loops as I–↓VII, as it does in “Hong Kong Garden” by Siouxsie and the Banshees (1978), but just like , it also Page 87 →appears frequently in other versions. Miami Sound Machine’s “Conga” (1985) loops I–↓VII in its chorus, but I–↓VII–I (with a doubly long ↓VII) in its verse, also hearable as an alternation of I–↓VII and ↓VII–I (“[I] Everybody [↓VII] gather ’round, now. [↓VII] Let your body feel the [I] heat”). Blues Traveler’s “But Anyway” also loops I–↓VII–I in its verse (though with a doubly long initial I), whereas it loops ↓VII–I in its chorus (“It’s a [↓VII] state of affairs and a [I] state of emotions”). Loops of also typically alternate a tonic (I) with a dominant (V). I–V runs throughout Robin Thicke’s 2013 date-rape anthem “Blurred Lines” featuring T. I. and Pharrell (with four bars per chord: “[I] Baby, can you breathe? .В .В .В [V] No more pretendin’”), while the Breeders build their bass and distorted guitar riffs on V–I in 1993’s “Cannonball” (in contrast, their single-line guitar riff suggests I–V simultaneously). The verses of the Crystals’ 1963 “Then He Kissed Me” loop as I–V–I with a long ending (“Well he [I] walked up to me and he [V] askedВ .В .В .”). also frequently appears as a pair of harmonic phrases, one phrased as I–V followed by another phrased as V–I, as we hear in two Christmas classics written by Jewish songwriter Johnny Marks: “Rudolph, the Red-Nosed Reindeer” recorded by Gene Autry in 1949 (“[I] RudolphВ .В .В . shiny [V] nose, [V] and if you everВ .В .В . it [I] glows”) and “Rockin’ Around the Christmas Tree” recorded by Brenda Lee in 1958 (“[I] Rockin’ aroundВ .В .В . at the [V] Christmas party hop. [V] MistletoeВ .В .В . tries to [I] stop”). is also frequently intimated by arpeggiations of the chordal root and fifth of a catatonic I; this is especially common in hip hop, as heard in Salt’n’Peppa’s 1993 “Shoop” (the ornamental notes in the bass amplify the effect: “[1] Shoop. Shoop ba [5] doop”). Another common looped schema matching a tonic with a neighboring dominant is . This schema is usually played very quickly as a I–↓III guitar riff, taking up only one bar in the first part of the Eddie Van Halen’s main riff in “Hot for Teacher” (1984), and only a half of a bar in the verse riff to Beck’s 2006 “Nausea” (although these two examples are roughly the same duration in real time); the I–↓III riff in the verses to Nirvana’s 1993 “About a Girl,” which we spent some studying in chapter 1, is likewise short, taking up one bar for each iteration. In many such I–↓III riffs, it is easy to hear one continuous I chord, with the notes of the ↓III serving as nonchord tones or actual chordal members of the I. Most progressions project strong pentatonic effects; numerous pentatonic-based schemas will be examined in detail in the next chapter.

Other than IV, the most conventional subdominant in looping two-chord schematic effects is either ↑VI or ↓VI. is heard looped in Beastie Boys’ half-jokingly misogynistic 1986 “Girls” (probably based on the fast-sectionPage 88 → vamp from the Isley Brothers’ “Shout”: [I] Girls! [↑VI] Yeah all I really want isВ .В .В .”) and in the verses of 2008’s “Sex on Fire” by Kings of Leon (wherein each chord persists for four bars: “Lay where you’re [I] layin’ .В .В . I know they’re [↑VI] watchin’”). appears in the verses of Elvis Costello and the Attraction’s 1978 “Watching the Detectives” (“[I] Nice girls, not one with a defect, [↓VI] cellophane shrink-wrapped”) and in the verses to Patrick Swayze’s 1987 “She’s Like the Wind” (which is phrased as the much less usual ↓VI–I, instead of I–↓VI: “[↓VI] She’s like the wind through my [I] tree”). Loops of are far less ordinary than any others so far identified, but these progressions are still widespread enough to project a schematic effect. Examples include the choruses to Carl Douglas’s campy, orientalist 1974 “Kung Fu Fighting” (“Everybody was [I] kung fu fighting. Those cats were [II] fast”) and the verses of Todd Rundgren’s 1972 “Hello It’s Me” (phrased as II–I: “[II] Hello, it’s me [I]”). Many two-chord loops in which the roots are a major second away do not strongly project the schema; many actually do not strongly project a two-chord schema at all, instead sounding more like IV–V or ↓VI–↓VII, especially if the potential II is a major triad (which would imply a lydian scale with its chordal major third, в™Ї4). We will devote more time to this issue in chapter 6 while discussing schematic ambiguity. Surprisingly, looped progressions probably appear with more frequency than , despite в™-II being less common overall than II in the repertory. (We will not bother calling в™-II a “♯I” in the context of a two-chord loop because it essentially always sounds like a neighbor to, and not a chromaticized version of, the I.) is a favorite of punk, heavy metal, and other hard rock styles. Examples include the riffs of Dead Kennedys’ 1979 “California Гјber Alles” (with в™-II ornamented by ↓III: “[I] I am Governor [в™-II] Jerry Brown”) and Everclear’s 1996 “Local God” (“[I] You do that, [в™-II] Romeo”). It is also a staple of hip hop, as heard in the riffs of Snoop Doggy Dogg’s 1993 “Gin and Juice” (“[I] Rollin’ down the street, smokin’ [в™-II] Indo”) and Nelly’s 2002 “Hot in Herre” (“[I] It’s gettin’ hot in here, [в™-II] so take off all your clothes”). It only rarely pops up in gentler settings, and in those more typically as a jolting bolt of chromaticism rather than as a loop, as is this case with the harmonic tag leading into the bridge of Shep and the Limelites’ 1961 doo-wop “Daddy’s Home” (under an extended vocalizing of “to say”). в™-II chords are ordinarily either major triads or power chords, and so the в™-II–I schema normally includes a lower subdominant (with књњ6 as the chordal fifth). The в™-II in “Local God,” however, is a major-minor seventh chord, and with в™-2 as its root and в™-1 (acting also as књ›7) as the chordal seventh this sonority additionally functions as an atypical lead dominant. в™-II can project a diatonic phrygian effect, especially if the I has a chordal minor third (књњ3, correspondingPage 89 → to the phrygian scale), but when I offers a chordal major third (књ›3), as is typically the case with punk’s and heavy metal’s distorted guitar riffs and their strong overtones, the scalar effect tends to be more chromatic, or perhaps one of the exotic-tinged “double harmonic major” scale (on E: E, F, Gв™Ї, A, B, C, Dв™Ї, heard melodically in the main riff to Dick Dale and His Del-Tones’ 1962 surf-guitar rendition of the classic Greek folk song “Misirlou”). Example 89.3. Two-chord schemas Looping progressions are extremely rare in the overall rock repertory. Although it is mostly confined to harder styles such as heavy metal and punk, the progression makes such a remarkable sound—with its chordal roots separated by a tritone—that its schematic effect is usually quite salient. We already have seen an example in chapter 2 with the main riff from Marilyn Manson’s “The Beautiful People”; we hear the same motion in the guitar riff in Nine Inch Nails’ 1992 “Last.” Ordinarily, as in these two cases, the в™ЇIV/в™-V functions primarily as a shocking post-tonic, providing a strong sense of

departure from the foregoing I but little forward motion toward resolution. loops are also not especially prevalent, and they are much blander than and , but they do appear across a variety of styles over the decades, so we will consider a true schema. We encountered an instance back in Example 1.8a with the choruses of Lady Antebellum’s “Need You Now”; other cases include the verses to the Rolling Stones’ 1971 “Wild Horses” (in the unusual phrasing ↑III–I: “[↑III] Childhood [I] living”) and the verses to Bruce Springsteen’s 1994 Academy Award–winning (for the soundtrack of Philadelphia) “Streets of Philadelphia” (“I was [I] bruised and batteredВ .В .В . I was [↑III] unrecognizable”). Most examples of this loop offer I as a major triad followed by ↑III as a post-tonic, mediant-functioning minor triad. The only remaining schematic possibility for a two-chord loop is ,Page 90 → which is fairly rare in the repertory at large. On the other hand, progressions by themselves—not looped—are standard, and moreover they are highly salient when both harmonies contain chordal major thirds, as heard in the verses of Brenda Lee’s 1960 “I’m Sorry” (“[I] I’m sorry, [↑VII] so sorry”) and in the verses of Elvis Presley’s 1957 “Jailhouse Rock” (where it actually does appear as a loop, although the ↑VII is really a brief ornament to I: “[↑VII] The [I] warden threw a party”). We will thus consider a schema, and with this schema we exhaust all the common numerals from Appendix C. See a summary of two-chord schemas in Example 3.1. The second standard way to articulate a harmonic phrase is to create a cadence. Meaning “fall” or “closing,” a cadence for our purposes is a chordal gesture that marks the end of one phrase and the beginning of another by offering a harmonic breathing point between them. The cadence is really only the ending portion of the phrase on some particular harmonic level, although it can also be considered a short phrase unto itself, a subphrase or gesture that is its own complete idea. (Loops may end in a cadence.) Each chord in a cadential gesture can be heard as projecting a cadential effect (in addition to schematic and functional effects), which we will define as the quality of driving toward, and delivering, a break in the flow of harmony. The shorter the phrase, the weaker the cadence will likely be, just as a speaking person would necessarily take shallow breaths if she breathed every two or three words while trying to maintain a sense of flow in her sentences. Cadences are thus akin to punctuation in grammar. Looped phrases may be heard as ending with cadences, but when the loops are short (less than four bars), any cadential effect will probably sound fairly weak. Cadences typically comprise one, two, three, or four chords and can be categorized according to whether they end with a pre-tonic or a tonic (a special case is the temporary resolution, which we discuss momentarily). Traditionally, pre-tonic cadences and tonic cadences are called “half” and “full” respectively, but since “half” usually means that the cadence ends not with a pre-tonic generally but with a dominant V specifically, we will use the more neutral term “partial,” paired with “whole.” A whole cadence requires at least two chords, a pre-tonic and tonic; a partial cadence needs only an ending pre-tonic. Both types of cadences can be heard in Billy Joel’s “Piano Man” (1973): “Sing us a song tonight [dominant V, partial cadence]В .В .В . and you’ve got us [dominant V] feelin’ all [tonic I, whole cadence] right.” (Joel’s cadences create a pair of phrases that classical musicians call “antecedent” and “consequent” phrases, which together form a phrasal “period.”) The term “partial” cadence is slightly misleading, as it implies that the pre-tonic chord that ends the phrase does not resolve; in reality, this chord ordinarily resolves to a tonic Page 91 →at the start of the next phrase. This is what happens in “Piano Man” (“Sing us a song tonight. [dominant V, partial cadence] Well, we’re [new phrase, tonic I] all in the moodВ .В .В .)” So while there is an important distinction between Joel’s partial and whole cadences, the harmonic schema is the same. We will therefore designate all schematic cadences as , just as we did with all two-chord loops. The schema common to both cadences in this excerpt from “Piano

Man” is . In between the partial cadence and whole cadence is the temporary cadence, which is our term from chapter 2 that substitutes for the Western classical terms “deceptive,” “interrupted,” or “false” cadence. A temporary resolution involves a pre-anchor resolving to an non-I, non-tonic anchor, a chord that is unstable enough itself that it projects its own need to continue on to greater stability (i.e., a tonic). While temporary resolutions such as V–↑VI, ↓VII–IV, ↓III–IV are indeed standard motions in the repertory, we will not consider these to be two-chord schemas in and of themselves, only because they are usually part of larger schemas and do not normally constitute their own independent phrases, cadential or otherwise. The most common two-chord cadences all involve resolution to a tonic; these are IV–I, ↓VII–I, V–I, and ↓III–I.6 The remaining two-chord schemas also can project strong cadential effects, save perhaps for . We will have much more to say about cadences in the next two sections on three-chord schemas.

Common Three-Chord Loops and Cadences Progressions involving three chords are overwhelming in number, not only because of their widespread use, but because of their various incarnations. The twelve common numerals from Appendix C support 440 possible combinations of three-chord series (assuming в™ЇI/в™-II represents one numeral, ditto for в™ЇIV/в™-V), and it is not always self-evident which should count as schemas. We will limit our discussion to only some of the most prevalent and interesting cases, yet even with such a limitation, the following pages will overflow with abstracts progressions and examples of their evocation, so the rest of this encyclopedia-like chapter will be less material to pursue casually and more material to examine slowly, in small chunks at a time, and in consultation with a comprehensive collection of recordings. This goes for all of chapter 4 as well. Appendix E serves as a summary of all schemas identified in this book. Example 3.2 lists common three-chord schemas. We have already sidestepped a few vital three-chord schematic effects in this chapter. The cadences in Billy Joel’s “Piano Man,” for instance, use the Page 92 →schema , but the cadential effects projected at the end of those phrases do not begin with the V chords, they begin with pre-dominants: “Sing us a song to- [pre-dominant II] -night [V].В .В . and [pre-dominant IV] you’ve got us [V] feelin’ all [I] right.” Both and are examples of three-chord schemas; when a progression projects one of these schemas, there are two schematic effects, one involving just two chords, , and the other all three. Looped three-chord schemas ordinarily last two or four bars and are often uneven in terms of the durations of their constituent chords: either the first or last chord (whatever that may be) is frequently twice as long as the other two. This is because most rock music features quadruple meter (straight or swung 4/4) and—except for the twelve-bar blues—phrases that do not divide evenly into three sets of bars. Yet even within this regular framework, the number of potential phrasings for three-chord schemas (including different rotations and relative durations) is considerably higher than that for two-chord schemas, as is the number of possible functional and hierarchical effects. Example 3.2. Common three-chord schemas , with its root line of descending perfect fifths, is most at home in older styles, which favor this kind of motion much more so than later rock. As a cadential motion, it often sends a bridge section back into the verse, relying on a chordal major third in the II to hoist us up to 5, creating a partial cadence that leads us gracefully into the earlier material. A classic example of this move occurs deep into Hank Williams’ 1953 “Your Cheatin’ Heart” (“you’ll toss a- [II] -round and call my [V] name. You’ll walk the [I] floor”). (Later in this chapter we will identify a larger “crossing schema” of which this cadence is also a part.) Within a loop, is more often encountered as part of a larger series of descending fifths, but at times it does constitute the entire

phrase: cases include the II–V–I verses of the Coasters’ 1959 “Three Cool Cats” (with a doubly long tonic I: “[II] Three [V] cool [I] cats”) and the I–II–V–I verses of Elvis’s 1956 folk-tune ballad “Love Me Tender” (each chord lasting the same amount of time: “[I] Love me tender [II] love me sweet [V] never let me [I] go”). Functionally, typically acts as a functional chain, Page 93 →with a basic dominantв†’tonic level (V–I) embellished by pre-dominant II. Since loops are slightly unusual, they have no real standard phrasing, although since three-chord looping progressions in general tend to make either the first chord or last chord twice as long as the others, Elvis’s I–II–V–I phrasing can be considered less typical than the Coasters’. is even more common than , having been popular among the earliest rhythm’n’blues artists through to the most current pop idols. It is widespread in loops, routinely phrased as I–IV–V with a doubly long I, and was particularly adored by new wavers and punks looking to simplify their sound. We hear it in the verses to the Cars’ 1978 “My Best Friend’s Girl” (“Here she [I] comes again, when she’s [IV] dancin’ ’neath the [V] starryВ .В .В .”) and in the choruses to the Ramones’ 1977 “Sheena Is a Punk Rocker” (“[I] Sheena is [IV] a punk [V] rocker.”). In both these songs, I lasts twice for a full bar, followed by half a bar each of IV and V. A common variation is to move from I/1 (“root position”) to I/књ›3 (“first inversion”) before proceeding to IV and V (each with its root in the bass), while the bass outlines 1–ꜛ3–4–5; the motion supports the verses to Shania Twain’s 1997 “You’re Still the One” (“[I] Looks like we [I/књ›3] made it. [IV] Look how far we’ve [V] come, my baby”). V can also last twice as long as I or IV, as it does in the choruses of Heart’s 1985 cover of “What About Love” (“What about [I] love? Don’t you [IV] want someone to [V] care about you?”) and the choruses of R.E.M.’s 1988 “Stand” (“[I] Stand in the [IV] place where you [V] live”). Less ordinary but still possible are phrasings of I–IV–V–I (each chord receiving equal duration), which occur in REO Speedwagon’s 1980 “Take It on the Run” (occasionally with a softening IV inserted before the last tonic: “[I] Heard it from a friend, who [IV] heard it from a friend, who [V] heard it from another you’ve been (IV) messin’ a- [I] -round”). The looped schema can also start with IV, in which case the final I is usually twice as long as the previous IV and V; this happens in the choruses to Jimmy Buffet’s 1977 “Margaritaville” (“[IV] Wastin’ a- [V] -way again in Marga[I] -ritaville”). As for cadences, no schema is more clichГ©d than this one; regardless of what happens beforehand, a IV–V–I progression will sound right as rain. The plodding verses of Led Zeppelin’s “Tangerine” (1970) perk up immediately with Jimmy Page’s IV–V–I acoustic-guitar gesture, landing us in the much more memorable psychedelic pedal-steel guitar chorus. The idiosyncratic string of arpeggiated chords that shift around various tonal centers in Chicago’s slow-dance “Colour My World” (also 1970) are roped in at the end by a simple IV–V–I cadence: “colour my world [I] with hope [IV] of [V] loving [I] you.” Just like , usually behaves as a functional chain of pre-dominantв†’dominantв†’tonic. The exception is the loop phrased as I–IV–V when the I is doubly long, as we heard in “My Best Page 94 →Friend’s Girl” and “Sheena Is a Punk Rocker”; in these cases, it is possible to hear an additional, competing, deep-level motion of I–IV, with the V as a dominant embellishment of the stronger progression subdominantв†’tonic. We will return to these competing hierarchical possibilities when we discuss functional ambiguity in chapter 6. I, IV, and V are probably the most widespread harmonies in the repertory, so it should come as no surprise that is one of the most frequently encountered schemas. A phrase can deploy these chords in any order; yet, following our earlier decision to label schemas with the resolving tonic I in the final position, we only have one other possible three-chord schema using these chords: .7 (The phrasings IV–V–I, I–IV–V, and the rarer V–I–IV represent , while the phrasings V–IV–I, I–V–IV, and the rarer IV–I–V represent .) is likewise ubiquitous in rock. It appears frequently as a whole cadence within the standard twelve-bar form (which we will dub the “blue schema” in the next chapter), a form that dates back to jazz era; early rock examples include Jackie Brenston and His Delta Cats’ 1951 style-defining “Rocket вЂ88’” (“Baby, we’ll [V] ride in style, [IV] movin’ all a- [I] -long”) and Ruth Brown’s 1952 “5-10-15 Hours” (“If you [V] ever need me,

baby, [IV] call me on the tele- [I] -phone”). The V in these cadences nearly always functions primarily as a dominant resolving to tonic I, with the IV functioning as a softening subdominant that ornaments a two-chord motion of V–I (which occupies the next deepest harmonic level). As a loop, typically is phrased starting with I, and most often features a IV that is twice as long as its I and V, as heard in much of Pete Townshend’s 1980 “Let My Love Open the Door” (“Let [I] my love [V] open the [IV] door”) and Bush’s 1994 “Comedown” (“[I] ’cause I don’t wanna [V] come back down from [IV] this cloud”). In chapter 2 we heard Townshend playing this same loop in The Who’s “Baba O’Riley” with all the chords in the same basic positions but with the I one beat longer and the V one beat shorter; Meredith Brooks follows these same proportions in the verses to her 1997 “Bitch” (“I [I] hate the world today [V] [IV]”). In these cases, the subdominant IV receives so much emphasis and the V receives so little that the V usually functions primarily as pre-subdominant rather than a dominant, resulting in a IV–I motion at the next harmonic level, as opposed to the V–I motion that normally emerges from the V–IV–I blues cadences. The exception occurs when the harmonic pulse is slow, as it is in the choruses of Reba McEntire and LeAnn Rimes’ 2007 duet “When You Love Someone Like That” (with a doubly long IV: “When you [I] love (when you love), [V] when you [IV] love someone like that”); in this case, the relaxed pace allows the dominant potentialPage 95 → of the metrically weak V to shine through, making the extra-long IV into a softening subdominant that embellishes V–I. Less often, can start with a I that is twice as long as V or IV. This happens in Alanis Morissette’s 1998 “Thank U” (“Thank you, [I] IndiaВ .В .В . Thank you, [V] disillusion- [IV] -ment”) and Cornershop’s 1997 homage to Indian singer Asha Bhosle, “Brimful of Asha” (“[I] Brimful of Asha on the [V] 45, [IV] well, it’s aВ .В .В .”). The harmonic levels in these cases are not entirely predictable. Sometimes the V is a more of a dominant, as in “Thank U” (making the next level V–I), while at other times the V is more of a pre-subdominant, as in “Brimful of Asha” (making the next level IV–I). We will discuss in detail the various factors influencing these levels—various types of functional “information”—in chapter 6. For right now, the important point is that there are two main interpretive possibilities here, the first a functional chain (the more common possibility), the second a motion from the first chord to tonic that is embellished by a softening IV. Still other hierarchical arrangements of these three chords are possible: under rare and very specific circumstances, the V or IV may serve as the chord being embellished by the other two. But the two main interpretive possibilities—a tonic I either being led into by a functional chain or embellished by an ensuing set of chords—will crop up again and again with the other three-chord schematic effects soon to be discussed. On rare occasions is phrased as I–V–IV–I, heard in much of Pearl Jam’s 1992 “Yellow Ledbetter” (“[I] Unsealed on a [V] porch a letter sat. [IV] Then you said вЂI wanna [I] leave again’”). can also begin with V, in which case the ending tonic is usually the longest chord; two iterations of such a phrase start each of the verses to Vampire Weekend’s South African–inspired 2008 “A-Punk” (“Jo- [V] hanna drove [IV] slowly [I] into the city”). Highly unusual is the doubly long initial V, as occurs in the choruses to the Beatles’ 1969 “Across the Universe” (“[V] Nothing’s gonna change my world, [IV] nothing’s gonna change my [I] world”). Phrasings of that start with IV are relatively rare, but when they do occur the V is usually twice as long as the other sonorities. Examples include the chorus loops of Creedence Clearwater Revival’s 1970 “Up around the Bend” (“they’re [IV] goin’ up a- [I] -round the [V] bend”) and the chorus loops of Toto’s 1978 “Manuela Run” (“You better [IV] run, run, Man- [I] -uela, -uela, [V] run”). In all these rarer phrasings—perhaps even more so than in “Thank U” and “Brimful of Asha”—the harmonic levels are not generalizable; the exception is the V–IV–I loop, which often (though not always) projects V–I at a deeper level because of its heavy emphasis on V. The I–V–IV–I and V–IV–I phrasing’s deeper motion Page 96 →can often be heard as either V–I or IV–I; the IV–I–V phrasing can project two very different deeper levels: V–I or IV–V. Such phrasings are best generalized as functionally ambiguous (chapter 6).

↓VII is probably the next most popular chord in the repertory (its root appearing in four of the five common rock scales: mixolydian, aeolian, dorian, and minor pentatonic). In combination with I, IV, and/or V, ↓VII forms four schemas, the least common of which might be , which is not to imply that it is in any way uncommon. It appears in cadential form in the choruses to the Beatles’ 1967 happy-go-lucky “Hello Goodbye” (“I don’t know [IV] why you say вЂgood- [↓VII] -bye,’ I say вЂhel- [I] -lo’”). The most widespread phrasing for loops of is I–IV–↓VII with a doubly long tonic I, as heard in the verses of Maria Muldaur’s 1974 easy-listening staple “Midnight at the Oasis” (“[I] Midnight at the o- [IV] -a[↓VII] -sis [I]). Various other loop phrasings are also possible. I–IV–↓VII–I appears in the choruses of Gordon Lightfoot’s 1974 “Sundown” (“[I] Sundown, you [IV] better take care if I [↓VII] find you’ve been creepin’ ’round [I] my back stairs”). Franz Ferdinand doubles the length of the final tonic and quadruples the length of the initial tonic in their I–IV–↓VII–I verses to 2005’s suggestive “Do You Want To” (a phrasing they probably got from Duran Duran’s 1983 single “Is There Something I Should Know?”: “[I] A-well do ya, do ya, do ya wannaВ .В .В . wanna [IV] go a-where I’ve [↓VII] never let ya before [I]?”). Also heard occasionally is the phrasing IV–↓VII–I with a doubly long I, as presented in the title track from Andrew Lloyd Webber and Charles Hart’s 1986 smash-hit musical The Phantom of the Opera (“In sleep he [IV] sang to me. [↓VII] In dreams he [I] came”). In most cases, projects chained functions of hyper pre-dominantв†’rogue dominantв†’tonic. Yet as with the analogous phrasing of , the I–IV–↓VII loop with doubly long I (“Midnight at the Oasis”) is torn between strong hierarchical possibilities: the functional chain with ↓VII–I as the deeper motion, and the I–IV schema with a dominant appendage (here, ↓VII instead of V). , the other combination of ↓VII with I and IV, is without a doubt one of the most important schemas to emerge during the rock era.8 It started off as a quick guitar gesture—as in the opening riff of Paul Anka’s 1959 “Lonely Boy” and the riff to the Everly Brothers’ original 1960 recording of “Love Hurts”—but it eventually came to appear in nearly every conceivable permutation during its height of popularity between the late 1960s and early 1980s. A standard looping phrasing of is I–↓VII–IV with a doubly long initial tonic. The entire loop sometimes fits all within one bar, as heard in the main riff of Ray Parker, Jr.’s 1984 “Ghostbusters”; Parker paid an out-of-court settlement to Huey Lewis and The News over the obvious similarityPage 97 → between his riff and the one from the 1983 hit “I Want a New Drug,” which itself bears a resemblance to the riff in M’s 1979 “Pop Muzik” as well as to Them’s 1964 “Gloria” (“[I] Glo- [↓VII] [IV] -ria”). (To date, no known lawsuits have been brought forth by M or Them.) More typically, the phrasing I–↓VII–IV lasts at least two bars, as it does in the verses to Richard Marx’s 1987 “It Don’t Mean Nothing” (“[I] Welcome to the big timeВ .В .В . and [↓VII] even if you don’t go all the way, I [IV] knowВ .В .В .”), or four bars, as in the verses of ZZ Top’s 1983 “Sharp Dressed Man” (“[I] Clean shirt, new shoes, [↓VII] and I don’t know where I am [IV] goin’ to”). I–↓VII–IV sometimes has a doubly long IV instead of long I, as heard in the verses of Bad Company’s 1974 “Can’t Get Enough” (“Well I [I] take what- [↓VII] -ever I [IV] want.”). may instead start with ↓VII and put the doubly long tonic at the end: we witness this in Fatboy Slim’s 1998 collage-ofsamples “Praise You,” the piano chords of which are taken from a recorded rehearsal of Hoyt Axton’s 1973 “Captain America” and the vocals of which are taken from Camille Yarbrough’s 1975 “Take Yo’ Praise” (“I’ve got to [↓VII] praise you [IV] like I [I] should”). Very rare is the doubly long initial ↓VII and short I in the Rolling Stones’ 1966 “Lady Jane” (“My sweet Lady [↓VII] Jane, when I see you a- [IV] -gain [I]”). The other widespread phrasing of is I–↓VII–IV–I, which normally appears at one of two different possible harmonic pulses. The first is one chord per bar, as heard in Bachman Turner Overdrive’s 1973 “Takin’ Care of Business” (“And I’ve been [I] takin’ care of business [↓VII] every day. [IV] Takin’ care of business [I] every way”). The second is one chord per two bars, as heard throughout Ike and Tina Turner’s last single together, 1975’s “Baby, Get It On” (“[I] Baby, baby, baby, get it on. You [↓VII] knowВ .В .В . So come [IV] onВ .В .В . baby get it [I] on”).

As a cadential gesture, is used widely. A typical example is the verse’s cadence in Johnny Nash’s 1972 pop-reggae hit “I Can See Clearly Now” (“It’s gonna be a [↓VII] bright, [IV] bright sun-shiny [I] day”). It can also appear as a quick tag after a strong, hyper (usually V–I) whole cadence, as a kind of cadential echo, as occurs in Elmo and Patsy’s 1979 novelty tune “Grandma Got Run over by a Reindeer” (based closely on the chords to Merle Haggard’s 1973 “If We Make It through December”: “But [V] as for me and grandpa, we be- [I] -lieve [↓VII] [IV] [I]”). A conventional historical explanation for the rise of , and the ↓VII–IV–I cadence in particular, is that it derives from the blues-defining V–IV–I cadence, by way of a chordal rotation and centric reorientation of that progression’s roots (BM–AM–EM with center E becoming AM–EM–BM with center B). It is hard to justify such a claim on a purely theoretical, explanatory level, seeing that the other possible rotation and reorientation of the V–IV–I cadence, V–II–I (EM–BM–AM Page 98 →with center A), has yet to emerge in the repertory as a standard cadential figure, or looping figure for that matter. This derivation also seems not to be the case on a historical level, as evinced in the dearth of examples of so-called twelve-bar blues (a form we will dub the “blue” schema in the next chapter) with ↓VII–IV–I cadences, which we should expect to find in excess due to the fact that the V–IV–I cadence is most associated with that sort of setting. Indeed, save for isolated cases like Buffalo Springfield’s 1967 “Mr. Soul” (heavily based on the Rolling Stones’ 1965 “Satisfaction”) and Link Wray and His Ray Men’s largely instrumental “The Shadow Knows” (1964), the ↓VII–IV–I cadence is essentially nonexistent in the twelve-bar blues; the schema’s cadential role seems to have developed after its role as a loop did.9 (When ↓VII is indeed incorporated in blues-based cadences, it normally appears after a V, resulting in V–↓VII–I, often with an extra IV or ↓VI.) This is not to say that V–IV–I and ↓VII–IV–I cannot be heard as functionally similar, or even as related historically with regard to particular songs (e.g., a cover version replacing one schema with the other); it is just that there is no compelling evidence, theoretical or historical, to support the notion that ↓VII–IV–I owes its existence in general to V–IV–I. (We likewise cannot rightfully claim that ↓VII in general is some sort of “substitute” V; this point will become clearer in chapter 5.) A more credible story is that it evolved out of the embellishment of , as heard in the Crickets’ earlier-cited “Not Fade Away” (1957, covered famously by the Rolling Stones in early 1964): the schema’s I is ornamented by a IV, and then the schema’s IV (different from the preceding ornamenting IV) is itself ornamented by ↓VII acting as a hypo pre-subdominant (IV of IV), a progression that upon repetition delivers ↓VII–IV–I (“[I–IV–I] I’m a-gonna tell ya how it’s gonna be. [IV–↓VII–IV] [I] A-you’re gonna give your love to me [I–IV–I]”). In terms of functions, functional strengths, and harmonic levels, yields one of two basic hearings. More often than not, the parallel movements of ↓VII–IV and IV–I, each with root motion down by a perfect fourth, dominates the progression’s sound, turning it into a chain of hypo functions with ↓VII as a hypo pre-subdominant to IV and IV as a (hypo pre-tonic) subdominant to tonic I. (This chain is sometimes referred to by music scholars as a “doubleplagal” motion. Since “plagal” is the traditional term for our “hypo,” we could call it a “double-hypo” motion were we so inclined.)10 In this hearing, a schema is embellished with a ↓VII–IV prefix; it is that survives at the next level, with ↓VII functioning as a pre-subdominant decoration of the stronger two-chord schema. The second possible hearing involves embellished by an interposing IV. In this case, ↓VII functions as a stronger rogue dominant, which moves to a weaker Page 99 →subdominant IV before resolving to tonic I; this is essentially analogous to our interpretation in chapter 2 of the V–IV–I progression from the Troggs’ “Wild Thing” (Example 2.5) and Ritchie Valens’ “La Bamba.” The difference here is the dominant ↓VII instead of dominant V. In certain cases, it is difficult to tell which, if any, of these hearings of is strongest. Another of the most important three-chord schemas to emerge in the rock era is .11 Arriving in the mid-1960s with songs such as the Beatles’ 1963 “P. S. I Love You” (“P. S. I love [↓VI] you, you, [↓VII] you, [I] you”), the ↓VI–↓VII–I schema soon became one of the most recognizable of cadential gestures: it appears in everything from Cream’s 1968 “White Room” (in the bridges: “where the [↓VI] shadows [↓VII] run from them- [I] -selves”) to the Misfits’ 1980 cryptic “We Are 138” (“We [↓VI] are [↓VII] one thirty [I] eight”) to Cyndi

Lauper’s 1983 celebration of masturbation “She Bop” (in the verses: “they [↓VI] say that stich in time saves nine. They [↓VII] say I better stop or I’ll go blind [I]”). In the Misfits’ song, the same schema also appears as a loop, and though the schema more frequently appears as part of loops that are slightly larger (especially ↓VII–↓VI–↓VII–I, which we will discuss later on), it does also appear with regularity as its own repeating progression. Phrased with a doubly long tonic at the end, ↓VI–↓VII–I supports the choruses of Stryper’s 1986 Christian heavy-metal anthem “To Hell with the Devil” (“To [↓VI] hell [↓VII] with the [I] devil”). Phrased with a doubly long tonic at the beginning, I–↓VI–↓VII can be heard in the choruses to Seal’s 1994 “Kiss from a Rose” (in triple time: “Ba- [I] by, I compare you to a [↓VI] kiss from a [↓VII] rose on the [I] grey”). A tonic at both beginning and end is also possible. We hear I–↓VI–↓VII–I in the verses to the Patti Smith Group’s 1978 “Because the Night” (“[I] Take me [↓VI] now, baby, [↓VII] here as I [I] am”). Much less common is a doubly long ↓VII at the end, as heard in the instrumental introduction to the Vibrators’ 1977 “Baby Baby” and throughout Milli Vanilli’s 1989 “Girl You Know It’s True” (“Girl you know it’s [I] true, [↓VI] ooh, ooh, ooh, I love [↓VII] you”). Even rarer are doubly long middle chords, like the long ↓VII in the ↓VI–↓VII–I pre-choruses of Bon Jovi’s 1986 “Livin’ on a Prayer” (“we gotta [↓VI] hold [↓VII] on to what we [I] got”) and the long ↓VI in the I–↓VI–↓VII loop of Marina and the Diamonds’ 2012 “How to be a Heartbreaker” (“Rule number [I] one [↓VI] is that you [↓VII] gotta haveВ .В .В .”). In all the above cases, the effect of evoking goes hand in hand with the effect of a functional chain, with hyper pre-dominant ↓VI driving toward rogue dominant ↓VII driving toward tonic I. This is the norm when ↓VI–↓VII–I constitutes its own harmonic phrase. In certain other cases, however, the ↓VI is clearly a stronger pre-tonic than the ↓VII; this results in a motion of lower subdominant ↓VI to tonic I on the next harmonic level, with Page 100 →a passing ↓VII. In the verses of Styx’s 1983 orientalist “Mr. Roboto,” the bass књњ6 of the ↓VI sonority continues through ↓VII, preventing the ↓VII from surpassing the ↓VI in hierarchical importance (“to keep me a- [↓VI] live, [↓VII] yes, keep me a- [I] -live”). ↓VII’s function as a passing chord is seen more often when the ↓VI–↓VII–I progression is contained within the larger schema ↓VII–↓VI–↓VII–I, to be identified later as the “watchtower.”

Rarer Three-Chord Loops and Cadences A schema closely related to , but slightly less common, is the highly salient , salient because of its distinctive semitone slide from ↓VI down to V. See Example 3.3. When evoked, this schema nearly always projects chained functions comprising a strong pre-dominant ↓VI leading to dominant V leading to tonic I. In the Chordettes’ 1954 “Mr. Sandman” we hear a cadential version, with the hyper pre-dominant ↓VI appearing as a major-minor seventh chord, the equivalent of classical theory’s “German augmented-sixth chord” (“his lonesome [↓VI] nights are [V] over. [I] SandmanВ .В .В .”). As for loops, the phrasing with a doubly long initial I seems to be the most widespread, heard in the verses of Eurythmics’ 1983 “Sweet Dreams (Are Made of This)” (“[I] Sweet dreams are [↓VI] made of [V] this”). Other phrasings are possible, including I–↓VI–V with a doubly long ending V—as heard in much of Santana’s (featuring singer Rob Thomas) 1999 “Smooth” (“[I] вЂthis [↓VI] life ain’t [V] good enough”)—and ↓VI–V–I with a doubly long ending I—as heard in Cheryl Lynn’s 1978 “Got to be Real” (“Watcha [↓VI] know [V] [I] to be [↓VI] real? [V] [I]”). In Backstreet Boys’ 1997 “Everybody (Backstreet’s Back),” the pronounced bass synth riff implies that the loop’s phrasing is the peculiar I–↓VI–V with a doubly long middle ↓VI, although the rest of the musical texture conforms to the expected version of a long initial tonic: “Every- [I] -body, [↓VI] yeah, [V] rock your [I] body.” is so similar to that the two are often used interchangeably, as heard in “Everybody” (most noticeably in the intro: “Every- [I] -body, [↓VI] rock your [↓VII] body [I] right”).

Another less-prevalent cousin of is . This schema can additionally be understood as a relative of , in that the latter schema often features IV as a major triad and in doing so it offers a motion of књ›6 (the chordal major third of IV) to књ›7 to 1—the same motion that serves as the roots of .12 Van Halen uses it cadentially to transition from their verses into their choruses in 1988’s “Finish What You Started” (“If [↑VI] I fall shy at all [↓VII] [chorus: I] Come on, baby, finishВ .В .В .”). Page 101 →It appears as ↑VI–↓VII–I with a doubly long ending tonic in the choruses to the Edgar Winter Group’s 1972 “Free Ride” (“[↑VI] Come on [↓VII] and take a [I] free ride”). Phrased with doubly long tonic I in the first slot, the schema loops within the choruses of Peter Gabriel’s 1986 “Big Time”: (“[I] Big time. I’m on my [↑VI] way, I’m [↓VII] making it.”); a doubly long rogue dominant ↓VII is heard in the I–↑VI–↓VII verse loops of Journey’s 1978 “Lights” (“When the [I] lights go [↑VI] down in the [↓VII] city”); an evenly distributed loop of I–↑VI–↓VII–I supports the verses to David Bowie’s 1977 “Always Crashing in the Same Car” (“[I] Every chance, every [↑VI] chance that I take, [↓VII] I take it on the road [I]”). Except in this last example, where ↑VI is more of a post-tonic than anything else, generally operates as a functional chain of hyper pre-dominantв†’rogue dominantв†’tonic, ↓VII–I being the underlying motion; indeed, in “Big Time” the progression is occasionally reduced to just ↓VII–I (as in the song’s gigantic, final ↓VII–I cadence). A distant relative of is , which also normally acts as a functional chain (the underlying motion being subdominant IV to tonic I) but which ordinarily lacks the књ›6–ꜜ7–1 motion (књњ7 not typically appearing as part of IV). When looped, this schema is normally phrased as I–↑VI–IV–I with equal duration on each sonority, as heard throughout Bruno Mars’s 2010 mega-hit “Just the Way You Are (Amazing)” (in an unusually elongated form with two bars per chord: “When I see your [I] face, there’s not a [↑VI] thingВ .В .В . a- [IV] -mazing, just the way you [I] are”). Only rarely does it offer a different phrasing, such as that of Creed’s 2001 “My Sacrifice” with its doubly long initial I and its ending IV (“Hel- [I] -lo, my friendВ .В .В . where should we begin? [↑VI] Feels like for- [IV] -ever”). The schema is also found in the longer schema , a clichГ©d series we will devote considerable attention to later in this chapter. is often multifaceted regarding its functional effects, because of its close relation to another schema, one of the most important in the repertory: . This longer schema, which we shall discuss later in this chapter, features a (normally dominant) V in between IV and I, and if we anticipate V after IV, then we will probably hear IV as a pre-dominant; when the V does not arrive, the progression can also project an effect of incompleteness, a type of quality that we will explore in chapter 5. Anticipating a dominant V is understandable not only because of the prominence of the ↑VI–IV–V–I schema but also because a V often does appear not long after the ↑VI–IV–I schema is evoked. In Enya’s 2000 “Only Time,” I–↑VI–IV–I in the verses (“[I] Who can say where the [↑VI] road goes, where the [IV] day flows? Only [I] time”) gives way to a ↑VI–IV–V–I progression supporting the nonsense syllables of the chorus; in David Bowie’s 1972 “Soul Love,” I–↑VI–IV is Page 102 →followed immediately by I–↑VI–II–V, the II having replaced the previous IV (“[I] Stone loveВ .В .В . A [↑VI] brave sonВ .В .В . the [IV] sloganВ .В .В . and her [I] eyes, [↑VI] for they penetrate [II] her breathing. [V]”). The schema’s hierarchy is thus difficult to generalize about. Even if we do not anticipate a dominant V after IV, the hierarchy is tricky: when the ↑VI is a minor triad, as it often is, it can project a weak effect of tonic function, in which case the underlying harmonic motion will be ↑VI–I, the IV functioning as relatively weak subdominant. (A IV chord with a chordal perfect fifth will also have tonic potential, but this potential is usually not realized in the context of this schema.) On the other hand, depending on the song, the ↑VI may not project a tonic effect at all (even a weak one), in which case this sonority will likely function as a medial pre-subdominant to IV, and the next harmonic level will comprise IV moving to I. Example 102.3. Rarer three-chord schemas

Closely related to but far less common is . Looped, this schema occurs as I–↓VI–IV–I with its sonorities evenly distributed in the choruses to Tears for Fears’ 1984 “Shout” (over eight bars: “[I] Shout, shoutВ .В .В . [↓VI] these are the thingsВ .В .В . Come [IV] on. I’m talking to you. Come [I] on”) and throughout Nirvana’s 1993 “Heart-Shaped Box” with a doubly long ending IV (over two bars, with the long IV projecting a weak tonic effect that creates a certain amount of ambiguity as to the tonal center: “[I] Hey, [↓VI] wait, [IV] I gotta new complaint”). Cadential examples include the Rolling Stones’ 1973 “Hide Your Love” (heard toward the end of the track: “Come [↓VI] on, come [IV] on, come [I] on”) and the choruses to The Who’s 1974 “Long Live Rock” (“[↓VI] long live [IV] rock, be it dead or alive [I]”). The distinction between loop and cadence is blurred in Moby’s 1999 “Honey,” with its sonorities constantly changing durations upon repetition, lasting anywhere between two and sixteen bars apiece. Unlike , the schema does not often lead to a dominant V, which is to say there is no schema ↓VI–IV–V–I to anticipate; this progression does occur on occasion, as in the verses of the Shangri-Las’ 1964 “Remember (Walking in Page 103 →the Sand),” but it is probably not common or salient enough to warrant status as a schema. This is to say, the IV of is not likely to project a pre-dominant effect, as it sometimes does in the previous schema. Instead, the IV here is typically a subdominant, and the ↓VI a weak pre-subdominant, forming a functional chain resolving with tonic I. By reversing the ↓VI and IV of , we get , heard in a cadential setting in the choruses to Tori Amos’s 1992 “Crucify” (“My [IV] heart is sick of bein’, I said my [↓VI] heart is sick of bein’ in [I] chains”). Somewhere between a loop and a cadence is the example in 1983’s “Islands in the Stream” by Kenny Rogers and Dolly Parton, a IV–↓VI–I progression with a doubly long I that occurs only twice but makes a big impact, effectively taking on the song’s entire narrative weight while Kenny and Dolly improvise a bit; the progression’s vivid effect lies in the post-tonic effect of the ↓VI, the root of which chromatically cross-relates with the chordal major third of the preceding IV, књ›6 (“[IV] oh, come [↓VI] sail away [I] with me”). Unequivocal loops support the verses of Black Oak Arkansas’s “Hot and Nasty” (1971), phrased as I–IV–↓VI with a doubly long initial I (“Yeah, they [I] call me hot and [IV] nasty. [↓VI] YeahВ .В .В .”), and the verses of La Roux’s 2009 “Bulletproof,” evenly spaced as I–IV–↓VI–I (“[I] Been that, done that, messed around, I’m [IV] having funВ .В .В . I’ll [↓VI] neverВ .В .В . my [I] feet”). When appearing in the larger progression IV–↓VI–↓VII–I, the ↓VI chord can sometimes sound as though it will lead to a dominant ↓VII (blossoming into a ↓VI–↓VII–I schema, as heard in the chorus’s cadences of 1975’s “SOS” by ABBA: “When you’re gone, [IV] how can [↓VI] I even [↓VII] try to go [I] on?”); however, the ↓VI ordinarily ends up functioning as a lower subdominant to tonic I, with IV acting as a presubdominant and a ↓VI–I serving as the underlying motion. One last three-chord schema, (G–B–E) is not particularly common but is noteworthy in its impressive ability to fortify a particular tonal center, which it does by arpeggiating a minor I triad in its root motion (third–root–fifth), a phenomenon on which we will elaborate in chapter 6. Looping examples include the ↓III–V–I guitar riff (with a doubly long ending I) heard repeatedly in Hole’s 1998 “Celebrity Skin,” and the I–↓III–V progression (with a doubly long ending V) that constitutes the second half of Radiohead’s 1998 “Pearly” (“[I] Hurts [↓III] [V] me. DarlingВ .В .В .”). ↓III–V–I cadences can be heard in the 1968 instrumental theme to the television show Hawaii Five-O (presented as a partial cadence on V, eight bars into the first main phrase), and at the end of the bridge in XTC’s 1986 “Dear God” (right after the line “after we made you?”). usually appears as a functional chain comprising pre-dominant ↓III to dominant V to tonic I, with V–I as its deeper motion. Page 104 →In these past two sections, we identified twelve three-chord schemas: , , , , , , , , , , , and

. Most of these tend to operate as functional chains when projected, involving a motion of pre-dominant to dominant to tonic I, or presubdominant to subdominant to tonic I. Of those that do not necessarily project chained functions, most of them tend to exhibit an underlying motion from the first chord (some kind of pre-tonic) to the third (a tonic), with the second chord (a subdominant IV in all the above cases) usually softening the larger motion.

Three Numerals in Four Slots Schematic effects involving four sonorities could simply be said to entail “four-chord schemas.” This designation, though, is ambiguous, since there are several schemas that change chords three times (adding up to four sonorities) that deploy one numeral twice. This was not possible with two- and three-chord schemas, because a repeated numeral would have reduced a two-chord progression to one chord and a looping three-chord progression to two chords (e.g., a I–V–I loop will project ). Thus, to circumvent possible confusion over how we count “chords” at this very general level, we will hereafter use the term slot schemas (and slot progressions) for series with room to repeat a sonority internally, the smallest of which are four-slot schemas. In contrast to most of two- and three-chord schemas, four-slot schemas do not often materialize within larger harmonic phrases. On the contrary, they normally constitute their own self-contained phrase, and thus are much more likely to be looped than serve as a cadence. Additionally, the widespread tendency is to start with a tonic-functioning I and to distribute all sonorities more or less evenly over the course of two or four (or occasionally eight) bars, with one chord per two or four (or eight) beats. Since it will become increasingly cumbersome to write out all the chords of schemas with four or more slots, we will give special names to the most important and longest of these schemas; for the remainder, numerals will suffice. Schemas will be named after one of their prominent examples, one of their aural qualities, or (preferably) both, in the hope of increasing the likelihood of them sticking. Several four-slot schemas comprise only three distinct numerals. See Example 3.4. The most prevalent sonorities in the repertory—I, IV, and V—combine to form three such schemas, each of which is quite common. The first is , normally starting with I and featuring equal durations Page 105 →for each chord. We hear this progression in the Tokens’ 1961 “The Lion Sleeps Tonight” (based on an African folk tune and first recorded by Solomon Linda and the Evening Birds’ in 1939 as “Mbube”: “[I] In jungle the [IV] mighty jungle the [I] lion sleeps to- [V] -night”) and in the considerably faster verses of Bruce Springsteen’s 1973 “Rosalita (Come Out Tonight)” (with each sonority lasting a mere half a bar: “[I] Spread [IV] out, now, [I] Rosie. [V] Doctor, come cutВ .В .В .”). Less often the schema will begin with IV, as it does in Fats Domino’s celebrated 1956 cover of “Blueberry Hill”: “I found my [IV] thrill on Blueberry [I] Hill, on Blueberry [V] Hill, when I found [I] you” and Santana’s 1999 “Maria Maria” (with singing duo the Product G&B: “Oh, Maria Mari- [IV] -aВ .В .В . west-side [I] storyВ .В .В . Spanish [V] HarlemВ .В .В . just like a [I] movie star”). While the V–I motion typically functions as dominantв†’tonic, the IV–I motion has two possibilities: neighboring subdominantв†’tonic, or deltaв†’pre-dominant. If both I chords function as tonic (as in the slow-moving “Maria Maria”), then the progression is broken up into two pre-tonicв†’tonic motions, and the deepest harmonic level will feature the strongest of the neighboring motions, I–IV–I or I–V–I (most likely the latter). However, when the middle I chord sounds more like a predominant than a tonic (as in the quick-paced “Rosalita”), the progression is a more unified gesture driving toward a single resolving tonic, with the next harmonic level likely featuring IV (now a pre-dominant instead of a delta) that presses directly to V, which resolves to I. Unlike most of its four-slot brethren, also frequently appears as part of larger progressions, of which one of the most important is the so-called twelve-bar blues progression (I–IV–I–V–I; this schema will be discussed toward the end of this chapter). The second four-slot schema composed of only I, IV, and V is , typically phrased as I–V–IV–V (which is palindromic when resolving

to the next phrase’s I: I–V–IV–V–I). This V-heavy progression can be projected simply by inserting two quick V chords into a progression (this happens in the verses of Cake’s 2001 “Short Skirt/Long Jacket”: “[I] I wanna a girl [V] with the [IV] right allocations [V] who’sВ .В .В .”), or by inserting a single quick V into a progression that has a doubly long initial tonic (i.e., a bar of I, followed by a bar of IV–V; this happens in the double-struck chords of Tommy James and the Shondells’ 1968 “Crimson and Clover”: “[I–I] [V–V] [IV–IV] Now, I [V] don’t hardlyВ .В .В .”). Other times, each harmony has roughly the same duration, as occurs in the verses of Belinda Carlisle’s 1987 “Heaven Is a Place on Earth” (across four bars: “When the [I] night falls [V] down, I [IV] wait for you, and you [V] come around.”) and in verses of Hanson’s 1997 “MMMBop” (across two bars: “[I] You have so many re- [V] -lationships in this [IV] life, but only [V] one or two willВ .В .В .”). The V–I portion of the V–IV–VPage 106 →–I schema typically operates as a dominantв†’tonic motion, with the preceding IV functioning as a neighboring pre-dominant. Since the IV chord is often accented metrically, the preceding V tends to sound like it a delta (pre-predominant) leading up to it, although depending on the harmonic pulse and other factors, the first V may also project dominant function, in which case the IV will sound like a neighbor to both dominant Vs (as happened in the previous chapter with Prince’s “When You Were Mine”). Whether the deeper harmonic level comprises IV–I or V–I depends on the strength of the IV as a predictor of tonic relative to that of the V. The third four-slot schema to include only I, IV, and V is , which is usually phrased in one of three ways. The first, much less common phrasing is the palindromic I–IV–V–IV–I, with a V and its ensuing IV half the length of each other sonority. This is heard in the verses of Jerry Lee Lewis’s 1957 “Great Balls of Fire” (each sonority lasting either one or two bars: “[I] You shake my nervesВ .В .В . [IV] Too much loveВ .В .В . [V] You broke my will. [IV] Oh, what a thrill. [I] Goodness”). The second, more standard phrasing is IV–I–IV–V, as heard in the nonlooping IV–I–IV–V choruses to Sammy Hagar’s 1984 “I Can’t Drive 55” (“[IV] write me up for 125. [I] Post my faceВ .В .В . [IV] Take my licenseВ .В .В . [V] I can’t drive 55”). The third, most widespread phrasing starts with I and gives roughly equal time for each sonority (creating a palindrome upon repetition), as heard in Phish’s 1994 “Sample in a Jar” (“[I] The [IV] binding belt’s en- [V] -closin’ me, a [IV] sample in a [I] jar”) and OK Go’s 2010 “This Too Shall Pass” (“Well, you [I] can’t keep lettin’ it [IV] get you down, and you [V] can’t keep draggin’ that [IV] dead weight around [I]”). Since is so commonplace and historically important, it merits a name; we shall call it the bamba schema, because one of the first important tracks to feature the evenly spaced I–IV–V–IV phrasing of this schema was Ritchie Valens’ 1958 “La Bamba” (heard throughout), and because “bamba” is probably corrupted Spanish for “bambolear,” meaning to swing, sway, or shake, a connotation the schema carries with it to this day.13 Harking back to our discussion of “Wild Thing” and “La Bamba” in chapter 2, we can summarize I-initiating phrasings of as projecting long-range motions of dominant V to tonic I, embellished by a pre-dominant (the first IV) and a softening subdominant (the second IV); in essence, it is a fusion of the most prevalent functional realizations of the and schemas. But in its IV–I–IV–V version, which is not generally looped, the initiating IV will not typically be a softener of a preceding pre-tonic (from a previous phrase), merely a subdominant. (We will return to the IV–I–IV–V version of the bamba in chapter 4 when we discuss the closely related “crossing” schema.) The common chords I, IV, and ↓VII form two palindromic four-slot schemas:Page 107 → and . The first is the rarer of the two, heard with even durations in Simple Minds’ 1985 “Don’t You (Forget About Me)” (“[I] Don’t you [↓VII] forget about me, [IV] [↓VII] don’t, don’t, don’t, don’t [I]”) and the choruses to the Guess Who’s 1970 “Hand Me Down World” (with a quick ↑VII filling in the semitonal space from ↓VII up to I: “[I] Don’t give me no [↓VII] hand me down [IV] shoes. [↓VII] [↑VII] [I] Don’tВ .В .В .”). As with the bamba schema, can arise simply by adding two brief sonorities to a two-chord schema, in this case ; this is heard in the verses of Lou Reed’s 1972 “Vicious” (“[I] Vicious [↓VII] [IV] You hit me [↓VII] with a [I] flower”) and

the verses of Bob Seeger’s 1976 “Night Moves” (“[I] I was a little too tall . . . [↓VII] [IV] tight pants, points, hardly renowned [↓VII] [I]”). When its chords are of relatively equal duration, a functional chain is usually created, the first ↓VII functioning as a weak delta, the IV as a pre-dominant, and ↓VII as a dominant to tonic I. The deeper harmonic levels comprise first IV–↓VII–I, and then ↓VII–I. This hearing is laid out clearly at the start of Paul Simon’s 1986 South African jam “I Know What I Know,” which gets its groove going by way of the chained functions of IV–↓VII–I, and then proceeding to loop I–↓VII–IV–↓VII for the rest of the track (with the first ↓VII shortened to one beat). On the other hand, when both ↓VII chords are quick and serve as passing chords between I and IV, the underlying motion will usually be heard as IV–I, subdominant→tonic.

name

Example 107.3. Four-slot schemas with three numerals other rotations I–IV–I–V I–V–IV–V

V–I–IV–I V–I–V–IV

I–V–I–IV IV–V–I–V

bamba I–IV–V–IV IV–I–IV–V V–IV–I–IV

I–↓VII–IV–↓VII ↓VII–I–↓VII–IV IV–↓VII–I–↓VII

I–IV–↓VII–IV IV–I–IV–↓VII ↓VII–IV–I–IV watchtower I–↓VII–↓VI–↓VII ↓VII–I–↓VII–↓VI ↓VI–↓VII–I–↓VII

I–V–↑VI–V V–I–V–↑VI ↑VI–V–I–V , the second combination of I, IV, and ↓VII, comes in three standard phrasings. The most prevalent one begins on I and presents each chord for the same length of time (usually two bars), a phrasing used in the verses to Smokey Robinson and the Miracles’ 1967 “The Tears of a Clown” (“Now, if there’s a [I] smile [IV] on my [↓VII] face, [IV] it’s only”). A second, less frequently encountered phrasing features I and IV each for a bar, then ↓VII and IV within a single bar, then a full bar of I; we hear this repeated Page 108 →throughout the choruses of the title track, “Superstar,” from Andrew Lloyd Webber and Tim Rice’s influential 1970 rock opera Jesus Christ Superstar (“[I] Jesus Christ, [IV] superstar, [↓VII] do you think [IV] you’re what they [I] say you are?”). The third standard phrasing is more flexible in terms of numbers of bars: it involves a I moving to IV, then a ↓VII embellishing IV as a kind of tag, resolving to I in the next iteration. (We noted earlier a similar role of the three-chord schema , as a tag after a whole cadence on I.) This final phrasing is presented in the verses to the Hollies’ 1967 “King Midas in Reverse” (with a bare I–IV progression turning into I–IV–↓VII–IV(–I): “[I] If you could only [IV] see me, [I] I’d know exactly where I [IV] am [↓VII] [IV]”), and in the verses to Queen’s 1979 neo-rockabilly number “Crazy Little Thing Called Love” (“This [I] thing called love, I [IV] just can’t [↓VII] handle [IV] it.”). The IV–↓VII–IV–I schema probably owes its widespread popularity to the Rolling Stones’ 1965 “(I Can’t Get no) Satisfaction,” which uses it as a loop in the choruses underneath Keith Richards’ famous fuzzbox-guitar riff (“вЂHey, hey, [I] hey [IV] [↓VII] that’s what [IV] IВ .В .В .”).14 The Stones’ chordal loop itself was likely based in part on that of Solomon Burke’s swinging 1964 sermon “Everybody Needs Somebody to Love” (which the Stones also covered in 1965, before recording “Satisfaction”: “[I] E- [IV] -very [↓VII] bo- [IV] -dy”); Burke’s track follows the lead of the Kingsmen’s “Louie Louie” and Marvin Gaye’s “Can I Get a Witness” (both 1963, the latter also covered by the Stones), neither of which presents a I–IV–↓VII–I loop but rather closely related loops incorporating a historically significant musical gesture we will identify in the next chapter as the “teetering schema.” In many cases of , the first IV is a delta, and the ↓VII acts as a

neighboring pre-subdominant to subdominant IV; the schema is thus an embellished IV–I motion. However, when the ↓VII is emphasized metrically or otherwise (in relation to the ensuing IV), the ↓VII may project a rogue dominant effect that is softened by a passing subdominant IV, and so the underlying motion would be ↓VII–I. At other times, the schema can project both hierarchies simultaneously. Another highly significant four-slot schema with just three numerals is the palindromic . Since its inception in the late 1960s, this schema has been one of the defining chord progressions of the repertory, in various different phrasings, most often employing some version of I–↓VII–↓VI–↓VII. The most prevalent phrasing features equal durations throughout, often over two bars total, as heard in the opening to Blue Г–yster Cult’s cowbell-heavy 1976 “(Don’t Fear) The Reaper” (“[I] All [↓VII] our [↓VI] times [↓VII] have”) and in the choruses to Gotye’s 2011 “Somebody I Used to Know” (“[I] But you [↓VII] didn’t have to [↓VI] cut me [↓VII] off”). A widespread variant on this phrasing states one or more of the ↓VII sonorities only briefly, Page 109 →in passing, as occurs over two bars in the Jimi Hendrix Experience’s 1968 famous cover of Bob Dylan’s “All Along the Watchtower” (“[I] There must be [↓VII] some kind of a way [↓VI] out of here [↓VII]”). Less common is the use of a passing ↓VII when the progression last four bars (instead of two bars), as it does in the choruses to Adele’s 2010 “Rolling in the Deep” (“We could have had it [I] all [↓VII], rollin’ in the [↓VI] deep. You [↓VII] had my heartВ .В .В .”). “All Along the Watchtower” may be the earliest hit recording to use this schema as a loop; we will hereafter refer to it as the watchtower schema, because of Dylan’s song and because the progression seems to move from side to side (from I to ↓VI), as if surveying the tonal terrain.15 An additional phrasing of the watchtower offers I and ↓VII for equal amounts of time, then ↓VI and ↓VII each for half that time, then I again within that same phrase (i.e., I–↓VII–↓VI–↓VII–I). We hear this for most of Cameo’s 1986 “Word Up” (over four bars: “вЂWord up,’ [I] every[↓VII] -body say. [↓VI] When you hear the [↓VII] call you’ve got to [I] get it under way”). The bookended I–↓VII–↓VI–↓VII–I phrasing is successfully combined with the earlier-cited, quickly passing ↓VII sonority in Vicki Sue Robinson’s 1976 “Turn the Beat Around”: “[I] Turn the [↓VII] beat a- [↓VI] -round. Love to hear [↓VII] per- [I] -cussion.” In all the above phrasings of the watchtower, the first passing ↓VII prepares the arrival of the ↓VI (either as a delta or a pre-subdominant, depending on the ↓VI’s functional qualities). The rest of the progression, ↓VI–↓VII–I, has the same functional and hierarchical possibilities as we discussed earlier with that three-chord schema: as a ↓VI–I schema (lower subdominantв†’tonic) embellished by passing dominant ↓VII, or a ↓VII–I schema (rogue dominantв†’tonic) embellished by hyper pre-dominant ↓VI. When the second ↓VII is quick (as in “All Along the Watchtower” and “Misled”), the chances are great that the ↓VI will be the hierarchically superordinate of the two, leading directly to tonic I as a subdominant. Nowhere is this possibility stronger than in the downright quirky phrasing of Fitz and the Tantrums’ 2010 “MoneyGrabber,” the choruses to which place ↓VI at the start of the phrase and I in the middle, with quick ↓VIIs in between (“Don’t [↓VI] come back any [↓VII] time. [I] I’ve already had your [↓VII] kind [↓VI]”). Our last three-numeral, four-slot schema is , which nearly always starts with tonic I. This schema often sounds like a I–↑VI loop with two quick, passing V chords. We hear this in two tracks by Sheryl Crow: 1993’s “Strong Enough” (“Are you [I] strong enough to [V] be my [↑VI] man? [V] MyВ .В .В .”) and 1996’s “Hard to Make a Stand” (“It’s [I] hard to make a stand. [V] [↑VI] Yeah [V]”). Loops with just one quick passing V are also possible, as heard in the Kinks’ 1970 “This Time Tomorrow” (the second V being the short one: “[I] This [V] time [↑VI] tomorrow [V]”), but more common are Page 110 →evenly spaced loops, like those in the acoustic guitar introduction to Weezer’s 1994 “My Name Is Jonas” and in Fleetwood Mac’s 1997 live version of their earlier “Landslide” (“[I] I took my [V] love and I took it down [↑VI] [V]”), both of which offer salient, stepwise lines of 1–ꜛ7–ꜛ6–ꜛ7(–1), the first portion of which constitutes a gesture we will identify as the “sliding schema”

in the next chapter. While the initial I–V–↑VI portion of all these examples tends to sound like an ornamented I–↑VI progression—with the first V functioning as both post-tonic and pre-anchor to anchor ↑VI—the functional and hierarchical status of the second V is often less clear. This is true even when this second V is brief: its proximity to the I of the next iteration usually strengthens its pre-tonic effect, and since ↑VI is generally not a strong pre-tonic to begin with, the ↑VI–V–I portion might sound like a functional chain favoring the V–I motion at a deeper harmonic level. Thus, tends either to operate as a large functional chain or as a I–↑VI motion embellished by two passing Vs.

Four Numerals in Four Slots: Part I Just as the three most common chords of the repertory form three-numeral four-slot schemas, so the four most common chords—I, IV, V, and ↓VII—constitute four-numeral, four-slot schemas. See Example 3.5. We will identify three such schemas. The first, , is looped in the opening of Freddie and the Dreamers’ 1965 “Do the Freddie” (two chords per bar: “Hear the [I] happy [↓VII] feet dancing [IV] to the [V] beat”) and in the bridge of virtual-band Gorillaz’s 2005 “Feel Good Inc.” (one chord per bar: “[I] Windmill, windmill [↓VII] for the land, [IV] turn forever [V] hand in hand”). This schema typically operates as a functional chain, with delta ↓VII pushing to pre-dominant IV pushing to dominant V pushing to tonic I. The second schema, , is the most prominent of the bunch and is heard not only in loops but also often—atypically for four-slot schemas in general—at cadences. Joe Jackson loops it in 1978’s “Is She Really Going Out with Him?” (“[I] Pretty [V] women out [↓VII] walkin’ with go- [IV] rillas”), and Nickelback repeat it in 2005’s “Photograph” (“[I] Look at this photo- [V] -graph.В .В .В . makes me [↓VII] laughВ .В .В . get so [IV] redВ .В .В .”). As a cadential gesture, V–↓VII–IV–I appears in a number of instances, including the refrains to Stealers Wheel’s 1972 “Stuck in the Middle with You” (“[V] Clowns to the left of me, [↓VII] jokers to the [IV] right, here I [I] amВ .В .В .”) and to Bon Jovi’s 1988 “I’ll Be There for You” (“[V] I’ll be [↓VII] there [IV] for [I] you”). The functions of depend on whether the progression arrives in a loop or a Page 111 →cadence. In loops, often evenly spaced, the first half of the phrase, I–V, forms a unit that is echoed by the second, ↓VII–IV; the root motions of each move a perfect fourth downward or perfect fifth upward, and this parallelism puts particular emphasis on the ↓VII, as an anchor to IV. Yet, the IV is usually also a strong predictor of tonic, and so the ↓VII–IV–I motion tends to be functionally multivalent in exactly the same way as the three-chord schema itself sometimes is. In other words, the underlying two-chord motion for a looped can be either ↓VII–I or IV–I, or perhaps both, with the V a mere post-tonic. In contrast, when appears at a cadence, the V is typically the strongest pre-tonic, with the ↓VII–IV–I portion acting as an embellishment of a deeper dominantв†’tonic motion. The third schema is . This is the least distinctive of the three, only because there seems to be no standard phrasing for it. It is realized as I–IV–↓VII–V–I (with the ↓VII–V portion as long as just one of the previous sonorities) in verses of the Beatles’ 1970 “I Me Mine” (“[I] All through the [IV] days, I me [↓VII] mine, I me [V] mine, I me [I] mine”), as ↓VII–V–I–IV in the choruses of Crash Kings’ 2010 “Mountain Man” (“[↓VII] I’m [V] sippin’ on some [I] sunshine [IV]”), and as the instrumental cadential IV–↓VII–V–I gesture in the choruses of Mott the Hoople’s 1972 “All the Young Dudes,” harmonizing a guitar and organ melody that ascends in semitones from књ›6 up to 1: књ›6 (the chordal major third of IV) to књњ7 (↓VII) to књ›7 (the chordal major third of V) to 1 (I). The fadeout coda of Elvis Costello and the Attractions’ 1977 “Alison” combines the schema’s looping and cadential potential: “[↓VII] My [V] aim is [I] true [IV].” The underlying motion of this schema is difficult to generalize about, since its phrasing is so malleable. The deeper motion depends on whether the V, the ↓VII, or the IV is the strongest pre-tonic (it can be V–I, ↓VII–I, or even IV–I in the case of “All the Young Dudes” with its strong chromatic ascent from an otherwise subdominant књ›6 up to 1).

Although , , and contain the most common individual chords, these progressions are far from being the most important four-slot schemas. Indeed, the whole rock practice of employing rhythmically even four-slot loops begins with one specific schema from the jazz era: , which we will dub the steady schema. The steady, which normally is phrased as an even I–↑VI–II–V progression when looped, features a series of descending perfect fifths or ascending perfect fourths (usually a combination of the two) between the chordal roots (књ›6 to 2, 2 to 5, 5 to 1). Its most famous manifestation is the jaunty “I Got Rhythm,” written by George and Ira Gershwin in 1930 (revised from an earlier, slower version from 1928) and first recorded with a vocalist in 1930 by Red Nichols and His Five Pennies (the singer being Dick Robertson): “[I] I [↑VI] got [II] Page 112 →rhy- [V] -thm.” The term “rhythm changes” eventually entered musicians’ vocabulary to signify the harmonic framework (aka harmonic “changes”) for this song, and rhythm changes spawned countless reworkings in every conceivable substyle of jazz. While the term “rhythm changes” actually refers to the chords of the entire song, the shorter schema ↑VI–II–V–I, which is looped in Gershwin’s verses starting with I and ending with V (its only standard phrasing), was extracted and used repeatedly by musicians early on in the rock era (the mid-1950s) in the singing style that came to be known eventually as “doo-wop.” Some doo-wop groups actually rerecorded songs from the 1930s; the most prominent of these covers was the Marcels’ 1961 cover of “Blue Moon” (penned by Richard Rodgers and Lorenz Hart and originally recorded by Connee Boswell in 1935: “Blue [I] mo[↑VI] -on, [II] you saw me [V] standing”). But for the most part the schema was simply incorporated into new material, such as the Chords’ 1954 “ShBoom” (made even more famous through the 1954 cover version by the all-white group the Crew Cuts: “[I] Life could be a [↑VI] dream [II] if I could [V] take you up”) and the Moonglows’ 1954 “Sincerely” (likewise upstaged by an all-white cover version, this time in 1955 by the McGuire Sisters: “Sin- [I] -cerely, [↑VI] [II] oh [V] yes”). The steady schema offers a steady, predictable motion to tonic I by way of the falling perfect fifths (or rising perfect fourths) between the chordal roots. A“ steady” is also colloquial American English for a girlfriend or boyfriend, an idiom dating from the late nineteenth century but that now is associated primarily with the 1950s; this etymology is similar to the history of the schema itself, which was popular in ragtime and jazz but now is widely remembered nowadays as a phenomenon of 1950s slow-dance ballads and doo-wop. In fact, the schema is sometimes called the “doo-wop” progression, although this title is also regularly given to the related but distinct schema (which we will discuss below). The term “ragtime” progression is also used to describe the steady, but usually only when all the sonorities feature chordal major thirds,16 as heard in innumerable jazz-era recordings such as Jelly Roll Morton’s 1924 “London Blues” (heard at each cadence) and Blind Willie McTell’s 1940 “Kill It Kid” (looped throughout), but also in the rock era with nostalgic tracks like Country Joe and the Fish’s 1967 Vietnam War protest song “The вЂFish’ Cheer/I-Feel-Like-I’m-Fixin’-to-Die Rag” (heard as a cadential figure: “There [↑VI] ain’t no time to [II] wonder why. Whoopee! [V] We’re all goin’ to [I] die.”). By the late 1960s, the popularity of the steady schema dropped off significantly, although in can still be heard from time to time, as in King Harvest’s 1973 “Dancing in the Moonlight” (with a brief, passing V inserted between I and ↑VI, and the phrases starting in the unusual position on II: “[II] Dancin’ Page 113 →in the moonlight. [V] Everybody’s [I] feelin’ (V) warm and [IV] bright”) and Queen’s 1975 “Bohemian Rhapsody” (in the verses, with an elongated II and abbreviated V: “[I] Mama, just [↑VI] killed a man, put a [II] gunВ .В .В . now he’s [V] dead”). In nearly all cases, regardless of the phrasings and the kinds of chordal thirds, the steady schema behaves as a functional chain: the V is a dominant predicting tonic I (V–I appears at the deepest level), the II is a pre-dominant predicting V (II–V–I at the next level), and the ↑VI is a weak delta (as much a departure from the I—a posttonic—as it is a predictor of things to come). Example 113.3. Four-slot schemas with four numerals: part I

name

other rotations

I–↓VII–IV–V V–I–↓VII–IV IV–V–I–↓VII

I–V–↓VII–IV IV–I–V–↓VII ↓VII–IV–I–V

I–IV–↓VII–V V–I–IV–↓VII ↓VII–V–I–IV steady I–↑VI–II–V V–I–↑VI–II II–V–I–↑VI king I–↑VI–IV–V V–I–↑VI–IV IV–V–I–↑VI

I–↑III–IV–V V–I–↑III–IV IV–V–I–↑III Nearly identical to the steady is , a schema much less common during the jazz era but probably originating as another variation on “I Got Rhythm.” Its popularity perhaps stems from 1938’s “Heart and Soul” (penned by Hoagy Carmichael and Frank Loesser) as performed by Larry Clinton and his Orchestra featuring singer Bea Wain. In this track, the sonority immediately before the V chord contains 4 in the bass along with 1, 2, and књ›6 above (with center C: F, C, D, A), and so can be interpreted as either a II (Dm/F) or a IV (F6) (“[I] Heart and [↑VI] soul, [IV] I fell in [V] love with you”). By the late 1950s, became fairly distinct from and came to be used so frequently that it is sometimes referred to simply as the “fifties progression,” a typical case being the Penguins’ 1954 “Earth Angel” (“Earth [I] angel, earth [↑VI] angel, [IV] will you be [V] mine [I]”). Yet it actually defined the rock sound well into the early 1960s; one of the schema’s most defining instances came in 1961 with Ben E. King’s “Stand by Me” (“[I] When the night has come, [↑VI] and the land is dark, and the [IV] moon is the [V] only light we’ll [I] see”), although in this case the progression features an atypically asymmetrical phrasing: I–↑VI–IV–V–I, with the ↑VI and the two I chords lasting two bars each, and the IV and V each lasting only one bar. (The Police’s 1983 “Every Breath You Take,” and the 1997 Police-sampling “I’ll Be Missing You” by Puff Daddy featuring Faith Evans and 112, are among the few hits to follow this unusual phrasing.) Still, King’s recording was a Page 114 →massive hit, and this schema is even sometimes referred to as the “Stand by Me” changes. We instead will give the less bulky title of the king schema, not only in honor of Ben E. King (who also cowrote and sang the Drifters’ 1959 classic “There Goes My Baby,” which likewise features this schema), but because of the schema’s absolute dominance during the formative years of the rock era. As with most four-slot schemas, the king is most typically phrased starting with I and gives equal duration to each harmony over the course of two or four bars. However, many songs after the doo-wop era initiate the king schema with IV (most often in their chorus section), as heard looped in the choruses of Marc Cohn’s 1991 “Walking in Memphis” (“walking in [IV] Memphis [V] [I] ’was [↑VI] walkin’ .В .В .”) and throughout Young Money’s 2009 “BedRock” (“[IV] you, baby, my [V] room is the G-spot. [I] Call me Mr. Flintstone. [↑VI] I can make your bed rock”). Regardless of the phrasing, the king schema works in exactly the same way as the steady schema, as a functional chain that leads gradually to tonic resolution, the only difference between the schema being the pre-dominant IV versus pre-dominant II. That said, there is often a 2 stated somewhere of the musical texture during the IV, and so the distinction between a king and a steady schematic effect can, in some situations, be difficult (or pointless) to make. Both schemas are often projected simultaneously. There have been so many songs to use the king that we should not be surprised to find it as a cadential gesture, even though four-slot schemas do not always form cadences separate from looped progressions. Cadential examples include the refrain of the Shirelles’ 1961 “Baby It’s You” (“what [↑VI] can I do? [IV] Can’t help myself, [V] when, baby, it’s [I] you”) and the refrain of the Bellamy Brothers’ 1979 playful country ballad “If I Said You

Had a Beautiful Body Would You Hold It Against Me?” (“[↑VI] If I [IV] said you had a beautiful [V] body would you hold it against [I] me?”). In both these cases, the ↑VI chord is more of an appendage to the primary cadential motion IV–V–I. A close relative of the king is , a schema popular as an evenly phrased I–↑III–IV–V progression in early-sixties tracks such as Peter, Paul, and Mary’s 1962 recording of Pete Seeger’s “If I Had a Hammer” (“If I had a [I] ham- [↑III] [IV] -mer I’d [V] hammer in theВ .В .В .”) and in retro songs such as 1986’s “Happy Hour” by the Housemartins (“It’s [I] happy [↑III] hour again. I [IV] thinkВ .В .В . if I [V] wasn’t out”). In both these examples, the ↑III chord is a minor triad; the ↑III can instead be major, in which case the momentum toward IV is greatly increased, and that chord’s arrival brings a certain degree of resolution (and projects a chromatic schematic effect that we will call the “stretch” in the next chapter). The major ↑III version of the progression can be heard looped in Arthur Alexander’s 1962 “Soldier of Love” Page 115 →(phrased with a quick IV and V that allow the phrase to end on a full bar of I: “There [I] ain’t no reason for [↑IIIM] you to declare [IV] war on the [V] one who loves you [I] so”) and in Bare Naked Ladies’ 1991 “Be My Yoko Ono” (“[I] And if there’s [↑IIIM] someone you can [IV] live without [V]”).17 Just like the king schema, ordinarily operates, regardless of the kind of ↑III, as a functional chain, except that its delta-functioning harmony is ↑III rather than ↑VI.

Four Numerals in Four Slots: Part II The same group of chords found in the king—I, IV, V, and ↑VI—are found in a few other important orderings. , which is not one so prominent as to warrant a special name, appears throughout Fine Young Cannibals’ 1988 “She Drives Me Crazy” (spread evenly over two bars: “She [I] drives me [IV] crazy [↑VI] ooh, [V] ooh”) and in the choruses of Faith Hill’s 1998 “This Kiss” (an embellishment on the chorus’s previous I–IV–V progression, and featuring a salient change of bass note under the I, from 1 to књ›3: [I] This [I/књ›3] kiss, this [IV] kiss, [↑VI] un- [V] -stoppable”). Another, more prominent ordering of these same four chords is the schema , which we hear in the verses to Prince and the Revolution’s epic 1984 “Purple Rain” (“[I] I never meant to cause you any [↑VI] sorrow. [V] I never meant to cause you any [IV] pain”) and in the verses to Spin Doctors’ 1991 “Two Princes” (“[I] One, two, [↑VI] princes kneel be- [V] -fore you. That’s [IV] what I said”). In both and , the strongest pre-tonic chord tends to be the V. In “Purple Rain,” Prince even ends the verses by leaving out the IV completely and protracting the dominant V by a half of a bar. In , ↑VI is usually a pre-dominant and IV a delta; in the IV normally acts as a softening pre-tonic (as in the V–IV–I schema), and the ↑VI a pre-dominant to V. At the deepest harmonic level both schemas reduce to V–I; whether the intermediary deepest level is IV–V–I, ↑VI–V–I, or V–IV–I depends on the exact attributes of the song in question. There are three other mathematically possible orderings for the chords I, IV, V, and ↑VI. See Example 3.6. Two of these, IV–V–↑VI–I and V–IV–↑VI–I, are not schemas, but the third is one of the most significant harmonic progressions to emerge in the last few decades: , which we will dub the journey schema.18 Of the four possible rotations of the journey, two are much less common. The first of these, V–↑VI–IV–I, we hear looped in the main sections of Marvin Gaye’s 1982 “Sexual Healing” (“And [V] when I get that [↑VI] feelin’, I want [IV] sexual [I] healin’”) and in the choruses of Page 116 →Spice Girls’ “Wannabe” (1996) “[V] If you wanna be my [↑VI] lover, you [IV] gotta get with my [I] friends”). The functions and levels of the journey are more complex than those of any of the other four-slot schema we have so far encountered. This particular phrasing typically operates as a prolonged dominant V sonority that is softened by ↑VI and IV en route to tonic I. This long-range

dominant V is even more obvious in the verses of James Blunt’s 2010 “Stay the Night,” wherein the journey appears with an extra V tacked on to the end and taking up half the duration of the I (“[V] It’s 72 de- [↑VI] -grees, zero chance of [IV] rain, it’s been a perfect [I] day [V]”); this extra V weakens the resolution to I and helps projects the additional—and stronger—effect of the I being a pre-dominant to V, a dominant that fully resolves only when the loop ends with the onset of the chorus. The second (of two) less common phrasing of the journey starts with IV and ends with ↑VI: IV–I–V–↑VI. This appears in the choruses to Rihanna’s 2007 “Umbrella” (four beats per chord: “[IV] Now that it’s rainin’ more than [I] everВ .В .В . each [V] otherВ .В .В . um- [↑VI] -brella”) and Taylor Swift’s 2012 “We Are Never Ever Getting Back Together” (two beats per chord: “[IV] We are [I] never, ever, ever [V] getting [↑VI] back together”). In Swift’s track, we can hear a passing V inserted between ↑VI and IV; this extra harmony is a standard addition to any phrasing. Functionally, this phrasing can operate in at least two ways. In Rihanna’s track, due to the relatively slow harmonic pulse (a new chord every bar, at a relaxed tempo), the anchoring potential of ↑VI shines through, with V likely acting as a pre-anchor to it. The initial IV resolves as a subdominant into tonic I; at a deeper level there is an oscillation between the two anchors, tonic I and post-tonic ↑VI. In Swift’s song, the fast pulse (a new chord every half bar, at a slightly brisker tempo), undermines the anchoring effect of the ↑VI and even that of the I. The progression might be heard as I–V at a deeper level, but it also can sound like IV–V (both chords being metrically accented) adorned by weak I and ↑VI chords. The extra passing V after Swift’s ↑VI further undercuts the latter’s weak anchoring function. The most standard phrasing of the journey, one which demands a fair amount of our attention here, is I–V–↑VI–IV, heard looped for the entirety of Journey’s 1980 “Any Way You Want It” (“[I] Any way you want it, [V] that’s the way you need it, [↑VI] any way you want [IV]”) and the entirety of Bruce Springsteen’s 1984 “I’m Goin’ Down” (“I’m goin’ [I] down, down, down, [V] down, I’m goin’ [↑VI] down, down, down, [IV] down”). The progressions in these two tracks have different bass notes for the V chord: in Springsteen’s it is the more common root 5, and in Journey’s it is the chordal third књ›7. A књ›7 or књњ7 permits a stepwise descent from the root of I, to the third of V, to the root of ↑VI (on center E: E–D♯–Cв™Ї); this three-note descent is often a highly Page 117 →salient version of an important gesture we will call the “sliding schema” in the next chapter. Another potential—but rarely fulfilled—downward motion within the journey is књ›6–ꜜ6–5 (on center E: C♯–C–B) from the chordal root of ↑VI to a chordal minor third of IV (књњ6), to the chordal fifth of the next I (5). This is rare because the IV is usually a power chord or a major triad, but the Chiffons insert IVm in the (nonloop) verses to the their 1963 “One Fine Day”: “[I] One fine day [V] you’ll look at me [↑VI, књ›6] and you will know our love was [IVm, књњ6] meant to be [I, 5].” In chapter 4 we will label the књ›6–ꜜ6–5 descent the “shrinking schema.” Example 117.3. Four-slot schemas with four numerals: part II name other rotations

I–IV–↑VI–V V–↓I–IV–↑VI ↑VI–V–I–IV

I–↑VI–V–IV IV–I–↑VI–V V–IV–I–↑VI journey I–V–↑VI–IV IV–I–V–↑VI ↑VI–IV–I–V zombie I–↓VI–↓III–↓VII ↓VII–I–↓VI–↓III ↓III–↓VII–I–↓VI In its standard phrasing as I–V–↑VI–IV, the journey’s initial tonic I typically moves to a post-tonic/pre-anchor V that resolves to an anchoring ↑VI,

which then proceeds to subdominant IV, leading back to tonic I at the following iteration. On the next harmonic level, the weak V gives way to the three-chord motion I–↑VI–IV(–I); the next level after that includes an oscillation between the two tonics, I and ↑VI. This interpretation becomes obvious when hearing the progression that ends the choruses of John Lennon’s 1971 “Oh Yoko!” The elongated ↑VI is clearly a temporary resting spot, followed by an elongated cadential IV that awaits final resolution to tonic I (“[I] Oh, [V] Yo- [↑VI] -ko. My [IV] love will turn youВ .В .В .”). We are calling the “journey” for two reasons: first, to convey the schema’s typical voyage from tonic I to anchor ↑VI, back to tonic I; and second, to honor the band Journey, whose “Any Way You Want It” was possibly the first hit song built entirely around a loop of this progression (“[I] Any way you want it. [V] That’s the way you need it. [↑VI] Any way you want [IV]”). Journey also used this schema to great effect a year later in the verses to 1981’s “Don’t Stop Believin’” (although there it alternates with the nonschematic I–V–↑III–IV). Examples of the phrasing I–V–↑VI–IV start to pop up with frequency in the early 1970s, probably due to the massive popularity of the Beatles’ 1970 “Let It Be” (“When I [I] find myself in [V] times of trouble, [↑VI] mother Mary [IV] comes to me”). (The Beatles’ IV might also, or instead, be heard as a II, since Paul McCartney’s right-hand piano chords rest on scale degree 2 at that point. This is yet another example of the overlapping effects of IV and II.) In Page 118 →“Let It Be,” the journey occupies only the first half of the verse, the larger, full progression representing a schema we will identify in chapter 4 as the “in-mind” schema. And even though the Beatles themselves used the journey as its own looping I–V–↑VI–IV phrase in 1965’s “In My Life” (albeit in a nonstandard phrasing, with two different IV chords presenting the chromatic descent књ›6–ꜜ6–5 heard earlier in the Chiffons’ “One Fine Day”: “There are [I] places [V] I re- [↑VI, књ›6] -member all my [IVM, књ›6] life, [IVm, књњ6] though [I, 5] some have changed”), it is “Let It Be” that seems to be the real fountainhead for this most-standard version of the journey. That song’s tonal center of C and Billy Preston’s gospel-organ atmosphere were recreated for the I–V–↑VI–IV loops in the verses to Bob Marley’s 1974 “No Woman, No Cry” (the V also giving the effect of a I/књ›7: “[I] Said, I [V] remember [↑VI] when we used to [IV] sit”). From there, the Rolling Stones took the loop for the verses of their 1978 “Beast of Burden” (in “[I] I’ve never [V] been your [↑VI] beast of [IV] burden”). Since the early 1980s, the I–V–↑VI–IV phrasing of the journey has been ubiquitous, appearing in every style from alt-punk (the verses of Green Day’s 1994 “When I Come Around”) to pseudo-classical (the choruses of Andrea Bocelli’s 1995 “Con te Partirò”) to dance-pop (the choruses of Lady Gaga’s 2008 “Paparazzi”) to Disney films (the choruses of Kristen Anderson-Lopez and Richard Lopez’s “Let It Go”—the title of which echoes “Let It Be”—from 2013’s Frozen). Its ubiquity has not gone unnoticed by rock practitioners; it has been the subject of comedic musical routines by Rob Paravonian (2006’s “Pachelbel Rant”)19 and the Axis of Awesome (2009’s “Four Chord Song”). The fourth and final possible rotation of the journey is ↑VI–IV–I–V, with equal durations throughout. This is heard as a repeated progression in Scott McKenzie’s 1967 hippie folk-rock anthem “San Francisco (Be Sure to Wear Flowers in Your Hair),” which is perhaps the first hit song to loop the journey (twice in a row at the start of the first two verses: “[↑VI] If you’re [IV] goin’ to [I] San Fran- [V] -cisco”), as well as in the choruses to 2011’s “Little Talks” by Of Monsters and Men (“Don’t [↑VI] listen to a [IV] word I [I] say. [V] Hey!”). Regarding its harmonic functions and levels, this phrasing is highly susceptible to ambiguity because of the prominence given to the ↑VI at the head of the progression. The ↑VI’s tonic potential often threatens the stability of the progression’s orientation toward the I, throwing weight toward the root of the ↑VI as another possible tonal center by itself. Thus, the ↑VI–IV–I–V phrasing of the journey typically projects, at least to some degree, numeric effects of I–↓VI–↓III–↓VII. The problem is deciding the degree to which any particular progression of, say, Em–CM–GM–DM projects the numerals ↑VI–IV–I–V versus I–↓VI–↓III–↓VII. This exact series of letter effects appears, for instance, in both the verses to McKenzie’s “San Francisco” and throughout Page 119 →the Cranberries’ 1994 “Zombie” (although the Cranberries use DM/Fв™Ї as opposed to McKenzie’s DM/D: “In your [I] head, in

your [↓VI] head, zombie, [↓III] zombie, zombie, [↓VII] -ie, -ie. What’s in your [I] head?”). Despite these progressions being nearly indistinguishable in terms of pitch-class content and rhythmic profile, they project different centric and numeric effects: in “San Francisco” the strongest center is G, and in “Zombie” it is E, and so the progression in the former is ↑VI–IV–I–V and in the latter is I–↓VI–↓III–↓VII. The I–↓VI–↓III–↓VII progression of “Zombie” deserves to be considered a schema in its own right and is probably on par with the journey in terms of its deployment in the repertory. It is known in some circles by the pointlessly sexist and awkwardly lengthy title “Sensitive Female Chord Progression, ” a term deriving from the schema’s use in mid-1990s rock by female artists (e.g., Joan Osborne’s 1995 “One of Us,” Ani DiFranco’s 1995 “Shy,” Sarah McLachlan’s 1997 “Building a Mystery”).20 We will instead refer to as the zombie schema, because the Cranberries’ song might be the first hit recording to loop the schema in all of its sections, and also because the schema has been tapped by musicians so many times that it seems almost supernatural in its endurance, as though it could never die or is already (un)dead. The zombie started to be looped for entire sections of songs as early as the mid-1970s, with tracks like folk artist Joan Baez’s 1975 “Diamonds and Rust” (in the verses: “Well [I] I’ll be damnedВ .В .В . [↓VI] ghost againВ .В .В . not un- [↓III] -usualВ .В .В . the [↓VII] moonВ .В .В . happen to [I] call”) and Boston’s 1976 “Peace of Mind” (in the introductory guitar riff and choruses: “[I] People [↓VI] livin’ in [↓III] compe- [↓VII] -tition. [I] All IВ .В .В .”). It was not until the late 1980s, however, that is started appearing regularly. Many contemporary rock musicians have acted like zombies themselves in their seemingly ceaseless fascination with this harmonic progression, a fascination that as of yet shows no signs of abating. The schema runs the complete stylistic gamut, from heavy metal (the choruses of Skid Row’s 1989 “18 and Life”) to hip hop (throughout Flo Rida’s 2012 “Whistle”), from Latin pop (alternating with I–↓VI–IV–↓VII in the choruses of Shakira’s 2001 “Whenever, Wherever”) to alt rock (the choruses of Red Hot Chili Peppers’ 1999 “Otherside”). The previously mentioned comedy routine “Four Chord Song” by the Axis of Awesome, which parodies the overuse of the journey schema, also include numerous examples of the zombie schema, layering examples of both schemas on top of one another. The zombie schema normally arrives in the phrasing I–↓VI–↓III–↓VII, with relatively equal durations throughout. No other rotation of this schema is standard, perhaps because when the I is placed in any position other than the first slot, its tonic quality tends to be much subtler, and the ↓III usually takes over as the strongest tonic. The chordal root of the ↓III then projects Page 120 →itself as tonal center, making the progression not a zombie at all but rather a journey (the ↓III acting as I and all the other numerals likewise adjusted). The only significant variations seen with the zombie are the lengths of the sonorities relative to one another: specifically, the ↓VI and ↓VII sometimes are sounded only briefly in between longer the I and ↓III chords, as heard in the verses of the Offspring’s 1994 “Self Esteem” (“[I] I wrote her off [↓VI] for the [↓III] tenth time today [↓VII] [I]”), although even in this track the zombie is looped with all the chords the same length when we move into the chorus. Regardless of the relative durations of its sonorities, the zombie schema tends to operate as a I–↓III motion, with the ↓VI functioning as a passing chord en route to ↓III (which also can project its own competing tonic effect) and the ↓VII functioning as a passing dominant. Since the journey and zombie schemas are so similar in certain ways, any given progression in a song might be heard as projecting both schemas simultaneously. The fundamental issue here is that some degree of tonic quality is usually projected by both the journey’s I and ↑VI and the zombie’s I and ↓III (the Em and GM chords in Em–CM–GM–DM). If one of the sonorities is clearly more a tonic, then the progression can be understood as a realization of one schema versus the other, but attempting to hear an invocation of the journey as opposed to the zombie, or vice versa, can be a difficult, or futile, task. We already noted the possibility of ambiguity between the two schemas, which we will investigate in chapter 6. For now, it will suffice to say that the journey and zombie schemas should considered inextricably linked structures—two sides of the same coin—and that it is often not clear whether a particular progression projects one versus the other.

Four Numerals in Four Slots: Part III Another schema related to the journey is . See Example 3.7. This progression, which is not quite common enough to warrant a special name, is only one chord different from the journey: II appears in place of ↑VI. Its normal phrasing is I–V–II–IV, spaced evenly. We hear this in Semisonic’s 1998 “Closing Time” (“[I] Closing [V] time. [II] Open all the [IV] doors”) and Katy Perry’s 2008 “Hot n Cold” [sic] (“’Cause you’re [I] hotВ .В .В . you’re [V] yesВ .В .В . you’re [II] inВ .В .В . you’re [IV] upВ .В .В .”). A second phrasing is possible but much less common: II–IV–I–V, as heard in the choruses of Toad the Wet Sprocket’s 1991 “Walk on the Ocean” (“Walk on the [II] ocean, [IV] step on the [I] stones [V]”) and Coldplay’s 2001 “Paradise” (the tonal center of which is slightly slippery: “[II] Para-, para-, [IV] paradise [I] para,- para, [V] paradise”). (These Page 121 →two phrasings correspond to the primary phrasings of the journey: I–V–↑VI–IV and ↑VI–IV–I–V.) The functions depend on the phrasing. With II–IV–I–V, there is usually a functional chain created by the pre-subdominant II and subdominant IV leading to tonic I, with the V functioning as a departure and a delta to the next iteration. With the more typical I–V–II–IV, however, the progression usually sounds more like a relaxed oscillation between I and II, with V and IV relegated to supporting roles as post-tonic/pre-anchor (V) and subdominant (IV). The same chords (II, IV, V, and I) form a separate, additional schema, with the II and IV swapped: . This schema, phrased normally as I–IV–II–V, is actually closer to the steady than the journey, with IV in place of the steady’s ↑VI. This somewhat less common schema is evoked in the verses of Bonnie Tyler’s 1976 “Lost in France” (“I was [I] lost in [IV] France. In the [II] fields the birds were [V] singin’”) and the choruses of Sister Hazel’s 1997 “All for You” (“It’s [I] hard to [IV] say what it [II] is I [V] see”). The functions and harmonic levels of this schema are usually identical to those of the steady and king schemas: a functional chain is created comprising a delta (IV) that predicts a predominant (II) that predicts a dominant (V) that predicts a tonic (I). There are two more major four-slot schemas, and one minor one, that need to be mentioned before closing this chapter. The first important one is , which features a series of ascending perfect fifths/descending perfect fourths in the bass. Typically phrased as I–↓III–↓VII–IV spread out evenly, this progression is looped in the titular portions of the Black Crowes’ 1992 “Remedy” (“[I] Can I [↓III] have some [↓VII] reme- [IV] -dy?”). A second possible phrasing is one that starts with ↓III. The evenly spaced progression ↓III–↓VII–IV–I is repeated in the chorus of the Rolling Stones’ 1968 “Jumpin’ Jack Flash” (“But it’s [↓III] all [↓VII] right [IV] now, in fact it’s a [I] gas”). Another, less common phrasing starts and ends with I, with various possibilities for the chords’ duration: I–↓III–↓VII–IV–I appears in the verses of the Kinks’ 1966 “Dead End Street” (“[I] There’s a crack up in the [↓III] ceil[↓VII] -ing [IV] and the kitchen sink is leak- [I] -ing”). is also regularly seen at cadences (one of the few four-slot schemas to be so), as evidenced by the verses of Electric Light Orchestra’s 1979 “Don’t Bring Me Down” (“I’ll [↓III] tell you once more, before I [↓VII] get off the [IV] floor, вЂdon’t bring me [I] down’”). This schema is essentially an expanded version of the three-chord , in the sense that the latter’s pair of ascending perfect fifths/descending perfect fourths between the chordal roots (IV to I, and ↓VII to IV) are enlarged by an additional fourth (↓III to ↓VII). These roots motions are usually so salient that the harmonic functions and levels cannot help but Page 122 →follow suit; the schema normally acts as a functional chain, with delta ↓III, pre-subdominant ↓VII, and subdominant IV all leaning into their following chord, until we reach tonic I. As we will later see, however, the looping version of the schema can also exhibit a fair amount of ambiguity regarding which chord is actually the I. Example 122.3. Four-slot schemas with four numerals: part III

name

other rotations

I–V–II–IV IV–I–V–II II–IV–I–V

I–IV–II–V V–I–IV–II II–V–I–IV

I–↓III–↓VII–IV IV–I–↓III–↓VII ↓VII–IV–I–↓III walk I–↓VII–↓VI–V V–I–↓VII–↓VI ↓VI–V–I–↓VII The last four-slot schema we will identify in this chapter has one of the longest histories of any we will discuss: . When starting with I and ending with V, as it usually does, this schema displays a root motion that is known among classical musicians as the “lamento” gesture: 1–ꜜ7–ꜜ6–5, all the while outlining the chordal root and fifth of the I (1 and 5). Dating back to Spanish Renaissance dance music, the lamento gesture, which usually occurs in the bass, has continued to play an important role in rock music in the form of .21 Typically phrased I–↓VII–↓VI–V with equal durations throughout, the schema is heard across two bars in Ray Charles’ 1961 “Hit the Road Jack” (“Hit the [I] road, [↓VII] Jack, and [↓VI] don’t ya come [V] backВ .В .В .”) and across four bars in the Bangles’ 1987 cover of “Hazy Shade of Winter” (looped in the song’s opening, and thereafter heard only one at a time: “Look a- [I] -round. Leaves are [↓VII] brown. And the [↓VI] sky is a [V] hazy shadeВ .В .В .”). This schema is also commonly deployed across eight bars, as heard in the Turtles’ optimistic 1967 “Happy Together” (“Imagine [I] me and youВ .В .В . [↓VII] day and nightВ .В .В . [↓VI] girl you loveВ .В .В . so happy to- [V] -gether”) and Zager and Evans’s pessimistic 1969 “In the Year 2525” (“[I] In the year 3535, [↓VII] ain’t gonna needВ .В .В . [↓VI] EverythingВ .В .В . [V] is in the pill”). Only very rarely is the schema realized with different durations for the chords, as it is in the verses of Dire Straits’ 1978 “Sultans of Swing,” with its short ↓VII and ↓VI but long V: “You get a [I] shiver in the dark, it’s [↓VII] raining in the [↓VI] park, but [V] meantime.” The ↓VII–↓VI–V–I schema deserves a name, but the traditional “lamento” title seems totally inappropriate given the schema’s typically upbeat nature in rock music; we will instead dub it the walking schema, or the walk, because its bass line usually takes an even pace downward from I to V, 1–ꜜ7–ꜜ6–5 (a “walking bass” is also a jazz term for a moving bottom line) and because the progression is sometimes used to conveyPage 123 → traveling imagery, as in “Hit the Road Jack,” and also the Ventures’ 1960 cover of the 1950s instrumental “Walk, Don’t Run.” The walk presents a diatonic stepwise descent between the I chord’s root and the root of V, although at a very deeper level it is conceivable to hear both 1 and 5 as belonging to the I, as the root and fifth respectively, an arpeggiation of I filled in with diatonic steps. The next harmonic level would usually exhibit V–I (with V as strong dominant), the next level ↓VI–V–I (↓VI as pre-dominant), and the next level the full ↓VII–↓VI–V–I (with ↓VII as delta). While this descent from 1 to 5 is a distinctive feature of the walk, it is also occasionally found in other progressions (if not always completely in the bass): I–I /књњ7–↓VI–V throughout Pink Floyd’s 1973 “Eclipse”; I–V/књњ7–↓VI–V in the verses to the Police’s 1978 “Roxanne”; I–↓III–↓VI–V throughout the Black Eyed Peas’ 2004 “Let’s Get Retarded”; I–↓VII–↓VI–↓III mid-phrase in the verses of The Moody Blues’ 1967 “Nights in White Satin” (the књњ6–5 repeats immediately afterward, but this time as the chordal perfect fifths of a в™-II–I cadence); and I–↓VII–↓VI–↓VII/5 in Madonna’s 1986 “Papa Don’t Preach” (which might be heard instead or additionally as the walk, with ↓VII/5 reinterpreted as V). The 1–ꜜ7–ꜜ6–5 descent almost meets the criteria for inclusion in chapter 4’s “metaschemas” in that it is a standard stepwise line harmonized in multiple ways (i.e., by multiple numeric series). However, the descent’s most prominent harmonization by far is indeed the walking I–↓VII–↓VI–V progression, the descent of which the roots (numerals) clearly indicate, so we will not further explore the meta-schematic potential of 1–ꜜ7–ꜜ6–5.

The affinity between the walk and the watchtower hinted at in “Papa Don’t Preach” is made plain in the choruses to Michael Jackson’s 1987 “Smooth Criminal,” which simply alternate the two (“[I] Annie are you [↓VII] ok? Will you [↓VI] tell usВ .В .В . [↓VII] okay? [I] There’s a signВ .В .В . [↓VII] window, that he [↓VI] struck you, a cre- [V] -scendo”). Such alternation is by no means specific to the walk or watchtower; it is representative of a much broader phenomenon of eight-slot loops that divide evenly into a pair of four-slot phrases, both halves of which may or may not be competing schemas. Earlier, we noted that the first four slots of the loop in the verses to Journey’s “Don’t Stop Believin’,” I–V–↑VI–IV, project a journey effect, while its next four slots comprise a slightly different but technically nonschematic (at least from this book’s perspective) I–V–↑III–IV progression (“[I] Just a [V] small town girl [↑VI] livin’ in a [IV] lonely world. [I] She took the [V] midnight train goin’ [↑III] any- [IV] -where”). We also noted the zombie effect of the first half of the loop in the choruses to Shakira’s “Whenever, Wherever” and that it was changed to a nonschematic I–↓VI–IV–↓VII progression for its second half (“[I] Whenever, [↓VI] forever, [↓III] we’re meant to [↓VII] be together. [I] I’ll be there and Page 124 →[↓VI] you’ll be near. [IV] And that’s the [↓VII] deal”) The roles are reversed in the eight-slot loops of Beyoncé’s 2008 “Sweet Dreams,” which first offers a nonschematic I–↓VII–V–↓VI progression followed by the schematic I–↓VII–↓III–IV: “[I] sweet dream or a [↓VII] beautiful nightmare. [V] Either way I [↓VI] don’t wannaВ .В .В . [I] sweet dream or a [↓VII] beautiful nightmare. [↓III] Somebody pinch me. [IV] Your love’sВ .В .В .” While eight-slot loops are common, their content does not appear to be standardized beyond their sometimes schematic four-slot halves. We will therefore define none of these eight-slot progressions as schemas unto themselves. (The second halves of these eight-slot progressions can often project a transformed schematic effect of their first halves via chordal substitution, but this idea will have to wait until chapter 5.) With this, we put the lid on four-slot schemas, all twenty-one of them. Admittedly, several of these schemas are very similar to one another, and it can be difficult to keep them all straight. While there might be even more four-slot progressions in the repertory that we could consider lesser schemas, there are in fact a whopping 3,630 possible four-slot combinations of the twelve common numerals from Appendix C (assuming в™ЇI/в™-II represents one numeral, ditto for в™ЇIV/в™-V), so even the longest list of schemas would pale in comparison to the total set of conceivable idiomatic progressions. (Rock musicians today appear especially interested in displaying their individual creativity through the exploration of weird combinations of chords while at the same time working completely within the confines of a seemingly mandatory four-slot loop.) It should also be said that this chapter has concentrated mainly on self-contained schematic phrases—on schematic loops and cadences—not because these are the only types of harmonic series that can project schematic effects, but because they are relatively easy to hear, and as such have probably contributed to the schematic status of these progressions for many rock listeners and especially for rock songwriters, who no doubt have subconsciously memorized these and other schemas, resulting in their further proliferation. In reality, not only can any self-contained harmonic phrase project a schema, but any part of a phrase—on any harmonic level—can potentially as well, while a single progression may project two or more different schemas. This point will be crucial to remember as we proceed to discuss meta-schematic, extended schematic, transformational, and ambiguous effects. As we close this lengthy chapter covering twenty-one four-slot schemas, twelve three-chord schemas, and eleven two-chord schemas, we should briefly return to one final, important topic, that of the possible physical motivations for the development and popularization of certain schemas. As we previously noted, a superficially good explanation for the prominence of, say, Page 125 →the looped progression I–↓VII–IV (a common realization of ) is that it results simply from the rearrangement of the combination of chordal positions already familiar to guitarists and keyboards as V–IV–I (e.g., EM–DM–AM.) Another such explanation pertains to ↓VI–↓VII–I, which can be played easily by moving the same barre position (a type of hand position) on a guitar up two frets for ↓VII and another two for I. While it is impossible for us to know for certain whether such speculations reflect the true history of how these progressions came into being, we can certainly judge them by their constructions as arguments. Unfortunately, their constructions are rather weak, because their logic tends also to explain the potential appearance of many other phantom schemas. For instance, assuming rock musicians reinterpreted EM–DM–AM as

I–↓VII–IV instead of just V–IV–I, it would follow that looping phrases of II–I–V (which is another possible interpretation of EM–DM–AM) would be prominent as well. But they are not. Similarly, if ↓VI–↓VII–I derived from the ease of playing the same barre position separated by two frets up the fingerboard, why is ↓VII–↑VII–I, which is same motion but with adjacent frets and thus even easier to play, so much less common? For that matter, why is II–в™-II–I not more widespread, and why is ↑III–II–I essentially unheard of, even though they likewise allow the same barre position but down the fingerboard? These physical-based arguments remain problematic because they predict patterns we should presumably, but in fact do not, find very often in practice; they may be provocative descriptions, but they are poor, or at least critically incomplete, explanations. This is not to say the physical reality of producing sound has no influence on musical composition. But most cases of such influence are probably either extremely general (e.g., sevennote chords have not been popular among solo singer-songwriters because a standard guitar sounds at most six notes at a time) or extremely specific (e.g., Joni Mitchell’s idiosyncratic guitar positions developed out of accommodation for her polio-weakened left hand). In any event, while it is perfectly reasonable to wonder what role physicality has played in the development of rock harmony, it is not a subject that will concern us in this book, because these types of explanations bear no obvious connection to hearing per se.

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Chapter 4 Pentatonic, Meta-, and Extended Schemas Pentatonic Schemas Nearly all of the forty-four schemas we identified in chapter 3 can be thought of as rooted in diatonicism; regardless of what other chordal members are present (assuming there are any), the chordal roots that define any one of these numeric series fit entirely within at least one of the four common white-key rock scales: ionian, mixolydian, dorian, aeolian. Presumably, then, these schemas will project a diatonic effect, even if other scalar effects—pentatonic or chromatic—are also present. Yet there are several important schemas that are not diatonic, or not entirely diatonic, in their effects. In this chapter, we will focus our attention first on pentatonic (black-key/open-string) schemas, then on (mostly) chromatic meta-schemas, followed by a discussion of lengthier extended slot schemas that often combine diatonic and chromatic motions. As with the previous chapter, the reader is advised to take the following pages at a relaxed pace, as these passages are dense with numeric series that can look very similar to one another in print and even sound similar to one another in recordings. As noted in chapter 1, rock progressions tend to project minor pentatonic effects only when there is motion between two notes three semitones apart. If we are to hear a numeric schema itself as contributing to a pentatonic effect, this three-semitone interval must necessarily be found somewhere between the chordal roots. (Any and all diatonic and chromatic chord tones beyond the roots must, in these cases, be heard as additions to a pentatonic framework.)1 The simplest schema to exhibit this sort of pentatonic potential is , which we first encountered in the repeating riff to Nirvana’s “About a Girl” (Examples 1.8b and 1.8d). Even with the strong pentatonic leanings of Nirvana’s pre-tonic ↓III, however, we chose to label it a “rogue dominant” because of its scalar hybridity, its projection of both a diatonic effect—via the roguish chordal perfect fifth књњ7—as well as a pentatonic effect—via the chordal perfect fifth again (this time as the minor-pentatonic fifth scale degree) but Page 127 →also via the chordal root, which can operate as the minor-pentatonic second scale degree. As we have stated, even in the most pentatonic of contexts diatonicism is never too far off; rock is defaulted to diatonicism. For three-chord schemas and up, the strongest pentatonic effects tend to be projected when the roots offer adjacent three-semitone and two-semitone intervals, corresponding to one of the four spots where this occurs in a black-key/open-string scale. In an E minor pentatonic scale, these sports would be E, G, A (or I, ↓III, IV), A, B, D (or IV, V, ↓VII), B, D, E (or V, ↓VII, I), and D, E, G (or ↓VII, I, ↓III).2 Not coincidentally, at least one of these combinations can be found in each of the pentatonic schemas to be identified below. This said, we should also note that these pentatonic-leaning intervallic combinations can likewise be found in four of the diatonic schemas from chapter 3: , , , and . For that matter, an additional thirteen of the previous chapter’s schemas feature roots that fit entirely within the minor pentatonic scale: , , , , , , , , , , the bamba , , and . We are bothering to designate nine other schemas below as especially pentatonic not because theirs are the only root motions that can project such a scalar effect, but rather because these schemas simply sound more pentatonic more often, meaning that the kinds of musical contexts in which they ordinarily occur are more prone to invite pentatonic hearings than are those for the merely pentatonic-tolerant schemas of chapter 3. The distinction is thus one of pentatonic theory versus pentatonic practice.

Ordinarily, the quintessentially diatonic will not support a pentatonic interpretation, but its intervallic content does permit the undeniably pentatonic effect of, for example, the guitar riff to “I Love Rock’n’Roll,” the famous 1982 cover by Joan Jett and the Blackhearts (“[I] I love rock’n’roll [passing pentatonic књњ3] so [IV] put another dime in the [V] juke box, baby”). Context, as always, is critical. We should also say a word here about the major pentatonic scale. It is an odd fact, but a fact nonetheless, that the major pentatonic scale does not normally serve as the basis for chordal roots in rock music. The chordal roots of rock’s foundational schema do not conform to this scale, and even in a case like that of (to be identified later as the “vaudeville schema”), in which the roots correspond exactly to the major pentatonic scale, the pentatonic effect is not especially strong (probably because the roots do not include a single interval that can be heard as a pentatonic step). Whatever the reason, major pentatonic effects projected by chordal root motions are faint, few, and far between. Unlike the minor pentatonic scale, which is found both in melodic and harmonic contexts, the major pentatonic Page 128 →scale is essentially a melodic phenomenon. Indeed, it is really only through melodic means that the scale can sporadically force its way into the realm of the harmonic, as heard in John Fred and His Playboy Band’s 1967 “Judy in Disguise (With Glasses)” (“Judy in dis-[I] -guise well that’s-a what you [V] are”), wherein the individual chords are adorned with major-pentatonic bass elaborations, making the harmonic roots sound as though they might actually be based entirely on the major pentatonic scale (at least until the unmistakably minor-pentatonic bridge). One last introductory generalization about pentatonic schemas: they are more likely than the previous schemas to be realized as quick single notes or power chords in riffs,3 which means that we should be less specific in summarizing their voice-leading inclinations. Whereas in chapter 3 we were a tad presumptuous in the degree of our specification about such tendencies, here we will be more reserved: a pre-tonic IV will not be assumed to function normally as a subdominant (which would require a real or imagined chordal third); a pre-tonic V will not be assumed to function normally as a dominant (which would require a real or imagined chordal third and chordal fifth). This is not to say that hyper, hypo, and medial effects are irrelevant in the current context, merely that they are not as generally applicable here by comparison to more inherently diatonic schemas. Accordingly, when summarizing a pentatonic schema’s functional penchants, we will avoid voice-leading labels like “dominant,” “subdominant,” “pre-dominant,” “pre-subdominant,” and the like, in favor of “pre-tonic, “gamma,” and so on. Now, on to the pentatonic schemas themselves. Just as the common chords I and IV combine with ↓VII to form two schemas, so do I and V: these are and . See Example 4.1. The first is a schema only because of its use in cadences; it does not often appear looped, although it does in the Pretenders’ 1983 “Middle of the Road” (phrased as I–↓VII–V: “Come on, now, [I] [↓VII] in the [V] middle of the road, yeah [I]”) and After the Fire’s 1982 Anglicized cover of Falco’s originally German-language rap “Der Kommissar” (“[I] one, two, three it’s [↓VII] easy to see, but it’s not that I don’t care [V] so, ’cause I [I] hear”). Cadential examples crop up in the choruses to the Monkees’ 1966 hit cover of “I’m a Believer” (“I couldn’t [↓VII] leave her if I [V] tried. [I] I thoughtВ .В .В .”) and throughout the 1978 theme to the television soap opera Dallas. (In this latter case, the gestures would be referred to as “cowboy cadences,” so-called because of their long-standing use in songs and film soundtracks about the American Old West.) typically operates as a functional chain, with ↓VII functioning as a gamma, V as a pretonic, and I as a tonic. However, in “Middle of the Road,” the Pretenders put a tremendous amount of emphasis on the V, resulting in a I that is less a tonic Page 129 →than a delta, which is subordinate to the ↓VII that follows it, making the next harmonic level not I–V but ↓VII–V. , the other schematic combination of I, V, and ↓VII, is often not clear with regard to its harmonic levels. The V may be heard as resolving directly to I, with a passing ↓VII (similar to the normal hierarchy of a V–IV–I cadence, without the softening effect), but it is often also possible to hear V as

a gamma that sets up the driving pre-tonic (possibly rogue dominant) ↓VII, in which case the next level is ↓VII–I. is a bit more common than as a looped progression. We hear loops of I–V–↓VII–I in the choruses of Blues Image’s 1970 “Ride Captain Ride” (“[I] Ride, Captain, ride, upon your [V] mystery ship, on your [↓VII] wayВ .В .В . others [I] mightВ .В .В .”) and in the verses of Ringo Starr’s 1971 “It Don’t Come Easy” (with a striking minor triad for V: “[I] Got to pay your dues if you [V] wanna sing the blues, and you [↓VII] know it don’t come [I] easy”). Much more typical of is its cadential role, heard in the verses of the Charlie Daniels Bands’ 1979 “The Devil Went Down to Georgia” (“вЂBoy, lemme tell ya what [V] [↓VII] I [I] guess you didn’t know it’”) and, most famously, in the Beatles’ 1963 “Not a Second Time,” the cadence of which has elicited much discussion (“[V] no, no, [↓VII] no, not a second [I] time”). The Beatles’ progression first caught the attention of music critics soon after the song’s release, the London Times calling it an “aeolian cadence” similar to the one in a symphonic vocal work by Austrian composer Gustav Mahler. Since then, the “aeolian cadence” has caused much mystification among critics and musicians alike, not the least of whom was singer and cowriter John Lennon himself, who commented that the esoteric term sounded to him like the name of an “exotic bird.”4 “Aeolian cadence” merely indicates that the cadence adheres to the aeolian scale, in this case E aeolian: Vm–↓VII7–Im, Bm–D7–Em. The fact that the Beatles’ progression is known as being aeolian—that is, diatonic—should cause us no distress; this particular incarnation of is indeed primarily diatonic in its effect (the cadence alone offering the entire E aeolian scale among all the chord tones), a testament not to a problem in calling inherently pentatonic but to our earlier caveat that individual contexts can override any of our assumptions about which scalar effects we may encounter when. (This caveat applies equally well to functional effects.) Other three-chord schemas that feature an adjacent diatonic minor third between their roots, and that will likely sound pentatonic given the chance, are , , , and . The most common of these are and , being especially prominent in blues-inspired tracks. Looped, is most often phrased as I–↓III–IV with an elongated starting tonic I, either featuring a doubly long Page 130 →tonic, as in Stevie Wonder’s 1973 “Higher Ground” (with a half bar for the tonic: “[I] People [↓III] [IV] [I] [↓III] keep [IV] on [I] learnin’”) and in the verses and choruses to the Black Keys’ 2011 “Lonely Boy” (with two bars for the tonic: “[I] Oh, oh, oh, oh, [↓III] I gotta a love that [IV] keeps me waitin’”), or featuring a tonic that lasts until nearly the end of the phrase, with ↓III and IV providing a surge of harmonic activity that projects a slight cadential effect, as heard in two recordings from 1968: Steppenwolf’s “Born to be Wild” (possibly the source of the term “heavy metal”: “[I] I like smoke and lightnin’ [↓III] [IV]”) and Canned Heat’s “On the Road Again” (“Well I’m [I] so tired of cryin’ .В .В . I’m on the [↓III] road [IV] again”). A less common phrasing is I–↓III–IV–I, with each harmony taking up the same amount of time: we hear this in the choruses to Sam and Dave’s 1966 Stax classic “Hold On, I’m Comin’” (“Hold [I] on, I’m [↓III] comin’. Hold [IV] on, I’m [I] comin’”) and in the choruses of Jet’s 2003 “Are You Gonna Be My Girl” (“[I] Well, I could see [↓III] you home with me. [IV] But you were with another [I] man”). Even less commonly, ↓III starts the loop and a long I ends it, as happens in the choruses to Ratt’s 1988 “Way Cool Jr.” (“[↓III] Way [IV] cool [I] junior”)5 and in the choruses to Information Society’s Star Trek-sampling 1988 “What’s on Your Mind (Pure Energy)” (“I wanna [↓III] know [IV] what you’re [I] thinking”). also materializes as a full-blown cadential gesture, as heard in the verses of the Beatles’ 1968 Who-emulating “Helter Skelter” (“come on [↓III] tell me the answer. Well, you [IV] may be a lover but you ain’t no dancer [I]”) and in the pre-choruses of Digital Underground’s 1990 “The Humpty Dance” (“The humpty [↓III] dance is your [IV] chance to do the [I] hump”). This schema normally results in chained functions: gammaв†’pre-tonicв†’tonic. , the other most popular schema with a diatonic minor third between its chordal roots, is often very close in sound to , so

close in fact that they are sometimes presented side by side, as though they were interchangeable.6 Living Colour alternates between the two schemas in their 1988 “Cult of Personality” (“Look in my [I] eyes what do you see? The [↓III] cult of person- [↓VII] -ality [I].В .В . I’ve been everything you wanna be. Ho, I’m the [↓III] cult of person- [IV] -ality [I]”), and ’Til Tuesday gives two statements of the first schema followed by two statements of the second in the verses of their 1985 “Voices Carry” (“[I] In the [↓III] dark I like to [IV] read his [I] mindВ .В .В . Oh there [↓III] must be something he’s thinking [↓VII] of to tear him away [I]”). Looped, typically appears in either two phrasings. The first is I–↓III–↓VII with a doubly long tonic, as used in Tom Petty and the Heartbreakers’ 1979 “Refugee” (“You [I] don’t have to [↓III] live like a [↓VII] refugee”) and in the choruses to Nine Inch Nails’ 1997 “The Perfect Drug” (“[I] You are the perfect drug, the [↓III] perfect drug, the [↓VII] Page 131 →perfect drug”). The second common looped phrasing is I–↓III–↓VII–I, with relatively even chordal durations throughout; this is the basis for the verses of Pink Floyd’s 1973 “Time” (“[I] Ticking awayВ .В .В . a [↓III] dull day. [↓VII] FritterВ .В .В . an off-hand [I] way”) and the White Stripes’ 2005 “Denial Twist” (“If you [I] think that a kiss is [↓III] all in the lips, c’mon, [↓VII] you got it all [I] wrong, man”). Equally at home in cadences and in tag endings of short progressions, is ordinarily realized either by power chords, as heard in the guitar tags to the verses of Billy Idol’s 1983 “Rebel Yell,” or by major triads supporting a descending diatonic књњ3–2–1 instrumental melody (2 as the chordal major third of ↓VII), as in the repeating fadeout cadences of the Beatles’ 1969 “You Never Give Me Your Money” (“[↓III, књњ3] One, two, three, [↓VII, 2] four, five, six, seven, [I, 1] all good children go to heaven”). The descending књњ3–2–1 is such a strong melodic figure that it gives any progression a sense of closure—i.e., a cadential effect—even when the progression is looped, as it is in the Beatles’ track. The same cadential effect is projected by the књњ3–2–1 loops found in the I–IV–↓III–↓VII guitar riff to the Rolling Stones’ 1981 “Slave” and in the I–↓III–↓VII phrases in the opening of the 1980 theme to Magnum, P.I. by ubiquitous TV composer Mike Post (who alternates I–↓III–↓VII with another short pentatonic progression as part of larger loop). In all the cases given above, ↓VII–I is the underlying motion, with ↓III often functioning as a gamma to a strong pre-tonic ↓VII. Example 131.4. Pentatonic schemas name other rotations

I–↓VII–V V–I–↓VII

I– V–↓VII ↓VII–I–V

I–↓III–IV IV–I–↓III

I–↓III–↓VII ↓VII–I–↓III

I–IV–↓III ↓III–I–IV

I–↓VII–↓III ↓III–I–↓VII I–↓III–IV–↓III IV–↓III–I–↓III ↓III–I–↓III–IV I–↓VII–↓III–IV IV–I–↓VII–↓III ↓III–IV–I–↓VII Compared to and , the schemas and are much less versatile; they turn up less frequently overall, and in fewer distinct kinds of settings. While more often than not appearing as part of larger progressions, both schemas do sometimes constitute their own phrases. , sometimes called the “axe fall” gesture when played quickly, appears in alternating statements with

in the choruses to the Cars’ 2011 comeback track “Keep on Knocking” (“They Page 132 →keep on [I] knockin’ [↓III] [IV] like the [I] party’s on. [IV] [↓III] They keep on [I] knockin’”). serves as a prominent cadential gesture in Harry Chapin’s 1972 “Taxi”: “[↓VII] she got [↓III] in at the [I] light.” Given their relative scarcity as self-contained looping or cadential progressions, and might very well not be considered schemas at all. Still, they do appear frequently as parts of progression, and they are so similar to the widespread schemas and respectively that they are more or less interchangeable with them (just as and are swappable with each other). We will thus consider all of them to be schemas, all with a decidedly minor pentatonic flavor. This blurring of schemas parallels the blurring of harmonic levels typical of and : while the simplest hearing of them involves a functional chain that comprises gamma IV or ↓VII leaning into pre-tonic (probably rogue dominant) ↓III leaning into tonic I, another possibility interprets the ↓III as an embellishment of a stronger IV–I or ↓VII–I progression, a hearing that recalls the typical underlying IV–I and ↓VII–I motions behind and (in terms of the numerals involved, not in terms of the placement of the chords within the three-slot progressions). The pentatonic schemas , , , , , and are often used in combination. Any grouping is possible, but in terms of loops or cadences, the standout is . See Example 4.2. Not typically a cadential gesture, this schema appears as the numeric palindrome I–↓III–IV–↓III–I in the guitar riff of the Everly Bothers’ 1957 “Wake Up Little Susie” and in the piano riff of the Contours’ 1965 “First I Look at the Purse” (“[I] Some fel- [↓III] -las look at [IV] the eyes [↓III] [I]”). The schema also creates a palindrome when looped as I–↓III–IV–↓III, as heard throughout the Sonics’ 1965 cover of “Louie Louie” (“[I] Louie Louie, [↓III] [IV] oh yeah, [↓III] [I] me gotta go now”) and in the verses of AC/DC’s 1976 “T.N.T.” (“See me [I] ride out of [↓III] the [IV] sunset on [↓III] your [I] color”). In contrast to , is rather predictable regarding functions and levels. Metric emphasis tends to favor the IV, pushing it deeper into the structure than the surrounding ↓IIIs, just as V is typically favored over the IVs in (as per our earlier discussion of “Wild Thing”; see Example 2.5); the IV then will function as a pretonic, embellished by the first (gamma) IV and second (softening pre-tonic) IV. (The pre-tonic strength of IV, however, is usually nowhere near that of the analogous V in .) The only other four-slot progression we will identify as a pentatonic schema is , which is nearly always phrased as I–↓VII–↓III–IV. Alanis Morissette loops this schema in the choruses of 1995 “You Page 133 →Oughta Know” (“And I’m [I] here to re[↓VII] -mind you of the [↓III] messВ .В .В . you [IV] went away”), as do the White Stripes in the verses of 2001’s “Fell in Love with a Girl” (“[I] Fell in love with a [↓VII] girl. I [↓III] fell in love once and al- [IV] -most completely”). In most of these cases, tonic I gives way to post-tonic, delta ↓VII, which then proceeds to gamma ↓III and pre-tonic IV, creating a functional chain. At slower tempos, however, the ↓III will assert itself as an alternative tonic and anchor to ↓VII and IV, as happens in the choruses to Moby’s 1999 Vera Hall–sampling “Natural Blues” “[I] Ooh, Lord-ay, my trouble’s so hard, [↓VII] ooh, Lord-ayВ .В .В . [↓III] Don’t nobody knowВ .В .В . [IV] Don’t nobody know”). Thus the underlying two-chord motion may be either IV–I or ↓III–I, depending largely on the harmonic pulse. Larger single-phrase combinations of pentatonic schemas are possible, but only one is worth consideration as its own schema: , which we will dub the multipentascent. By no means common but most definitely distinctive, the multipentascent was featured prominently in 1980s and early 1990s pop-rock hits like “Rock You Like a Hurricane” (1984) by the German heavy-metal troupe Scorpions (“[I]

Here I am. [↓III] [IV] [↓VI] Rock [↓VII] you like aВ .В .В .”), “Lovin’ Every Minute of It” (1985) by Loverboy (“[I] Turn that dial [↓III] all the way. [IV] Shoot me like a rocket [↓VI] into [↓VII] space”), and the unsubtle “Cherry Pie” (1990) by Warrant (“[I] She’s my [↓III] cherry pie. [IV] Cool drink of water, such a [↓VI] sweet sur- [↓VII] -prise”). This schema usually projects a strong pentatonic effect, and it is nearly an unblemished ascent up the minor pentatonic scale; the only problem is the ↓VI, where we might expect V. A similar progression with V in place of ↓VI can be heard in the opening brass chords of Eddie Floyd’s 1967 “Knock on Wood,” an ascent from I up the minor pentatonic scale to ↓VII (which we could call a “pentascent”) plus an extra V at the end: I–↓III–IV–V–↓VII–V. (We will not consider the pentascent a schema.)7 The pentatonic wrinkle in Scorpions’, Loverboy’s, and Warrant’s riffs might lead us to speculate that the schema originates in a pentatonic scale other than the standard minor version, a hypothetical alternative resulting from a rotation of the black-key/open-string pitch-class set. On center E, this specifically would be E, G, A, C, D (as opposed to the minor rotation of A, C, D, E, G, or the major rotation of C, D, E, G, A).8 Yet there is a better explanation, one that will make sense of the name “multipentascent.” Consider the 1962 instrumental “Green Onions” by Booker T. & the M.G.’s, a track that is likely responsible for sparking an explosion of pentatonic harmony in the mid-1960s. “Green Onions” starts with an organ riff looping I–↓III–IV (the schema ), with roots E–G–A. (We are transposing down from the actual center of F.) After several bars, the chords Page 134 →switch to IV–↓VI–↓VII, A–C–D, which is not a schema in itself but is related by exact transposition to the original three-chord sequence: it is the same riff starting on IV instead of I (conforming to a larger schema known widely as the twelve-bar blues, to be discussed later in this chapter). Since we can hear I–↓III–IV as based on the first, second, and third scale degrees of a minor pentatonic scale, it is likely we will carry this hearing with us when we arrive at IV–↓VI–↓VII. In other words, we can hear another pentatonic effect, this time on 4 (A, C, D, E, G), with IV built on the first scale degree, ↓VI on the second, and ↓VII on the third; see Example 4.2a. The last new riff the song offers is V–↓VII–I, B–D–E, which is its own schema, but more importantly is another transposition of the main riff, this time starting on V, and represents another wholesale transposition of the minor pentatonic scale (B, D, E, Fв™Ї, A). In “Green Onions,” then, the chordal roots represent three separate partial minor pentatonic scales centered on 1, 4, and 5 in relation to the original tonal center. Similar partial minor pentatonic scales on 1, 4, and 5 can be heard in the Animals’ 1964 “I’m Crying” and Link Wray and His Ray Men’s 1966 “Hidden Charms.”9 The relevance of this discussion for the riffs of “Rock You Like a Hurricane,” “Lovin’ Every Minute of It, ” and “Cherry Pie” lies in the numerals based on the partial minor pentatonic versions on 1 and 4: I–↓III–IV and IV–↓VI–↓VII. This pair of three-chord progressions overlaps by one harmony (IV) to create a single fluid motion of I–↓III–IV–↓VI–↓VII, the multipentascent; see Example 4.2b. This schema is an “ascent” in that its roots rise through a scale; it is “pent” in that this rising scale is minor pentatonic; it is “multi” in that it shifts pentatonic scales halfway through, from a scale on 1 (E–G–A) to a scale on 4 (A–C–D). This shift is not so difficult to hear; in all three of our multipentascent examples, the schema lasts two bars, with the downbeats occupied by I and IV. Moreover, in the Loverboy song, the two-bar multipentascent alternates with a simple two-bar I–IV progression (accompanying the titular refrain), as if to make sure we can hear the metric emphasis and thus too the pentatonic transposition. Yet it is no less feasible to hear two overlapping three-chord progressions even when the rhythmic profile is very uneven, as it is in the Knack’s possibly pedophiliac 1979 “My Sharona.” The Knack’s multipentascent is presented over six bars with the harmonic pulse growing faster over the course of the progression (“[I] Never gonna stopВ .В .В . [↓III] I always get it upВ .В .В . [IV] my my [↓VI] my-y-y [↓VII] whoa!”), but the pentatonic transposition at IV is still eminently hearable. (In the middle of the song, the Knack even repeat the IV–↓VI–↓VII portion by itself, as if to highlight its autonomy from I–↓III(–IV).) The multipentascent, then, normally operates at its deepest level as a IV–I, pre-tonicв†’tonic Page 135 →motion, with an embellishing ↓III, ↓VI, and ↓VII; the ↓VI and ↓VII are easily heard as gamma and pre-tonic respectively, while the ↓III might be an

epsilon and the IV (on the surface level) might be a delta. Example 135.4. 4.2a. I–↓III–IV and IV–↓VI–↓VII in “Green Onions” (transposed from main center F) minor pentatonic degrees: first second third fourth fifth center E: E (I) G (↓III) A (IV) B D center A: A (IV) C (↓VI) D (↓VII) E G center B:

B (V) D (↓VII) E (I)

Fв™Ї A

4.2b. Multipentascent minor pentatonic degrees on I: first second third minor pentatonic degrees on IV: I

first second third – ↓III | IV – ↓VI – ↓VII

Minor pentatonic scales in rock most often are built on 1 or 4 (5 is still standard but less common).10 It is perhaps unsurprising, then, that there are numerous other progressions that might be discussed in their light, progressions that do not constitute schemas but that cast potentially problematic shadows on the usefulness of the very notion of partial pentatonic transposition itself. Particularly significant in this regard are progressions nearly identical to the multipentascent but that are missing the seemingly crucial IV. For instance, we get the nonschematic I–↓III–↓VI–↓VII looped in Devo’s first single from 1977, the unfortunately themed “Mongoloid” (“[I] Mongoloid. He was a [↓III] mongoloid, [↓VI] happier than [↓VII] you and [I] me”), and in the choruses of the B-52s’ 2008 “Dancing Now” (“[I] Dancin’ now [в™-III] [в™-VI] dancin’ [VII] now”). The nonschematic ↓III–I–↓VI–↓VII–I forms the main guitar riff to the Rolling Stones’ saucy “Brown Sugar” (1970) (appearing right after the chorus: “just like a young girl should”). And tight-knit combinations of the three-chord schemas and can be heard in the chorus to Rick Derringer’s 1973 solo version of “Rock and Roll Hoochie Koo” (“[↓VI] Rock and roll [↓VII] hoochie koo [I].В .В . lordy, mama, [↓III] light [↓VII] my fuse [I]”) and in the opening riff to Ozzy Osbourne’s 1981 “Crazy Train” (“[I] [↓III] [↓VII] [I] Ay, ay, ay [↓VI] [↓VII] [I]”). Not one of these progressions offers a IV, so there is little chance of hearing the ↓VI and ↓VII in these songs as built on pentatonic scale degrees arising from 4 (although “Crazy Train” does contain a prominent 4 in Randy Rhoads’ lead guitar line). These examples need not Page 136 →undermine our interpretations of our multipentascent examples, but they do call into question just how far we are willing to push the claim that ↓VI can be heard as projecting a minor pentatonic effect, because there is no obvious way to hear it in relation to that scale. Rather, the (I–)↓VI–↓VII(–I) portions of these alternative examples are much more likely to project diatonic effects; if a pentatonic effect is created by the chordal roots of that riff, it will probably be confined to the I and the ↓III.11 Before leaving pentatonic schemas, we should briefly return to a three-chord schema mentioned in chapter 3, , because of its potential relationship to partial pentatonic transposition. We noted beforehand that this schema typically appears as part of a longer progression, but there is one particular realization that would lend itself to being heard as built on transposed scales: ↓III–IV–↓VI–I. We get this progression in the Monkees’ 1966

rendition of “(I’m Not Your) Steppin’ Stone” (“[I] I-I- [↓III] -I-I- [IV] -I’m not your [↓VI] steppin’ [I] stone”) and in the verses to Max Frost and the Troopers’ 1968 “Shape of Things to Come” (alternating with straightforwardly pentatonic I–↓III–IV–V: “There’s a [I] new sun [↓III] risin’ up [IV] angry in the [↓VI] sky”). Phrased as I–↓III–IV–↓VI, the progression naturally splits into two halves of equal length, I–↓III and IV–↓VI, and each can be heard as outlining the first and second degrees of a pentatonic scale (on 1 and 4 respectively). While we will not consider ↓III–IV–↓VI–I to be a schema in itself (though it can possibly project a “meta-schematic” effect we will later define as the “dropping” effect, involving 1–ꜜ7–ꜛ6–ꜜ6–5), it is relevant here in that it is only one chord short of the multipentascent ↓III–IV–↓VI–↓VII–I, and the same parallelism between that schema’s two halves are clearly audible in this slightly shorter progression. Such a hearing would probably result in different functions compared to the interpretation of the in the previous chapter, where we construed ↓VI–I as the fundamental motion, and the IV as a pre-subdominant to lower subdominant ↓VI. But if ↓VI is heard as being built on the second degree of a minor pentatonic scale on IV, then the IV is clearly the hierarchically superordinate harmony, functioning as a pre-tonic that directly predicts resolution to tonic I; in this hearing, the ↓VI would still be a pre-tonic, but it would be confined to a surface harmonic level. In this section we identified nine progressions of assorted lengths that typically project both schematic and pentatonic effects: , , , , , , , , and the multipentascent . In the next two sections, we will turn toward a particular brand of schemas that are largely chromatic in nature, before concluding the larger, “extended” slot schemas that often involve layerings of many different schematic types. Page 137 →

Meta-Schemas: Part I There is a class of harmonic schemas whose identity hinges largely on one or more scale degrees beyond the chords’ roots.12 Consider the I–↑III–↑VI–IV loops heard in the chorus to Roy Orbison’s 1989 “You Got It” (with two beats per chord: “[I] Any- [↑III] -thing you [↑VI] want, you [IV] got it”) and the chorus to Timbaland’s 2009 “If We Ever Meet Again” (with four beats per chord: “[I] I’ll [↑III] never be the [↑VI] same [IV] if we ever meet again”). The numerals of these sonorities, which denote only their roots, give no indication of the prominent ascending string of semitones that starts with the 5 of the I (the chordal fifth), stretches up to the ♯5 of the ↑III (the chordal major third), and stretches once more to the ꜛ6 in the ↑VI (the root). (The IV sounds like a mere afterthought and does not participate in the ascent.) This stretching ascent is heard at various times in the lead vocal lines of both songs. In relation to center E, these notes would be B–B♯–C♯; see Example 4.3. This progression can be heard as projecting an effect of familiarity—a schematic effect—but one not determined as much by its chordal roots as by the chromatic line 5–♯5–ꜛ6 (and especially by the second chord’s ♯5, which lends the chord a pronounced departing, post-tonic effect). But in focusing on scaledegree motions other than merely that of chordal roots, we must consider the possibility that a different series of numerals could just as well project the same line, the same effect. And because any numeral can hypothetically include any scale degree, there is a sizeable number of possible root harmonizations of this little 5–♯5–ꜛ6 line. Indeed, in the repertory at large, this chromatic ascent is heard just as frequently with ꜛ6 as the chordal major third of a IV as opposed to the root of ↑VI, the progression thus being I–↑III–IV. We hear this, for instance, at the start of the verses to Johnny Burnette’s 1960 “You’re

Sixteen” (“Ooh, you [I, 5] come on like a dream, [↑III, в™Ї5] peaches and cream, [IV, књ›6] lips”) and at the start of the choruses in Tammy Wynette’s 1968 country classic “Stand by Your Man” (“[I, 5] Stand by your [↑III, в™Ї5] man. [IV, књ›6] Give himВ .В .В .”). Other possible realizations of this ascent include the I–↑III–II progression heard in the verses of Mary Wells’ 1964 “My Guy” (with a long opening I, and with the књ›6 provided by the chordal perfect fifth of II: “[I, 5] Nothing you could sayВ .В .В . I’m stuck like glue to [↑III, в™Ї5] my guy. I’m [II, књ›6] sticking”) and the I–↓VI–IV opening to the Beau Brummels’ 1965 “Just a Little,” a progression we identified in the previous section as a possible phrasing of the three-chord schema (the root of the ↓VI acts as в™Ї5 in addition to acting as књњ6, the ascent clearly stated in the backing vocals: “I can’t [I, 5] stay. Yes, I [↓VI, в™Ї5] know. You know [IV, књ›6] IВ .В .В .”). In 1968’s “Honey Pie,” the Beatles similarly harmonize в™Ї5 with a “crazy” ↓VI, but resolve it even Page 138 →more crazily to ↑VI (“[I, 5] Honey pie, you are making me [↓VI, в™Ї5] crazy. [↑VI, књ›6] I’m in love”). Another standard way to create this rising chromatic line is by stretching the chordal perfect fifth of a I to make a I+ before moving to књ›6. This happens in Jay and the Americans’ 1965 cover of the Rodgers and Hammerstein song “Some Enchanted Evening” (“[I, 5] You may see a stranger [I+, в™Ї5] ’cross the [IV, књ›6] crowded room”). Example 138.4. Stretching schema B – Bв™Ї – Cв™Ї (center E) 5 – в™Ї5 – књ›6 I5 – ↑IIIM – ↑VI (“You Got It,” “If We Ever Meet Again,” “Only You”) I5 – ↑IIIM – IVM (“You’re Sixteen,” “Stand by Your Man”) (“My Guy”) I5 – ↑IIIM – II5 5 M (“Just a Little”) I – ↓VI – IV I5 – ↓VI – ↑VI (“Honey Pie”) – IVM (“Some Enchanted Evening”) I5 – I+ The upwardly stretching chromatic line common to all these progressions is so immediately recognizable that the chordal roots are almost demoted to secondary features. At the very least, the chromatic line will be familiar to experienced listeners of rock as a recognizable, standard series of notes—as a kind of schema, which enables progressions that offer it to project a schematic effect. This chromatic figure, however, is not a harmonic schema in the same way that each of the previously cited schemas is, in that it is not identifiable as a series of chordal roots (numerals). We could think of 5–♯5–ꜛ6 as a melodic schema, but as we will see, this and similar schematic figures are frequently present partially or exclusively as abstract, register-indifferent scale-degree motions dispersed throughout a musical texture, as opposed to being confined to actual melodies; in other words, these figures are better understood as harmonic in nature. Yet from a harmonic perspective, we can see that this new breed of schema is not bound to any particular group of numerals, or even any number of numerals (e.g., “Some Enchanted Evening” harmonized 5 and в™Ї5 with two different versions of I). To convey these schemas’ numeric flexibility, we will christen them harmonic metaschemas (a special type of schema) and their effects harmonic meta-schematic effects (a special type of schematic effect). Compared to root-defined schemas, metaschemas are less predictable regarding their manifestations: the former are often projected solely by bass lines, because rock music overwhelmingly tends to feature roots in the bass, while the latter can be projected in any number of conceivable combinations of instruments, voices, and pitch registers. That Page 139 →said, in learning meta-schemas, listeners will likely need to encounter these patterns at least some of the time as actual melodic lines, otherwise their memorability—their

schematic potential—will never come to fruition. There are hundreds of potential meta-schemas. We will limit our discussion to a few of the more significant, salient ones that regularly appear on the harmonic surface in multiple numeric contexts and that specifically involve chromatic stepwise lines of three notes or more (with two diatonic exceptions). Each meta-schema will be receive a unique name, and otherwise will be identified by its defining scale-degree line without less-than and greater-than brackets because meta-schemas are not normally rotatable. Since there will be numerous unique names to keep straight, we will embed mnemonic devices in them: names starting with “s” will designate short (three-note) meta-schemas; names starting with “d” will designate meta-schemas descending from tonal center; names starting with “t” will designate meta-schemas that travel both up and down (not just in one direction). We will call the short 5–♯5–ꜛ6 meta-schema the stretching schema, or just the stretch. The list in Example 4.2 is necessarily only a sampling of possible stretching progressions; hypothetically, any numeric series, on any harmonic level, may project a stretching effect. When referring to the numerals of a particular progression that projects a meta-schema, we will hereafter add superscript symbols to convey the chordal members (beyond the roots) required to realize the metaschematic scale-degree line. So the stretching version of I–↑III–↑VI will be I5–↑IIIM–↑VI; the stretching I–↑III–IV will be I5–↑IIIM–IVM; the stretching I–↑III–II will be I5–↑IIIM–II5; the stretching I–↓VI–IV will be I5–↓VI–IVM; the stretching I–I+–IV will be I5–I+–IVM. The 5 does not mean the Is must specifically be power chords, nor does the M signify that the ↑IIIs and IVs must be major triads, nor does the + indicate necessarily an augmented triad. Additional tones may also be present, but the specified tones are mandatory, as real or imagined notes. Mandatory thirds will be either m or M; mandatory fifths will be 5, o, or +; mandatory sixths will be 6 or m6; mandatory sevenths will be 7, M7, or o7; mandatory ninths will be 9 or в™-9 or в™Ї9 (see also Appendix B). This superscript notation occupies a middle ground between bare-numeral notation and numeral-plus-sonority notation. For instance, “V” indicates at least one scale degree, 5; “V7” indicates at least two scale degrees, 5 and 4; “V7” indicates exactly four scale degrees, 5, књ›7, 2, and 4. The stretch is usually projected within a larger harmonic progression (often at the beginning) as opposed to constituting its own separate harmonic phrase. Because of this fact, a whole assortment of different sonorities can immediately follow the third chord. Hence the exact functions of the stretch’s constituent harmonies are not fully generalizable, although the initiating Page 140 →chord (typically I5) most often functions as a tonic, and the second chord will usually relax into the third chord, making the second chord hierarchically subordinate to the third. The next harmonic level, therefore, generally comprises the first and third chords, most often either I–↑VI or I–IV. Continuations of the stretching schema are also possible. In fact, “Just a Little” extends the upward gesture by one more semitone: 5–♯5–ꜛ6–ꜜ7, with књњ7 as the root of ↓VII (I5–↓VI–IVM–↓VII). Our second meta-schema is one slot longer than this, and is a traveling meta-schema (with a “t” name) in that it goes up and down: the touring schema stretches chromatically upward from 5 to књњ7, fully touring the space of this minor third, before falling back down књ›6. The full figure is 5–♯5–ꜛ6–ꜜ7–ꜛ6; with E as center, the line would be B–B♯–C♯–D–Cв™Ї. See Example 4.4. At the beginning of the verses in the Platters’ 1955 “Only You (And You Alone”), the tour starts as a stretching I5–↑IIIM–↑VI progression, continuing upward to књњ7 (in the form of a chordal minor seventh of a I7) only to descend immediately to књ›6 (the third of IVM), as though it simply overshot the goal note (“Only [I5, 5] you can make ah-this [↑IIIM, в™Ї5] world seem right. Only [↑VI, књ›6] you can make the [I7, књњ7] darkness bright. Only [IVM, књ›6] you”). The I5–↑IIIM–↑VI–I7–IVM progression is a standard touring series; we hear it also in the verses of the Joe Jeffrey Group’s 1969 “My Pledge of Love” (“[I5, 5] I woke up this morning, baby. [↑IIIM, в™Ї5] I had you on my mind.

[↑VI, књ›6] I woke upВ .В .В . [I7, књњ7] You know [IVM, књ›6]”) and in the verses of the Carpenters’ 1976 cover of “There’s a Kind of Hush (All Over the World)” (“There’s a [I5, 5] kind of hush [↑IIIM, в™Ї5] all over the [↑VI, књ›6] world tonight. [I7, књњ7] All over the [IVM, књ›6] world”). Much wilder is the touring I5–↑IIIM–↑VI–↑VIm9–II5 that sets up the refrain of Billy Joel’s 1980 “Don’t Ask Me Why,” the chordal minor ninth of ↑VIm9 providing књњ7 and the chordal perfect fifth of II5 offering the second књ›6, all over a descending stepwise bass ([I5, 5] “Don’t [↑IIIM, в™Ї5] wait for [↑VI, књ›6] answers. Just [↑VIm9, књњ7] take your [II5, књ›6] chances”). Another standard touring series fills the second slot (в™Ї5) with I+ in place of ↑IIIM, and the third slot (the first књ›6) with I6 in place of ↑VI, making the entire ascending portion of the gesture an elongated I, changing its root only with IVM. We hear this touring progression in the verses to Otis Redding’s 1962 “These Arms of Mine” (“And if [I5, 5] you [I+, в™Ї5] would let [I6, књ›6] them [I7, књњ7] hold you [IVM, књ›6]) and in these verses to the Guess Who’s 1969 “Laughing” (“Time goes [I5, 5] slowly but carries [I+, в™Ї5] on and now the [I6, књ›6] best years have come and [I7, књњ7] gone. You took me by sur- [IVM, књ›6] -prise”). With this long I it is easy to see one of the two main hierarchical possibilities of the tour in general: the initial 5, which is ordinarily the chordal fifth of I5, moves gradually to the књ›6 in the last slot, which is typically the chordal third of IVM. At a Page 141 →deep harmonic level, then, the entire progression is I–IV, with IV functioning as a post-tonic. (What happens—or what is predicted to happen—after the IVM is entirely dependent on the individual song). The other basic hierarchical possibility was heard in “Only You”: the slow harmonic pulse allows us to savor the књ›6 in the third slot, harmonized with a distinct ↑VI (as opposed to another I). Thus the ensuing motion of књњ7–ꜛ6 sounds more like an embellishment of the primary motion—the stretch (5–♯5–ꜛ6)—with the I7 functioning as a low-level pre-IVM (which can function in any number of ways, depending on the circumstances). Whether the intervening књ›6 (↑VI or I6) is an anticipation of the true arrival of књ›6 in the last slot (as is normally the effect of the long I progressing to IVM and of faster harmonic pulses), or instead the first књ›6 sounds like the real arrival point that is temporarily overshot and must come back down (an effect more likely projected by tours that do not stay on I, and of slower harmonic pulses) is a matter to be decided based on the musical particulars of a given song. In 1975’s “You’re My Best Friend,” Queen fills the second slot with a I augmented major-seventh chord, otherwise hearable as a ↑III major triad over a dissonant bass 1: “[I5, 5] Ooh, [I+ or ↑IIIM, в™Ї5] I’ve been [↑VI, књ›6] wan- [I7, књњ7] -derin’ [IVM, књ›6] ’round.” Queen’s brisk harmonic pulse and metric emphasis on the IVM override the fact that we change chords before the IVM; in this case, it is the last slot that delivers the strongest arrival of књ›6. Example 141.4. Touring schema B – Bв™Ї – Cв™Ї – D – Cв™Ї (center E) 5 – в™Ї5 – књ›6 – књњ7 – књ›6 – ↑VI – I7 – IVM (“Only You,” “My Pledge of Love,” “There’s a Kind of Hush”) I5 – ↑IIIM – I6 – I7 – IVM (“These Arms of Mine,” “Laughing”) I5 – I+ – IVM (“You’re My Best Friend”) I5 – I+ (↑IIIM) – ↑VI – I7 In both “You’re My Best Friend” and “Laughing,” the semitonal motion continues downward two more chromatic steps: 5–♯5–ꜛ6–ꜜ7–ꜛ6–ꜜ6–5. The three-note descending motion at the end, књ›6–ꜜ6–5, or C♯–C–B in relation to center E, is the exact retrograde of the stretch (књњ6 being the same pitch class as в™Ї5; C is Bв™Ї). See Example 4.5. This short, ubiquitous meta-schema, which we will dub the shrinking schema, can appear at any point in a harmonic phrase. While “You’re My Best Friend” and “Laughing” offer shrinks of

IVM–IIo–V and IVM–IVm–↑IIIm respectively, the shrink’s most common incarnations are IVM–IVm–I5 and IVM–IIo–I5; књ›6 appears as the chordal major third of IVM, књњ6 as the chordal minor third of IVm or chordal diminished fifth of IIo, and 5 as the chordal perfect fifth of I5. IVM–IVm–I5 begins the choruses of the Page 142 →Temptations’ 1969 “I Can’t Get Next to You” (“[IVM, књ›6] But my [IVm, књњ6] life is incom- [I5, 5] -plete”), and IVM–IIo–I5 is placed within the larger progression I5–↑IIIM–IVM–IIo–I5 in both Johnnie Ray’s 1957 “You Don’t Owe Me a Thing” (“[I5] Don’t [↑IIIM] be nice to me [IVM, књ›6] just because I’m your [IIo, књњ6] used-to-be. [I5, 5] Forget me”) and the verses of Ronnie Milsap’s hyper-nostalgic 1985 “Lost in the Fifties (In the Still of the Night),” a song inspired partly by the Five Satins’ hit mentioned in the subtitle (the ↑IIIM possibly again a I+, and with a slight entity effect of a Vm9 between IIo and I5: “[I5] Close your eyes, baby. [I+ or ↑IIIM, в™Ї5] Follow my heart. [IVM, књ›6] Call on the memories [IIo, књњ6] here in the dark [I5, 5]”). We will have more to say about these last two examples shortly.

C♯ – C – B ꜛ6 – ꜜ6 – 5 IVM IVM IVM IVM II5 II5 ↑VI IVM II5 IVM ↑VI IVM ↑VI II5 II5

Example 142.4. Shrinking schema (center E)

– IIo – V (“You’re My Best Friend”) – IVm – ↑IIIm (“Laughing”) – IVm – I5 (“I Can’t Get Next to You,” “Sleep Walk”) – IIo – I5 (“You Don’t Owe Me a Thing,” “Lost in the Fifties”) – IIo – I5 (“Lonely Teardrops,” “This Girl Is a Woman Now”) – IVm – I5 (“Nowhere Man”) – IVm – I5 (“My Prayer”) – ↓VI – I5 (“Beautiful Stranger”) – Vm9 – I5 (“Put Your Head on My Shoulder”) – IIo – ↑IIIm (“I’m Not in Love”) – IVm – V (“Sleep Walk”) – IVm – V (“Sleep Walk”) – в™-II5 – V (“Sleep Walk”) – ↓VI – I5 (“Personal Jesus”) – в™-II5 – I5 (“Personal Jesus,” “Alma Mater”)

Of all the meta-schemas we will identify, the shrink has the most numeric possibilities. (This is not a result of inherent abstract properties of the melodic line, but rather merely how the shrink is evoked in practice.) We hear II5–IIo–I5 in the verses of Jackie Wilson’s 1958 “Lonely Teardrops” (“[II5, ꜛ6] lonely teardrops. [IIo, ꜜ6] My pillow never dry up [I5, 5]”). II5–IVm–I5 appears in the verses’ cadences from the Beatles’ 1965 “Nowhere Man” (“[II5, ꜛ6] making all his [IVm, ꜜ6] nowhere plans for [I5, 5] nobody”). ↑VI–IVm–I5 is used in the Platters’ 1956 cover of “My

Prayer” (the ↑VI being an unusual fully diminished seventh chord, creating other descending lines in addition to the shrink: “to linger with [↑VI, књ›6] you at the end of the [IVm, књњ6] day in a dream that’s di- [I5, 5] -vine”). IVM–↓VI–I5 projects the shrink at the end of the Page 143 →chorus progressions from Madonna’s 1999 “Beautiful Stranger” (“[IVM, књ›6] da da [↓VI, књњ6] da da [I5, 5] da. Beautiful stranger”). II5–Vm9–I5 (the Vm9 being a major triad with minor seventh and minor ninth, the ninth providing the књњ6) is employed in Paul Anka’s 1959 “Put Your Head on My Shoulder” (“[II5, књ›6] Hold me [Vm9, књњ6] in your arms, [I5, 5] baby”). IVM–IIo–↑IIIm does the job in the verses of 10CC’s 1975 soft-rock “I’m Not in Love” (“[IVM, књ›6] I’m not in love, [IIo, књњ6] so don’t forget it [↑IIIm, 5]”). In Santo & Johnny’s 1959 steel-guitar instrumental “Sleep Walk,” the shrink appears in four different forms: ↑VI–IVm–V, as the back end of the verse’s looping I–↑VI–IVm–V king progression,13 with the root of the V providing the 5; IVM–IVm–I5, in the opening of the bridge; IVM–IVm–V, in the bridge’s second phrase; and the accidental ↑VI–в™-II5–V (with the fifth of в™-II5 as књњ6), heard at the very beginning of the track when Johnny—clearly unintentionally—hits an additional, open string while playing the IVm as part of his otherwise I–↑VI–IVm–V rhythmguitar vamp. The shrinking schema commonly appears at the start of bridge sections (as in “Sleep Walk”), a point we will return to later on. Additionally, the shrink can appear as part of other, larger meta-schemas, which we shall discuss in due time. Note that some of these shrinking progressions, including ↑VI–IVm–I5, IVM–↓VI–I5, and II5–Vm9–I5, represent their own individual threechord schemas (sans the nonroot tones) when we strip them down to their chordal roots. Because it has so many different numeric incarnations—some with their own unique schematic effects—and because it can arrive at any point within a larger phrase, the shrink is difficult to generalize about in terms of functions. Nonetheless, in all cases, the third chord (5) is the overall harmonic goal, functioning as an anchor to the second chord and possibly also to the first chord. The second sonority (књњ6) is usually a pre-anchor, either a lower subdominant to a tonic I5 or a pre-dominant to a dominant V. The first chord (в™Ї5) may attach itself either to the second or third chord; in the latter case, the second sonority will sound more like filler within this larger motion. In “You Don’t Owe Me a Thing” and “Lost in the Fifties,” which we cited as examples of a shrinking IVM–IIo–I5 progression, we hear the shrink being led into by I5 and ↑IIIM, which means these phrases also can project a stretching effect (overlapping with the shrink with the IVM): I5(5)–↑IIIM(в™Ї5)–IVM(књ›6)–IIo(књњ6)–I5(5). This combination of the two meta-schemas, B–B♯–C♯–C–B with center E (5–♯5–ꜛ6–ꜜ6–5), is its own traveling meta-schema; we will refer to it as the teasing schema, because it stretches upward two semitones before shrinking back down to where it started. See Example 4.6. Although the tease has appeared at various points during the rock era—we hear it in the choruses to David Bowie’s 1969 “Space Oddity” (“[I5, 5] This is Ground Control Page 144 →to Major [↑IIIM, в™Ї5] TomВ .В .В . the [IVM, књ›6] grade, and the [IVm, књњ6] papers want to [I5, 5] know”), as the main riff in Metallica’s 1986 “Master of Puppets” (an embellishment of a long tonic I, with I5 followed by I+ followed by I6 and then back down), throughout Radiohead’s 1992 “Creep” (“I’m a creep. [I5, 5] I’m a [↑IIIM, в™Ї5] weirdoВ .В .В . doin’ [IVM, књ›6] here? I don’t belong [IVm, књњ6] hereВ [I5, 5]”),14 and in the choruses of Toby Keith’s 2012 “Hope on the Rocks” (“Where did they [I5, 5] go? They come [↑IIIM, в™Ї5] here to [IVM, књ›6] drownВ .В .В . and [IVm, књњ6] cryВ .В .В . they’re in [I5, 5] need”)—it is primarily a creature of 1950s and early 1960s rock, like “You Don’t Owe Me a Thing” and the 1962 surf-rock/jazz instrumental known as “The James Bond Theme” (written for the film Dr. No), the latter featuring the tease in the upright bass, brass, and vibraphone parts (which can be heard as either as a melodic embellishment of a big I, or, especially because the motion is in the bass, as a harmonic effect with the teasing notes as the roots of separate chords: I5–↓VI–↑VI–↓VI–I5).15 It is also a staple of retro pastiches, such as “Lost in the Fifties” and Morrissey’s 1992 “I Know It’s Gonna Happen Someday” (“My [I5, 5] love, wherever [↑IIIM, в™Ї5] you are, whatever [IVM, књ›6] you are, don’t lose [IVm, књњ6] faith. I [I5,

5] know”). The tease normally operates as a functional chain leading to a final tonic I5: the penultimate chord (usually IVm or IIo) is a subdominant, and the preceding sonority (most commonly IVM) is both a pre-subdominant and an anchor that resolves the pre-anchor second chord (↑IIIM or I+). On the next harmonic level, the progression reduces to the shrinking schema. Like most meta-schemas, the tease in rock music probably derives from jazz practice, where its most famous appearance was probably the gloomy brass riff to Artie Shaw and His Orchestra’s 1938 big-band instrumental “Nightmare,” heard throughout the entire track as a melodic embellishment of an unchanging, catatonic I. The choruses of “Hope on the Rocks” open with a teasing I5–↑IIIM–IVM–IVm–I5 progression, but they continue from there with I5–↑IIIM–IVM–IIM–I5, the previous IVm being replaced by IIM. This latter progression, similar to but distinct from the teasing schema, does not offer a shrinking line, as each of the II5 chords here is a major triad with no књњ6. Yet this IIM does feature as its chordal third a salient в™Ї4, so we might suspect that this scale degree is some kind of colorful substitute for the more common књњ6. If we were to hear this в™Ї4 involved in some sort of semitonal melodic line that is analogous to the shrinking line, it would probably be the ascent of natural 4 (the root of IVM) to в™Ї4 (the third of IIM) to 5 (the fifth of I5): on center E, this is A–A♯–B, as shown in Example 4.7. This motion would mirror the shrink in its approach to 5 via two semitones: the shrink involving two steps down, this other motion entailing two steps up. This three-note rising line will define Page 145 →another short meta-schema, the swelling schema. The larger traveling motion of the stretch overlapping with the swell we will define as the twirling schema: 5–♯5–ꜛ6/4–♯4–5, or B–B♯–Cв™Ї/A–A♯–B with center E. More examples of the twirl include the verses to Eric Hutchinson’s 2008 “Rock and Roll” (“[I5, 5] He’s been waitin’ ’round for the [↑IIIM, в™Ї5] weekendВ .В .В . to [IVM, књ›6, 4] sneak in. Fancy [IIM, в™Ї4] drinks and $50 cover [I5, 5] charge”), 1959’s “Sea of Love” by Phil Phillips with the Twilights (“[I5, 5] Come with me, [↑IIIM, в™Ї5] my love, [IVM, књ›6, 4] to the sea, the [IIM, в™Ї4] sea of love. [I5, 5] IВ .В .В .”), and Otis Redding’s 1968 “(Sittin’ on) The Dock of the Bay” (“[I5, 5] Sittin’ in the mornin’ [↑IIIM, в™Ї5] sun, I’ll be [IVM, књ›6, 4] sittin’ when the evenin’ [IIM, в™Ї4] comes. [I5, 5] Watching”). Example 145.4. Teasing schema B – Bв™Ї – Cв™Ї – C 5 – в™Ї5 – књ›6 – књњ6 I5 – ↑IIIM – IVM – IIo I+ – IVM – IIo I5 – (↑IIIM)

– B (center E) – 5 – I5 (“You Don’t Owe Me a Thing”) – I5 (“Lost in the Fifties”)

(“Space Oddity,” “Creep,” “Hope on the Rocks,” “I Know It’s Gonna Happen Someday,” “The Air that I Breathe”) – I6 – I+ – I5 (“Master of Puppets,” “James Bond Theme,” “Nightmare”) I5 – I+ – ↑VI – ↓VI – I5 (“James Bond Theme”) I5 – ↓VI – IIo – I5 (Hoagy Carmichael’s “Georgia”) I5 – ↑IIIM – II5 I5 – ↑IIIM – IVM – IVm

– I5

Admittedly, in “Hope on the Rocks,” “Rock and Roll,” “Sea of Love,” and “The Dock of the Bay,” the swells are not nearly so obvious as the stretches. One factor here is that these two meta-schemas overlap in time but not in notes, with the swell beginning on 4 as the stretch is ending on ꜛ6. This overlap was also present in the earlier tease examples, but in those cases the constituent stretching and shrinking lines respectively ended and started in the same place; in the twirling examples, we are less likely to notice the beginning of the swell and thus less likely to notice the swell at all. Affecting hearability even more is the fact that these swelling lines are never presented as an actual melody in any instrumental or vocal part. Twirling effects in general are often not as aurally apparent as teasing effects, although there are exceptions, such as that in the last chorus of Chuck and Mac’s 1970 soul ballad “Powerful Love,” which clearly projects interweaving stretching and swelling effects with a progression of I5–↑IIIM–IVM–♯IV–I5, right before the drums kick into overdrive: “So, baby, [I5, 5] try it my [↑IIIM, ♯5] way. Oh, and [IVM, ꜛ6, 4] please don’t make me wait too [♯IV, ♯4] long, ’cause I [I5, 5] love you.”16 Example 146.4. Twirling schema B – B♯ – C♯/A – A♯ – B (center E) 5 – ♯5 – ꜛ6/4 I5 – ↑IIIM – IVM I5 – ↑IIIM – IVM

– ♯4 – 5 – IIM – I5 (“Hope on the Rocks,” “Rock and Roll,” “The Dock of the Bay,” “Sea of Love”) – ♯IV – I5 (“Powerful Love”)

Page 146 →Unlike those in the previous examples, the average swell is a fairly prominent part of its musical texture; most instances are not part of a twirling motion and so do not involve any kind of overlap with a stretch. As illustrated in Example 4.8, obvious swells occur with the IV–♯IV–I5 progression leading to the refrain in Ray Charles’ 1956 “Hallelujah I Love Her So” (the в™ЇIV being a playful, fully-diminished seventh chord: “[IV, 4] she bring my coffee in my [в™ЇIV, в™Ї4] favorite cup. That’s why I [I5, 5] know”), the IV–♯IV–V progression heard in leading to the chorus in Lenny Kravitz’s 2001 “Dig In” (“[IV, 4] Don’t let it beat you. [в™ЇIV, в™Ї4] Say вЂnice to meet you’ and [V, 5] вЂbye’”), the IV–IIM–I5 progression in the pre-choruses of the Beach Boys’ 1965 “Help Me, Rhonda” (originally spelled “Ronda”: “and I [IV, 4] know it wouldn’t take much [IIM, в™Ї4] time for you to [I5, 5] help me, Rhonda”), and the IV–IIM–V progression in the bridges of the Lovin’ Spoonful’s 1966 “Daydream” (the lyrics of which perhaps countering an earlier Rolling Stones hit cover: “[IV, 4] And even if [IIM, в™Ї4] time ain’t really [V, 5] on my side”). Just like the stretch and the shrink, the swell usually appears as part of a larger harmonic phrase and thus too is not wholly generalizable in terms of functional effects. Whether the third chord is I5 or V, it is always the immediate hierarchical goal of the gesture, with the second chord (most often a IIM or в™ЇIV) strongly pulled toward it and hierarchically subordinate to it. The first chord, ordinarily a IV, also is subordinate to the third chord (as a subdominant or pre-dominant), but the nature of its relation to the second chord is determined by the specific musical attributes of the individual song. The twirling schema, on the other hand, normally operates as a functional chain leading to a final tonic I5 or dominant V, and in this manner is just like the tease: the final sonority is predicted by the penultimate chord (likely IIM or в™ЇIV), which is predicted by the preceding chord (probably IV or ↑VI), which itself is predicted by stretching ↑IIIM (in all these cases). On the next harmonic level, the progression might reduce to the swelling schema if its effect is strong enough; otherwise, the stretching portion will take precedence. The reverse motion of the swell is also a short meta-schema, which we will dub the slouching schema: 5, down to в™-5 (identical in pitch class to в™Ї4), Page 147

→down to natural 4 (B–Bв™-–A on center E). By far the most common numerals for the slouch are I5–IIM–IV, with the chordal fifth I as natural 5, the third of IIM as в™-5 (doubling as в™Ї4); see Example 4.9. The Grateful Dead cadence with a slouch in the verses of their 1970 “Brokedown Palace” (“In my [I5, 5] time, in my [IIM, в™-5] time, I will [IV, 4] roll”). But more often than not the slouching I5–IIM–IV progression appears as part of the self-contained loop of I5–IIM–IV–I, as heard in the verses of Procol Harum’s 1967 “Homburg” (again, over a bass line stuck on 1, and the slouching line constituting the lead vocal melody: “[I5, 5] Your multilingual [IIM, в™-5] business friend [IV, 4] has packed her bags and [I] fled”) and Cee Lo Green’s often-edited 2010 “Fuck You” (“I see you [I5, 5] drivin’ ’round town with the [IIM, в™-5] girl I love, and I’m like [IV, 4] вЂfuck you’ [I]”). This looping version appears to have been popularized by the summer 1964 Anglophone-version of the bossa nova “The Girl from Ipanema” as recorded by Astrud Gilberto, JoГЈo Gilberto, Stan Getz, and Antonio Carlos Jobim, although the identities of the chords in that case are flexible due to the jazz sonorities and the improvisatory nature of the playing (“[I5, 5] Dark and tanВ .В .В . the [IIM, в™-5] girl fromВ .В .В . and [IV or ↑VIm6, 4] when she passesВ .В .В . goes [I]“ah”).17 The I5–IIM–IV–I progression was codified later that year by the Beatles in “Eight Days a Week” (“[I5, 5] Ooh, I need your [IIM, в™-5] lovin’. [IV, 4] Yes, you know it’s [I] true”). Example 147.4. Swelling schema – Aв™Ї – B (center E) – в™Ї4 – 5 – IIM – I5 (“Hope on the Rocks,” “Rock and Roll,” “The Dock of the Bay,” “Sea of Love,” “Help Me, Rhonda”) – в™ЇIV – I5 (“Hallelujah I Love Her So”) – в™ЇIV – V (“Dig In”) – IIM – V (“Daydream”) в™ЇIM – в™ЇIV – V (“Judy’s Turn to Cry”) A 4 IV IV IV IV

In all these cases, the slouching line can be traced past the 4 (IV) to књ›3 (the chordal major third of the resolving I). There are many other examples, however, that do not continue the pattern in this way, and so we will not include the final књ›3 as requirement for the slouching schema. For instance, I5–IIM–IV can be found moving to a књ›3-less V in the loops of Marianne Faithfull’s 1964 “As Tears Go by” (“[I5, 5] It is the [IIM, в™-5] evening of the [IV, 4] day [V]”) and Puddle of Mudd’s 2001 “She Hates Me” (“She fuckin’ [I5, 5] hates me, [IIM, в™-5] [IV, 4] lo-, lo,- lo-, [V] love”). While it is possible to think of 5–в™-5–4 and 5–в™-5–4–ꜛ3 as two separate meta-schemas, it is the в™-5 that defines both these Page 148 →lines’ sound; therefore, only the three-chord 5–в™-5–4 will be classified as a meta-schema here. Example 148.4. Slouching schema B 5 I5

– Bв™-– A (center E) – в™-5 – 4 (“Brokedown Palace,” “Homburg,” “Fuck You,” “The Girl from Ipanema,” “Eight Days a Week,” – IIM – IV “As Tears Go by,” “She Hates Me”)

I5 V V

– IIM

V

– IIM

– IIm (“Right Here, Right Now,” “This Girl Is a Woman Now”)

– IIM – IV – в™-V – IV 7 ↑VI – IIM – IV ↑VI7 – IIM – V7

(“Drops of Jupiter”) (“My Michelle”) (“Yesterday”) (“The Puppy Song”)

– IIm (“The Chipmunk Song”)

Other possible realizations of the slouch include the I5–IIM–IIm loops of Jesus Jones’ 1990 “Right Here, Right Now” (the chordal third of IIm providing 4: “[I5, 5] Right here, right [IIM, в™-5] now. There is no [IIm, 4] other place”), the V–IIM–IV portion of the choruses to Train’s 2001 “Drops of Jupiter” (the root of V offering 5: “[V, 5] Tell me, did you sail across the [IIM, в™-5] sun? Did you make it to the Milky [IV, 4] Way”), the V–в™-V–IV portion of the main guitar riff to Guns N’ Roses’ 1987 “My Michelle” (the root of в™-V presenting в™-5), the ↑VI7–IIM–IV(–I) cadences of the Beatles’ seminal 1965 “Yesterday” (the chordal minor seventh of ↑VI7 offering natural 5: “Oh, [↑VI7, 5] I be- [IIM, в™-5] -lieve in [IV, 4]”), and as part of the ragtime-steady verse loop (with a chordal major thirds) of Nilsson’s self-consciously naive 1969 “The Puppy Song” (in the verses: “[↑VI7, 5] I’d call myself so very lucky [IIM, в™-5] just to have some company to [V7, 4] share”). In the Chipmunks and David Seville’s 1958 “The Chipmunk Song (Christmas Don’t be Late),” the slouch is a continuation of a downward trajectory initiated by a shrink, resulting in a semitonal line starting with књ›6 (the third of IVM) and ending with 4 (the third of IIm): “[IVM, књ›6] We can [IVm, књњ6] hardly [V, 5] stand the [IIM, в™-5] wait. Please, [IIm, 4] Christmas.” The slouch and the shrink are nearly concurrent in the verses to Gary Puckett and the Union Gap’s 1969 “This Girl Is a Woman Now.” The progression I5–IIM–IIo–I5 (over a pedal 1) starts the slouch with its first I5 (I5–IIM–IIm) then starts the shrink with its IIM (II5–IIo–I5): “[I5, 5] This girl walked in [IIM, в™-5, књ›6,] dreams, [IIo, 4, књњ6] playing in a [I5, 5] world of her own.” (Note the mix of superscript and nonsuperscript symbols here to indicate all the relevant tones.) In the verses of Billy Joel’s 1980 “Don’t Ask Me Why, ” the previously cited touring progression I5–↑IIIM–↑VI–↑VIm9–II5 births a slouchingPage 149 → ↑VI7–IIM–V7 series that resolves to књ›3 with IM ([I5, 5] “Don’t [↑IIIM, в™Ї5] wait for [↑VI, књ›6] answers. Just [↑VIm7(m9), књњ7, 5] take your [IIM, књ›6, в™-5] chances. Don’t [V7, 4] ask me [IM, књ›3] why”). Even more so than the previous meta-schemas, the slouch does not offer up easy generalizations about its chordal functions or harmonic levels. This said, the schema in its most common form starts with a tonic I; the second chord (scale degree в™-5) normally functions as a highly salient post-tonic to the I, and as a pre-anchor to the third chord (scale degree 4). Our next two short meta-schemas are another mirror pair: 1–♯1–2 and 2–в™-2–1. The former, E–E♯–Fв™Ї on center E, we will name the soaring schema, after its use in the Beatles’ 1963 cover of “Till There Was You.” In the second verse, Paul McCartney pronounces “saw” in a rhotic dialect, making the word sound like “soar” (which is appropriate to the lyrical topic of flying: “There were [I, 1] birds in the [в™ЇI, в™Ї1] sky, but I [II, 2] never saw them”). The soar nearly always starts at the beginning of a phrase on a tonic I, whose root is thrust upward chromatically via в™Ї1 to a temporary resolution on 2 (usually harmonized by II or V5); see Example 4.10. The soar’s most frequent deployment is as the chordal root-bass line of I–♯I–II (в™ЇI often as a diminished triad or fully-diminished seventh chord), as heard in the verses to “Till There Was You,” and in the verses to Elton John’s 1973 “Bennie and the Jets” (where it appears in the middle of the harmonic phrase, resolving across the lyrics: “The spot- [I, 1] light’s hittin’ somethin’ that’s been [в™ЇI, в™Ї1] known to change the weather [II, 2]”). However, it is by no means restricted to root-bass lines: we hear 2 harmonized as the chordal perfect fifth of V5 in the 1940s’ radio/TV theme song Happy Trials sung by Roy Rogers and Dale Evans (“Happy

[I, 1] trails to you until we [в™ЇI, в™Ї1] meet a- [V5, 2] -gain”), while in the verses to Leslie Gore’s 1963 “Judy’s Turn to Cry” V5 is preceded not only by в™ЇI (this time a major triad, with 4 as its chordal major third) but also by the в™Ї1-containing в™ЇIV5, and simultaneously projecting a swelling ascent of 4–♯4–5 to boot ([I, 1] I sat down and cried my [в™ЇIM, в™Ї1, 4] eyes out now. [в™ЇIV5, в™Ї1, в™Ї4] That was a foolish [V5, 2, 5] thing”). The soar’s в™Ї1 is also regularly offered by ↑VIM, as part of I–↑VIM–II; this series is inherent to the ragtime version of the steady schema ( with all major thirds), and in fact to any steady progression wherein the ↑VIM offers a chordal major third. We hear this in the verses of Patsy Cline’s 1961 “Crazy” (“[I, 1] Crazy I’m [в™ЇVIM, в™Ї1] crazy for feelin’ [II] so lonely”), and the verses of the Four Seasons’ 1962 “Big Girls Don’t Cry” (with one of the backing vocal parts clearly articulating the soar: “[I, 1] Big [↑VIM, в™Ї1] girls [II, 2].В .В .”). Although the steady is nearly identical to, and often interchangeable with, the king schema , a soaring line makes these schematic Page 150 →effects relatively distinct. The resolving 2 will likely prevent the harmonizing chord from projecting any numeric effect other than II, and thereby prevent the progression from projecting any numeric schema other than the steady. Example 150.4. Soaring schema E – Eв™Ї – F (center E) 1 – в™Ї1 – 2 I – в™ЇI – II (“Till There Was You,” “Bennie and the Jets”) I – в™ЇI – V5 (“Happy Trails”) I – в™ЇI–♯IV5 – V5 (“Judy’s Turn to Cry”) I – ↑VIM – II (“Crazy,” “Big Girls Don’t Cry”) The opposite of the soaring schema is the short slumping schema, 2–в™-2–1 (F♯–F–E on E); see Example 4.11. Ending on 1, the slump is a prime candidate for the ends of phrases, particularly for whole cadences, as found in the instrumental intro to U2’s 1995 “Hold Me, Thrill Me, Kiss Me, Kill Me” (in the form of V5–в™-II–I) and several times throughout Depeche Mode’s 1989 “Personal Jesus” (II–в™-II–I: “[II, 2] [в™-II, в™-2] Reach out and touch me [I, 1].”) (“Personal Jesus” alters one of these cadences in the middle of the song, making it I5–↓VI5–I5, an unusual shrinking cadence.) These two harmonizations, V5–в™-II–I and II–в™-II–I , are the primary carriers of the slump; other examples include the Jefferson Airplane’s 1968 “Crown of Creation” (“You [V5, 5] are the [в™-II, в™-2] crown of cre- [I, 1] -ation”) and Alice Cooper’s 1972 “Alma Mater” (“To- [II, 2] -morrow, like the [в™-II, в™-2] rain, I’ll be back [I, 1] home again”). More unusual harmonizations of the slump include Weezer’s II–↑VIM–I progression (в™-2 as в™Ї1, the chordal major third of ↑VIM), heard in the verses of their 1996 emo-landmark “The Good Life” (“[II, 2] I can’t believe what I [↑VIM, в™-2] see [I, 1]”), and Stevie Wonder’s II–IIM7–II7 (the chordal major seventh of IIM7 providing в™-2 as в™Ї1) in his 1967 cover of “For Once in My Life” (among many other meta-schemas: “For [II, 2] once una- [IIM7, в™-2] -fraid I can [II7, 1] go”). In cases where the slump’s 1 is harmonized by something other than I, as in “For Once in My Life” and in the similar progression in the bridges of Elvis Costello’s 1989 “Veronica” (“Do you sup- [II, 2] -pose that waiting [IIM7, в™-2] hands on eyes Ve- [II7, 1] -ronica”), the initial moment (2) tends to be the most stable, with the remaining notes moving toward some future point of predicted resolution. Otherwise, the I(1) is almost always the harmonic goal. When projected specifically by II–в™-II–I as its root-bass line, the slump usually travels with a simultaneous књ›6–ꜜ6–5 shrink, hovering above in the (real or imagined) chordal perfect fifths (I5–♯I5–II5); this is the case in both “Personal Jesus” and “Alma Mater.” In this

way, the slump is dissimilar to the soar: while the soar also often appears as a root-bass line, and thus might project a Page 151 →simultaneous stretch (5–♯5–ꜛ6 in I5–♯I5–II5), its middle chord in these settings more often than not features a diminished, not perfect, chord fifth (в™ЇIo).

F♯ – F

Example 151.4. Slumping schema – E (center E)

V5 II

– в™-2 – в™-II – в™-II

II II

– ↑VIM – I (“The Good Life”) – IIM7 – II7 (“For Once in My Life,” “Veronica”)

2

– 1 – I (“Hold Me, Thrill Me, Kiss Me, Kill Me,” “Crown of Creation”) – I (“Personal Jesus,” “Alma Mater”)

Our final meta-schema of this section is a relative of the teasing schema. Like that other gesture, the very important teetering schema is an up-down traveling motion starting on 5, but one that moves upward a whole tone and a semitone, then downward in the reverse order. On E, it is B–C♯–D–C♯–B; see Example 4.12. This is only one of three meta-schemas to be identified that includes a whole tone (the others being the upcoming slide and drop), and only one of two that is not inherently chromatic (the other being the slide). Its inclusion as a meta-schema is justified by its kinship to the chromatic tease and by the fact that no other schema adequately covers this aurally distinctive and historically important harmonic gesture. The teeter is commonly heard against a single I seventh chord with 5 acting as the I’s chordal fifth and the књњ7 as its minor seventh, as happens in the main guitar riff of the Sweet’s 1973 “Ballroom Blitz.” Yet it can also appear across two or more chords (i.e., as a harmonic effect), always involving a move away from and back to a tonic I5. It is possible for a teetering progression to move away from I5 just once, as happens with the I5–I6–↓VII–↓VIIM7–I5 loop in The Who’s pubescent 1965 “My Generation,” the књ›6 harmonized once by I6 and once by ↓VIIM7 (as the chordal major seventh): “[I5, 5] Talkin’ [I6, књ›6] ’bout my [↓VII, књњ7] gene- [↓VIIM7, књ›6] -ration [I5, 5]” (the backing vocals stating the melodic motion very clearly). When a teetering progression includes only two distinct numerals, it more typically features two motions away from I, specifically to IVM (with its chordal third as књ›6), the non-Is thus tending to function as passing post- and pre-tonics. I5–IVM–I7–IVM–I5 appears often in the Ad Libs’ 1964 “The Boy from New York City” (the teetering line presented clearly in the doo-wop backing vocals) and in Santana’s 1969 “Evil Ways” (“You got me [I5, 5] runnin’ and [IVM, књ›6] hidin’ [I7, књњ7] all over [IVM, књ›6] town. You got me [I5, 5] sneakin’”). The teeter is really a particular version of a more general figure that arpeggiates any harmony’s chordal perfect fifth and chordal Page 152 →minor seventh while filling in the gap with a passing chordal major sixth. This more general figure regularly ornaments Is and IVs (heard in “The Boy from New York City”), and less often Vs (heard at the end of the instrumental introduction to the Chicago Transit Authority’s 1969 “Does Anybody Really Know What Time It Is?”), and dates back to the piano and guitar accompaniments of blues and boogie-woogie.18

B – C♯ – D 5 – ꜛ6 – ꜜ7

Example 152.4. Teetering schema – C♯ – B (center E) – ꜛ6 – 5

I5 – I6 I5 – I6 I5 – IVM I5 – IVM I5 – II5 I5 – IVM

– I7

– I6

– I5 (“Ballroom Blitz”)

– ↓VII – I7 – ↓VII – ↓III5

– ↓VIIM7 – I5 (“My Generation”) – IVM – I5 (“The Boy from New York City,” “Evil Ways”) – IVM – I5 (“What I Like about You,” “Best of Me”) – II5 – I5 (“Living for the City,” “Walkin’ on the Sun”)

– Vm

– IVM

– I5 (“Louie Louie,” “Why Do I Cry”)

There are two longer, palindromic chordal series that consistently project a teetering effect. The first, more common one is I5–IVM–↓VII–IVM–I5, already familiar to us in the form of the schema from chapter 3. We hear this teetering progression in most of the Romantics’ 1979 “What I Like about You” (“[I5, 5] Keep on [IVM, књ›6] whisperin’ [↓VII, књњ7] in my [IVM, књ›6] ear. [I5, 5] Tell meВ .В .В .”) and in the choruses of Morningwood’s 2009 “Best of Me” (“[I5, 5] You think you’ve [IVM, књ›6] got the best of me. [↓VII, књњ7] You think you’ve [IVM, књ›6] got the best of me [I5, 5]”). (We identified IV–↓VII–IV–I as its own separate schema because it seems to have a life of its own, with various possible phrasings and with strong chordal roots that often do not harmonize the full teeter, as when a power chord IV does not offer књ›6.) The second, less common palindrome is I5–II5–↓III5–II5–I5, the teetering melody harmonized as a chordal fifth throughout and often accompanied with a pedal 1 in the bass that strengthens the reach of the I5 and weakens the entity effects of the II5 and ↓III5; this occurs in the main keyboard riff of Stevie Wonder’s 1973 “Living for the City” (“[I5, 5] A boy is born [II5, књ›6] in [↓III5, књњ7] hard-time Missis- [II5, књ›6] -sippi [I5, 5]”) and in the choruses to Smash Mouth’s 1997 “Walkin’ on the Sun” (“[I5, 5] So don’t de- [II5, књ›6] -lay, act now. [↓III5, књњ7] Supplies are [II5, књ›6] runnin’ out [I5, 5]”). A third palindrome, I5–IVM–Vm–IVM–I5 (a bamba progression) can also project a teetering effect (with its Vm offering the subtonic as its third), yet it is very rare Examples include the Kingsmen’s 1963 cover of “Louie Louie” (“[I5, 5] Louie Louie, [IVM, књ›6] [Vm, књњ7] oh no, [IVM, књ›6] said [I5, 5] me gotta go”) and the Remains’ 1965 “Why Do Page 153 →I Cry” (“I would [I5, 5] lose all my [IVM, књ›6] blues if you [Vm, књњ7] promised that your [IVM, књ›6] love was [I5, 5] true, now”). Despite the rarity of I5–IVM–Vm–IVM–I5, this progression as part of “Louie Louie” was hugely influential in the development of rock harmony from the mid-1960s onward. It is likely responsible not only for the popularization of the teetering schema as a harmonic effect (as opposed to it its use as a melodic ornament, which we noted dates back to the earliest days of the jazz era), but also for the popularization of the more general bamba schema (which typically features a V with a chordal major third rather than a minor third) as well as the standardization of the two-bar, four-slot loop as the basis for an entire track.19

Meta-Schemas: Part II Our remaining meta-schemas all feature stepwise scale-degree descents starting from the tonal center, descents we will name with words starting with “d.” Our first center-descending meta-schema is the only necessary exception to our naming rule, because it descends from center and is short (three notes). We will give it the name sliding schema, the “s” signifying its brevity and its internal “d” indicating its centric descent (no other s-named meta-schema contains a “d” anywhere). The slide starts on 1 and moves two steps (one half, one whole) down to ꜛ6 via the leading tone ꜛ7.20 On center E, it is E–D♯–C♯; see Example 4.13. This is one of the most important bass motions in all of rock music, although it is by no means limited to the lowest register. It makes regular appearances in three of the most important numeric schemas we studied in the previous chapter: the steady phrased as I–↑VI–II–V, the king phrased as I–↑VI–IV–V, and the journey phrased as I–V–↑VI–IV. Within the steady and the king, the slide

appears as part of a longer descending line to scale degree 5 (E–D♯–C♯–B), and in fact frequently appears as part of even longer stepwise diatonic descents, although it is equally at home in a self-contained three-chord loop. The middle књ›7 can serve as a passing chordal seventh in IM7 between I and ↑VI; this version is looped in the verses of John Lennon’s 1970 “Instant Karma! (We All Shine on)” (“[I, 1] Instant karma’s [IM7, књ›7] gonna get you [↑VI, књ›6]”) and alternated with ↓VI–↓VII–I in the intro and verses of Peter Frampton’s talk-box 1977 Frampton Comes Alive hit “Show Me the Way” (“I [I, 1] wonder how you’re feelin’. There’s [IM7, књ›7] ringingВ .В .В . and [↑VI, књ›6] no one”). (Lennon’s progression loops until a cadence of ↓VI–↓VII–I, while Frampton’s progression is part of a larger six-slot loop that moves repeatedly from I–IM7–↑VI to the same ↓VI–↓VII–I.) Sometimes the ↑VI does not project a very strong entity effect, making the third sonority more of a continuation Page 154 →of the initial I than its own chord. This is true of the down-up loops of Blink-182’s 2003 “I Miss You,” wherein the bass’s slide sounds utterly detached from the guitar riff’s persistent I (“Hel- [I, 1] -lo there, the [IM7, књ›7] angel from my nightmare, the [I6, књ›6] shadow”). Example 154.4. Sliding schema E – Dв™Ї – Cв™Ї (center E) 1 I I I I I I

– ꜛ7 – ꜛ6 – IM7 – ↑VI – IM7 – I6 – VM – ↑VI – VM – IVM – ↑III5 – ↑VI – VM – II5

(“Instant Karma!,” “Show Me the Way”) (“I Miss You”) (“A Case of You,” “Dust in the Wind”) (“Helpless,” “Mr. Brightside”) (“Bell Bottom Blues”) (“The Man Who Can’t Be Moved”)

The slide’s ꜛ7 may also be harmonized as the third of its own separate VM, usually progressing from there to either ↑VI or IVM (ꜛ6 as IVM’s chordal major third). Sliding I–VM–↑VI progressions are featured prominently in Joni Mitchell’s 1971 “A Case of You” (“[I, 1] I could drink a case [VM, ꜛ7] of [↑VI, ꜛ6] you”) and in the verses of Kansas’s 1977 “Dust in the Wind” (“I [I, 1] close [VM, ꜛ7] my [↑VI, ꜛ6] eyes”). Sliding I–VM–IVM progressions appear in Crosby, Stills, Nash and Young’s 1970 “Helpless” (“[I, 1] There is a [VM, ꜛ7] town in north [IVM, ꜛ6] Ontario”) and in the verses to the Killers’ 2004 “Mr. Brightside” (wherein the slide is heard behind the guitar riff’s more conspicuous 1–ꜛ7–4 line: “[I, 1] Comin’ outta my [VM, ꜛ7] cage and I’ve been doin’ just [IVM, ꜛ6] fine”). Other possible numeric realizations of the slide include I–↑III5–↑VI (the fifth of ↑III5 as ꜛ7), as heard in Derek and the Dominos’ 1970 “Bell Bottom Blues” (which simultaneously projects a stretching schema, the ↑III5 having a chordal major third ♯5 that raises the 5 of the I: “Bell bottom [I, 1] blues, you [↑III5, ꜛ7] made me cry [↑VI, ꜛ6]”) and I–VM–II5 in the choruses of the Script’s 2008 “The Man Who Can’t Be Moved” (“I’m not [I, 1] movin’. [VM, ꜛ7] I’m not mo- [II5, ꜛ6] -vin’”). Since the slide starts with the tonal center, and since this 1 is usually presented as the root of a tonic I, sliding progressions normally begin on their most hierarchically important chord. With ꜛ7, the slide may continue with tonic I, move to a post-tonic VM, or move to a pre-anchor ↑III5. The chord harmonizing ꜛ6 will likely be a subdominant when part of a short loop, otherwise this chord can function in various ways (including as an anchor to a preceding ↑III5). In all cases, the chord under ꜛ7 is the low person on the hierarchical totem pole.

In our last two examples—“Bell Bottom Blues” and “The Man Who Can’t Be Moved”—the sliding effect is projected by the beginning of a larger progressionPage 155 → that continues descending even further. In the rock repertory more generally, the longer lines 1–ꜛ7–ꜛ6–5 and 1–ꜛ7–ꜛ6–5–4 are absolutely standard bass motions. In a very strong sense, then, they are schematic, yet these longer lines start to bleed into the domain of mere diatonic scales. A span of three diatonic notes seems as good an arbitrary divider as any to separate our meta-schemas from mere scales, so we will not theorize as meta-schemas purely diatonic motions that are four notes or longer. (The slide and the teeter, the only meta-schemas we will define that can be considered purely diatonic, both span three diatonic notes; the walking schema spanned four, 1–ꜜ7–ꜜ6–5, but we theorized this as a series not of plain scale degrees but of chordal roots, .) The slide itself might seem an odd choice to include as a meta-schema, since it is just three notes of a descending ionian scale (or the rare lydian); however, it will serve as the basis for two more chromatic meta-schemas, the dip and the drop. (In this way, the slide differs significantly from the important diatonic arpeggiating descents књњ3–2–1 and књ›3–2–1, which do not normally blossom into larger chromatic patterns and hence will not be theorized here as meta-schemas.) Our final three, related meta-schemas—the dip, the droop, and the drop—will receive names that represent their lengths relative to each other: the dip is the briefest (four notes), the droop is the longest (six notes), and the drop is in-between (five notes). The dipping schema spans the same three semitones as the slide but includes the scale degree that the slide skips over, the subtonic, resulting in the line 1–ꜛ7–ꜜ7–ꜛ6. With center E, this is E–D♯–D–Cв™Ї; see Example 4.14. The dip usually moves slowly through its three semitones, sometimes adorning a static I, as heard in the opening to the Turtles’ psychedelic 1967 “She’s My Girl” (“[I, 1] Mor- [IM7, књ›7] -nin’ [I7, књњ7] mor- [I6, књ›6] -nin’ .В .В .”), but more frequently starting on I and ending on IVM. Often, I and IV are the only numerals involved, with I supporting the first three scale degrees (1 as the chordal root, and књ›7 and књњ7 as chordal sevenths) before moving to IVM for књ›6 (the chordal major third). Indicating all requisite scale degrees, we would write this progression as I–IM7–I7–IVM. We hear this in the Beatles’ 1963 cover of “A Taste of Honey” (“I [I, 1] dream of [IM7, књ›7] your first [I7, књњ7] kiss and [IVM, књ›6] then”) and in their 1969 Abbey Road favorite “Something” (“[I, 1] Something in the way she [IM7, књ›7] moves [I7, књњ7] attracts me like no other [IVM, књ›6] lover”). 1 is normally held in the bass through the first three scale degrees—as the root of the three I chords—but occasionally this root evaporates with the dipping descent and instead only the third and fifth of the initial I are held until the IV. In MГ¶tley CrГјe’s 1985 power ballad “Home Sweet Home,” this results in the progression I–↑III5–↑IIIo–IVM, with the fifths of ↑III5 and ↑IIIo supporting the leading tone and the subtonic Page 156 →respectively (“I’m a [I, 1] dreamer but my [↑III5, књ›7] heart’s of gold. I had to [↑IIIo, књњ7] run away high, so I [IVM, књ›6] wouldn’tВ .В .В .”). (In such cases, it is still possible for us to imagine a static 1, a perfectly reasonable hearing given the prevalence of the version with three I chords and the aural complexity of many records’ mixes.) In place of ↑IIIo, ↓VII can appear (its root offering the књњ7), as part of the dipping I–↑III5–↓VII–IVM, heard in Joe Walsh’s 1991 “Ordinary Average Guy” (“[I, 1] I’m just an ordinary [↑III5, књ›7] average guy. My [↓VII, књњ7] friends are all boring, [IVM, књ›6] and so am I”). In contrast, the dipping progression of She Wants Revenge’s 2006 “Tear You Apart” never lets go of its 1 in the vocal line, resulting in the pseudo-progression I–IM7–I7–I6 (“Gotta [I, 1] big planВ .В .В . at the [IM7, књ›7] right placeВ .В .В . in a [I7, књњ7] whisperВ .В .В . wanna [I6, књ›6] make out”).

E 1 I

Example 156.4. Dipping schema – D♯ – D – C♯ (center E) – ꜛ7 – ꜜ7 – ꜛ6 – IM7 – I7 – I6 (“She’s My Girl”)

I

– IM7

– I7

– IVM (“A Taste of Honey,” “Something”)

I I I I

– ↑III5 – ↑III5 – IM7 – VM

– ↑IIIo – ↓VII – I7 – ↓VII

– IVM – IVM – I6 – IVM

(“Home Sweet Home”) (“Ordinary Average Guy”) (“Tear You Apart”) (“A Natural Woman”)

– ↑III5 – ↓VII – II5 (“Lay Lady Lay”) – ↑VII – ↓VII – IVM (“Everybody Is a Star”) – IVM (“Her Majesty”) ↑VIm – ↑VI2 – I7 I – VM – ↓III5 – IVM (“Let It Grow”) I I

Many other progressions can project the dip. I–VM–↓VII–IVM, which will likely also project the previously cited schema, is heard in Aretha Franklin’s 1967 “(You Make Me Feel Like) A Natural Woman,” the third of VM offering књ›7 (“[I, 1] Lookin’ out [VM, књ›7] on the mornin’ rain, [↓VII, књњ7] I used to feel [IVM, књ›6] so uninspired [I]”). I–↑III5–↓VII–II5, the fifth of II5 harmonizing књ›6, is looped in Bob Dylan’s 1969 “Lay Lady Lay” (“[I, 1] Lay lady [↑III5, књ›7] lay, [↓VII, књњ7] lay across [II5, књ›6] myВ .В .В .”). Also from 1969 is the dipping I–↑VII–↓VII–IVM progression in the verses to “Everybody Is a Star” by Sly and the Family Stone (“[I, 1] Everybody is a [↑VII, књ›7] star, [↓VII, књњ7] who can rain and chase the [IVM, књ›6] dust”). An unusual ↑VIm–↑VI2–I7–IVM progression, the third and second of the ↑VI chords supporting 1 and књ›7 respectively, appears in the Beatles’ 1969 Abbey Road encore “Her Majesty”: “[↑VIm, 1] I wanna tell her that I [↑VI2, књ›7] love her a lot, but I [I7, књњ7] gotta get a belly full of [IVM, књ›6] wine.” In general, the dipping schema entails a hierarchy Page 157 →favoring the first and fourth slots—usually occupied by I and IVM—which, when looped, are normally tonic and subdominant in function. The dip sometimes will descend one more semitone to књњ6. Occasionally this motion appears within a larger progression, as it does in the verses to Eric Clapton’s 1974 “Let It Grow” (“[I, 1] Standing at the [VM, књ›7] crossroads, [↓III5, књњ7] tryin’ to read the [IVM, књ›6] signs [↓VI, књњ6]”), but more commonly this motion appears within its own four-slot loops, and since the dip typically starts with I—which usually features 5 as its chordal fifth—this descending line can often be heard as extending from 1 all the way through 5 (and thus offering a shrink within it, књ›6–ꜜ6–5). On E, the full gesture is E–D♯–D–C♯–C–B; see Example 4.15. This can be heard in five-bar I5–IM7–I7–IVM–↓VI phrases in Naked Eyes’ 1983 cover of “(There’s) Always Something There to Remind Me” (only the first part of the progression is looped, but it is enough to completed the descent to 5: “[I, 1] I walk along [IM7, књ›7] the city [I7, књњ7] streets you used to [IVM, књ›6] walk along with [↓VI, књњ6] me [I5, 5]”) and in the constantly changing four-bar phrases to Lenny Kravitz’s so-retro-it-hurts “Ain’t Over ’til It’s Over,” (1991), which is at various times I–IM7–I7–II5–IVm, I–VM–Vm–II5–IVm, and I–VM–Vm–II5–IIo (“[I, 1] So many tears I’ve cried, [IM7, књ›7] so much pain inside, [I7, књњ7] but, baby, it ain’t over ’til it’s [II5, књ›6] o- [IVm, књњ6] -ver [I5, 5]”). The longer descent from 1 all the way to 5, which overlays a dipping gesture on a shrinking gesture (књ›6–ꜜ6–5), is its own meta-schema, which we will call the drooping schema (“droop” being two letters longer—and two notes longer—than “dip”). In Kravitz’s and Naked Eyes’ droop loops, the descent is completed only by continuing into the next iteration—the 5 arriving with the same I that offers 1 for the start of the next iteration. The droop’s full descent to 5 also can appear fully within a single phrase, frequently as the beginning part of a larger progression. (This is a separate

phenomenon from the shorter, uncommon descent cited above in “Let It Grow,” which also appeared within a longer phrase but which fell only to књњ6.) There is no single, prototypical numeric version of such larger drooping progressions, but they tend to be eight bars long, with one chord per bar. In the verses of the Eagles’ cryptic 1976 “Hotel California,” a drooping effect is projected by the initial I–VM–↓VII–IVM–↓VI–↓IIIM progression, which alternates its harmonization of the descending line between chordal roots (in the bass) and chordal major thirds (in other instrumental parts) (“[I, 1] On a dark desert highway, [VM, књ›7] cool windВ .В .В . [↓VII, књњ7] warm smellВ .В .В . [IVM, књ›6] risin’ .В .В . [↓VI, књњ6] up aheadВ .В .В . [↓IIIM, 5] I sawВ .В .В .”). The Eagles’ ↓IIIM is a less common harmonizer of 5 than is V; the latter we hear as part of I–VM–↓VII–IVM–↓VI–V at the start of the choruses in David Bowie’s 1999 “Something in the Air” (“a thing to [I, 1] say. Lived [VM, књ›7] with the best times. [↓VII, књњ7] Left with the [IVM, књ›6] Page 158 →worst. [↓VI, књњ6] I’ve danced with you [V, 5] too long”). I–VM–↓III5–IVM–IVm–I5–V is used by Radiohead for the start of the verses to 1997’s “Exit Music (For a Film),” the fifth of ↓III5 as књ›7, the minor third of IVm as књњ6 (“[I, 1] Wake, from your [VM, књ›7] sleep. The [↓III5, књњ7] dryin’ of your [IVM, књ›6] te- [IVm, књњ6] -ars. To- [I5, 5] -day”). The Left Banke uses I–VM–Vm–II5–↓VI–I5 at the beginning of the verses to their 1966 “Walk Away RenГ©e,” Vm offering its third as књњ7 (“[I, 1] And when I [VM, књ›7] see the sign that [Vm, књњ7] points вЂOne [II5, књ›6] Way,’ [↓VI, књњ6] the lot we [I5, 5] used”). The song “Super Heroes” from Richard O’Brien’s 1975 The Rocky Horror Picture Show, opens with a slow, solemn drooping progression from I through ↓III+ (the result of holding the previous I’s 5 (the chordal fifth) and књњ3 (the chordal third) while shifting 1 to књ›7) through ↓III5 (shifting the књ›7 of the previous ↓III+ to књњ7) to IVM–↓VI–V: “[I, 1] I’ve done a lot. [↓III+, књ›7] God knows I’ve tried. [↓III5, књњ7] To findВ .В .В . [IVM, књ›6] I’veВ .В .В . [↓VI, књњ6] But allВ .В .В . [V, 5].” David Bowie’s earlier effort “Wild Eyed Boy from Freecloud” (1969) offers a series of I chords occupying the first four slots—an even longer series of Is than seen in previous examples—as part of the progression I–IM7–I7–I6–IVm–V (“[I, 1] Solemn faced the [IM7, књ›7] village settles [I7, књњ7] down, unde- [I6, књ›6] -tected by the [IVm, књњ6] stars. And the [V, 5] hangmanВ .В .В .”).

E – D♯ – D 1 – ꜛ7 – ꜜ7 I – IM7 – I7 I – IM7 – I7 I – VM – ↓VII I – VM – ↓VII I – VM – ↓III5 I – VM – Vm I – ↓III+ – ↓III5 I – IM7 – I7

Example 158.4. Drooping schema – C♯ – C – B (center E) – ꜛ6 – ꜜ6 – 5 – IVM – ↓VI – I5 (“Always Something There to Remind Me”) – II5 – IVm – I5 (“Ain’t Over ’til It’s Over”) – IVM – ↓VI – ↓IIIM (“Hotel California”) – IVM – ↓VI – V (“Something in the Air”) – IVM – IVm – I5 (“Exit Music”) – II5 – ↓VI – I5 (“Walk Away Renée”) – IVM – ↓VI – V (“Super Heroes”) – I6 – IVm – V (“Wild Eyed Boy from Freecloud”)

The drooping schema is an old figure in Western classical music, and its treatment in some of the preceding examples—especially “Exit Music” and “Super Heroes”—is indicative of its historical usage as a protracted, lamenting gesture. (“Exit Music” was specifically written to accompany the mournful end of Baz Luhrmann’s 1996 film Romeo + Juliet.) But the two traditions’ use of the figure differ in two significant ways. First of all, the classical

drooping figure normally appears in the bass, while the rock droop, like all rock schemas, tends to feature a bass line made up largely of chordal roots, which Page 159 →means the defining scale-degree motion is often scattered throughout the musical texture, as already seen in “Hotel California.” (And a progression of I–↑VII–↓VII–↑VI–↓VI–V is not customary.) Second of all, classical practice frequently, though not always, pairs the droop with a variation technique wherein a repeating drooping bass is heard under continuously changing upper melodies; such a variation technique is foreign to rock. In terms of functions, functional strengths, and harmonic levels, the droop is unpredictable. Drooping progressions often emphasize every other slot, meaning that 1, књњ7, and књњ6 all tend to be given more metric weight, and with the eventual motion to 5, the meta-schema can sound like a chromatically rich—and thus more aurally arresting—relative of the walking schema (which has a root motion 1–ꜜ7–ꜜ6–5), otherwise known as the baroque-era “lamento.” We have picked the name “droop” partly because the lamento’s sad associations apply fairly well to many rock deployments of this chromatic descent; in this regard, the droop is different from the walk, since the latter is typically used in more energetic progressions (hence the term “walk”). In phrasings where the droop’s final 5 comes only with the onset of the next looping phrase, the penultimate slot of the descent—ꜜ6, the final chord of the phrase—will often project a subdominant function to an ensuing tonic I. In the version that sits within a single larger phrase, the first chord is always a strong tonic I, and the string of sonorities that follows usually leads gradually to a dominant V, whether that V comes at the end of the descent (harmonizing 5) or at the end of the larger progression (beyond the end of the dip itself). Our last meta-schema is a combination of the slide and the shrink; it descends from 1 to 5 that passes over the leading tone (one slot short of the droop). See Example 4.16. On E, it is E–D–C♯–C–B; we will dub this the dropping schema. In one of its familiar forms it operates as a I–V gesture that will end a phrase (as a partial cadence) in blues-styled songs such as George Thorogood and the Destroyers’ 1977 reworking of “One Bourbon, One Scotch, One Beer.” After the lyrical refrain and an implied 1 (implied only in the sense that the 1 is not obviously articulated as the initial step in a descending motion), Thorogood fills time with a stereotypical guitar riff starting on the subtonic and dropping three semitones to 5, with the arrival of 5 heralding dominant V. Such a V is traditionally referred to as “turnaround dominant,” since the primary purpose of the chord—and of the drop itself—is to prepare the tonic I that will commence the next phrase. Since the harmony does not sound as though it is changing until the V (i.e., the V is the next sonority after I to project a strong entity effect), the I is active throughout most of the descent: I–I7–I6–I(m6)–V. We saw similar situations crop up with the dip and the droop, where I chords take up the first several slots of the schema.

– D – ꜜ7 – I7 – I7 – I7 I–IIm7 – ↓VII I – ↓III5 I – ↓III5 E 1 I I I

Example 160.4. Dropping schema – C♯ – C – B (center E) – ꜛ6 – ꜜ6 – 5 – I6 – Im6 – V (“One Bourbon, One Scotch, One Beer”) – I6 – IVm – V (“25 or 6 to 4”) – I6 – ↓VI – V (Les Misérables prologue) – IVM – IVm – V (“Fly by Night”) – IVM – ↓VI – I5 (“Ante up,” “Soul Sister, Brown Sugar”) – IVM – IVm – I5 (“For Your Love”)

I

– ↓VII – ↑VI – ↓VI – V (“Black Hole Sun”)

I7 I I I

– I7 – I7 – I7 – I7

– IVM – IVM – IVM – I6

– ↓VI – I5 (“I Saw Her Standing There”) – ↓VI – I5 (“I Am the Walrus,” “While My Guitar Gently Weeps”) – IVm – I5 (“Till There Was You,” “You Won’t See Me,” “Magical Mystery Tour”) – Im6 – I5 (“Lucy in the Sky with Diamonds,” “Dear Prudence”)

I

– I7

– I6

– ↓VI – I5 (“Lucy in the Sky with Diamonds”)

Page 160 →The five-slot dropping schema most often spans four bars, which means at least one of its chords will be shorter than the others. (The tease and the twirl are also five-slot meta-schemas that typically last four bars, but they usually loop back onto themselves, with the final I5 of one iteration serving as the initial I5 of the next. The five-slot tour is less predictable as to its phrasing.) In the I–I7–I6–IVm–V progression of Chicago’s 1970 “25 or 6 to 4,” bar-long I chords occupy the first three slots, giving way to half-bar IVm (the chordal third as књњ6) and V chords (“[I, 1] Waiting [I7, књњ7] for the break of [I6, књ›6] day [IVm, књњ6] [V, 5]”). A similar I–I7–I6–↓VI–V progression is heard in the prologue to Claude-Michel SchГ¶nberg and Herbert Kretzmer’s 1985 English version of the musical Les MisГ©rables, with the ↓VI and V each shortened to just one beat in order to accommodate an extra tonic I for the last two beats (“Tell His [I, 1] Reverence your story, let us [I7, књњ7] seeВ .В .В . you were [I6, књ›6] lodgingВ .В .В . the [↓VI, књњ6] honest [V, 5] bishop’s [I] guest”). In the opening of 1975’s “Fly by Night,” Rush harmonizes their 1 with two different chords, I and IIm7 (1 as the chordal seventh), each lasting a full bar, while their remaining slots receive only half a bar each, resulting in the progression I–IIm7–↓VII–IVM–IVm–V (“[I, 1] Why try? [II7, 1] Now why? This [↓VII, књњ7] feeling in- [IVM, књ›6] -side me says it’s [IVm, књњ6] time I was [V, 5] gone”). In 2000’s “Ante up,” M.O.P. gives equal durations to the first four slots of their dropping I–↓III5–IVM–↓VI–I5 progression (which we Page 161 →earlier identified as a kind of shortened version of the multipentascent); each of these chords is half a bar each, totaling two bars, but the final I5 lasts four times as long, making the entire riff four bars (M.O.P.’s loop is a sample from the opening of Sam and Dave’s 1969 “Soul Sister, Brown Sugar”: “[I, 1] Ante up. [↓III5, књњ7] Yap that fool. [IVM, књ›6] Ante up. Kid- [↓VI, књњ6] -nap that fool. It’s the [I5, 5] perfectВ .В .В .”). The Yardbirds wrap the drop around the four-bar loop I(5)–↓III5–IVM–IVm in the verses of their 1965 “For Your Love,” the resolving I5 serving as the initiating I for the next iteration (“[I, 1] I’ll give you [↓III5, књњ7] everything and [IVM, књ›6] more that’s for [IVm, књњ6] sure. For your [I5, 5] love”). In “Black Hole Sun” (1994) Soundgarden slithers downward using root motions the entire way as part of a larger, contorted chordal loop that is clearly meant to make the familiar meta-schema sound as unsettling as the lyrics (“In my [IM, 1] eyes, indis- [Im/књњ3, 1] -posed, in dis- [↓VII, књњ7] -guises no one [↑VI, књ›6] knows. Hides the [↓VI, књњ6] face, lies the [V, 5] snake”).

Page 188 →

Chapter 5 Transformational Effects Altering the Aurally Prior The distinctive guitar bass line in Led Zeppelin’s “Moby Dick” (1969) begins with a two-bar minorpentatonic riff on a tonic I; see Example 5.1a (rewritten with center E instead of the original D for comparison with other examples). After playing this riff four times, guitarist Jimmy Page and bassist John Paul Jones transpose the riff to IV. This new harmony not only projects a schematic effect (the blue) and a new functional effect (subdominant), it also gives the impression of altering what we just heard (the riff on I). The riff is the same, yet different. When Zeppelin’s blue schema moves to its third and final section, the instrumentalists predictably transpose the riff yet again, this time to V, although the riff’s melodic contour unravels as the large harmonic phrase comes to a cadence back to I via softening IV. At each point that we notice Zeppelin’s riff changing, we are hearing a transformational effect. Similar effects can be heard in the riffs to “I’m Not Talking” (1965) by the Yardbirds (a band that essentially morphed into Led Zeppelin) and “I Feel Fine” (1964) by the Beatles; see Examples 5.1b–c, where they are all written on center E. The Yardbirds follow the blue schema and transpose their two-bar riff up to IV; the Beatles offer only the blue schema’s cadence, starting their two-bar riff on V, then transposing it down to IV, then down to I (later, when John Lennon begins singing, the phrase is elongated into I–V–IV–I). All three British songs not only harmonically transform their individual two-bar riffs, they also melodically transform in subtle ways the same underlying American model riff found in Bobby Parker’s “Watch Your Step” (1961); see Example 5.1d (unchanged from its original center E). The similarities between all these tracks are not limited to the riffs. Except for one, each recording opens with two distinctive musical events: Parker features two brass chords, the Yardbirds feature two guitar chords, and the Beatles feature a single plucked guitar note and then its eventual feedback; Zeppelin, the odd band out, features a quick drum solo by John Bonham. There is obviouslyPage 189 → a historical influence at work here, but actually experiencing the Brits as transforming Parker’s riff requires that we be familiar with the original and that we make a mental comparison between them with our inner ear.1 If we do not make this mental comparison, then this account is all talk. Talk is not bad; it should just not be conflated with hearing, when possible. Only when we are hearing an alteration are we encountering a transformational effect. Example 189.5. Riff transformations 5.1a. Led Zeppelin, “Moby Dick,” transposed to E 5.1b. The Yardbirds, “I’m Not Talking,” transposed to E 5.1c. The Beatles, “I Feel Fine,” transposed to E 5.1d. Bobby Parker, “Watch Your Step” In these examples we can perceive transformations melodic and harmonic. The latter—represented here by the transposition of a riff from one chord to another—will naturally receive the bulk of our attention in this chapter. Still, the former melodic kind—represented by the reworking of Parker’s model riff in subsequent songs and by contour changes within individual tracks (as witnessed in “Moby Dick”)—often plays a significant role in transformational harmony, and so we will occasionally touch upon melodic makeovers as well. The riffs in Example 5.1 also reveal two dissimilar contexts for hearing transformational effects: obvious moment-to-moment alterationsPage 190 → within a single song, and esoteric comparisons between recordings by different artists in different years on different sides of the Atlantic. Despite the obvious contrast in these contexts, they both embody the same essential experience: they represent a transformation of something that is aurally prior, an alteration of a musical object that we will call a transformee. (By extension, the changed object would be a transformed, but since this word looks more like an adjective, we will not use it as a noun.) There is one other chief context in which to hear musical transformations: our auditory imagination. In such cases, we are never actually presented with the pretransformed object, the transformee. Nevertheless, the musical object in question evokes in us a sense that it is an alteration. This is precisely how the Western classical notion of a musical “ornament” works.

With the ornamental trills that pepper Little Walter’s harmonic solos in songs like “Juke” (1952) and “Thunderbird” (1955), we must use our inner ear to create a hypothetical unornamented sound: the note not trilled, just as it would be depicted in written notation with a “tr” or squiggly line over it. This untrilled note must exist somewhere, if only in our minds, for the notion of ornamentation (a kind of melodic transformation) to make any real sense. So regardless of where the transformee resides—immediately prior, years prior, or prior only in our imagination—we will call the aural effect “transformation.” Over the years, “transformation” has been used to describe music in very different ways, three of which are worth mentioning here. The most established is undoubtedly the “motivic transformation” associated with large orchestral and operative works of nineteenth-century European composers such as Franz Liszt and Richard Wagner, wherein small melodic fragments are altered over long stretches of music.2 The transposition of two-bar riffs in “Moby Dick” would be a highly simplified, abbreviated example of this kind of transformation. Another significant way the term has been used is in the “voice-leading transformations” or “transformation levels” of Schenkerian music theory, which represent what we might call a sort of linguistic grammar diagram for music.3 In a Schenkerian analysis, a musical composition is understood as growing from a hypothetical, fundamental musical structure, which, by way of certain specific procedures, is ornamented (melodically transformed) with nonchord tones, themselves being made into chord tones (harmonically transformed) on another transformation level, which then are further ornamented on yet another transformation level, and so on, until one arrives at a full piece of music.4 Little Walter’s trills work in a similar way, in that they ornament a structure that is not literally heard but only imagined, a structure that is hidden within the music at a level removed from the audible surface. The third principal use of “transformation” by musicians Page 191 →occurs in Transformational theory and its subarea neoRiemannian theory5; the word’s meaning in that context comes (mostly) from mathematics and is essentially unrelated to the work we are doing in this chapter. Even though the term “transformation” might at first seem appropriate only for describing cases of radical conversion, it is actually suitable as an umbrella term for denoting all aural effects of musical change, regardless of degree. This loose approach to “transformation” makes sense if we consider difference and sameness as musical properties to be defined only according to some degree of abstraction—so that, for instance, two objects we indeed would consider different objects in one context might very well be considered the same object in another context, as happens whenever the current theory identifies two sonorities with different letter designations (e.g., EM versus E7) but that share the same numeric designation (e.g., I), or two sonorities with different letter designations (e.g., EM and AM) but that share the same pitch-class intervals (e.g., a major triad). A transformation, which by definition relates two different objects that are the same at some degree of abstraction, can accordingly occur on any order of magnitude. In the next section we will flesh out the common kinds of harmonic transformees. But first we should further clarify what we mean by saying that a transformation involves alteration of a musical object. In this context, the word “object” (or “structure,” “instance,” or “entity”) should be taken in its broadest sense, including, and not in opposition to, “effect” (or “quality”). While we started off in this book’s introduction by dividing musical objects/structures into one camp and musical effects/qualities into another, this distinction has been gradually blurred by our theorizing the traditional harmonic objects of pitches, chords, and progressions as effects. This traffic is not one-way: we can also construe any harmonic effect to be an object. In other words, the appropriateness of the label “object” versus “effect” (or “structure” versus “quality,” etc.) depends almost entirely on our frame of mind and the circumstances of the situation. When speaking of harmonic transformational effects, we are free to include as potential transformable objects any prior harmonic thing so long as it is hearable as a transformee. This includes, most importantly, the effects of schema and tonal center, transformed examples of which will soon follow.

Harmonic Transformees When we hear a specific musical instance being transformed, whether that instance was earlier in the same song or

in some other song we have heard Page 192 →before, we will call the transformee a precedent.6 All transformations in which the original transformee is actually heard, which is usually the case, involve a precedent. When “Moby Dick” transforms its riff on I by transposing it to IV, it is transforming the precedent that is the riff on I. If we hear “Moby Dick” melodically transforming the riff of “Watch Your Step,” this is also a transformation of a precedent. Precedence may seem a perfectly obvious idea, but since we are talking specifically about transformation as an experiential effect, the transformee is whichever object is heard as prior, irrespective of which object first came into the world, which is to say that the chronology of experience is independent of, and sometimes different from, the chronology of music making. For instance, “Moby Dick” is much more famous than “Watch Your Step”; for those many listeners who hear Bobby Parker’s recording only after already knowing Led Zeppelin’s, the transformational effect will initially run backwards in history, meaning that Parker will be heard as altering Zeppelin. To be sure, such effects are usually temporary, in that by becoming aware of the earlier-recorded song we will eventually hear Zeppelin’s as the transformed version rather than Parker’s. But this reversal of the effect can require many rounds of listening, and in any event the original transformation can only fade into a memory; it cannot be undone. Such antihistorical transformational hearings are understandable and, in a certain sense, to be expected. They are a reality of experience, and in the current theory, experience is what matters most. When we hear a transformation of a more general structure, one that is not tied to any specific instance, that transformee will be referred to as a norm.7 By “norm” we do not mean something that is better or more desirable, nor necessarily something clichГ©d. Norms are simply stylistic models abstracted from many different particular concrete examples, always memorable and often representing something very common. Norms can reside at any level of style—from a single artist’s own idiolect to the conventions of the rock repertory at large (or even beyond)—so long as there multiple examples to engender a generic standard. We might say, though, that certain norms are more normal than others, based solely on their statistical prevalence. All the schemas identified in chapters 3 and 4 can operate as norms, from two-chord series like , to the meta-schemas, to the extended slot series like the saint. Most of these represent common progressions, although we noted that certain ones are memorable—are schematic—despite their relative rarity; these latter, less widespread schemas can still serve as norms so long as they are experienced as imaginary, as abstract, free from any specific musical context. (If a progression remains wedded to a particular instance in one’s memory, then it is debatable whether it should count as a schema; however,Page 193 → under transformation it is definitely not a norm but rather a precedent.) But schemas are a uniquely slippery sort of transformee, in that the stronger the transformational effect the weaker the schematic effect. In the stop-time section that ends the choruses to the Bee Gees’ “Stayin’ Alive” (1977), we get an Fm–Eв™-M–Fm–Cm7 progression that is very close to the walking schema (I–↓VII–↓VI–V) but that does not actually give the ↓VI; see Example 5.2a. The Gibb Brothers sing three-part descending lines (reduced to C–Bв™-–Aв™-–G, Aв™-–G–F–Eв™-, and F–Eв™-–C–Bв™-) that approximate all the descending lines that would constitute walking triads (on the prolonged “alive”), but the crucial књњ6 (Dв™-) is missing, having been replaced by 5 (C), transforming the schema into a I–↓VII–I–V progression. In this case, the schematic effect is strong and the transformational effect is barely noticeable. The opposite is true of the choruses to Metallica’s thrash-metal anthem “Master of Puppets” (1986), which transforms so much that our hearing the schema itself requires quite a bit of effort (and it may not even occur to us to hear a schematic and transformational effect until the progression is nearly finished); see Example 5.2b. Metallica’s I–↓VI–↓VII–I realization of the schema (on the words “Master, ” “twisting,” “Blinded,” and “Just”) becomes apparent when we pay attention to largescale metric accents and ignore the adorning sonorities closer to the harmonic surface: “[I] Master of puppets, I’m [II] pullin’ your [↓III] strings, [↓VI] twistingВ .В .В . [V] smashingВ .В .В . [IV] dreams. [↓VII] BlindedВ .В .В . [↓VI] can’tВ .В .В . [V] thing. [I] JustВ .В .В . [↓VII] I’llВ .В .В . [↓VI] scream.” As for transformations of meta-schematic norms, they depend on our hearing a change to the defining melodic line. In the fadeout of Kim Wilde’s “Kids in America” (1981), a loop of I5–↓VI–IV4–IVM projects a transformed teetering schema in the synthesizer (5–ꜛ6–ꜜ7–ꜛ6–5), with ↓VI offering књњ6 in place of the normal first књ›6 (“[I5, 5]

We’re the kids, [↓VI, књњ6] we’re the kids, [IV4, књњ7] we’re the kids in A- [IVM, књ›6] -merica [I5, 5]”). In the Rivieras “California Sun” (1964), a soaring schema (1–♯1–2) is set up during the cadential refrain, only to quit before the final step, instead moving back down to center (creating 1–♯1–1); the resulting king progression (I–↑VI–IV–V–I), in this light, is probably also a transformed normal steady progression (I–↑VI–II–V–I), because had the aborted soar fulfilled its potential, the resolving 2 likely would have projected itself as root, and with it a steady effect: “Well, they’re [I, 1] out here a-havin’ [↑VIM, в™Ї1] fun in that [IVM, 1] warm Cali- [V] -fornia sun [I].” A base is a basic, relatively simple transformee that undergoes some sort of complication, and it is also often—though not necessarily—a precedent or norm. Tom Cochrane’s 1991 “Life Is a Highway” uses a simple IV–I–V progression for its verses (“[IV] Life’s like a road that you travel onВ .В .В . [I] one day hereВ .В .В . Some- [V] -times you bend”) which is ornamented in the choruses Page 194 →by significant scalar runs and two smaller IV–I–V phrases embedded within the space of the long V (“[IV] Life is a highway. I wanna [I] ride it [IV] all [I] night [V] long [IV] [I] [V]”). In “Love Me Two Times” (1967), the Doors project a blue schema that gets creative in its cadential third part by erasing the basic V–I cadence and replacing it with a long-winded ↓VII–↓VI–↓III–↓VII–↓VI–V–I progression (D7–C7–GM–D7–C7–B7–E7(в™Ї9)), giving the effect of a temporary change of tonal center to the root of ↓III (from center E to G, in which case the weird cadential progression starts as V–IV–I on G: “Love me two times, [D7] girlВ .В .В . once just for today. [C7] [GM] Love me two [D7] times. [C7] I’m [B7] goin’ a- [E7(в™Ї9)] -way”); the lyrical theme of seeking extra “love” is mirrored by the extra time and energy put into jazzing up the basic blue. Although most bases are also either precedents or norms, some need not be either. These exceptions are mainly limited to two kinds: conventional “ornaments” such as the trills in Little Walter’s harmonic solos, and scalar embellishments. Minor pentatonic scales are regularly embellished; the main riff to Cream’s 1967 “Sunshine of Your Love” features a chromatic note, Aв™-(a sort of in-tune blue note в™-5), between the fourth and third D minor pentatonic scale degrees (D-D-C-D-A-Aв™--G-D-F-D). This same в™-5 is heard as Eв™-in the context of A minor pentatonic in the lead guitar descents of Rick Derringer’s 1973 “Rock and Roll Hoochie Koo”: (A–A–A–G–E–Eв™-–D–C–A). All chromatic scalar effects, whether in a pentatonic or diatonic context, can be understood as transformations of an underlying base scale (although we have noted that chromaticism can additionally be heard as departing from a scale, which Page 195 →technically is not transformational). Trill-like ornaments and scalar embellishments can also transform precedents, but they always transform a base. Example 194.5. Transformation versus schema 5.2a. “Stayin’ Alive,” vocal refrain 5.2b. “Master of Puppets,” chorus “MasterВ .В .В . twistingВ .В .В . BlindedВ .В .В . JustВ .В .В .” surface level: I II ↓III ↓VI V IV ↓VII ↓VI V I ↓VII ↓VI middle level: I : I

↓III ↓VI ↓VI

IV ↓VII ↓VII

VI I

↓VI

Our last two kinds of transformees both operate on a notion of completeness. A whole is a complete object that undergoes removal of one or more of its parts. The most common way this occurs is via a transformation of a complete precedent or complete norm, or both. In “Mannish Boy” (1955), Muddy Waters loops a major /minor pentatonic riff similar to that featured in his earlier “(I’m Your) Hoochie Coochie Man” (1954).8 The “Mannish Boy” riff itself can be heard as melodically transformed, but it is the harmonic content that is relevant here: in “Hoochie Coochie Man,” the riff is featured on I in the verses (“[I] The gypsy woman told my mother”) before giving way to the second and third parts of a blue schema in the chorus (“but you know I’m here [IV] . . . [I] . . . I’m the [V] hoochie coochie man [IV] . . . [I]); but in “Mannish Boy,” the riff never leaves the catatonic-functioning I, and in this withholding of the rest of the blue schema we can hear a transformation of a precedent (the earlier track), a norm (the blue schema), and a whole (both the precedent and the norm). This process of removing elements from a complete structure can

naturally be run in reverse, meaning that we can generate a whole by filling in an incomplete structure—a structure representing another kind of transformee that we will call a fragment. While the word “fragment” often connotes a small chunk of something, in our hands it will cover all degrees of incompleteness. Completion of a fragment is absolutely a standard effect of the repertory; however, in every one of these cases, a fragment is also a precedent. This makes sense, since it is difficult (or impossible) to envision an imaginary harmonic object that is both independent of a specific musical instance and yet also somehow inherently incomplete. In other words, only when we hear some specific harmonic fragment can it serve as a transformee for eventual completion. And yet for such a transformee to be heard as a fragment in the first place, we must already have a sense of the unfragmented whole, which is to say that every fragment already necessarily projects a transformational effect involving some sort of complete transformee, whether that be a precedent or norm, or just a whole by itself. When a whole is not also a precedent or norm, it is a purely imaginary object. Such imaginary wholes are relatively rare, and like bases, they are mainly limited to scales. In the first chorus to “Hash Pipe” (2001), Weezer offers a stepwise diatonic descending root motion starting on књњ6 and ending on tonal center, supporting the progression ↓VI–V–IV–↓III–II–I (the I arriving with the start of the ensuing section: “kick me. [↓VI] Come on and kick me [V] .В .В . [IV] I’ve got my ass wipe [↓III] .В .В . [II] I’ve got my hash pipe [I]”); the only missing numeral is ↓VII (much less likely: ↑VII). It is with the Page 196 →arrival of the tonic I that we hear the effect of incompleteness. The decision to describe this effect as “transformational” is not nearly as self-explanatory as the decisions to give transformational descriptions to the earlier examples of precedents and norms, because hearing a fragmented version of something is not necessarily the same as hearing that something changed. Still, we are free to interpret Weezer’s progression not just as ignoring but as deleting a note from the abstract whole that is a diatonic scale, in which case the effect is indeed transformational and the imagined, whole scale is a transformee. This aural interpretation fits well with the song’s second and third choruses, when the first chorus’s transformed, partial scale becomes its own transformee, a fragment/precedent. In these later choruses, Weezer delivers the missing note in the form of књњ7, supporting ↓VII, placed prominently right before the resolving tonic, thereby transforming the fragmented precedent set by the first chorus (the phrase extends two extra bars to accommodate the new harmony: “[II] I’ve got my hash pipe. [↓VII] I’ve got my hash pipe [I]”). Example 196.5. Five common kinds of transformees norm: a general prior structure, usually very common; includes all schemas and meta-schemas precedent: a particular prior structure base: a prior structure that is simpler than the transformed version; often also a norm or precedent whole: a complete prior structure; often also a norm or precedent fragment: an incomplete precedent Precedents, norms, bases, wholes, and fragments, summarized in Example 5.3, are such common types of transformees that we could not help but make repeated references to them in earlier chapters (although not always by those names). By systematically isolating and identifying these transformees, we now have a better chance at being able to describe to ourselves and to our fellow listeners precisely what transformational effects we hear. These labels are particularly useful when describing a chord or progression that serves as both a transformed object and transformee simultaneously, a very common phenomenon. For instance, many schemas—which may all operate as norms—can also be heard as embellished versions of more basic schemas; indeed, several of our extended schemas include in their very definitions some room for additional chords, so that, for example, one complicated version of a blue schema might be heard as a transformed version of a more basic blue. In this way, any given song can weave a complex web of transformational relationships,Page 197 → connecting objects within that song to themselves as well as to other real and imagined objects we as listeners bring to the conversation. One thorny linguistic-conceptual issue that plagues the term “norm” should be addressed here. A norm for

us is always a transformee, and like all transformees it is evoked only through its absence; it is the transformed objects that projects the effect of the absent norm, which has been replaced by some changed version of the original. If we get too loose with our employment of “norm,” we might think that every conceivable object could qualify as one—even the craziest distortion of a schema—since it is normal for rock to transform normal structures. Indeed, we have theorized the category of transformational effects precisely because they are so normal for the repertory. It is true that since rock is normally transformative, then every object it presents can be considered normal under that broad definition. But this really has nothing to do with our norm transformee. In the above example of a simple blue schema versus a complicated one, both versions are schematic and both are normal, yet only the simple version serves as a transformee, as a norm and a base. We would only hear this complicated blue schema as a norm if it were itself evoked as a transformee in relation to some other progression down the road. Before moving on to the transformations themselves, we must address a deep and complex issue that emerges in this context, that of the arbitrary standard. It makes perfect sense to hear cover versions in terms of one another, even when we hear a transformation running backwards in history. It also is perfectly reasonable to hear a complicated blue progression as a transformed version of a simple one. But other conceivable transformational relationships are more problematic. For example, those readers trained extensively in Western classical theory might expect a rock song to emphasize, or at least offer, a dominant VM or V7, since these sonorities are more or less central to all tonal theories of Western classical music. While VM–I and V7–I are indeed among the most common progressions in rock, IV–I is even more common, and there are many, many rock songs that do not feature any sort of dominant function, let alone a dominant V. Hence, our hearing any particular rock song as missing a dominant—perhaps as altering some whole transformee—is dubious, because the transformee in this case is not necessarily appropriate; indeed, it seems completely at odds with our stated goal in this text of building a rock theory from within the repertory itself and minimizing outside influences as much as is practical. We could frame this problem as a tension between descriptive and prescriptive music theory, harking back to the distinction we made in the introduction and chapter 1: Page 198 →is the theory addressing what we can hear, or what we should hear? If we are only interested in describing the former, then inappropriateness and arbitrariness are irrelevant; what we hear is what we hear, case closed. We would thus not take issue with a listener who hears the trip hop of Tricky as transforming the twelfth-century polyphonic organum of LГ©onin. Equally, if we think that historical and cultural knowledge should play at least some part in how we aurally interpret pieces of music, then we have opened the door to prescriptive theory. And as stated in previous chapters, every theory, by its very nature, is to some degree prescriptive, so the question then becomes how much prescription to let in. In the case of our expecting a dominant VM or V7 in every rock song, we will take the position that, since a listener very familiar with, and only with, rock-era harmony would be highly unlikely to arrive at such an expectation, it is not reasonable to expect rock song to produce a dominant VM or V7. At some less abstract level, however, this expectation could gain legitimacy, as when a particular recording artist’s personal idiolect includes so many dominant VMs and V7s that its absence will be aurally apparent; its absence projects a transformational effect in relation to an artist-defined norm. The same question of arbitrary standards crops up elsewhere, too. Since we have defined the repertory of “rock” in this book largely on the basis of its two normal sonority types—the power chord and the triad—we might wonder whether so-called chordal “extensions” (sixths, seventh, ninths, elevenths, thirteenths) are inherently transformational. It is certainly possible that a many-noted chord could be heard as transforming some more basic version, but it is not clear whether the transformee would be a power chord or triad, unless a particular song were to set up a standard sonority type, in which case the transformee would lie somewhere between an abstract norm and a concrete precedent. A related, but more pressing, issue is that of socalled chordal “alterations,” notes that do not conform to the most common version(s) of a given chordal member.9 This is a pressing problem because our sonority notations might seem to suggest such notes are indeed inherently transformational, for instance, “M7” versus “7.” (For that matter, our scale-degree and numeric notations might seem to imply something similar: natural 1 and I, 4 and IV, and 5 and V versus sharp or flat versions.) This is certainly not the intent of these notations. Our assumption of certain versions of chordal members (or scale degrees or numerals) reflects not transformation but relative commonness; these structures are

more “normal” only in the sense of being more “routine,” not in the sense of enabling a transformational effect. (Letter notation does not even imply relative commonness: Fв™Ї is not less ordinary, let alone a transformation of, F-natural.) As for the Page 199 →most normal sonorities themselves—power chords and triads—one cannot be convincingly shown to serve as a transformee for the other, at least at any general level. There are two other important specific cases of standards that are worth addressing here. The first is involves black-key/open-string pentatonic versus white-key diatonic scales, and whether the former are justifiably understood and heard as incomplete versions of the latter. In The Who’s “I’m Free” (1969), Pete Townshend’s guitar riff starts off by projecting a pentatonic effect with I–↓III–IV, but it immediately pulls us out of a pentatonic context a bar later when we hear the same gesture transposed up a major second, as II–IV–V. With this transposition comes not only another pentatonic effect (because of the roots’ minor third and major second) but also a diatonic effect,10 since the previous pentatonic step between the roots of I and ↓III now has the root of II inserted into it, retroactively redefining that first pentatonic step as a diatonic leap and turning it into a fragment to be completed by the missing diatonic scale degree 2. By comparison, Stevie Wonder’s 1973 “Higher Ground” offers a similar situation with very different results: while The Who alternate I–↓III–IV and II–IV–V, Wonder loops I–↓III–IV by itself for a while before moving briefly to the other progression, so that by the time it arrives, the initial pentatonic effect is so wellestablished that the potential transformational effect has little chance to assert itself (“[I] People [↓III] [IV] [I] [↓III] keep [IV] on [I] learnin’ .В .В . [II] World [IV] [V] [I]”). To hear the pentatonic scales in Wonder’s songs as gapped would require that we simply assume that all pentatonic scales are in general fragments of diatonics, an assumption that seems to have no real justification. While in The Who’s case there was a particular contextual motivation for hearing the transformational effect of (partial) completion, there is absolutely no reason to take for granted such incompleteness as though it were innate to pentatonicism. Indeed, hearing every pentatonic melody as diatonically incomplete makes as much sense as hearing every fully diatonic melody as incomplete “chromatic scales” (sets of all twelve pitch classes) or, conversely, as an ornamented pentatonics, which is to say it makes no sense at all.11 (Note that, in “I’m Free,” both the (pentatonic) fragment and the (diatonic) transformed fragment are mere portions of their respective scales; each portion—each fragment—is disposed to becoming a transformee in a transformation wherein the rest of the pentatonic and diatonic notes respectively are added.) The last case of transformational standards we will address is that of “blue notes.” The notion of the blue note was first developed in reference to the blues style, and over the decades it has gone through many different incarnations. The two primary meanings of “blue note” are (1) a note that creates a Page 200 →pungent dissonance when sounded with a particular chord, and (2) an out-of-tune version of a pentatonic scale degree (what we called a “blue-note effect” in chapter 1).12 Succinct examples of both these kinds of blue notes are found in the main guitar riff in the Jon Spencer Blues Explosion’s “Talk About the Blues” (1998). The riff is simply two notes, first an out-of-tune (flat) 5, then an in-tune в™-2, both of which are heard against an atmospheric catatonic I chord. The в™-2 simply creates a jarring dissonance and is an example of the first kind of blue note. The flat 5 would hardly be noteworthy as part of the I were it not for the note’s obvious intonational independence; it is an instance of the second kind of blue note. With regard to a general rule about whether blue notes necessarily involve transformation, we can differentiate between these two kinds. A dissonant note (the first kind) does not necessarily represent a transformed base—just as we said a chordal “extension” or “alteration” is not inherently transformative—unless the major or minor pentatonic scale itself is taken as the base (a dubious idea given that pentatonicism is generally interspersed with diatonicism). On the other hand, an out-of-tune note (the second kind) is transformative by nature; the description “out-of-tune” itself appropriately implies that the note is being heard against a standard that is in tune, a standard acting as a base that is transformed via complex intonation. It is only this latter, inherently transformative kind of tone that we are considering a candidate for a blue-note effect.

Kinds of Harmonic Transformation: Part I

We will now turn our attention to the transformations themselves; there are several standard kinds to identify. Transposition, one of the simplest and most common kinds, is usually not heard unless there is some reason to consider a group of pitches as cohering into some sort of especially significant entity. Thus a single pitch is usually not heard as transposed into another single pitch; a power chord does not normally project a transpositional effect when followed by a different power chord. What constitutes an “especially significant entity” is not something easily defined, but transpositions nearly always involve transformed precedents, and the most common ones include riffs and progressions (i.e., at least two chords in a row). An exception to this informal significant-entity rule is the case of registral change; a pitch (not pitch class) that leaps to a different octave can project the effect of transposition. Another exception is the case of intonation, as we just encountered in the riff from “Talk About the Blues”: the lone out-of-tune “blue note” can be heard as transposing an imaginary norm (not a precedent)—an in-tune Page 201 →scale degree 5. A specific kind of transpositional effect available (primarily though not exclusively) to listeners with absolute (perfect) pitch is transposition between recordings with parallel material built on different tonal centers. For instance, “Moby Dick” is centered on D, “I’m Not Talking” on C, “I Feel Fine” on G, and “Watch Your Step” on E. Aurally comparing one riff to another could include hearing transposition across recordings. Across these recordings, one could also hear modulation, the traditional term for a change in key but that for us will more specifically denote the effect of changing a previous musical progression’s orientation on one pitch class (a precedent) to orientation on another, with the underlying, invariant object being the orientation effect itself. (We could say the form of a centric effect includes the centric pitch class, which is susceptible to be being transformed, that is, modulated.) By theorizing modulation as a kind of transformation, we are bringing the term “transformation” into better alignment with “change” in its everyday use (a term we have been using, along with “alteration,” as a synonym for “transformation”); change can refer not just to modification (as when we “change our appearance”) but also to exchange (as when we “change our clothes”). This inclusion of “exchange” within our conception of transformation will be of great benefit when we get to chord substitution. One acutely interesting, complex version of modulation is reorientation. This sort of centric transformation usually involves a short chordal loop that projects multiple (usually two) different centric effects at different times. For instance, the Gm7–FM7 loop heard for the entirety of Lily Allen’s “Smile” (2006) begins by projecting G as the strongest center. But at some point later—the precise timing of which depends on how closely we are paying attention—we will probably reorient ourselves to center F, the only pitch class heard in both chords (“[Gm7] At first, when you I see you [FM7] cryВ .В .В .”). The numeric and schematic effects are thus I–↓VII (the normal phrasing of ), then later II–I; the functional effects are at first tonic and rogue dominant, then later upper subdominant and tonic. (This all works well with the lyrics, which summarize the narrator’s progression from being broken-hearted to laughing and smiling.) The reorientation effect always arrives with new numeric, functional, and schematic effects as well. The same reorientation occurs with the instrumental loop to Jackie Mittoo and the Soul Brothers’ “Free Soul” (1966), a rocksteady track that Lily Allen sampled to build the loop for “Smile.” Such two-chord loops featuring chords with roots spaced a major second are prime candidates for reorientation as well as centric ambiguity, a phenomenon we study examine closely in chapter 6. Modulations are pervasive in the repertory, to the point of being standardized. One of the most important modulatory conventions is the shift Page 202 →from one tonal center in one section of music to another tonal center a three semitones (a minor third) higher in another section. We will refer to such modulation as breakingout. In its standard form, breaking-out occurs when the center of a verse is changed at the start of a chorus, with the chorus bringing a general sense of heightened activity in assorted musical parameters, including pitch, loudness, rhythm, texture, timbre, and lyrics.13 (A chorus effect is, to a great extent, predicated on such an increase in intensity. This facilitates the chorus’s normal role as the dramatic focal point of a song, although the ways these increases can work are highly varied.)14 A break-out modulation can be simple or complex. In 1982’s “Down Under,” Men at Work create contrast between the verses and choruses by shifting the tonal center from B to D. Their I–↓VII–I–↓VI–↓VII progression centered on B that loops in the verses (“[Bm I] Travelling in a [AM ↓VII] fried-out combie [Bm I] [GM ↓VI] [AM ↓VII]”) is

replaced in the choruses by a looping I–V–↑VI–IV–V progression centered on D (this is a journey schema with an extra dominant V at the end: “[DM I] Do you come from a [AM V] land down under? [Bm ↑VI] [GM IV] [ [AM V]”), a change that merely involves altering the first chord of the progression: Bm to DM. (Built into this standard, simply break-out structure is a letdown upon returning to the verses, which modulate back down, but Men at Work mitigate this effect by simultaneously building in intensity between each verse in the lead vocal line, which always reaches higher than it did in previous verses.) In Foo Fighters’ intricate “Everlong” (1997), the verse’s center of B is slightly masked by the fact that first chord in each progression is DM7 (“[DM7 ↓III] Hello. I’ve [B2 I] waited here for you”); in the chorus, the center switches to D, but we must wait for its arrival as the root of a D chord, because that progression actually starts with a B5 (“[B5 ↑VI] If everything could ever [G5 IV] be this real for- [D5 I] -ever”). In other words, the initiating chords of Foo Fighters’ verse and chorus loops seem to be swapped. Despite the complication, however, the break-out is still clearly projected, as the chorus section increases in intensity with regard to loudness, melodic pitch height (in the vocal line), textural density, and timbral noise. In both “Down Under” and “Everlong,” the relationship between the tonic Is is that which is called “relative” in the North American traditional of tonal theory: Bm is the relative minor of DM, and DM is the relative major of Bm. The “relative” relationship is the most common form for the competing tonic Is in a break-out, which often exploits the special closeness of an aeolian-based minor I triad and an ionian-based major I triad a minor third above: aeolian and ionian share the same pitch-class set when separated by three semitones (e.g., B aeolian and D ionian). In essence, this is an example of reorientation within a single white-key set. This said, we should not associate break-outs Page 203 →entirely with reorientation, since break-outs can involve competing tonics still a minor third up but that are not “relative.” In “The Rubberband Man” (1976), the Spinners flirt with F major diatonic and F minor pentatonic scales throughout the verse, but the tonic I sonorities are mostly F major triads or major minor-seventh chords, both with chordal major third A-natural (“[F7 I] Hand me down my walkin’ cane”); the choruses break-out with tonic Aв™-major I triads (“Hey y’all, pre- [Aв™-M I] -pare yourself for theВ .В .В .”). The most common variation on breaking-out is a simple swapping of the centers, meaning that we move a minor third down rather than a minor third up between verse and chorus. This happens in Irene Cara’s 1983 themesong hit “FlashdanceВ .В .В . What a Feeling,” where Bв™-M I triads in the verse (“[Bв™-M I] First when there’s [FM V] nothing”) fall away in favor of Gm I triads in the chorus (“What a [Gm I] feelin’”). In 1997’s soundtrack mega-hit “My Heart Will Go On (The Love Theme from Titanic),” Celine Dion glides downward from EM I triads in the verse (“Every night in my dreams”) to Cв™Їm I triads in the chorus (“Near, far, wherever you are, I believeВ .В .В .”). In both these examples, the swapped break-out involves replacing a mostly ionian scale with a mostly aeolian one (i.e., from “relative major” to “relative minor”). This movement is usually not as convincing as the opposite motion, in that the chorus’s centric effect tends to be weaker than the verse’s (though not always), probably because the ionian I chords benefit from being led into by functionally strong lead dominants (especially V major triads) whereas the aeolian Is can only be reinforced by relatively less-strong rogue dominants, subdominants, and mediants if they are to adhere strictly to their aeolian scales. The swapped break-out is thus typically stronger when the motion does not involve the “relative” relationship, as heard in Paul Davis’s 1984 “It Takes Two to Tango,” with its DM Is in the verses (“[DM I] Life, life has a way”) and BM Is in the choruses (“It [BM I] takes two to tango”), and in Survivor’s 1985 “The Search Is Over,” with its Eв™-M Is in the verses (“[Eв™-M I] How can I convince you?”) and its CMs in the chorus (“I was livin’ [CM I] for a dream”). There are two other common kinds of variation on breaking-out. One is to offer the modulation at a spot other than between the changeover between verse and chorus. Since many songs offer a pre-chorus effect before their chorus effect, it makes sense that break-outs can occur between verses and pre-choruses, as heard in Def Leppard’s 1987 hyper-sexed “Pour Some Sugar on Me”: the verse’s Cв™Ї (“Love is a like bomb, baby, come and get it on”) shifts to the pre-choruses’ E (“Shake it up. Break the bubble”). A break-out can in fact appear between any two points in a song, as evidenced by Darlene Love’s 1964

“Stumble and Fall,” wherein the center shifts up a minor third within a few seconds of the start of the verse: “[Bв™-M I] Bet you think I’m stayin’ home Page 204 →every night. [Dв™-M I] Bet you think I can’t wait to hold you tight.” While Love’s recording certainly can be heard as a break-out, it projects outright centric ambiguity, a kind of effect we will define in chapter 6. The final common variation on breaking-out we will identify is modulation at a pitch-class interval other than the minor third. Any distance is possible. Movement by perfect fourth or fifth might be the next most common interval (both five semitones), as happens from Bв™-down to Eв™-in the Four Tops’ 1964 “Baby I Need Your Loving” (verse: “Some say it’s a sign of weakness”; chorus: “Baby, I need your lovin’. [Eв™-M I] GotВ .В .В .”) and from Bв™-up to F in Shania Twain’s 1997 “Man! I Feel like a Woman!” (verse: “I’m goin’ out tonight, I’m feelin’ all right”; chorus: “Oh, oh, oh, go totally crazy”). Break-outs by major second also occur with some frequency. The Pointer Sisters jump up from G to A in 1983’s “Jump (For My Love)” (verse: “Your eyes tell me how you want me”; chorus: “Then jump for my love”), while Aerosmith falls out of love from G down to F in 1989’s “What It Takes” (verse: “There goes my old girlfriend”; chorus: “Tell me what it takes to let you [FM I] go”). A major third is less ordinary still but can be heard in the modulation from A down to F in Carole King’s 1971 “It’s Too Late” (verse: “Stayed in bed all mornin’”; chorus: “And it’s too late, baby, now, [FM7 I] it’s too late”) and swapped, from F magically up to A, in David Bowie’s 1986 Labyrinth-soundtrack number “Magic Dance,” although with a pass through center C in the pre-chorus (verse: “I saw my baby cryin’ hard as babe could cry”; pre-chorus: “What kind of magic spell”; chorus: “Dance magic, dance magic”). (Such extra modulations are more typical of the less common break-out pitch-class intervals.) Break-out modulations by semitone and tritone, the two remaining possibilities, are extremely rare, but do happen respectively in Mick Jagger’s 1986 Stones-less single “Ruthless People,” from center B to C (verse: “They love the smell of the killin’, the flesh”; chorus: “Hey, stand up, ruthless people”), and in No Doubt’s 2003 cover of “It’s My Life,” wherein the relocation from E to Bв™-occurs at a pre-chorus, making that section project a chorus effect up until we get the true chorus immediately afterward (verse: “It’s funny how I find myself in love with you”; pre-chorus and chorus: “And I’ve asked myself вЂhow much do you [Bв™-m I] do’”).15 Often a modulation and a transposition are heard in combination, generating a special kind of transformation we will refer to as pumping-up.16 In most cases, a pump-up pulls us upward by a minor or major second; only occasionally is it by a larger interval. As the name indicates, the sound of a pump-up is one of intensification and is often saved for the latter part of a song that may otherwise suffer from the fatigue of repetition. When Genesis moves into the final iterations of the chorus to 1986’s “Invisible Touch” (“She Page 205 →seems have to have an invisible touch, yeah”), they inject a little shot of adrenaline by pumping-up the original progression, lifting us up from center F to center G and transposing all the sonorities accordingly. A song’s coda—usually a repeating chorus—is the most common place for pumping-up, although another standard location is the beginning of an instrumental break that immediately precedes the coda, as heard with George Harrison’s Spanish-inflected guitar solo in the Beatles’ “And I Love Her” (1964). Through the 1960s (and still to this day in deliberately old-fashioned arrangements), multiple pump-ups were often distributed throughout a track. In his 1965 rendition of the originally orchestral “Sleigh Bells,” Andy Williams inundates us with five pump-ups—totaling six tonal centers—within the span of a mere two minutes. Extremely rare is the pump-down, although we hear one near the end of MGMT’s 2007 “The Youth” (center F down to E) and at least five brief ones in a row (creating a complete whole-tone scale of centers) during the fadeout of Yes’s 1971 “I’ve Seen All Good People” (center E down to D, to C, to Bв™-, to Aв™-, to Gв™-). Seldom will a lone pump-up be heard in the first half of a song, although we get one in Ace Frehley’s 1978 cover of “New York Groove” after the first chorus (one-third of the way through the track) from Eв™-to E (the original 1975 recording by Hello has the pump-up in the same unusual spot). Pumping-up has been a standard technique in pop genres since the 1950s, although its use extends well back into the jazz era (e.g. we can hear it in Irving Berlin’s “Happy Holidays” as recorded by Bing Crosby for the 1942 film Holiday Inn). Yet it is by no means restricted to pop; indeed, it seems no style is immune to the

pump-up’s charms, not rhythm’n’blues (Sam and Dave’s 1967 “Soul Man”), not country (George Strait’s 1990 “Love Without End, Amen”), not contemporary R&B or hip hop (Sisqó’s 1999 “Thong Song”). Older songs even get pumped-up by covering artists: The Rolling Stones (1963) add one to Chuck Berry’s “Come On” (1961), and Barry Manilow (2008) adds one to Rick Astley’s “Never Gonna Give You Up” (1987). Unlike a harmonic schema, a break-out modulation, or even a localized transposition like those of Bobby Parker–based riffs, a pump-up is not something an instrumentalist can play without being aware of it on some level. A musician can record an entire album that is littered with schemas and break-outs and localized transpositions—or even write the songs for such an album—but may not be conscious of any of those progressions as schemas or as involving break-outs or localized transpositions. Yet when one is suddenly playing an entire section of a song at a slightly higher pitch level than before, one can hardly miss the transformational effect. Even someone using a sampler must make a physical adjustment to the machine at the appropriate time, at least during the Page 206 →recording process. (Singing a pump-up is a different story: a singer can simply feel the change without consciously noticing that the notes have all risen.) Pumping-up, then, seems tied to authorial intentions in a much more obvious way than any other kind of effect we have studied (or will study). We will have more to say about breaking-out and pumping-up in the book’s conclusion. Another common kind of harmonic transformational effect is reordering. Most often, reordering entails a simple rotation of a progression. In “Midnight Rambler” (1969), the Rolling Stones repeat several times a I–↓VII–IV progression with a doubly long IV (a normal phrasing of the schema) for the first half of the verse (“Did you [I] hear about the [↓VII] midnight [IV] rambler?”). In the verse’s second half, the progression is changed to ↓VII–IV–I with a doubly long I (which projects the same schematic effect), and with this change comes a reordering effect, specifically a rotation, meaning that we simply start and end in a different place in the schema than we did previously: “He [↓VII] don’t give a [IV] hoot of a [I] warning.” (Note that both phrasings are standard for the norm; the transformee in this case is the precedent set by the beginning of the song.) But not all reorderings are rotations. A reversing effect occurs in the Stones’ 1968 “Jigsaw Puzzle.” The verses offer a descending V–IV–II–I loop (“[V] There’s a tramp sittin’ on my [IV] doortstep [II] tryin’ to waste his [I] time”), while the choruses start with the ascending version, I–II–IV–V (counting the pickup I as part of the progression: “[I] Me, I’m waitin’ so [II] patiently [IV] lyin’ on the [V] floor”). At other times, a reordering effect involves a progression whose harmonies are rearranged in a unique pattern. This is the case with the scat choruses of Madonna’s 1999 “Beautiful Stranger,” which weakly project the Jimi schema, , even though her ↓III–↓VII–IV–↓VI–I dropping progression does not exactly line up with that normal series, the Jimi schema’s epsilon ↓VI shifting into the beta position while the other non-I chords shift one slot to the left (“[↓III] da na na na [↓VII] da ’n da ’n [IV] da da [↓VI] da da [I] da, beautiful stranger”).17 In light of the reordering effect, it is worth mentioning again that a transformational effect is something we hear. In the previous two chapters on schemas, we derived several different schemas from the same set of chords. For instance, I, IV, V, and ↑VI combined to form (the king), , , and (the journey). To the extent that each of these schemas does indeed represent its own effect, we are likely not to hear any given incarnation of one of them as a reordered version of another. In other words, assuming each one of these schemas is present in our aural memory, they will exhibit independent identities that suppress the likelihood of hearing a given progression as projecting a transformation of another schema that is a different ordering of the same chords in the actual Page 207 →progression. A I–↑VI–IV–V loop will probably not sound like a transformed ; a I–↑VI–V–IV loop will likely not give the impression of being a reordered . Of course they all do use the same chords, but this fact embodies a transformational rationalization, not a transformational effect.

Kinds of Harmonic Transformation: Part II Another major transformational effect is chordal subtraction. In the verses of the Wreckers’ “My, Oh

My” (2006), a looped ↓VII–IV–I progression is streamlined to ↓VII–I right before the chorus: “[↓VII] long before the [IV] Sonic and the [I] Walgreens. [↓VII] Not no [I] more.” This subtractive effect is heightened by the lyric “Not no more” and by the fewer number of beats given to the ↓VII–I motion: ↓VII and IV as part of ↓VII–IV–I last two beats each, whereas the ↓VII in ↓VII–I lasts only one beat. Chordal addition is the opposite effect. In Chuck Berry’s “No Particular Place to Go” (1964), the V–I blue cadences in the sung sections are adorned with softening IVs during the guitar solo (a harmony projected primarily by the bass’s 4), creating V–IV–I progressions. In a sense, all complete softening motions can project chordal addition, because the pre-tonic that is being softened (in Berry’s song, a dominant V) predicts direct resolution to tonic I; in other words, to hear V–IV–I as a softened progression is to compare it to an imaginary, unsoftened V–I motion (i.e., a base). In “No Particular Place to Go,” we actually hear the addition of IV to an earlier V–I progression, yet all cases of complete softened motions, regardless of what comes earlier in any given song, can be heard in this manner. The last major kind of harmonic transformation we will identify is the highly complex chordal substitution. Substitution is a central theme in traditional jazz theory, in which it usually describes the improvisational practice of playing a different chord from the one indicated in the lead sheet (typically comprising a staff-notated melody underneath letter-notated chords, sometimes with lyrics). A chordal substitute does not have to bear any particular relation to the original sonority, although the new chord often projects the same basic function as the original. In rock, improvisation is a much less prominent stylistic feature, and so rock chordal substitution is mostly (but of course not exclusively) compositional, decided upon ahead of time by the entire ensemble. The quintessential substitution in jazz is the “tritone substitution,” so called because the root of the original chord is a tritone away from that of the substitute, and because the same harmonic tritone appears Page 208 →in both the original and new sonority (spelled differently, but the same pitch classes). The exemplar of this practice is в™-II7 substituting for V7, where both are major-minor seventh chords and both function as dominants. In rock, the tritone substitute is uncommon, occurring really only in jazz-rock hybrid settings such as the opening of the Casinos’ intentionally old-fashioned cover of “Then You Can Tell Me Goodbye” (1967), which we cited in chapter 1 as featuring an unusual dominant Bв™-7(в™Ї9) V7(в™Ї9) on center A; see Example 5.4a. (The Casinos add a sharp ninth to the required major-minor seventh chord, which is notated here as a true sharp ninth (Cв™Ї) and not a flat tenth (Dв™-); the chordal seventh (Aв™-) is notated as the semitonally equivalent augmented sixth (Gв™Ї).) Yet to qualify as a transformational aural effect, this substitution must give us some reason to hear it as transformed V; see Example 5.4b. The issue of the tritones is relevant only to the specific, traditional notion of tritone substitution; what matters to us now is the motivation for trying to experience в™-II as a numeric substitute for V. Since V–I and в™-II–I both represent schemas, there is no reason in the abstract to hear the latter as a norm or a base or any other type of transformee. In the particular case of the Casinos, however, we have two clear precedents: Johnny Nash’s 1964 recording of the same song, and the original 1962 recording by Don Cherry, both of which feature V–I instead в™-II–I.18 For the exactly the same reason, we will not treat rogue dominants (with књњ7) as substitutes for lead dominants (with књ›7) unless there is some clear reason to think so in some specific case; this is an especially important point to make considering the pervasive use of the term “dominant substitute” by professional music theorists to characterize any pretonic sonority that is not VM or V7 (which we already argued is under no inherent pressure to make an appearance in a rock song). Although chordal substitution is conventionally theorized as a type of harmonic transformation, as it is here as well, the two concepts on face value would appear to be antithetical. Transformation changes one object into another version of itself, while substitution removes one object and replaces it with another object. This apparent contradiction echoes our earlier discussion about treating modulation as a type of transformation. With modulation, the transformee is the precedent of a prior centric effect, of which the governing pitch class is replaced by another. In substitution, we can think of the transformee as the chord progression within which the individual chord is contained, so that, for instance, when в™-II substitutes for V, the progression of V–I transforms into в™-II–I. By some measure, the progression remains the same, in this case by numeric and functional measures. On the other hand, it is also possible to think of both the substitutional object and transformational object as one individual harmony. Given that our theory includes Page 209 →multiple kinds of

chordal identity, we have the option of identifying any and every chord in more than one way, and the distinct chordal identities of a single harmony can be used to distinguish between substitutional and transformational objects. Example 209.5. The Casinos, “Then You Can Tell Me Goodbye” 5.4a. в™-II7 as tritone substitute 5.4b. Hypothetical V7 transformee So in the song “Funkytown” (1980) by Lipps, Inc., as the tonic I major triads in the verses (“[IM] Gotta make a move to a town that’s right for me”) give way to tonic I minor minor-seventh chords in the choruses (“[Im7] Oh, won’t you take me to Funkytown?”), we can hear the first I transforming into the second I, and still also hear a major triad substituting for a minor minor-seventh chord. The chord’s intervallic structure (and thus pitch content), which contributes to the chord’s color, changes between the song’s sections, even though its numeral—the root’s diatonic position in reference to tonal center—stays the same. The exact opposite of this transformation, which is a more common phenomenon, occurs in Hall & Oates’ 1981 “I Can’t Go For That (No Can Do),” wherein the tonic minor minorseventh triads of the verse (“[Im7] Easy, ready, willing, overtime”) are contrasted with the tonic major triads in the pre-chorus (“Yeah-ah-ah [IM] I”). In these two songs, the two versions of I are simultaneously the same chords and different chords. They are different because they have dissimilar letter identities—i.e., letter effects—but they are the same chord (repeated several times) in terms of function and numeral. Thus the harmonies are replaced by substitute, transformed versions of themselves. Two points need reiteration here. First, as we stated in chapter 1, there is no Page 210 →the tonic in the current theory. The aural comparisons we are drawing between the differently colored I chords above are not predicated on an assumption that a given song should have a single, coloristically invariant tonic. It so happens that all these entities project the same numeric and functional effects; this makes them instances of the same chord from the perspective of numeral and function. But it is quite a different thing to believe in a general rule that songs, as a matter of course, offer a monochromatic, abstract tonic harmony beyond the individual centric pitch class. The second point to reiterate is that transformations are not predicated on expectations. When we first hear the transition from verse to chorus in “Funkytown” and “I Can’t Go For That,” we will likely be surprised when the color of the tonic I chords change, because we have no reason to expect it to happen; yet the transformational effect is loud and clear. In this case, it is the functional and numerical resemblance that invites us to make the aural comparison and thus to hear a change. The substitutions in “Funkytown” and “I Can’t Go For That” are quite a different phenomenon from what is traditionally indicated by the term “chordal substitution.” It thus makes sense to specify this as coloristic substitution, in contrast to the conventional sort, which we will dub numeric substitution. Coloristic substitution might at first seem like a straightforward transformational subtype, but in reality it is much more complicated than numeric. The complications arise with the concept of color itself, which, like many traditional music-theory terms, is widely used but poorly defined. “Color” can refer to a harmony’s pitch-class content, but also its pitch content, its timbral qualities, and even the relative loudness of each of its constituent parts. Thus the range of possible coloristic differences is incredibly broad. An E5 chord and an Eв™-9(-5), which do not have a single pitch class or interval in common, are obviously distinct from one another with regard to color, yet so are two EM triads played in the guitar-fret position (EBEGв™ЇBE) when, in between strumming them, we simply adjust our electronics to bring out the overtones a little more clearly. For one harmony to substitute coloristically for another, then, the change need only be barely noticeable; simple mistakes such as an instrumentalist playing a wrong note or a vocalist singing off-key can transform a chord’s color. We could go some way to dissolve a bit of this subtype’s opacity by dividing it up into its own subcategories such as pitch substitution, pitch-class substitution, timbral substitution, and loudness substitution, although we will not pursue that level of precision in this book. Instead, we will simply leave ourselves the option of defining “color” in a manner relevant to a specific situation, with the understanding that what counts as coloristic substitution in one case may not rise to that same description in another. Page 211 →Coloristic and numeric substitution are not mutually exclusive transformational types. Even though

the changes of color in “Funkytown” and “I Can’t Go For That” happen against a fixed numeral of I, this is not always the case; changes in color can happen concurrently with changes in numeral. Indeed, numeric substitution essentially necessitates a change in color, since a change in numeral is a change in root, and in most cases this means a change in the root’s pitch-class. The only possible exception would be when there is an attendant reorientation (modulation), so that the original chord and the substitute chord could potentially have the same letter designation but not be in the same scalar relation to both tonal centers. However, describing the aural effect of such a reorienting numeric change as a “chordal substitution” seems intuitively wrong, precisely because none of the notes change. Thus we will define numeric substitution, and all kinds of chordal substitution, as always entailing coloristic substitution. A typical numeric substitution like the one we encountered in “Then You Can Tell Me Goodbye” involves a change in both color and numeral, but not a change in the chord’s strongest functional effect. Yet like color, function is a manifold notion. When we listen to Limp Bizkit’s 1997 cover of “Faith” against George Michael’s 1987 original, we can hear ↓VII substituting for IV in the verses (Michael’s original: “it would be [I] nice if I could touch your body. I know not [IV] everybody has got a body like [I] you”; and Bizkit’s transformed: “it would be [I] nice if I could touch your body. I know not [↓VII] everybody has got a body like [I] me”), an alteration that augments the concomitant lyrical and stylistic modifications, all pointing to a change in the meaning of the song, namely, into hypermasculine, antigay parody. If we hear Bizkit’s ↓VII as a dominant and Michael’s IV as subdominant—or hyper pre-tonic versus hypo pretonic—then the ↓VII will project the effect of functional substitution, a change in function. Alternatively, we might hear the functions of these two chords simply as pre-tonic or pre-anchor, in which case there is no change in function and the only transformative effects would be coloristic and numeric substitutions. Just as with coloristic substitution, functional substitution is an open subtype of transformation, one that needs to be defined in every particular situation according to what a given listener hears and depending on the specific purpose of the transformational labels. In certain cases, general pre-tonic function may be the best description; in others, we may want or need to be as specific as possible, as when, for instance, citing a substitution of a rogue hyper pre-V predominant IV with a lead hyper pre-V pre-dominant в™ЇIV. This goes not only for “pre-” functions but for all functions. Temporary resolutions (e.g., “deceptive” cadences) can be heard as substituting some other numeral for tonic I, but depending on whether we Page 212 →hear the substitute (↑VI, ↓VI, IV or whatever) as a non-tonic or as simply a different kind of anchor (of which a tonic is a particular type), the effect will be either functional or numeric substitution respectively. This is all assuming we are willing to assign merely one essential functional designation for a given chord; the subtleties of functional multivalence that we cultivated in the earlier chapters exponentially complicate the categorization of functionally substitutional effects. A further complication is that numeric substitution is not exactly a subset of functional, which is not say that while a change in function normally involves a concomitant change in numeral, the latter is not a requirement for the former. (However, functional and numeric substitution each require coloristic.) At the start of each verse in Hank Williams’ “I’m So Lonesome I Could Cry” (1949), an EM I triad gives way to E9 I chord, and with this coloristic substitution comes a functional one as well (“[EM I] Hear that lonesome whippoorwill. He sounds too blue to [E9 I] fly. The [AM IV] midnightВ .В .В .”). The tonic quality of the initial sonority is replaced by the second I’s prediction of resolution to the upcoming subdominant IV; we have no alteration in numeral but a clear alteration of function from tonic to gamma (hyper pre-subdominant), a common occurrence in early rock music. While the distinction between functional and numeric substitution is highly flexible, there are in fact limits to the overlap, which is to say that there is a significant number of cases that are clearly on one side or the other. In the earlier-cited “California Sun” by the Rivieras, because of the transformation of the meta-schematic soar 1–♯1–2 to the non-schematic 1–♯1–1, the harmonizing numeric series of I–↑VI–IV–V (the king) can project a transformed I–↑VI–II–V (the steady), with (likely) predominant II substituting for pre-dominant IV. Without knowing what other notes the hypothetical II would have included in this song, and thus possibly being able to distinguish functionally between the II and the IV along the lines of some specific anticipated voice-leading motions, we can say at most this is a coloristic and numeric

substitution. On the other end of the spectrum are functional substitutions that are clearly not merely numeric (or not numeric at all). In the verses of Beck’s “Lost Cause” (2002), a repeating IV–I–V phrase makes a left turn toward ↑VI, with this newly anchoring, quasi-tonic ↑VI taking over the position previously occupied by subdominant IV (“[IV] Your sorry [I] eyes [V] [IV].В .В . they make it [I] hard [V] [↑VI] to leave you alone”). This is no measly substitution of numeral; the functional effect has unquestionably been altered. While we could always create another functional category to subsume any two other functions—in this case by fashioning the incredibly general function “non-tonic” to cover both the ↑VI and the IV—the term Page 213 →“numeric substitution” is simply a poor description of the ↑VI’s sound. This is a clear example of substitution of function. We will posit one more subtype of substitution: hierarchical. This transformation, the most drastic of our four substitutions, we already encountered in its simplest form in “I’m So Lonesome I Could Cry”: the superordinate EM I transforms into the subordinate E9 I. More often, a hierarchical substitution entails a concomitant change in numeral. In the verses to Black Sabbath’s 1970 cover of “Warning” (1970), we hear a blue schematic effect that cadences not with but with the pentatonic , a phrase with a completely different hierarchy (“I was [↓III] warned about you, baby, but my [IV] feelings were a little bit too [I] strong”). While the normal progression features a strong dominant V softened by a passing subdominant IV en route to tonic I, Sabbath’s cadence starts with a ↓III that is a pre-subdominant to subdominant IV, meaning that Sabbath’s cadence is a functional chain of which the deeper motion is IV–I, not V–I. When compared with the normal, imagined dominant V, Sabbath’s pre-subdominant ↓III is a coloristic, numeric, functional, and, most strikingly, hierarchical substitute. It is subordinate to the IV, rather than the other way around (as in the V–IV–I cadence). The IV’s hierarchical effect is thus also affected, since it is now an anchor to ↓III rather than a post-anchor to V; rather than the IV ornamenting the V, the ↓III ornaments the IV. It is certainly easy to hear the ↓III substitution for V as a wholesale replacement rather than a transformation between two versions of the same chord; nevertheless, we can consider this a transformational effect if we identify the chord in terms of its position within the harmonic phrase, which is to say that the norm that ordinarily starts the blue cadence undergoes a change in its color, numeral, function, and hierarchical position. (This argument entails the notion of positional identity, and thus a harmonic positional effect.) These four types of chordal substitution represent not only four different subtypes of transformational effects but also, generally speaking, four different transformational degrees, with coloristic generally being the weakest effect, numeric ordinarily being stronger, functional usually stronger still, and hierarchical often the strongest. As we have already seen, however, these four substitutions do not nest neatly inside one another. Furthermore, certain transformational effects are not clearly substitutional versus additional/subtractive; they seemingly project all three effects simultaneously. In “Why Didn’t You Call Me” (1999), Macy Gray’s blue schema offers a cadence of II–IV–I (“[II] we had such a good time, hey, [IV] why didn’t you call me? [I]”), the II being a major triad that might be heard as a strong, hyper pre-V to the dominant V that never arrives (grouped with the preceding I, this meta-schematic I5–IIM–IV–I progression also projects a slouching effect). The II thus can Page 214 →be a coloristic and numeric—and possibly functional and hierarchical—substitutive for V, but it can also sound like a pre-dominant addition to an imagined, normal blue cadence from which the V has been subtracted. The latter hearing is aligned with the conventional way of thinking about such progressions, which is that any chord may be replaced by its own V, in this case, II (AM) being V of V (DM). In this relatively short chapter, we have investigated the widespread transformational effects of transposition, modulation, reorientation, breaking-out, pumping-up, reordering, rotation, reversal, subtraction, addition, and substitution. These transformations represent a mix of centric, chordal, and progression effects, evoking a range of other real and imaginary transformees: precedents, norms, bases, wholes, and fragments. We also touched upon the fundamental issue of deciding whether we wish to enforce any limits on transformational distance. Do we embrace the descriptive ideal of all possible hearings being equally valid, or do we incorporate more prescriptive measures and allow ourselves the freedom to criticize hearings we deem exceedingly idiosyncratic or too

dependent on nonrock music? We took the latter stance with regard to the absence of a dominant VM or V7, to extended and altered chords, to pentatonic and diatonic scales as alterations of each other, and to blue notes, but our generic answer to the broader question was to decide such matters more or less matters on a case-by-case basis. Things will only get messier as we proceed through the final chapter, which deals with the most complex of all harmonic effects: ambiguity.

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Chapter 6 Ambiguous Effects Disambiguating Ambiguity The famous figure in Example 6.1 can be interpreted as a duck facing left or as a rabbit facing right. An additional interpretation is the duckrabbit, the higher-order combination (for want of a better term) of the first two interpretations. Describing what the duckrabbit actually looks like is no simple task, because our perception of the rabbit seems to preclude our simultaneous perception of the duck, and vice versa. Yet the duckrabbit is palpably real, a case of visual ambiguity.1 A similar kind of ambiguity exists in music. Ambiguity is an especially favorite discussion topic among rock musicians and music lovers, although these discussions usually concentrate on ambiguous lyrics, on the difficulty we face in figuring out exactly what, if anything, a song’s text means. (For the widespread tradition of writing incomprehensible lyrics, we can thank Bob Dylan, who paved the way with nonsense songs like 1965’s “Subterranean Homesick Blues.”) Rock music can also be ambiguous with regard to its harmony, but we will need to spend a fair amount of time exploring exactly what “ambiguous harmony” might possibly entail before exploring the nitty-gritty of its workings. “Ambiguous” literally means “uncertain” or “having multiple meanings.” (Technically “ambi” means “both,” but it usually understood in this context as “two or more.”) “Uncertain harmony” would probably describe chords that do not project obvious schematic, functional, letter, scalar, numeric, root, or even entity effects. We could distinguish this phenomenon as vague harmony. Harmonic vagueness is surely an effect of the verses to Steely Dan’s “Babylon Sisters” (1980), which seem to drift aimlessly in a wash of unpredictable progressions and ever-resolving (i.e., never-resolving) dissonances, all without a clear sense of tonal center.2 Steely Dan also avoid using a single standard scale for any length of time, which contributes to the confusion. In other situations, however, it is strict allegiance to a single scale that is considered Page 216 →by musicians to be a primary marker of ambiguity. This kind of ambiguity is often referred to as “modality.” Example 216.6. Duck-rabbit The term “modality” carries so many denotations and connotations that it can be difficult to know what the word means in any given setting. “Modal” can simply indicate the presence of a white-key (as we labeled them in chapter 1) diatonic “church mode” or “jazz mode,” although popular-music scholars frequently save “modal” for addressing only some of these modes, namely, those that contain the subtonic (књњ7) instead of the leading tone (књ›7): dorian, phrygian, mixolydian, aeolian (or natural minor), and locrian.3 (By this criterion, we might call these the “rogue modes,” because their subtonic supports rogue dominants but not lead dominants.) This kind of “modality” is often distinguished from “tonality,” the latter defined as a characteristic of music that makes extensive use of lead functions, which lend the progressions a great deal of forward momentum. “Modal harmony,” in contrast, exclusively features rogue, hypo, or medial functions, which, all other musical factors being equal, tend to be weaker than lead functions in their propulsion toward tonic resolution. These relatively weaker progressions can, so the argument goes, be thought of as another form of vague harmony and thus another form of “ambiguous harmony.” In the memorable saxophone introduction and verses to George Michael’s “Careless Whisper” (1984), the aeolian scale is used exclusively, and even though we get a prominent rogue dominant Vm7 at the end of phrases (“the [predominant ↓VIM7] careless whispers [rogue dominant Vm7] of a good friend [tonic Im]”), Michael’s avoidance of the leading tone helps maintain the aural smoothness of this “modal” song, and makes it, in a limited sense, “harmonically ambiguous.”

Since relatively weak hypo functions are traditionally defined according to 4 instead of our књњ6 or књ›6, it is not surprising that another kind of use of Page 217 →“modal” as a code word for “harmonically ambiguous” occurs in accounts of progressions with descending perfect fourths and ascending perfect fifths in the root-bass line (e.g., ↓VII–IV–I). Such falling-fourths progressions, which frequently are hypo chains (but only if we hear a chordal third in the “pre-” chords: e.g., књњ6 or књ›6 in IV, and 2 in ↓VII), often have less forward momentum—and hence are more vague, more “ambiguous”—than the progressions with descending fifths and ascending fourths root-bass motions that typify so-called “tonal” music (with its emphasis on lead-hyper progressions such as IIM–VM–I). This brand of vagueness might be heard in relation to the aeolian I–↓III–↓VII–IV power-chord guitar riff (the normal phrasing of ) that opens Kiss’s 1976 “Calling Dr. Love.” And since the falling fourths form a mirror-image of the falling fifths, the former are occasionally labeled “modal” to contrast with the latter “tonal” progressions.4 Thus when a series such as is called “modal,” there is frequently an additional implication that the progression is “ambiguous.” (In truth, falling-fourths progressions are indeed prone to ambiguity, but not because of their supposed “modality”; we will explore this point toward the end of the chapter.) We should note that such “ambiguous” falling-fourths progressions do not always conform to a single scale. The ↓III–↓VII–IV–I schematic progression in the bridge of the Beatles’ 1969 “Here Comes the Sun” (“[FM ↓III] sun, [CM ↓VII] sun, [GM IV] sun, here we [DM I] come”) is a series of major triads—as opposed to Kiss’s power chords—and these triads will not all fit in any one diatonic scale.5 Of course, the roots of the progression by themselves do fit this definition of modal, and in this way the progression could be “modal” in the same way that pentatonic progressions often are pentatonic (that is, solely based on their roots). Pentatonic harmony, in fact, just like so-called modal harmony, is also conventionally understood to be inherently vague and thus ambiguous (even though the term “pentatonic,” for whatever reason, is not ordinarily used as a code word for “ambiguous” in the way that “modal” so often is). The charge of ambiguity (of the vague type) against both modality and pentatonicism is sometimes framed in terms of their being more “melodic” in nature, as compared with diatonicism, which is supposedly more “harmonic.” The melodic argument is founded on the idea that the goal-directedness of lead-hyper (i.e., “tonal”) functions is the defining characteristic of “harmony” itself, so that the term “tonal harmony” is in effect redundant, while the terms “modal harmony” and “pentatonic harmony” are essentially oxymoronic.6 From this perspective, the relative weakness or vagueness of modal and pentatonic harmony automatically disqualifies them from even counting as harmony at all. Page 218 →The above examples of harmonic vagueness paint a rather lackluster portrait of harmonic ambiguity. But what about the other sense of “ambiguous” as “having multiple meanings”? “Multivalent harmony” would probably mean a progression that suffers from the opposite problem: offering multiple strong schematic, functional, letter, numeric, root, or entity effects, or more than one assertive tonal center. Yet it is not self-evident how such multiple effects—except for multiple centers—could be well described as “ambiguous,” not because there is dearth of examples but indeed because there are so many. We have already seen several cases in the previous chapters where a single chord functions in multiple ways; chords typically project multiple functional effects. Multiplicity is also characteristic, although to a lesser extent, of root, numeric, letter, and entity effects. In complex rock textures, it is frequently difficult to differentiate all chord tones from nonchord tones, to determine which note is the root, and to ascertain the scale degree of that root (i.e., to hear precise letter effects, root effects, and numeric effects), as we noted in chapter 2 regarding the common phenomenon of chords that can be heard as both IV and II, or I and ↑VI, or ↓VI and IV, or ↓VII and V (with reference to a single tonal center). As for entity effects, it is extremely common for tones to project multiple entity effects simultaneously. This fact is the very foundation for the notion of harmonic levels; several distinct chords on different levels may be heard at any given moment. Another form of multiple, competing entity effects is known among rock and jazz musicians as the “polychord,” a harmony that is seemingly two chords in one (e.g., Aв™-7/Eв™-7) because of how the notes are often stratified in the musical texture. Polychords are a particularly common phenomenon in mashups that feature recordings that are not quite harmonic matches. (For instance, listen to the layered progressions at the end of Girl Talk’s 2010 mashup “Let It Out,”

which superimposes the pop vocals of Rihanna’s 2009 “Rude Boy” onto the hardcore guitars of Fugazi’s 1988 “Waiting Room.”) It usually makes more sense, however, to hear these sonorities as having a single root, and in any event, even if we did hear two chords simultaneously, we could understand this multiplicity of entity effects as occurring on two different harmonic levels (depending on the specifics of the song), not unlike how a dominant V maintains at a deeper level even while it is softened by a passing IV on the way to a tonic I. As for schematic effects, every schema larger than two chords will be multiply schematic in itself, in that it contains at least one two-chord schema nested within it (e.g., contains , contains , etc.), to say nothing of the many two-chord, three-chord, four-slot, and metaschemas typically heard within extended schemas. Scalar effects likewise very often intermingle, with 3, 6, and 7 moving freely between upper and lower versions, a fact Page 219 →we noted in chapter 1 while jettisoning the traditional term “key.” To boot, scales are frequently incomplete and fleeting, making it almost trivial to call a particular case of simultaneous scales with the same center “ambiguous.” It does not seem especially helpful to define a whole category of ambiguity that simply describe aspects common to almost all rock harmony, aspects that in fact informed our theorization of functional, letter, root, numeric, entity, schematic, and scalar effects in the first place. In contrast, the label “ambiguous” applies less universally, and thus less trivially, to cases of multiple tonal centers. Since a centric effect is almost kinesthetic in nature, our hearing two simultaneous centers is like facing two different directions at once, or, as with the drawing of the duckrabbit, involving a flickering or oscillating quality generated by two or more competing and mutually exclusive interpretations. This harmonic quality we will call an ambiguous effect, specifically one of centric ambiguity (or centric disorientation). In the context of centric ambiguity, a more specific, more useful sense of ambiguity of function, of schema, and of scale also emerges. If, say, a two-chord loop of E5–A5 were to project both E and A as tonal center, we would likely hear the schemas (as I–IV) and , and the functions tonicв†’pre-tonic and pre-tonicв†’tonic. These schemas and functions are not simply multiple, they are hierarchically contradictory: if the first chord is a tonic and resides at a deeper harmonic level, the same cannot also be true of the second chord. And yet when we hear both tonic effects, both sets of levels, the sum effect is one of ambiguity, specifically schematic ambiguity and functional ambiguity (in addition to centric). Likewise, if two simultaneous scalar effects were not to share centric allegiance—say E ionian and A minor pentatonic—their mutually exclusive orientations could result in an aural quality of scalar ambiguity.7 While it is useful to take the idea of hierarchical contradiction that is inherent in centric ambiguity and apply it to schematic, functional, and scalar ambiguity, it is not similarly helpful to apply it to letter, root, numeric, and entity ambiguity. The notion of hierarchical contradiction simply does not relate in any obvious way to an entity effect. Comparatively, the notion applies more readily to letter, root, and numeric effects (although their hierarchies involve only individual notes in relation to a single sonority, not multiple chords in relation to one another); however, there is no clear way to distinguish between letter, root, and numeric contradiction versus letter, root, and numeric multivalence, and so these types of ambiguity are still as general—and still as trivial in any particular musical case—as they were before. Hence, we will leave behind these other potential brands of harmonic ambiguity in the interest of the hierarchical contradiction of centric, schematic, functional, and scalar ambiguity. Page 220 →It cannot be stressed enough that the contradiction we are discussing here is experiential in nature. Ambiguity, just like but even more so than transformation, can be either an effect or a rationalization. In the latter formulation, the term “harmonically ambiguous” sometimes denotes a progression for which there is a set of conflicting interpretations posited either by a single person, in a conscious attempt to convey the progression’s contradictory aspects, or by different people who disagree with one another.8 Contradictions of this nature are not outside the scope of this book; indeed, if by “ambiguity” we mean a rationalization of conflicting interpretations, we could say the entire theoretical project here has been one of building a theory of ambiguity, of building a primarily descriptive system in which any number of mutually exclusive listening experiences may be faithfully mapped. But our topic in this chapter is the narrower, more personal definition of the word: the aural quality that arises only in our subjective experiences and under certain harmonic conditions. To be certain, rationalization in some form will necessarily play a role in every discussion of ambiguity, insofar as

the attitudes we hold toward the very notion of ambiguous harmony greatly influence where we draw the line between the ambiguous and unambiguous. (Listeners who are inclined toward hearing single tonal centers, schemas, and functions will probably hear fewer ambiguous effects than other listeners who are not so singleminded.) However, ambiguous effects depend not solely on our own subjective tendencies or interpretive choices but also greatly on what we might call the “objective realities” of the music. Identifying these objective realities, as well as some other relevant factors, is vital if we wish to articulate with precision—to ourselves and to others—why, and in which ways, certain harmonic objects sound ambiguous. In describing how ambiguous harmonic effects arise, we return to the kind of discussion we offered in chapter 2 concerning the aural criteria for distinguishing chord tones from nonchord tones. Related, but different (and many more) factors influence our hearing of centric, schematic, functional, and scalar effects, and thus too centrically ambiguous, schematically ambiguous, functionally ambiguous, and scalarly ambiguous effects. Schematic and scalar effects are the simplest to explain: they are dependent on the tonal center itself, as well as the pitch-class intervals of the chords involved. Given a certain center, every harmony in a progression can be heard numerically in relation to that 1, and if the numerals match one of the generic numeric patterns we know (i.e., a schema), then we will probably hear a schematic effect. (And we already noted that the numerals of known schemas and the numerals given in a particular song do not have to correspond exactly in order to yield a schematic effect; this mismatch can, depending on the exact circumstances, lead to Page 221 →a schematic effect combined with a transformational effect.) The stronger our sense of where the tonal center is, the stronger the potential schematic effects will be. Yet a centric effect is not a prerequisite for hearing a schema (or hearing schematic ambiguity). Even though we defined all our schemas according to scale degrees (including numerals), the pitch-class intervals represented by those scale degrees can be mapped onto the pitch-class intervals of a passage without recourse to a 1. In this way, schemas themselves can influence our hearing of tonal center, a point to which we will return shortly. When two schemas, phrased in a particular way, offer the same intervallic pattern—say, major second down, perfect fourth down, as and offer when the latter is phrased as I–↓VII–IV (examples of which appear below)—the effect can be one of schematic ambiguity. Scales work in exactly the same way. Like schemas, they are defined by a predetermined intervallic pattern hierarchically oriented to a single centric pitch class. The stronger the centric effect, and the greater the degree of alignment between a familiar scale and the pitch-class intervals of a musical passage (or some portion of a passage), the more likely we will hear a strong scalar effect. And also like schemas, scales do not require a center to be in place beforehand; thus scales themselves can likewise influence centric effects. Competing scales in fact tend to be more significant as indicators of centric ambiguity rather than of scalar ambiguity per se, which is to say that scalar ambiguity is not often a very strong effect in and of itself. By comparison with the process that results in schematic and scalar effects, the process for hearing centric and functional effects is incredibly complex and slightly mysterious. Nevertheless, we will, for the sake of discussion, treat the various musical factors involved in centric and functional hearing as taking the form of discrete, articulable streams of harmonic information that flow around us as we listen.9 We will spend the next two sections exploring just how these streams influence which centric and functional effects we hear and how strongly each of these effects is felt.

Centric and Functional Information: Part I Example 6.2 offers a list of thirteen types of information pertinent to hearing centric and functional effects, and thus too centric and functional ambiguity.10 These thirteen types additionally influence centric and functional strengths and the makeup of harmonic levels. The numbers attached to each type are meant only to facilitate discussion of that type’s role in specific musical examples. They do not denote a ranking of any kind, because such Page 222 →matters are difficult to generalize about (although we will eventually propose a rough, practical generalization). For now, we will explore each and every one of these types as they operate in particular cases to create hierarchically contradictory centric and functional effects, and sometimes centrically and functionally ambiguous effects. The most expedient way to illustrate them is to examine multiple musical passages that share

some common aspect, an invariant musical parameter that can serve as a reference point for measuring how any other musical differences contribute to differing effects. We could engineer such musical passages, as is common in music scholarship on perception and cognition, or we can find actual examples from the repertory. The former would afford the greatest precision in its findings, but the latter would be more representative of the experience of listening to actual music (since they are the actual music). There is room for both types of study, but we will forgo hypotheticals here in favor of real songs. Example 222.6. Types of centric and functional information (1) schema (correspondence) (2) meter (emphasis) (3) phrasing (emphasis) (4) repetition (emphasis) (5) texture (emphasis) (6) scale (correspondence) (7) duration (emphasis) (8) pedal (articulation) (9) arpeggiation (articulation) (10) penultima (correspondence) (11) loudness (emphasis) (12) parallel (correspondence) (13) expression (correspondence) Warren Zevon’s “Werewolves of London” (1978) and Lynyrd Skynyrd’s “Sweet Home Alabama” (1974) are excellent examples to compare, and we will spend a good deal of time engaging their similarities and dissimilarities.11 Both of these tracks offer the same basic chordal loop with the same durations: a chord on D for two beats, a chord on C for two beats, and a chord on G for four beats. Unsurprisingly, the exact note makeup of each sonority in each iteration is not always the same, but more often than not the chords are all major triads: DM–CM–GM. “Werewolves” repeats this basic progression for its entirety; “Alabama” interrupts it only twice, briefly, with the progression FM–CM/E–DM. First off, we will notice that the DM–CM–GM progression common to both songs can evoke two different three-chord schemas Page 223 →(Type 1). The first, , would make the progression into V–IV–I with a doubly long I, which is a common phrasing for this schema. The second, , would make the progression into I–↓VII–IV with a doubly long IV, which is likewise a common phrasing for that schema. The issue with these two schematic effects is that they are centered on two different pitch classes—G and D—with tonic function being projected at the end of V–IV–I and at the start of I–↓VII–IV. If we were to hear both simultaneously, we would be experiencing two contradictory sets of chordal hierarchies. In the first case, a dominant V is softened by passing subdominant IV on the way to resolution; in the second, we start in the most stable position, then move to a post-tonic ↓VII that glides into a lackadaisical subdominant IV. (There is no three-chord schema that suggests hearing center as C. While DM–CM–GM could hypothetically be II–I–V, this is not one of our schemas and is certainly not a standard progression for a three-chord loop.) It might seem backwards to say that a schema can influence our sense of tonal center, since all of our schemas—including the meta-schemas—are themselves defined by scale degrees in reference to a 1. But as we stated above, when we recognize familiar patterns in the pitch-class intervals of a song, we can then link up these intervals with those between a schema’s chordal roots, or between the notes in a meta-schema’s melodic line. This is what is meant by “correspondence” in parentheses in Example 6.2. Once we hear the schematic effect, we know where center should be, and we will thus hear the relevant pitch class projecting a centric effect (at least to some degree). Schematic effects are often very strong factors in hearing functional and centric effects, and thus too functional and centric ambiguity; indeed, the main reason we waited until this final chapter to dissect

the absolutely critical topic of centric and functional information is that we needed to spell out all our schemas—and their common transformations—first. While the main DM–CM–GM loop constitutes the entirety of “Werewolves,” there are three other brief cadential statements of FM–CM/E–DM in “Alabama” (“In Birmingham they loved a governor. [FM] Boo, [CM/E] boo, [DM] boo!”). These cadences each project a strong schematic effect of , with that schema’s characteristic књњ3–2–1 line heard in the bass-root line. In the context of this other schema, center would be D, the cadential I would be a tonic, the ↓VII would probably be a rogue dominant, and the ↓III would likely be a rogue hyper pre-dominant. Corresponding schemas are but one type of musical information at play in “Werewolves” and “Alabama.” The metric position (Type 2) of chords and individual pitch classes can assert itself in the process, with such emphasis making those chords and notes more likely to be heard as hierarchically Page 224 →superordinate to those around them. This is quite a different sort of information from schematic correspondence, and as such is indicated parenthetically as “emphasis” in Example 6.2. Metric emphasis can occur on any durational level—a beat, a bar, a four-bar phrase—so long as one event is heard in a stronger metric position relative to some other event. Metric strength in rock music is essentially the same as in all steadypulse Western music: the start of any duple rhythmic unit tends to be the strongest position, followed by the midpoint (e.g., the third beat of a standard bar), followed by quarter-points (e.g., beats two and four), and so on; triple rhythmic units likewise are strongest at the beginning, but their next strongest tends to be the last third (e.g., the third beat of a three-beat bar), followed by the second third. In the loops of “Werewolves” and “Alabama,” the most salient form of metric emphasis occurs in relation to the triads at the one-bar and twobar levels. The DM triad is metrically stronger in relation to CM (which is at the midpoint of the bar), and the DM triad is metrically stronger than GM (which is at the midpoint of the two-bar loop). As opposed to the corresponding schemas we cited above, which suggested both D and G as potential centers and DM and GM as potential tonic-functioning chords, the metric emphasis of the chordal loop clearly favors D and DM over all other possibilities. The loop, however, is not the only area where metric emphasis occurs: every articulated pitch in a track can be heard as metrically related to every other pitch. Short of presenting such a long and tedious analysis, we can summarize here that there seems to be more metric emphasis on G elsewhere in the texture of “Werewolves,” especially in the vocal refrain (which essentially repeats G throughout, even in its upward octave leap on the wolf call, “Ah, ooo!”). In “Alabama,” D is metrically stressed more than any other note, particularly in the main vocal line (most notably in the downbeat stress of “Alabama”: “[Fв™Ї] Sweet [E] home [D] A- [C] -la- [D] -bama”). Care should be taken in our pinpointing metric emphasis—and musical emphasis more generally (six of the types in Example 6.2)—as a causal force in determining hierarchical superordination, because such superordination does not necessarily translate specifically into tonic function or tonal center. In “Werewolves” and “Alabama,” if we hear (for argument’s sake) the GM triads and G roots as more emphasized than other chords and notes, these G notes might simply operate as the roots of the superordinate GM chords, which themselves might be heard as, say, subdominant IVs in reference to tonal center D. In this hearing, the DM I triads in the loop, while potentially tonics, would not project tonic effects strong enough to resolve those GM pre-tonics. Instead, the GM IVs would be anchors to the DM Is. The issue here is that metric emphasis, and musical emphasis in general, can only really Page 225 →tell us what is hierarchically superordinate at a given moment, not what is hierarchically superordinate overall (i.e., 1, which is the definition of center and a requisite for tonic function). Center and tonic are only ever specified by schemas and scales (discussed below). Another sort of emphasis, that of phrasal position (Type 3), denotes the weight inherent to the first and last events in any given harmonic or melodic phrase simply by virtue of their being first or last. (And like metric emphasis, it cannot by itself indicate whether a chord is a tonic or its root 1, merely that they are superordinate to surrounding events.) In the DM–CM–GM loop, DM (and D) and GM (and G) acquire greater hierarchical value in relation to CM (and C). Hence, phrasing is not overwhelmingly helpful here. The position of every note in every phrase in each track could be considered as well, which would lead us eventually to the slightly more useful

conclusion that G is the most phrasally emphasized note in “Werewolves,” and D is in “Alabama” (again, the vocal refrains are illustrative of this point). Repetition is another sort of emphasis (Type 4). Repetition works in two main ways, depending on the type of object being repeated. A pitch class can be repeated at any given moment, but an abstract harmony usually can be repeated only when we hear it separated by another harmony (e.g., two DM triads in a row tends to sound like one big DM triad). Since the chordal loops of “Werewolves” and “Alabama” present each abstract harmony only once, repetition, like phrasing, is not especially illuminating. Looking at the individual notes in melodic lines throughout the textures, however, we can notice that G is clearly the most repeated note in “Werewolves” and D in “Alabama” (as heard in their respective vocal refrains: “[G] Ah, [G] ooh! [G] were- [G] -wolves [G] of [G] Lon- [G] -don” versus “[D] A- [C] -la- [D] -ba- [D] -ma”). Repetition refers to the number of articulations of an event, separate from the event’s duration. Durational emphasis is its own type of information, which we will deal with momentarily. A note can be emphasized via texture (Type 5) by virtue of its being texturally unique and being removed from other things going on. In “Werewolves,” the most obvious instance of textural emphasis occurs in the chorus, on the vocal’s “Ah, ooh!,” emphasizing the high G. Something similar happens in “Alabama” during the guitar solo: Ed King wails on a sustained G high above everything else going on. Textural emphasis also includes textual (lyrical) emphasis, meaning the attention given to notes or chords that arrive at a particularly important point in the lyrics, the most important being the titular refrain. In “Werewolves,” the title is set entirely with G; in “Alabama,” the title occurs over a figure whose most stable note is D. A scale is another form of information (Type 6), but one that works not Page 226 →through emphasis. Like schemas, they work through correspondence to a structure that is oriented around a single, specific tonal center, and so they too are less useful in creating effects of harmonic function than effects of center. Yet even in this limited capacity scales are equivocal. Consider that white-key diatonic scales are traditionally theorized as being generated by the rotation of the same pitch-class set (e.g., a piano’s white keys) through every possible position. Thus, when a song prominently employs such a white-key diatonic set—as does “Werewolves” and “Alabama” with their set C, D, E, Fв™Ї, G, A, B—then that set can theoretically be oriented in seven different ways: as G ionian, A dorian, B phrygian, C lydian, D mixolydian, E aeolian, or Fв™Ї locrian. Yet this hypothetical rotation of a white-key set is more a theoretical contrivance than a musical reality. Complete, unadulterated examples of locrian are almost unheard of in the rock repertory at large, with lydian and phrygian being not far behind them. (At best, we get bits of these scales combined with other scales, in bass lines or individual melodic parts (e.g., riffs), and usually only in the esoteric styles of jazz-fusion and prog rock and in the harder styles of heavy metal, punk, and gansta rap.) The most common manifestation of any of these scales is undoubtedly the schema, which often has a phrygian flavor. The white-key scales that we get frequently, fully, and plainly in the repertory at large are ionian, dorian, mixolydian, and aeolian (Appendix C).12 Thus, it is reasonable to hear only four strong suggestions for tonal center from the one main pitch-class set in “Werewolves” and “Alabama”: G (ionian), A (dorian), D (mixolydian), and E (aeolian). As opposed to white-key diatonic scales, black-key/open-string pentatonic scales are better at indicating center because, as we discussed in previous chapters, they commonly come in only two forms: major and minor. While there is no obvious pentatonic material in “Werewolves,” there is in “Alabama.” Skynyrd’s guitar fills are sometimes pentatonic, as is much of the guitar solo section; the pentatonic set is consistently D, E, G, A, B, so that the tonal centers implicated are E and G (minor and major pentatonic respectively). (As an aside, it should be pointed out that these fills act as anacruses—or pickups—to imminent harmonic changes on the next downbeat; an anacrusis emphasizes the forthcoming event, and constitutes another form of Type 2, metric emphasis.) The only rock scales that do not have common rotational counterparts are so-called harmonic minor and melodic minor, so they really do implicate just one tonal center apiece. However, the very existence of these two scales as their own unique structures—as clearly distinguishable from aeolian and dorian—is a longstanding controversy in harmonic theory, one that we will not attempt to resolve here. Durational emphasis (Type 7) can be heard when a progression has an Page 227 →uneven harmonic pulse. (A

steady rate of harmonic change precludes any one sonority from lasting longer than others.) In our two DM–CM–GM loops, durational emphasis is placed on GM by virtue of its lasting the same amount of time as DM and CM combined. As for individual notes, G is held for longer than any other pitch class in the vocal refrain of “Werewolves.” In “Alabama,” Skynyrd gives no clear durational priority to any one pitch class in the vocal lines; on the other hand, D is held the longest in the song’s opening lead guitar part (see Example 6.3), and the high G in the guitar solo gives a sense of one long duration because its articulations are not separated (but if we were to hear them as separately attacked notes, the emphasis would be repetitive rather than durational in type). These examples of durational emphasis all are of a relative kind, known traditionally as “agogic accent.” Durational emphasis can also be of an absolute kind, but since that variety is not relative to these two tracks we will delay discussion of it. Example 227.6. Lynyrd Skynyrd, “Sweet Home Alabama” (from intro) In Example 6.3, the long Ds in the lead guitar are held over all three chords of the loop. These long tones not only emphasize D durationally, they articulate D as a pedal (Type 8). “Pedal” is an old term deriving from the use of a pipe-organ pedal (played by an organist’s foot) to sound an unchanging tone while various notes and chords are played (by the hands) on the keyboards. A pitch or pitch class is a “pedal” when it persists through at least two chords, normally starting with one chord and lasting at least until that same chord is stated again. A pedal is an example of articulation as opposed to emphasis, the difference being that the former describes the actual presentation of a particular pitch class, while the latter is a kind of weight given to a pitch class (or chord) that is already present. In the case of Ed King’s held D, the note starts as the root of DM, becomes a major ninth against CM, and then ends its tenure as the fifth of GM; this D pedal is also echoed in the second guitar part on the fourth beat of the example’s first bar (although it is not an actual pedal in that part). A pedal is a fairly literal manifestation of a passage’s harmonic levels: when we hear such a held note, its effect is one of hierarchical superordination, making everything else that happens sound like embellishment. A pedal will most often project the quality of being a chordal root, although hypothetically a pedal can operate as any part of a chord. In the “Alabama” Page 228 →opening, the D enters as the root of DM, making the CM and GM sound subordinate to that initial harmony. Ed King’s high G during his solo indicates that GM is the hierarchically superordinate harmony during that later section of the song. The most prominent pedal in “Werewolves” is a bit more disguised than these: the vocal refrain’s Gs embody not a pitch pedal but a pitch-class pedal (with octave leaps) heard across all chords, in this case the anticipated root of GM. Pedals can wield a tremendous amount of influence on our hearing centric and functional effects because they articulate a pitch class that unequivocally resides at the deepest harmonic level. A similar kind of articulation comes in the form of melodic lines that change pitch, when those lines can be interpreted as arpeggiating a particular real or imaginary chord. Arpeggiation (Type 9) appears in both “Werewolves” and “Alabama,” although in a subtle way. In “Werewolves,” the piano riff heard throughout the song features a melodic descent of B–A–G, which can be heard as arpeggiating the GM triad: the chordal third B moves to the chordal root G via a passing, decorative A. (Such an arpeggiation, when filled in with a stepwise passing motion, is called a “linear progression” in Schenkerian music theory.) The important point here is that this melodic descent, which we are interpreting as a decorated, partial arpeggiation of GM, occurs across all three chords of the loop, which places GM at the loop’s deepest harmonic level. This is despite the fact that the B is presented as a nonchord tone above DM, resolving immediately to A; the outline of GM is still clear. In “Alabama,” the same sort of thing is heard in the vocal refrain, except this time arpeggiating. The chordal third Fв™Ї (“Sweet”) moves to the chordal root D (“Alabama”) via a passing, decorative E (“home”), thus indicating DM is the deepest harmony of the three. (The D on “Alabama” is additionally decorated from below by C, while the last pitch on “-ma” is unclear: “[D] A- [C] -la [D] bama.”) Yet in Skynyrd’s guitar solo we hear an altogether different arpeggiation, this time in one of the female backing vocal lines, filling in the chordal fifth (D) and third (B) of GM with the descent D(DM)–C(CM)–B(GM). While hearing arpeggiations is real and reasonable, it would be a mistake to think that it is an entirely objective enterprise. Compared to pedals and most of the other types of information we will identify, arpeggiation requires a greater degree of aural imagination and interpretation. This is especially true

when the arpeggiation in question is filled in with a passing motion, as both examples here are.13 To summarize: We have taken stock of nine distinct types of information in “Werewolves” and “Alabama.” We hear two equally viable schemas for the main chordal loop ( on G and on D), plus on D as a cadential figure in “Alabama.” Metrically, D is the strongest in the Page 229 →loop of both tracks, although “Werewolves” does emphasize G in the vocal parts. With regard to phrasing and repetition, G is strongest in “Werewolves” and D is strongest in “Alabama.” The texture of “Werewolves” emphasizes G consistently, while the texture of “Alabama” is torn between D in the vocal refrain and G in the guitar solo. The white-key diatonic scale is not of much help in either track—D, E, G, and A are all equally viable, yet the more focused pentatonic guitar parts in “Alabama” give us a clear choice between G and E (and to boot, the latter is not really a contender, since it is ignored by every other type of information). Regarding duration, “Werewolves” emphasizes G, whereas “Alabama” splits its emphasis again on D (in the opening) and G (in the solo). Pedals and arpeggiations appear on G/GM in “Werewolves,” and on both G/GM and D/DM in “Alabama.” From all this detailed analysis, we can see fairly clearly that “Werewolves” is centered G, because G is the only pitch class supported by every type of information discussed so far. The same is not true for “Alabama”; this is a more complicated situation, with G and D both being viable. It is interesting to note that the members of Lynyrd Skynyrd themselves disagree about whether the song’s tonal center is G or D.14

Centric and Functional Information: Part II For “Alabama,” a simple tally of all centric suggestions is inadequate. In order to understand what is really going on, we will need to tease out two more aspects of the information: (1) the relative strength of the different streams, and (2) the timing of those streams. While informational strength is difficult to objectify on a large scale, it is certainly true in the case of “Alabama” (and in many other cases too) that articulation and correspondence are stronger kinds of information than is emphasis. Emphasis (including metric, phrasal, repetitive, textural, and durational) only makes certain events more prominent; it does not offer a hierarchy per se, as opposed to the articulation of pedals and arpeggiations, which actually present a particular pitch class or chord across other events. Most kinds of correspondence not only present a hierarchy for the immediate context, they specifically indicate the tonal center, which articulation cannot quite do. Correspondence thus has the potential for being the strongest kind of centric information. Yet this potential is often not fulfilled because the pitch-class intervals of a given progression can correspond to multiple scales or differently centered schemas, as we saw with the white-key diatonic scales and the progressions V–IV–I and I–↓VII–IV. (Later on, we will address three additional kinds of correspondence, none of which is center-specific like scales or schemas.) Of all the song’s harmonic Page 230 →information, the schematic ↓III–↓VII–I cadence on D, with no competition from other schemas, is probably the strongest single indication of center. Nevertheless, this progression is only ever heard twice, and it appears for the first time fairly late in the track, during the second verse (after the intro, first verse, and first chorus). Informational timing, the second issue we are to address here, is obviously an important consideration. The earlier we encounter a stream, and the more times we encounter it, the more of an impact it will likely have. Considering strength and timing together, we can make a crude but extremely useful generalization about centric information: early- and often-heard schemas, scales, pedals, and arpeggiations will commonly be the most significant factors in determining tonal center in a song. But the proof of the pudding is in the eating. If we apply this generalization to “Alabama,” it becomes clear that the song establishes D and G as center at different times. The opening pedal on D (Example 6.3) and the filled-in arpeggiation of DM in the titular vocal refrain of F♯–E–D—an arpeggiation also heard continuously throughout the verses—trumps the strongest early indications of center G, those being the few sporadic G major pentatonic fills in the guitar. (Although before the voice enters for the first time, G is perhaps just as feasible as D.) The remaining informational types we identified above (the various emphases) merely confirm that D has the strongest support for the first portion of the song; the D is compellingly confirmed later by ↓III–↓VII–I. The switch to center D comes at some point in the guitar solo, far away from the pedal intro and arpeggiating lead vocals. While having to contend with the D center that came before it, this

instrumental section is able to define the center anew, with its strong emphasis on, articulation of, and correspondence to G (through texture, pedal, arpeggiation, and a pentatonic scale). The return of the lead vocals after the solo brings us immediately back to the original D, confirmed again by ↓III–↓VII–I. Perhaps predictably, the instrumental coda, with its lack of vocals and prominent G pentatonicism, tries to shift (and perhaps succeeds in shifting) our centric orientation back to G as the track fades out. Despite some competing streams—which are to be found in every song in the repertory—“Werewolves” is straightforwardly centered on G, with its primary scalar effect being G ionian and its primary schematic effect being . “Alabama” requires more effort to crack. It seems to reorient (modulate) a few times, but not in any systematic or obvious way, and not at clear, precise moments. Rather, the centric effects are fluid, bleeding into one another as old information is replaced with new. Even when D holds the strongest centric effect, G seriously challenges it, just as the G-centered sections are seriously challenged by D, and for this reason it is reasonable to call Page 231 →“Alabama” weakly centrically ambiguous, weakly schematically ambiguous ( versus ), and weakly scalarly ambiguous (D mixolydian versus G ionian). The centric ambiguity in “Alabama” is a weak effect because we can indeed hear D and G as center simultaneously; were a single pitch class not in the lead at any given moment, we would not need to qualify the ambiguous effect as “weak,” which some listeners might argue is the case with certain passages of “Alabama.” When there is no strong profile to centric effects—i.e, when there is not one center clearly stronger than all others—then centric ambiguity will likely be generated. Skynyrd’s reorientations are related to the ambiguity, but they result from the slight yet significant changes that gradually occur in the kind, amount, and strength of information favoring D versus G. In other words, reorientation and centric ambiguity both are effects resulting from multiple centers, but in reorientation the centers are consecutive and in ambiguity the centers are concurrent. That said, the distinction is porous, and we will spend some time in the next section discussing their overlap. Now that we have given a thoughtful answer to the question of centricity (and schema and scale) in these two tracks, we may proceed to answer the simpler question of harmonic function. In “Werewolves,” every GM triad sounds like an anchor; of all the informational types we listed, the relentless B–A–G arpeggiation is probably the most salient indication of GM’s position in the hierarchy. Hearing this anchor more specifically as a tonic is no big feat, since it is already at the deepest harmonic level and there is no real centric rival to G anywhere in the song. The CM triads, by virtue of their repeated and consistent motion to GM, will project a pretonic effect; turning our attention to CM’s chordal third of књ›6, we can specifically hear upper subdominant function. The IV here is repeatedly heard as the penultima (Type 10), which is the position immediately before an anchor (especially a tonic). This special form of phrasing is one of the most important factors in hearing preanchor and pre-tonic functions; it is different from the Type 3 phrasing in that it works not through emphasis but rather correspondence, by mapping the chords onto an abstract functional chain of pre-anchorв†’anchor or even pre-tonicв†’tonic. (Penultimas are also different from the previous informational types that work through correspondence—schemas and scales—because penultimas do not necessarily specify a particular pitch class as center.) The DM triads are more complicated, as they can be heard both as pre-anchors to CM (as hypo presubdominants) and as pre-anchors to GM (as lead dominants). It is fair to say the DM chords are weakly functionally ambiguous, since their pre-subdominant and dominant roles are hierarchically contradictory. If DM is Page 232 →a pre-subdominant to CM, then the deeper progression is CM–GM (IV–I); if DM is a dominant to GM, then the CM will additionally function as passing, softening subdominant, and the deeper progression is DM–GM (V–I). As we already noted in chapter 3, often projects such functional ambiguity. Whether a particular progression is functionally ambiguous or not is principally determined by emphases of various sorts (Types 2–5, 7); emphasis is largely responsible for non-tonic functions in general. In the “Werewolves” loop, V is metrically and phrasally emphasized (Types 2 and 3) compared to IV; this weakens V’s pre-subdominant effect and strengthens its pre-tonic effect. Yet IV’s arrival immediately before the tonic reinforces its pre-tonic effect and undermines V’s, hence the ambiguity. The functional ambiguity between V and IV in “Werewolves” is not tied to equally strong centric or schematic ambiguity; it is completely independent. In fact, functional ambiguity in general is independent of other

kinds of ambiguity, and in this regard it is unique. In contrast, centric ambiguity more or less necessitates functional, scalar, and schematic; scalar necessitates centric, functional, and schematic; schematic necessitates centric, functional, and scalar. (For this reason, functional ambiguity will demand some separate, additional discussion at the end of this chapter.) In “Alabama,” the weak centric ambiguity will thus naturally accompany weak functional, scalar, and schematic ambiguity. To the extent that both D and G are heard as centers simultaneously in “Alabama,” we will also hear DM and GM simultaneously as anchors—and probably as tonics too—while projecting scalar effects of D mixolydian and G ionian concurrently. Similarly, we will hear and schematic effects on their respective centers, and the appropriate functional effects of pre-anchor and post-anchor with V, ↓VII, and IV. On top of all this, the G-based hearing of “Alabama” will exhibit the exact same kind of functional ambiguity for V and IV that we can hear in “Werewolves.” The D-based hearing of “Alabama” will most likely not provide any extra functional ambiguity, because unlike the V compared to its IV (on G), the ↓VII will not sound like a pre-tonic softened by its IV en route to tonic I DM; rather, the penultimate IV is emphasized metrically, phrasally, and durationally in comparison to the ↓VII, so the ↓VII will function merely as a pre-subdominant (and post-tonic). Our extended investigation into centric, functional, and ambiguous effects in “Werewolves” and “Alabama” has exposed various musical aspects involved in hearing centric and functional effects generally, aspects ranging from the relatively objective—e.g., pedals—to the relatively subjective—e.g., arpeggiation—to things in between—e.g., schemas, which are objective in their correspondence to pitch-class intervals but subjective because their existencePage 233 → depends on listeners’ stylistic knowledge. There are in fact three more types of information listed in Example 6.2 that we did not engage. The first of these, emphasis from loudness (Type 11), is of no relevance to “Werewolves” or “Alabama,” and so we will wait a bit to explore it. The remaining two types offer at least a hint of influence on these two tracks. A parallel (Type 12) is a similar musical instance from our aural past that informs the aural present; it is a precursor that carries with it centric, and possibly functional, baggage. A parallel can simply be something we have heard earlier in the same song (or in a previous hearing of the same song), in which case the DM–CM–GM loop itself operates as its own parallel. Our tonal interpretation of the loop at the any given moment will guide, to some degree, our tonal interpretation of the loop elsewhere. (Thus the transformational effect of reorientation is innately at odds with parallel centric information.) But a parallel can come from anywhere, even outside the song in question; in this light, our tonal hearing of “Alabama” can inform that of “Werewolves,” and vice versa. The degree of similarity required for a structure to qualify as a parallel is as flexible, and as personal, as that required to qualify as a transformational precedent; indeed, a precedent is a specific kind of parallel, a parallel that has been altered. And just like in situations of transformed precedents, the chronology of parallels is amorphous, so that a newer track (Zevon’s is from 1978) is just as likely to affect our experience of an older track (Skynyrd’s is from 1974) as the other way around. Relevant parallels to “Werewolves” and “Alabama” include, but are not limited to, the Rolling Stones’ “Stray Cat Blues” (1968), Led Zeppelin’s “Your Time Is Gonna Come” (1969), and Kid Rock’s “All Summer Long” (2008).15 The earliest of these, “Stray Cat Blues,” has more chordal variety than “Werewolves” and “Alabama,” but it does feature a prominent loop of DM–CM–GM–FM across two bars, wherein the fourth chord is stated briefly, in passing, and clearly operates as a passing ornamentation of the same basic three-chord riff (“[DM] I hear the [CM] click-clack of your [GM] feet on the stairs [FM]”). Yet with this decoration comes a significant piece of information, the pentatonic schema (GM–FM–DM), reinforcing D as center; further schematic progressions in addition to the main loop confirm center D and squelch any potential ambiguity. Zeppelin’s song, written and recorded shortly before the Stones’ track was released but still likely inspired by it thanks to personal contact between the bands, which loops DM–CM–GM across two bars for its verses and the simpler DM–GM across two bars for its choruses, also favors D, largely because of the many књњ3–1 melodic licks that, like the Stones’ ↓III–I motion, suggest a D minor pentatonic scale (“[DM] Lyin’, [CM] cheatin’, [GM] hurtin’, that’s all you seem [DM] to do”). Page 234 →But these licks by themselves are not enough to keep ambiguity completely at bay; like “Alabama,” “Your

Time” is laced with weak centric, functional, scalar, and schematic ambiguity throughout, not least because G is firmly established as center in John Paul Jones’ fifty-second organ solo preceding the start of the loop. Kid Rock’s track actually quotes the “Werewolves” piano riff for most of the track, solidifying center G for most of the track, but for two bars Zevon’s riff is replaced by the opening rhythm-guitar riff of “Alabama” (Example 6.3 minus the pedal D), right after lyrics refer to Skynyrd’s song by its title (“singin’ [DM] вЂSweet Home Ala- [CM] -bama’ all [GM] summer long”), and for that brief moment there is a whiff of center D, and with it faint, but very real, ambiguous effects. Still, Kid Rock’s textural emphasis on this parallel progression (including the textual reference to “Alabama,” but also the titular refrain of his own song) must battle not only with Zevon’s parallel progression but also Kid’s own progression from earlier in his track, so center G is never under serious threat. Our hearings of any of these songs—“Werewolves,” “Alabama,” “Stray Cat,” “Your Time,” “All Summer Long”—can potentially affect our hearings of any other one. But the magnitude of these influences is hard to summarize, and is probably so dependent on our personal experiences that any attempt at generalization would be futile. We should also note that parallels work through correspondence; in this way they are more like penultimas and less like schemas and scales, but they do not necessarily suggest a single tonal center. For instance, with “Alabama” operating as a parallel for “All Summer Long,” both of Skynyrd’s two centers of D and G would presumably inflect our hearing of Kid Rock’s loop (assuming we are hearing the parallel at all). The final type of information is expression (Type 13), or musical meaning. We will deal with expression in detail at the end of this chapter, but we must acknowledge expression here as a possible, albeit flimsy and roundabout, influence on our hearing center and function. Though never a strong or unique indicator, expression can sometimes magnify certain effects already generated by other informational types. For instance, in “Alabama, ” expression can be understood to bolster our hearing centric ambiguity throughout the track (a hearing affected by most of the other informational types) if we understand the lyrics as ambiguous in their own right. Counterbalancing the celebratory “sweet home” refrain” are Skynyrd’s three “boos” during the second ↓III–↓VII–I cadence, right after the first mention of the governor being loved in Birmingham (an obvious reference to the notorious segregationist George Wallace), as well as the line “Watergate does not bother me—does your conscience bother you?” both of which might suggest that the narrator loves his homeland despite its checkered past, just as a presumed California or D.C. Page 235 →resident might be proud of hers regardless of the moral and ethical blunders of one of her own representatives, Richard Nixon. On the other hand, Skynyrd’s relatively passionless “boos” could easily be sarcastic (or representing voices other than that of the narrator), and various other lines in the lyrics would seem to suggest pure admiration for everything having to do with the American South.16 At the very least, the song’s expression is not altogether clear, and thus reinforces the centric, schematic, scalar, and functional ambiguities we can hear in the notes. Expressive information can likewise inform our hearing of harmonic functions, although, as before, expression really can only amplify other informational types. To illustrate, we will finally turn our attention away from “Werewolves” and “Alabama” in favor of other examples. In Vanilla Fudge’s psychedelic cover of “You Keep Me Hangin’ On” (1967), we hear a four-slot loop that ends with ↓VI, which, upon repetition of the phrase, moves directly to tonic I: “[I] You really don’t [↓VII] want me. You just [V] keep me hangin’ [↓VI] on [I].” The ↓VI, as the penultima, is likely to be heard as a pre-tonic (lower subdominant). Yet ↓VI also projects the quality of a gamma (hypo pre-dominant), largely because of the parallel represented by the Supremes’ original 1966 recording of the song, in which the same ↓VI progresses to a dominant V before resolving to I (although even the Supremes’ V requires effort some effort on our part to hear the voice-leading specific to a dominant). A rogue dominant ↓VII might have worked just as well; in fact, Kim Wilde moves from ↓VI to ↓VII to I in her 1986 cover of the song. At any rate, Vanilla Fudge’s refusal to move to a dominant after ↓VI corresponds perfectly with the lyrics: we are to hang on to the chord’s pre-dominant potential, which hierarchically contradicts its function as a subdominant seeking I. This is an example of functional ambiguity in the absence of centric and schematic ambiguity; we will discuss additional such cases below. Care must be taken in making too much of expression as a type of centric and functional information. When we

write about music, it can be tempting to stretch our analytical claims to tolerate as many correspondences between expression and other harmonic effects as we can muster. This is a perfectly understandable strategy in certain situations (which we will investigate later in this chapter), but when trying to pinpoint the information truly involved in hearing centric, functional, and ambiguous effects, we should be extra cautious in attributing the emergence of these effects to the influence of expression. Expression is the most intellectual, the most conscious of all the thirteen types of information in Example 6.2, and for that reason its influence on experience is the greatest in danger of being overstated. For instance, it is fair to say that much of Morrissey’s 1994 track “Speedway” is centrically ambiguousPage 236 → between E and Cв™Ї, the choruses slightly favoring the former (“[Cв™Їm] All of the [BM] rumors keeping me [AM] grounded, I never [EM] saidВ .В .В .”) and the verses slightly favoring the latter (“So when you [Cв™Їm] slam down the hammer, [EM] can you see it in your [AM] heart? Can you delve [Gв™ЇM]”). Yet the lyrics toward the end of the song, including “In my own strange way, I’ve always been true to you,” might inhibit our acknowledgment of these otherwise obvious ambiguities, since they would seem to run counter to the presence of an “always”-present, “true” tonal center. Conversely, because Morrissey has publicly promoted an “ambiguous sexual point of view,”17 we might push ourselves to exaggerate the harmonic ambiguities for each of the song’s sections and for the song as a whole, in order to align the harmony better with the artist’s general persona. We could even go so far as to claim that hearing the song’s lyrics in the context of Morrissey’s general persona makes it seem like he is being ambiguous about his own ambiguity, and so on. This infinite series of interpretations is obviously so far from our aural experience of the harmony that it could not possibly have any real, direct consequence for hearing center, function, or harmonic ambiguity. The point here is that while musical expression can indeed color our hearings, we should not allow our interpretive imaginations to marginalize other types kinds of harmonic information simply because those types point us in a different tonal direction. Before we move to the next section, where we will cite some of the most common incarnations of centric, scalar, schematic, and functional ambiguity, we must clarify and supplement our explanation of a few of Example 6.2’s informational types. First up is loudness (Type 11), which we merely mentioned in passing because it did not apply to “Werewolves” or “Alabama.” Loudly performed chords and pitch classes will be heard, unsurprisingly, as emphasized in comparison with those softer ones, as is obvious in the introduction and verses of Stone Temple Pilots’ “Adhesive” (1996). STP’s oscillating, evenly spaced loop of AM–Cв™Їm9 (“[AM] My friend Blue he runs the showВ .В .В . [Cв™Їm9] His family trees”) suggests both chords as tonic Is, with A and Cв™Ї as equally viable centers. Cв™Ї is strongly supported by a Cв™Ї minor pentatonic vocal line (Cв™Ї aeolian overall) and schema, while A is emphasized metrically, by a schema, and through loudness: the mellow, soft Cв™Їm9 chords alternate with crashing AM triads. STP’s strong centric, functional, and schematic ambiguities also shed light more on durational emphasis (Type 7), an information type that we earlier saw in its relative form (agogic accent) but that we noted can come in an absolute form. In “Adhesive,” the slow tempo of the song, in combination with the slow harmonic pulse (every two bars), lingers on—and thus emphasizes—every individual AM and Cв™Їm9. This kind of durational emphasis can have two possible,Page 237 → mutually exclusive effects. Either it will strengthen the tonal center and chordal function that we were already hearing, or, in the face of potential centric ambiguity, it will make the current chord and chordal root sound more stable than they otherwise would, making them candidates for tonic I and tonal center respectively. The second of these scenarios applies to “Adhesive”: the fact that we hear Cв™Їm9 for 7.5 seconds each time, combined with the Cв™Ї minor pentatonic vocal line, means that Cв™Ї is going to be a major contender for center. Of course, since the two-chord loop is evenly spaced, the loud AM triads likewise receive absolute durational emphasis; yet durational emphasis also applies beyond chords to individual pitch classes, meaning that Cв™Ї is at a distinct advantage over A because of its inclusion as a chord tone in both chords (as the third of AM). C♯’s omnipresence results in both a relative and absolute forms of durational emphasis, and additionally counts as a pedal (Type 8). Our final example of this section allows us to flesh out two informational types, the first being metric emphasis (Type 2), specifically the anacrusis, which we only mentioned in passing with regard to the pentatonic guitar fills in “Alabama.” An anacrusis typically emphasizes the event—the pitch class or chord—on the next

strong beat, but an anacrusis can also operate as a syncopation, an early statement of something that would more naturally fall on the upcoming strong beat. Such syncopation tends to emphasize the early event itself and is commonly heard in conjunction with arrival of an anchoring chord, and especially a tonic I. We see this fact play out in an interesting way in Jackson Browne’s “Somebody’s Baby” (1982). Browne’s versechorus form weakly projects break-out modulation as the initial chorus sections of the song give way to the first verse. As the verse starts, we get the rising progression GM–AM–Bm, possibly a schema on B, which would in fact fit the model break-out by contrasting with the chorus’s clear center D and DM tonic Is. However, the chorus is full of syncopation and elaborate nonchord tones, so when the verse’s rising progression arrives with absolutely no such complications, we are right to be suspicious of Bm as a new tonic I. Our suspicions are validated a few beats later, when the progression continues up one more unsyncopated step to AM/Cв™Ї before resolving to an anacrusis of DM. In other words, the lack of emphasis of an anacrusis on Bm weakens the hearing of Bm as tonic I and B as center, both of which pale in comparison to the tonic DM I and center D that are emphasized by the only anacrusis in the entire harmonic phrase. The metric emphasis here is able to override both pieces of information in favor of center B: the schema and the potential break-out. The latter clearly operates as something like a schema in this case, which brings us to our last second informational type to flesh out. Even though a break-out modulation is really a transformational effect, it can Page 238 →be considered a pseudo-schematic effect for the purposes of hearing center and function, falling under Type 1, since it can lead to an expectation that a certain kind of modulation will occur, to wit, modulation from one center to another, up a minor third between verse and chorus; in “Somebody’s Baby,” we are anticipating the opposite process, a minor third (back) down from the chorus to a new center in the verse. Another pseudo-schema to include under Type 1 would be the trio of different of pentatonic-scale transpositions we encountered while discussing the multipentascent schema ; this set of standard versions can contribute to our sense of which pitch class is scale degree 1 in a centrally ambiguous song like the Kinks’ 1964 “All Day and All of the Night”: the pentatonic riff ↓VII–I–↓VII–↓III–I is heard on three different temporary 1s, but only by hearing a tonic arrival in the third and final one (under the titular refrain) can we align all three versions with the standard 1-version, 4version, and 5-version (“[↓III] I’m [IV] not con- [↓III] -tent” moving to “[IV] your [V] side [IV]” moving to “[↓VII] [I] girl, I [↓VII] want”). We will have the opportunity to further refine our sense of centric and functional information in the ensuing section, during our investigation into some of the most frequently encountered forms of centric, scalar, schematic, and functional ambiguity. As the last several pages have made perfectly plain, the factors that go into hearing centric, functional, and centrically and functionally ambiguous effects are multiple and complex. While many streams of information in any given song will ultimately be outdone by others, we should not ignore their potential influence if our goal is to gain access to, and understanding of, the manifold experiences of hearing harmony. Indeed, it is incumbent upon us to be on the lookout for even more informational types, especially timbre, since it is not yet obvious to this author how timbre might influence center and function in a manner distinct from Type 5, texture.18 A thorough understanding of the objective and subjective forces behind these aural effects is nearly as important as the effects themselves, as this understanding brings different experiential possibilities to our attention and thus helps us to expand the kinds of hearings we are able to have; in addition, understanding why we hear certain songs in certain ways helps us determine why and how our own hearings can differ from those of our fellow listeners.

Centric and Scalar Ambiguity In the next three sections we will identify some relatively common and striking manifestations of centric, scalar, schematic, and functional ambiguity. The organization of these sections will be somewhat fluid, a natural outcome Page 239 →considering that schematic and scalar ambiguity are intrinsically linked with centric contradiction; one could almost (but not quite) say that schematic and scalar ambiguity are specific forms of centric ambiguity (although, as we know, a centric effect is not a prerequisite for schematic and scalar effects). Roughly speaking, we will first spend our energies on centric and scalar ambiguity, then schematic, and then functional. In the process we will cite many different songs in quick succession (yet not quite as quick as in the schema chapters);

an appropriate pace is thus recommended to readers. Centric ambiguity is possible between any two (or more) pitch classes. Yet there are two intervallic pairings that are most common by far: a perfect fourth apart and a minor third apart. The first kind, which we will dub wide centric ambiguity, was exhibited by the weak D/G ambiguity in “Alabama.”19 The second, and much more widespread (almost omnipresent) version, occurs between centers a minor third apart, of which we saw a weak case in “Somebody’s Baby” (D and B); we will name this narrow centric ambiguity. (Note that “narrow” covers, but is not limited to, ambiguity within the traditional “relative major” and “relative minor” relationship. The interval of the minor third is the same, but “narrow” carries no requirements for scales or kinds of tonic-functioning sonorities.) The terms “wide” and “narrow” are in some sense arbitrary, because the intervals between centers can be measured in a “short” way (D to G is a perfect fourth, D to B is a minor third) and a “long” way (D to G is a perfect fifth, D to B is a major sixth). In any event, songs projecting narrow centric ambiguity do usually offer D pitches and B pitches a minor third apart, which is a smaller interval than is at all possible between D pitches and G pitches, so there is an aural reason to employ “wide” and “narrow” in this manner. Wide and narrow centric ambiguity are not always distinct phenomena. Depeche Mode’s “Enjoy the Silence” (1990) glides effortlessly across various tonal centers separated by both minor thirds and perfect fourths. In the Cm–Eв™-M–Aв™-M loop of the verses, Cm and Eв™-m both project effects of I and of tonic (with C and Eв™-as their respective centers): “[Cm] Words like violence [Eв™-m] break the silence.” In the Fm–Aв™-M–Cm–Eв™-M/Bв™-progressions of the choruses, each chord is a possible tonic I, exhibiting wide narrow ambiguity between F and Aв™-and between Cm and Bв™-, but also wide ambiguity between F and C and between Aв™-and Eв™-: “[Fm] All I ever wanted, [Aв™-M] all I ever needed is [Cm] here in my [Eв™-M/Bв™-] arms.” Ultimately, Eв™-is probably the strongest possible center in the song, with Eв™-M being arpeggiated in various vocal and instrumental lines; but to determine a single local center would seem to violate the expressive information of the lyrics, which specifically warn against the verbalization of complex experience. Page 240 →While the harmonic ambiguity in “Enjoy the Silence” is almost palpable, many other instances straddle the line between simultaneous tonal centers and sequential tonal centers, that is, between ambiguity and modulation. Consider the ending section of “The Flesh Failures (Let the Sunshine In),” the powerful finale of Galt MacDermot, James Rado, and Gerome Ragni’s hippie musical Hair (1968). The lyrics encourage us to let in not only the sunlight but also a new, brilliant center D, in place of a previous, bleak B. Each center is supported by its own tonic I triad, but the motion between them takes place entirely within the span of a single sixbar looping phrase, I–V–I on B repeatedly giving way to IV–I on D: “[Bm] Let the [Fв™Ї7] sunshine, let the [Bm] sunshine in, the [GM] sunshine [DM] in.” Competing schemas are complemented by competing interpretations of the vocal line’s descent of F♯–E–D that is heard twice across the entire six-bar progression (“[Fв™Ї] Let the sun- [E] -shine, let the sun- [D] -shine in, the [Fв™Ї] sun- [E] -shine [D] in”). This descent operates as a filled-in arpeggiation of the chordal fifth and third of Bm, but also of the chordal third and root of DM. Despite the lyrics’ clear message of hope and the extremely celebratory mood of the performance, center B is just too strong to be dismissed (or perhaps the progression is reminding us of how far away we are from universal love). Yet is this narrow centric ambiguity, or does the progression simply modulate over the course of its six bars? The problem here is that concurrent aural effects are not always so easily separable from consecutive effects, because the very notion of centricity, as we have stated before, is like facing a particular direction in space, so that hearing centric ambiguity is like oscillating between points of view. But oscillation implies a temporal order—one thing, then another—simply at a rapid pace. Just like when viewing the duckrabbit, we usually must shift between one interpretation or another when considering the tonal center of a progression, since it is often very difficult—or indeed impossible—to experience both versions simultaneously in the strictest sense. In this light, centric ambiguity is merely a fast kind of reorientation, which itself is a kind of modulation wherein the notes do not change (only our perspective changes). The question then is where to draw the line between centric simultaneity and succession, or perhaps where successive centric effects are so close together that they should be classified as a special brand of consecutive centric effect—as centric ambiguity. In

this case, the decision to claim one versus the other is best considered according to the specific circumstances of any individual progression. In the Hair finale, “centric ambiguity” does seem to be a reasonable description of the effect. The label “reorientation” actually feels a bit wishy-washy in this context, since we can split the progression into two constituent schemas, one on each center. Simple “modulation” might be a better alternative to “reorientation”Page 241 → here, were we so inclined to highlight the successive quality of B and D over their quality of simultaneity. Centric ambiguity within a single harmonic phrase is often of a narrow or wide sort. Additionally, there are two other standard distances for such phrases: a major second and a major third. The former can be heard in the Moody Blues’ “The Story in Your Eyes” (1971), the verses of which swing from center A (supported by three statements of I–IV and a dorian scale) to center G (with V–I and IV–I and an ionian scale) over the course of the verse’s eight-bar harmonic phrase: “I’ve been [Am7 I] thinkin’ ’bout our fortuneВ .В .В . deep inside us now [GM I] is still the same.” The latter occurs in the verses to America’s “Sister Golden Hair” (1975), which start with an apparent EM I that immediately progresses to a Gв™Їm I, with a noodling three-note vocal line that suggests not only E major and Gв™Ї minor pentatonic scales but a Cв™Ї minor pentatonic scale as well (the song’s intro also suggests center Cв™Ї): “Well I [EM I] tried to make it Sunday but I [Gв™Їm I] got so damned depressed.” (America’s Gв™Ї is weaker than its E, meaning the centric ambiguity between these two pitches classes itself is weak.) These two examples are typical of their respective intervallic distance between competing centers. When shifting by a major second, the tendency is to move down by major second, so that the initial I becomes a II (the Moody Blues’ Am7) and the second I is also a ↓VII (GM). When the centric interval is a major third, it is usually pushed up, with the initial I normally becoming ↓VI (America’s EM) and the second I also being a ↑III (Gв™Їm). The pentatonic scale fragments in “Sister Golden Hair” are suggestive of competing tonal centers but they are exemplary of scalar ambiguity. While it is true that any song projecting centric ambiguity will necessarily also project scalar ambiguity (because scalar ambiguity is not simply the presence of multiple scales but more specifically the presence of multiple scales with competing centers), scalarly ambiguous effects are at their most salient when the individual scalar effects are crystal clear. The clearest scales are those that are complete and that display little to no chromatic alteration or scalar mixture. Yet even the strongest cases of scalar ambiguity pale in comparison to the often intense effects of centric, schematic, and functional ambiguity. While it is certainly easy to understand a song like “The Story in Your Eyes” as swinging A dorian and G ionian, the effect of this swinging is likely going to be drowned out by its other ambiguities. More worthy of our attention than individual cases of scalar ambiguity is the conventional wisdom that certain scales are more inherently ambiguous than others. We already confronted this idea briefly at the start of this chapter, in the context of “modality,” a term we elected not to perpetuate. But there is an aspect of the conventional wisdom deserving closer scrutiny, that of Page 242 →pentatonicism supposedly having greater inherent ambiguity in comparison to diatonicism. Justification for the inherent ambiguity of black-key/open-string scales, when it is given at all, usually arrives in the form of appeals to intervallic content.20 This argument sometimes relies on the abundance of a single intervallic pattern, specifically the pentatonic-defining threesemitone interval in combination with a two-semitone interval (e.g., D–E–G or E–G–A), which we used in chapter 4 to identify several “pentatonic” schemas that feature this combination in their root motions. The idea is that when we hear such a pattern we do not know what the other notes of the pentatonic set are (what “position” the pattern occupies in the larger pentatonic set), because each one of these patterns can appear in two distinct sets: e.g., D–E–G fits in G, A, B, D, E (G major/E minor pentatonic) and also C, D, E, G, A (C major/A minor pentatonic). Yet this ambiguity in no way makes pentatonicism more inherently ambiguous relative to diatonicism. In fact, it indicates the opposite, because the same D–E–G pattern can be heard in four distinct white-key sets: G, A, B, C, D, E, Fв™Ї (G ionian, etc.); C, D, E, F, G, A, B (C ionian, etc.); F, G, A, Bв™-, C, D, E (F ionian, etc.); and D, E, Fв™Ї, G, A, B, Cв™Ї (D ionian, etc.). The interval of a tritone might seem to represent a better hypothetical argument for the relative ambiguity of pentatonicism, because a white-key set helpfully features just one tritone (a so-called “rare interval”) while a black-key/open-string set features none.21 But again, this really does not indicate pentatonicism’s greater inherent ambiguity,

because knowledge of our position in a white-key set requires at least three notes: even though the tritone appears only once, it is self-inverting, so we need at least one other tone to know whether we are hearing, say, the augmented fourth B–F in the set C, D, E, F, G, A, B (C ionian, etc.) or the diminished fifth B–Eв™Ї in the set Fв™Ї, Gв™Ї, Aв™Ї, B, Cв™Ї, Dв™Ї, E (Fв™Ї ionian, etc.). By contrast, position in a pentatonic set can sometimes be deduced from just two notes, because there is only one major third, which is not self-inverting; thus G–B together as black-key/open-string notes can only mean the set G, A, B, D, E (G major/E minor pentatonic). The same distinction holds true for all the other intervals and combinations of intervals.22 In sum, pentatonic intervals are no less revealing of their set than are diatonic intervals, and in actuality it is the white-key scale that is more ambiguous at a theoretical (inherent) level. This claim also obtains at a practical level. We have identified the six most common scales in the rock repertory as ionian, dorian, mixolydian, aeolian, minor pentatonic, and major pentatonic. When faced with the pentatonic set G, A, B, C, D, there are really only two strong options for hearing a tonal center: G (major) and E (minor). This claim is based on aural expectations arising from a familiarity with the repertory at large—familiarity with how Page 243 →such scales are most often used in actual songs. The same logic applies to the diatonic set G, A, B, C, D, E, Fв™Ї, which has four strong options for center: G (ionian), A (dorian), D (mixolydian), and E (aeolian). We are reiterating here a point we made in our earlier discussion of centric and functional information, but the point is so important that it is worth repeating. A pentatonic set’s strongest centric orientations are both absolutely and relatively fewer than those of a diatonic set: 2 of 5 pitch classes as possible center, as opposed to 4 of 7. This is not to deny important musical differences between pentatonic and diatonic scales. (One such difference is the play of dissonance, which is much freer in the former than in the latter.23) But the charges of ambiguity (as we mean it here) against pentatonicism are simply false, and are possibly rooted in a much broader exoticization of African-based culture (and its pentatonicism) from a European-based perspective (and its diatonicism). This kind of exoticization is not just an academic issue, it inflects how musicians use these materials in their music; pentatonic scales are obviously coded to some degree as representing Others—such as “black” or “Asian” or “countercultural”—just as Otherness can be represented by certain singing styles and instrumental timbres. As stimulating a topic as this is, harmonic Othering is far too massive and thorny to attempt to cover here; we must instead continue on with the nuts and bolts of harmonic ambiguity.

Ambiguous Two-Chord Loops Because of their simplicity, two-chord loops represent an interesting microcosm of centric, scalar, schematic, and functional ambiguity. But not all two-chord schemas are regular carriers of such ambiguity. Only the perfect fourth ( and ) and the minor third ( and ) offer this sort of ambiguity with regularity; these two distances represent our categories of narrow and wide centric ambiguities. More specifically, in Lauryn Hill’s “Everything Is Everything” (1998), we get a four-bar loop of EM–Am–EM projecting wide centric ambiguity: “[EM] I wrote these words [Am] for everyone who struggles [EM] in their youth.” The equally viable, contradictory schemas or , along with the equal durations for each chord (two bars for Am, and one bar for each of the two EMs) are only barely offset by metric and phrasal emphases on EM, which is probably the stronger tonic I of the two. EM being first, the effect is as if our tonal center E is yanked out from under us by the Am (although since the loop opens and closes on EM, the E is a bit stronger overall). The primary pitch-class set is E, Fв™Ї, Gв™Ї, A, B, C, D; centered on E, the scale is nonstandard, possibly a mix Page 244 →of E mixolydian and E aeolian; centered on A, the scale is the so-called jazz minor scale or ascending melodic minor. Wide centric ambiguity seems to be a stronger possibility when the roots ascend by perfect fourth within the loop, as they do initially in Hill’s song, although this may be true only because such ascending-fourth loops are more common in general than descending-fourth ones. Ambiguity is still possible, however, when the perfect fourth descends. In Janet Jackson’s “When I Think of You” (1986), an AM–EM loop (complicated by various tones in the synthesizer lines) projects slow oscillation between centers A and E, each backed by a standard diatonic scale: ionian for the former and mixolydian for the latter (“’Cause when I think of [AM] you, ba- [EM] -by”). The schematic possibilities for all ambiguous two-chord loops are given in Example 6.4. (The remainder of the chapter will engage a multitude of different ambiguous examples; the reader is encouraged to take them at an appropriate

speed.) Narrow centric ambiguity can be heard in the two-chord loops of Van Morrison’s “Wild Night” (1971), which starts its verses with Em–GM (the GM ornamented by neighboring CM triads), offering the competing schemas (phrased as I–↓III) and : “As you brush your [Em] shoes and stand before the [GM] mirror.” The white-key diatonic set here allows easy sliding between E aeolian and G ionian positions. The reverse root motion (by descending minor third) situation in the verses of Blondie’s “One Way or Another” (1978) is even more ambiguous, seemingly because the two competing tonic Is, DM and BM, do not fit in a single standard scale, as was the case with the EM and Am triads in “Everything Is Everything (“[DM] One way or anotherВ .В .В . [BM] One way or another”). Blondie’s constant motion back and forth between these two tonics unsubtly reflects the song’s refrain. Two-chord loops are not confined to ambiguity between two-chord schemas; some loops project ambiguity by invoking parts of longer schemas. (Recall that a schematic effect can be projected by fewer chords than are contained with the schema itself; this is an ordinary starting point for the effect of chordal subtraction.) There are four notable versions (at different root-distances) of this phenomenon. The first is a motion of a perfect fourth up from the initial chordal root to the second, yet resulting not in competition merely between and , but with II–V thrown into the mix. This II–V is the first portion a schema, compelled to resolve to a tonic I once the loop ends. In truth, this loop usually only projects II–V as a possibility once we have heard the loop actually complete a II–V–I progression. We hear such a loop in George Harrison’s heartfelt 1970 “My Sweet Lord” (“[My sweet [II] lord, [V] mmm, my [II] lord”), a song for which Harrison was successfully sued due to its similarities to the Chiffons’ 1962 “He’s So Fine” Page 245 →(“He’s so [II] fine, [V] wish he were [II] mine.” No suits were brought against Merry Clayton when she recorded the original 1963 version of “The Shoop Shoop Song (It’s in His Kiss)” (later a hit for Betty Everett, whose version we cited early in chapter 1), even though the harmony of that song’s verses starts in exactly the same way, but with a faster harmonic pulse (“Is it [II] in his [V] eyes? Oh, [II] no”). We should also note that there are many more numeric possibilities for a loop such as this: в™ЇI/в™-II–♯IV/в™-V, ↓III–↓VI, ↑III–↑VI, IV–↓VII, в™ЇIV /в™-V–↑VII, ↓VI–в™-II, ↑VI–II, ↓VII–↓III, and ↑VII–↑III (these are all the pairs of common numerals from Appendix C separated by an ascending perfect fourth). Such loops, however, almost never (if ever) project these numerals, probably because most of them are not close to being a full schema; the exceptions are IV–↓VII and ↓VII–↓III, which could hypothetically evoke the three-chord schemas , , , or . For whatever reason, IV–↓VII and ↓VII–↓III are not standard effects for two-chord loops. Likewise, each of the other kinds of partially schematic, centrically ambiguous two-chord loops below has its own numeric possibilities that do not regularly crop up; we will ignore these in favor of focusing on what does normally occur. Example 245.6. Ambiguous two-chord loops root examples E–A; A–E E–G; G–E E–F; F–E E–D; D–E

potential schemas ; ; incomplete ; ; incomplete ; ; incomplete ; incomplete

; ; ; incomplete

The second kind of an ambiguous, partially schematic two-chord loop starts off as and then quickly adds an even stronger effect of ↓VII–V, a fragment of . (This is another case of three-

semitone, “narrow” centric ambiguity.) Returning to the 1968 musical Hair, we hear such a loop at the beginning of “Easy to Be Hard” (“[Eв™-M7(9)] How can people [CM] be so heartless?”). The initial effect in this case is of a diatonic-pentatonic rogue dominant ↓III resolving tonic I, but after only a few iterations of the loop, the progression cadences on an FM I (“[C7 V] Easy to be [FM I] cold”). The Eв™-M7(9)–CM is then not only ↓III–I on C but also ↓VII–V on F (wide centric ambiguity). Something similar happens in Creedence Clearwater Revival’s 1969 “Proud Mary”: the opening CM–AM oscillation of the signature guitar riff begins as a simple ↓III–I loop, but it quickly becomes ↓VII–V as we fall downward as part of ↓VII–V–IV–↓III–I (CM–AM–GM–FM–DM, a “pentdescent”). Page 246 →The third kind of partially schematic two-chord loop entails root motion up or down by a semitone. Typically, the first chord initially sounds like a tonic I, making the second chord a в™-II or ↑VII. In the absence of further cues regarding center, we may float over to the в™-2 as the orientating pitch class, in which case the schema simply changes from to . In Slipknot’s “Psychosocial” (2008), the simple riff of Eв™-5–D5 during the screamed verses defaults to I–↑VII (center Eв™-), although a hearing of в™-II–I (center D), and thus of weak ambiguity at the distance of a minor second, is a distinct possibility (“I did my [Eв™-5] time and [D5] I want out”). Yet upon Slipknot’s arrival at the sung choruses (“[Eв™-5] And the [Bв™-5] reign will [F5] kill us [D5] all”), the strongest centric effects come from Eв™and G. If we hang on to the latter effect as the riff returns, the progression will be ↓VI–V, a numeric series likely to project the three-chord schema (and centric ambiguity of a major third). A different three-chord schema is intimated in the Fв™Їm–GM riff in the verses to Jefferson Airplane’s “White Rabbit” (1967). The first chord here likewise defaults to tonic I, making the progression I–в™-II on center Fв™Ї; and although G is never a real contender for center, and thus the progression never projects a ↑VII–I effect, the onset of the chorus projects a break-out effect with a new AM tonic I (F♯’s ↓III). In relation to the chorus’s center A, the preceding (and ensuing) riff is ↑VI–↓VII, which can clearly project a fragment (and narrow centric ambiguity). The fourth and final kind of an ambiguous two-chord loop that projects a schematic fragment is most complex of the bunch. It involves a root motion up by a major second, resulting not just in I–II versus ↓VII–I but including the possibility of at least one of the following pairs: IV–V or ↓VI–↓VII. Neither of these is a schema in itself, but the former will likely project an incomplete schematic effect of , and the latter . (Just as with the perfect-fourth loop, the major-second loop can hypothetically project other numeric effects: в™ЇI/в™-II–↓III, II–↑III, ↑III–♯IV/в™-V, в™ЇIV/в™-V–↓VI, V–↑VI, and ↑VI–↑VII. But none of these is very close to a schema.) It is possible for these numeric pairs to compete with a true two-chord schema, that is, or . In David Bowie’s “Rebel Rebel” (1974), the main guitar riff of DM–EM projects ↓VII–I and IV–V, both strongly. Center E is suggested by the early, syncopated arrival of EM, the descending filled-in arpeggiation of chordal root E and fifth B (the riff’s highest notes E–D–C♯–B, which are echoed when Bowie begins scatting: “[E] do [D] do [Cв™Ї] do [B] do do do [Cв™Ї] do [B] do”), and the riff’s quick concluding E major (or Cв™Ї minor) pentatonic descent of C♯–B–G♯–E. Yet at two points in Bowie’s track, there is a strong arrival on AM (“They put you down”), projecting either IV on center E (if Page 247 →the main riff is ↓VII–I), or the long-awaited tonic I on A (if the main riff is IV–V); the gender confusion expressed in the lyrics encourages us to hear both centers equally. In “Jane Says” by Jane’s Addiction (1988), the strongest numeric effects of the primarily loop of GM–AM are ↓VII–I on A and IV–V on D as (“[GM] Jane says [AM]”). The durational emphasis (syncopation) on AM leads credence to the A-centered hearing, as does the lack of a D chord. On the other hand, the D-centered hearing is supported by the prominent A (“Jane”) and Fв™Ї (“says”) in Perry Farrell’s vocals, as though he were arpeggiating a DM triad’s chordal fifth and third. While a D chord is never heard in the studio recording of “Jane Says” (a definite strike against D as center), the 1997 live-recorded single begins with a minute-long vamp on DM before drooping into the GM–AM loop (although DM never returns, and the track is left unresolved on GM). The centric ambiguity in all these cases is some combination of centers that are spaced widely (by perfect fourth or fifth).

Major-second loops project IV–V more often than ↓VI–↓VII, probably because IV and V are a bit more common in the repertory (although ↓VI and ↓VII are of course absolutely standard). But sometimes these two numeric pairs are the only ones in competition. As opposed to the loops in “Rebel Rebel” and “Jane Says,” which respectively featured I–II and ↓VII–I as strong possible hearings, the FM–GM loop in Fleetwood Mac’s 1977 “Dreams” does not project either of its roots as strong possible centers (except perhaps in the first couple iterations) because of the lead guitar’s and vocal’s largely C major/A minor pentatonic vocal line (“[A] Now [C] here [D] you [D–E–D] go [D] a- [C] -gain [A] you [C] say”).24 The track creates a trance-like state of tonic anticipation, although it is not altogether clear whether the scale degree 1 we seek is C, , or A . A is certainly the stronger candidate, mostly due to the vocal line’s subtle arpeggiation of an Am triad. When Fleetwood Mac finally gives us an subdued Am triad in the instrumental middle of the song (after “you’ll know”), the narrow centric ambiguity is not really dispelled; our dream-state is not so easily broken. A similar situation can be heard in the choruses of Talking Heads’ “Psycho Killer” (1977), in which the FM–GM does not loop by itself, but rather takes turns resolving to both Am and CM: “[FM] Psycho killer [GM] qu’est-ce que c’est? [Am].В .В . better [FM] run, run, run, run, [GM] run, run, run, a- [CM] -way.” Talking Heads’ verses are strongly center on A, a fact that bolsters our hearing the choruses in parallel fashion (i.e., the progression as ↓VI–↓VII); yet we can also hear a possible break-out modulation between these sections, lending support to the C-centered interpretation (IV–V). Hearing the potential ambiguity would seem to be supported by the expressive content of the track, with its quick Page 248 →vacillation between English and French lyrics and its stark contrast between the disturbing thoughts conveyed by the narrator and David Byrne’s purposefully nerdy performance of them. An argument could be made that the progression IV–V (and perhaps ↓VI–↓VII) by itself should be considered a schema, since it is a common and recognizable progression for both loops and cadences. There are certainly cases of IV–V that project no ambiguity at all; this is true, for instance, of the loop to Carly Jae Jepsen’s 2011 Internet sensation “Call Me Maybe,” which includes center-loyal passing I and ↑III chords: “[IV] Hey, I just met you, [I] [V] and this is cra- [↑VI] -zy”). But these instances are exceptional; most IV–V loops are indeed ambiguous to some degree. Additionally, the overwhelming impulse with the progression IV–V is always to resolve to a tonic I as part of a functional chain; it is thus not self-contained like all the rest of our numeric schemas. We are thus justified in considering IV–V schematic only as a part of ; the same is true of ↓VI–↓VII as part of . Since all four of the above examples of major-second loops have featured two major triads, we might suspect that scale plays the decisive role in determining the center and numerals. To be sure, none of these examples projected a real possibility of I–II, likely because this interpretation would not have been supported by a strong piece of scalar information; if FM–GM were our loop, then an F center would entail the rare lydian scale, a scalar effect that would surely be outmatched by C ionian, D dorian, G mixolydian, and A aeolian (not to mention the A minor / C minor pentatonics heard in “Dreams”). This said, scale is not the sole determining factor, as evidenced by examples that do indeed project the first chord as a tonic I, as part of . In Tears for Fears’ “Head over Heels” (1985), the song opens and closes with a CM–DM loop (“la la la la la”) that definitely favors C, because of the pedal C, E, and G that shade the DM half of the loop. C is a strong contender for center, but the loop can also reasonably be heard as part of on G, which is the center established in the choruses (“Something happens and I’mВ .В .В .”), and as part of on the verses’ center of A (“I wanted to be with you alone”). Hence, while scalar information can be important, especially when steering us away emphasis from a potential center, scales are not omnipotent; other informational types can conspire to overpower them. David Bowie was fond of such conspiracies (despite what we saw in “Rebel Rebel”), as heard in the I–II loops of 1973’s “Panic in Detroit” (“He [DM I] looked a lot like Che Guevara. [EM II] Drove a diesel van”) and 1976’s “TVC15” (“[CM I] Oh, my TVC15, [DM II] oh, oh”). Another example worth discussing in this context is BjГ¶rk’s “So Broken” (from the 2003 Homogenic box set), which alternates Cm7 and D7(m9), with C and G projecting the Page 249 →strongest centric effects (“My heart [Cm7] was so broken. It was [D7(m9)] in pieces”). When she starts to sing in Icelandic, BjГ¶rk moves a few times to Gm(M9), center G thus being suggested by , resolving much of the previous ambiguity.

BjГ¶rk’s center C is undermined by its own exotic scale: dorian with a lydian в™Ї4 (jazz musicians sometimes call this “dorian в™Ї11” or “dorian в™Ї4”: C, D, Eв™-, Fв™Ї, G, A, Bв™-). We have so far encountered five intervallic distances for schematic ambiguity, the two most common being narrow (a minor third) and wide (a perfect fourth), followed by a major third, a major second, and a minor second. The only remaining possibility is the tritone. The dearth of examples of this form of centric ambiguity is surely related to the fact that I chords—the most common chords in the repertory—would in this context double for в™ЇIV/в™-V, the least common of our twelve common numerals. Even when a simple loop such as E5–Bв™-5 is used, the second chord is nearly always an obvious ornament to the first (melodically, metrically, etc.). Ambiguity is never really part of the picture.

Ambiguous Three-Chord and Slot Schemas Identical root pitch-class intervals, and thus a potential for schematic ambiguity, can be observed in three pairs of three-chord schemas: and (which can exhibit wide centric ambiguity); and (wide again); and (narrow); and and (wide). See Example 6.5a. (The other pair of three-chord schemas that align are and , but these are not standard bearers of ambiguity; a progression is normally just one or the other.) The first pair, and , we discussed at length in “Alabama” and in “E-Pro.” The second pair, and , can be found by returning once again to Hair. In the opening number, “Aquarius” (1968), the loop of the verses features Bв™-m7 and Eв™-M each for a half a bar, then Fm for a full bar (“When the [Bв™-m7] moon [Eв™-M] is in the [Fm] seventh house”). The numeric effects are simultaneously I–IV–V on Bв™-, and IV–↓VII–I on F. Center Bв™-is suggested by the long vamp on Bв™-m7 that constitutes the preceding instrumental intro and by the metric emphasis on Bв™-m7 in the loop. Center F is indicated by the relatively longer duration of Fm, the vocal line’s descending filled-in arpeggiation of the Fm’s chordal third Aв™-and root F (“When the [Aв™-] moon is in [G] the [F] seventh house”),25 and the large break-out pseudo-schema (F–Aв™-) when the verse gives way to the chorus (“and love will steer the Page 250 →[Aв™-M I] stars”). Overall, the Bв™-hierarchy is slightly stronger, but there is no denying the ambiguous effects in this track. The third pair of ambiguous three-chord schemas, and (both often strongly pentatonic), can be heard in the Fв™Їm–AM–BM loops of the verses to David Bowie’s 1972 “Hang on to Yourself” (“Ooh, she’s a [Fв™Їm] tongue-twisting storm, [AM] (she’ll) come to the show tonight, [BM] praying to the lightnin’ machine [Fв™Їm] [AM] [BM]”). The primary factors here are the metric emphasis on Fв™Їm and the durational emphasis on BM. These two chords are equally matched; Bowie’s progression is as strongly ambiguous as progressions get. The fourth and most widespread pair of ambiguous three-chord schemas is and . We can observe this couple at work in Daft Punk’s 1997 house-music hit “Around the World.” The striking bass line (modeled, though not exactly, on that of Chic’s 1979 “Good Times”), supports Am–CM–Em (and possibly a fourth chord during the bass’s tumble downward, although this chord’s entity and letter effects are hazy: “[Am] Around the [CM] world, around the [Em] world”). The potential schematic ambiguity here involves wide centric ambiguity between A and E. In favor of a tonal center of A and a schematic progression of I–↓III–V are the A dorian scale, the metric emphasis on the initial Am chord, and, most importantly, the arpeggiation of an Am triad in the chordal roots A, C, and E. Center E and its accompanying schematic IV–↓VI–I progression are supported by the durational emphasis on Em. The possible fourth chord, a DM or GM or maybe both, is much clearer in Daft Punk’s 2013 mega-hit “Get Lucky” (featuring Pharrell Williams, and cowritten with Nile Rodgers, who also co-wrote “Good Times”), which offers a nearly identical loop but a major second higher: Bm–DM–Fв™Їm–EM (EM corresponds to a DM fourth chord in “Around the World”). In “Get Lucky,” we can hear the same

ambiguity between and , although the full loops here are either I–↓III–V–IV on B, or IV–↓VI–I–↓VII on Fв™Ї. Hearings of “Around the World” on C and of “Get Lucky” on D and E, are also not out of the question, although these interpretations do not involve schematic ambiguity (since no schemas line up with those potential centers).26 In this light, we could compare Daft Punk’s songs to the choruses of Sara Bareilles 2007 “Love Song,” which offer a similar loop but one with a fourth chord (FM) corresponding to a GM in “Around the World”: Gm7–Bв™-M(9)–Dm–FM. (In the earlier-cited “Enjoy the Silence” by Depeche Mode, the earliest of these schematically ambiguous examples, we encountered a chorus loop of Fm–Aв™-M–Cm–Eв™-M /Bв™-, the fourth chord of which corresponds to a GM in “Around the World” while that chord’s bass Page 252 →note Bв™-corresponds to D, almost as though the sonority were a compromise between the two possibilities for the fourth slot.) Page 251 → Example 6.5. Ambiguous three-chord and slot schemas 6.5a. Three-chord progressions root examples potential schemas E–B–A; B–A–E; A–B–E ; E–A–B; A–B–E; B–E–A ; E–G–A; G–A–E; A–E–G ; E–A–C; A–C–E; C–E–A ; 6.5b. Slot progressions potential schemas

root examples E–C–G–D; C–G–D–E; zombie ; journey G–D–E–C; D–E–C–G E–B–F♯–A; B–F♯–A–E; ; ; F♯–A–E–B; A–E–F♯–B E–A–F♯–B; A–F♯–B–E; steady ; ; ; F♯–B–E–A; incomplete ease I–IV–↓VII–↓III B–E–A–F♯ 6.5c. Hypothetical interpretations of a falling-fourths loop G5 – D5 – A5 – E5 ↓III – ↓VII – IV ↓VII – IV – I IV – I – V I – V – II

– I ↓III–↓VII–IV–I> – V

– II

– ↑VI not a schema

6.5d. Hypothetical interpretations of a falling-fifths loop E5 – A5 – D5 – G5 ↑VI – II – V – I steady II – V – I – IV

V – I – IV – ↓VII I – IV – ↓VII – ↓III I–IV–↓VII–↓III, easing fragment Three-chord loops do not regularly project ambiguity involving parts of larger schemas as we saw with the twochord loops with roots a perfect fourth apart (I–IV and V–I versus II–V), a minor third apart (↓III–I

versus ↓VII–V), a minor second apart (I–↑VII versus в™-II–I versus ↓VI–V; and I–в™-II versus ↑VI–↓VII), and a major second apart (I–II versus ↓VII–I versus IV–V versus ↓VI–↓VII). But of course larger, slot progressions can be ambiguous in themselves. In chapter 3 we took special note of the ambiguity between the zombie and the journey . As we know, the zombie is standard only in its I–↓VI–↓III–↓VII phrasing probably because the tonic potential of the ↓III is so great in the other three possible phrasings that we will instead not hear a zombie at all but rather a journey. Even in its standard phrasing, the zombie tends to have at least weak narrow centric ambiguity between its own 1 and its књњ3, the latter being the 1 of the ↑VI–IV–I–V phrasing of the journey. This is definitely the case with Jewel’s 1995 “Foolish Games,” the verses of which float between Dв™Їm tonic I (in the zombie) and Fв™ЇM tonic I (in the journey) (“[Dв™Їm] You took your [BM] coat off and stood in the [Fв™ЇM] rain. You were always [Cв™ЇM] crazy like that”). In the choruses, Jewel switches to the IV–V–I–↑VI phrasing of the king schema on center Fв™Ї, although even there the progression gives a hint of on Dв™Ї embellished by ↓III: “And [BM] these foolish [Cв™ЇM] games are [Fв™ЇM] tearing me a- [Dв™Їm] -part.” With this kind of zombie/journey ambiguity we get a consistent oscillation from one center up three semitones to another center, often between “relative” minor and major tonic chords from aeolian and ionian orientations of the same white-key diatonic pitch-class set. In this way, Jewel’s and similar progressions represent a kind of microcosm of break-out modulation: that originally long-range modulatory scheme has evolved into quick, incessant reorientation within a short harmonic loop (i.e., a kind of centric and schematic ambiguity). Sometimes these progressions appear in the verse only to be rotated over two slots (to the standard journey phrasing) in the chorus, making the incestuous relationship between the zombie, journey, and break-out all the more graphic. We hear this in Keith Urban’s 2002 “You’ll Think of Me,” offering competition between centers Fв™Ї and A in the verse (I–↓VI–↓III–↓VII and ↑VI–IV–I–V) giving way to a clearer center A in the chorus (I–V–↑VI–IV), the Fв™Їm–DM–AM–EM loop becoming AM–EM–Fв™Їm–DM (verse: “[Fв™Їm] I woke up early this mornin’, ’round [DM] 4am with the [AM] moonВ .В .В . on [EM] the interstate”; chorus: “[AM I] Take your records. Take your [EM V] freedomВ .В .В . I don’t [Fв™Їm ↑VI] need themВ .В .В . your [DM IV] reasons”). A related though distinct situation can be found in Audioslave’s “I Am the Highway”—alsoPage 253 → from 2002—although in this case the zombie/journey loop in the verse (FM–CM–GM–Am) is in the unusual phrasing of ↓VI–↓III–↓VII–I within an A aeolian scale, and IV–I–V–↑VI within a C ionian scale (“[FM] Pearls and [CM] swine be- [GM] -reft of [Am] me”). Audioslave’s progression mutates halfway through the verse in such a way that the competing CM and Am tonic Is are split into quick CM–Am progressions in themselves, creating miniature competing and schemas (“I was [FM] lost in the [CM] ci- [Am] -ties, a- [GM] lone in the [CM] hi- [Am] -lls”). Audioslave’s chorus loop, on the other hand, is not a rotation of either of these verse progressions but rather is built on a series of descending perfect fourths between the chordal roots, starting on C and landing on A (and projecting both ends as center) as either I–V–II–↑VI or ↓III–↓VII–IV–I (“[CM] I am [GM] not your rolling [Dm] wheels. I am the [Am] highway”). The fact that I–V–II–↑VI (on C) is not a schema while ↓III–↓VII–IV–I (on A) is lends support to the chorus’s orientation about A; furthermore, the chorus features an additional progression of CM–GM–Dm–EM, whose final triad projects a strong effect as lead dominant to Am I. Yet center C is supported phrasally, metrically, and by the break-out modulation (which would favor A in the verse moving up to C in the chorus). However we interpret all the details, it is clear that, harmonically speaking, “I Am the Highway” is a truly ambiguous song. The series of perfect fourths heard in Audioslave’s song are at the heart of all our final examples of schematic ambiguity. Whenever a harmonic root pattern is repeated verbatim, there is a good chance that our ears will lose track of where we are. A root pattern of falling fourths such as that in the chorus to “I Am the Highway” is particularly ambiguous because at every step we get a new schema: one fourth gives us the most common progression in the repertory, ; another fourth yields us the highly visible ; another produces ; yet another fourth creates the Jimi, . Root patterns of rising fourths, or falling perfect fifths, feature the

same kind of inherent schematic ambiguity: one fifth gives us ; another yields ; another produces the steady, ; one more creates the vaudeville, . In addition to leading into I, however, falling fifths also participate in schemas leading out of I: one fifth is I–IV (); two fifths yields I–IV–↓VII (); three fifths produce I–IV–↓VII–↓III (a fragment of the easing schema, which otherwise is I–IV–↓VII–↓III–↓VI || V); four fifths create I–IV–↓VII–↓III–↓VI (all but the cadential V of the ease). Beyond I–V, falling fourths do not form such schemas leading entirely out of I (I–V–II, I–V–II–↑VI, and I–V–II–↑VI–↑III are not schemas). That said, falling fourth and fifth motions each may feature I in the middle of the phrase: falling fourths can hence form IV–I–V Page 254 →(), IV–I–V–II (), and ↓VII–IV–I–V (); falling fifths can additionally form V–I–IV (), V–I–IV–↓VII (), and II–V–I–IV (). In other words, when we encounter, say, a song with a four-slot loop built with falling fourths in the chordal roots, it is perfectly natural for us to be unsure about the location of the I (assuming there is one at all), because three out the four possible rotations of that loop are their own complete schemas: a G5–D5–A5–E5 loop might be a schematic ↓III–↓VII–IV–I on E, a schematic ↓VII–IV–I–V on A, or a schematic IV–I–V–II on D, not to mention the nonschematic I–V–II–↑VI on G; see Example 6.5c. The extent to which any one of these numeric series is projected by an individual example depends, of course, on the particulars of that passage and the outlook of the listener, but it should be noted that such ambiguities will be even more pungent if the progression begins a new section that could easily have its own unique, unpredictable tonal center (like a chorus). This was the case in the choruses to “I Am the Highway”; other comparable examples include the looped choruses to Precious Wilson’s 1985 soundtrack single “Jewel of the Nile” (“[Eв™-M] We’ll go [Bв™-M] searchin’ for the [FM] jewel of the [CM(9)] Nile”), and the choruses to Guns N’ Roses’ 1988 bigoted diatribe “One in a Million” (“[BM] You’re one in a [Fв™ЇM] million. [Cв™ЇM] Yeah, that’s what you [Gв™Їm] are”). The potential for schematic ambiguity is even greater when a four-slot loop features falling fifths, because not only are three of the rotations schemas in themselves but the fourth is an easing fragment. An E5–A5–D5–G5 loop might be a steady ↑VI–II–V–I on G, a schematic II–V–I–IV on D, a schematic V–I–IV–↓VII on A, and an incomplete easing I–IV–↓VII–↓III on E; see Example 6.5d. Representatively ambiguous examples include the verses of the Kinks’ 1968 “Picture Book” (“[EM] Picture your- [AM] -self when [DM] you’re getting [GM] old”); the verses of Def Leppard’s 1987 “Love Bites” (“When you make [Dm] loveВ .В .В . the [Gm9] mirrorВ .В .В . think [CM] ofВ .В .В . like [FM] me?”); the verses of Blood, Sweat & Tears’ 1969 “Spinning Wheel” (with the brass pouring a thick layer of jazz-flavored chromaticism over the already disorienting loop, making each sonority into a major minor-seventh sharp-ninth chord) (“[E7(в™Ї9)] Spinnin’ [A7(в™Ї9)] wheel [D7(в™Ї9)] all a- [G7(в™Ї9)] -lone”); the choruses of Earth, Wind & Fire’s 1975 “Shining Star” (coming off the centric E established in the verses “[E7(в™Ї9) I] “You’re a [A9] shinin’ star [D9] no matter [G9(6)] who you are [C7(6)]”); and the main sections of the Velvet Underground’s 1969 “Beginning to See the Light” (with an odd phrasing that places one of the falling fifths between the last and the first chord, leaving a minor third between the final two, “[GM] Well, I’m be- [CM] -ginning to see the [FM] light [DM]”). Progressions with five or more slots can also be schematically ambiguous,Page 255 → yet there are only a few schemas longer than four slots and none of these schemas features identical root intervals with another schema. Therefore, the potential for longer progressions to be schematically ambiguous always involves at least one shorter schema, and often more than one. In 1964’s “Laugh Laugh,” the Beau Brummels move from center Gв™Ї to E over the span of each of the verse’s phrases, but then leap up to an Fв™ЇM triad at the start of the chorus, which may or may not be a new I. We fall downward by six perfect fifths until we are at C—a tritone away from the F♯—and then sink down to BM, a clear dominant V of E (“[Fв™ЇM] Laugh, laugh, I [BM] thought I’d die. [EM] It seemedВ .В .В . [AM] me. [DM] LaughВ .В .В . [GM] metВ .В .В . [CM]

taughtВ .В .В . to [BM] be”). The progression is thus simultaneously I–IV–↓VII–↓III–↓VI–в™-II–в™-V–IV on Fв™Ї, an easing schema that veers off course (with в™-II, в™-V, and IV but not moving to a cadential V), and also II–V–I–IV–↓VII–↓III–↓VI–V on C, comprising overlapping with a full easing schema. We should take note that progressions containing any kind of falling-fourths or -fifths series are not always schematically ambiguous. This is most obviously true when the repeating intervals are not all perfect fourths or fifths, and too when the intervals are not all the same chordal part (such as a root). For instance, in Neil Diamond’s “Love on the Rocks” (1980), falling fifths populate most of the vocal line, but they are a mixture of perfect and diminished fifths (C–F–B–E–A–D♯–Gв™Ї); they also alternate as chordal thirds and roots (“[Am I (C)] Love on the rocks. [FM ↓VI (F)] Ain’tВ .В .В . [GM ↓VII (B)] Just pourВ .В .В . [Em V (E)] tellВ .В .В . [FM ↓VI (A)] Had nothin’ .В .В . [B7(6) II (Dв™Ї)] just sing the blues all the [E7 V (Gв™Ї)] time”). Diamond’s progression projects the effect of a walking schema (I–↓VII–↓VI–V) that has been transformed via chordal addition (an extra chord in between each chord of the schema). There is no strong sense of schematic ambiguity here despite the clear pattern of fifths. As we wrap up our discussion of schematic ambiguity, we should say something about the oddballs: metaschemas and pseudo-schematic break-outs. Hypothetically, meta-schemas can be ambiguous in the same way as any other schema, by virtue of one meta-schema’s defining pitch-class intervals being identical to those of another meta-schema. For instance, the stretch’s 5–♯5–ꜛ6 ascent might be heard on a different tonal center as the swell’s 4–♯4–5 ascent. In practice, however, this simply does not happen with any regularity, maybe because meta-schemas simply permit too many possibilities for centrically unambiguous harmonizations that, statistically speaking, possible ambiguities get lost in the shuffle. As for break-out modulation, ambiguity must mean something different from the other forms of schematic ambiguity we have discussed; break-out ambiguity probably resides somewhere between Page 256 →centric and schematic ambiguity, entailing centric with regard to at least one of its two sectional centers. We have already seen several cases in which this has happened to some degree: “Somebody’s Baby,” “White Rabbit,” “Psycho Killer,” “Foolish Games,” “You’ll Think of Me,” and “I Am The Highway.” These songs represent different incarnations of break-out ambiguity; the only main form not covered by these tracks is that which fails to offer a tonic on the new tonal center. In Jay-Z’s 2009 “Empire State of Mind,” the rapped Fв™Ї-centered verses loop a simple I–IV progression (“Yeah, I’m out that [Fв™ЇM I] BrooklynВ .В .В . I’m the new Si- [BM IV] -natra”) until the end of the section, when they prepare the onset of Alicia Keys’ sung chorus by offering two ↑IIIs, Aв™Ї4–Aв™Ї7 (the 4 really operating as a nonchord tone resolving to the chordal major third of the Aв™Ї7). This Aв™Ї7 strongly projects an effect of dominant V predicting a tonic Dв™Ї chord, which is to say that this Aв™Ї7 sets up a modulation from center Fв™Ї down a minor third to center Dв™Ї, which would be the opposite of the model break-out (a standard variation we cited in chapter 5). However, when the chorus begins, Aв™Ї7 swerves upward a semitone to BM, which then falls to Fв™ЇM (“[Aв™Ї7] .В .В . that I’m most definitely from/in [BM] New YorkВ .В .В . dreams are [Fв™ЇM] made of”). This BM might be a delaying ↑VI on center Dв™Ї, temporarily resolving Aв™Ї7 V, but it is clearly also IV on center Fв™Ї resolving to Fв™ЇM I, so perhaps we never left our original center of Fв™Ї at all. The break-out center Dв™Ї is never hypostasized by its own tonic I in the chorus, though it makes a weak appearance in the song’s bridge, toward the end of the track: “[Cв™ЇM ↓VII] No place in the world that can compare [Dв™Їm I].” (This is a weak tonic Dв™Їm because the section’s centricity could likewise be Fв™Ї, in which case the chords would be Cв™ЇM V–Dв™Їm ↑VI.) The ambiguous break-out effect depends on the song’s parallelism to the intro from 1969’s “Love on a Two-Way Street” by the Moments, from which “Empire” samples its signature riff—in the Moments’ recording, the pregnant V does indeed come through with a modulation a minor third down (all chords a semitone lower from those of “Empire,” so the seeking V is A7 and it predicts a tonic D chord: “[A7 V] I found [GM7 IV] love on a two-wayВ .В .В . lonely [DM9 I] highway”).

Functional Ambiguity

While functional ambiguity is part and parcel of centric and schematic ambiguity, it does also occur independently of them. Even when the centric and schematic effects are perfectly singular, functional ambiguity can still be rampant, because tonal centers and schemas do not dictate any one hierarchy for a given progression or function for any given chord, nor do they preclude Page 257 →the possibility of progressions projecting multiple, contradictory hierarchies and sonorities projecting multiple, contradictory functions. Indeed, we have already encountered schemas that are predisposed to functional ambiguity, most notably , , , and . In chapter 3, we noted the two main functional interpretations of : a rogue dominant ↓VII to tonic I motion that is softened or delayed by a passing subdominant IV, and a subdominant IV to tonic I motion that is preceded by a hypo pre-subdominant ↓VII (creating a functional chain). The latter effect is the most common by far, and the former effect seems always to have to fight for its right to exist; this is to say, when we hear as an ornamented ↓VII–I, it is usually accompanied by functional ambiguity because it is in direct competition with effect of as a functional chain. In the main guitar riff for Billy Squier’s “Lonely Is the Night” (1981), we hear two first harmonic phrases: I–↓VII–I, then I–↓VII–IV (“[I] Lonely [↓VII] is the [I] night, when you [I] find your- [↓VII] -self a- [IV] lone”). The first is an obvious tonicв†’dominantв†’tonic motion. The second would seem to be a strong case of IV as a delayer of tonic resolution within a larger ↓VII–I, based on the precedent set by the immediately preceding phrase. Yet even in this example the ↓VII can sound subordinate to IV. IV arrives on a beat that is stronger than the ↓VII’s (metric emphasis), at the end of the phrase (phrasal emphasis), and lasts twice as long as ↓VII (durational emphasis). Indeed, the IV is so strong that it could be heard as overpowering the I at the beginning of its phrase, in which the riff would sound like a big I–IV motion, the I a reduction of the first phrase (I–↓VII–I) and the IV a reduction of the second phrase (I–↓VII–IV). So while there is never any confusion about Squier’s tonal center or schemas, functional ambiguity is a primary effect of the riff, and it is more generally a constant companion of any hearing of as a ↓VII–I progression. is a bit more complicated than . In the latter, the ↓VII’s potential as a pre-tonic is slightly stronger than the IV’s by virtue of its stronger generic voice-leading potential—the hyper књњ7 and presumed 2 anticipating 1—as opposed to that of the IV—the presumed hypo књ›6 anticipating 5. Yet this advantage for the ↓VII is equally matched, and in fact normally outmatched, by the IV’s sheer proximity to the I, that is, the IV’s placement as the penultima. In the case of , the IV is still the penultima, but the potential pre-tonic strength of the V is much greater if it contains књ›7 (as a lead dominant), which is more strongly attracted to 1 than the farther књњ7 inherent to ↓VII; even V as a power chord will tend to be a stronger dominant than a ↓VIIM or a Vm because we can easily imagine a књ›7. Thus the two main competing hierarchies for are defaulted in the opposite way compared to those of : V–I is the customary deep motion, while IV–I is merely Page 258 →a contender that emerges only under certain circumstances and then often (though not always) in competition with V–I, creating a functionally ambiguous effect. For this ambiguity to arise, the V’s strong pre-tonic potential needs to be undermined in some way, either by materializing as a rogue dominant instead of a lead dominant (featuring књњ7 and not књ›7), or by receiving little metric, durational, or phrasal emphasis relative to the IV. The rogue dominant Cm V that starts the chorus’s loops in “Get Down Tonight” (1975), by K. C. and the Sunshine Band, is in the strongest possible position in the phrase—at the very beginning—yet its chordal third (Eв™-) is књњ7 and can sound both superordinate and subordinate to the subdominant IV: “[Cm V] Do a little dance, [Bв™-M IV] make a little love, get [F7 I] down tonight.” The deeper motion can simultaneously be V–I and IV–I; the progression is functionally ambiguous. The de-emphasis of V in occurs most readily in the phrasings I–V–IV and I–V–IV–I, both of which we discussed in chapter 3. The first, I–V–IV normally features a doubly long IV when it is looped, in which case the V receives no metric, durational, or phrasal emphasis and so functions as a passing chord between I and IV with little or no functional ambiguity to the progression. Such is the case with the Eagles’ 1974 “Already Gone” (“Cause I’m [I] al- [V] -ready [IV] gone and I’m [I] fee-В .В .В .”). However, when the phrasing of I–V–IV gives two lengths of I and only one

each for V and IV, the V is usually emphasized metrically against the IV, so the progression tends to be at least somewhat functionally ambiguous; we can hear this in Spin Doctors’ 1991 “Little Miss Can’t Be Wrong” (“[I] Little miss, little miss, little miss [V] can’t be wrong [IV]”). The other main phrasing, I–V–IV–I, usually holds each sonority for the same length, placing little emphasis on V and thus favoring functional ambiguity. In Social Distortion’s 1990 “Ball and Chain” (“Take a- [I] -way, take a- [V] -way, take a- [IV] -way this ball and [I] chain”), the V is a post-tonic and the IV is a pre-tonic, producing no clear, single deeper-level progression. and are related motions that we previously said most often operate as functional chains: pre-dominantв†’pre-tonicв†’tonic. Yet when the I–IV–↓VII and I–IV–V phrasings of these schemas are looped with a doubly long I (typically lasting one full bar, followed by two beats of IV and then two beats of either ↓VII or V), the IV is emphasized metrically compared to the ↓VII or V, facilitating the hierarchical possibility of a deeper I–IV progression (IV as post-tonic and subdominant) with a ↓VII or V as a weaker pre-tonic tacked on to the end. (The fact that I–IV is the most common two-chord schema also may influence our hearing.) In the verses to the Kinks’ kinky “Lola” (1970), I–IV–↓VII offers this opportunity for hearing functional ambiguity, the ↓VII sounding as much as a post-anchor to IV as a pre-tonic to I: “I [I] met her in a clubВ .В .В . where you [IV] drink champagne and Page 259 →it [↓VII] tastes just like Coca- [I] -Cola”). In Billy Stewart’s 1956 “Billy’s Blues, ” Jody Williams’ signature guitar riff emphasizes the I and IV much more than the V (“[I] Baby, [IV] you’re [V] my inspi- [I] -ration”); the same happens in the derivative but much more famous 1956 hit “Love Is Strange” by Mickey and Sylvia (“[I] How do you call your lover boy? [IV] вЂCome [V] here, lover boy!’”). While it is still possible to hear I–↓VII or I–V as the deeper motion in these tracks, I–IV is a definite alternative. As for limiting a V’s potential dominant strength by using књњ7 instead of књ›7 (like in the V–IV–I progressions in “Get Down Tonight”), this seems not to be much of an option in this context, which is to say that the series IV–V–I nearly always sounds like a functional chain regardless of the types of sonorities involved. It seems that phrasing the loop to allow a deep I–IV motion—the most common progression in the repertory—is the primary factor in enabling functional ambiguity in IV–V–I. We have so far seen one basic kind of functional ambiguity in , , , and . These ambiguous effects all involved a pre-tonic IV competing with either a pre-tonic V or pre-tonic ↓VII for hierarchical superordination. Yet sometimes exhibits an altogether different sort of functional ambiguity, wherein the primary hierarchical competition is not between IV and V but IV and I. This phrasing normally features IV and I for two beats each, followed by a full bar of V, as heard throughout Len’s 1999 “Steal My Sunshine” (a looping riff sampled from the middle section of the Andrea True Connection’s semipornographic 1976 “More, More, More”: “I [IV] know it’s [I] up for [V] me. If you steal my sunshine”). The V is a strong lead dominant. In contrast, the potential tonic function of the I faces stiff competition from the metrically and phrasally emphasized IV. This prominently placed IV has a distinct pre-dominant quality, driving directly to the V and making the I into a passing hypo predominant. Functional ambiguity emerges from the balance achieved between this tonic-less hearing and a blander interpretation of subdominant IV resolving to tonic I. All these functionally ambiguous examples have been loops. Yet, barring one chief exception, these three-chord schemas are equally ambiguous in cadential settings. The exception is the V–IV–I cadence as it occurs at the end of a blue schema. The blue’s V is usually such a strong arrival point—so highly anticipated as the head of the final section and deliverer of the b lyric—that its pre-tonic function is never in serious jeopardy of being outdone by that of the following subdominant IV (assuming there even is a potential subdominant, since the blue’s cadence can also be simply V–I). A more likely scenario—although only slightly more likely—is ambiguity generated by the addition of a turnaround dominant V after the I, anticipating the arrival of Page 260 →the next phrase’s initial tonic I. In this situation, the third portion of the blue is V–IV–I–V, and functional ambiguity can arise between the Vs and I: the first V can be an ordinary dominant resolving (through a softened motion) to tonic I, followed by another dominant (and post-tonic) V. Yet

under the right circumstances, the entire motion can be heard as a big dominant V predicting resolution to the I coming at the beginning of the next phrase, in which case the two Vs are the same chord at a deeper harmonic level while the IV and I are embellishments. In the latter, fancier hearing, the I functions not as a tonic but as a neighboring hypo pre-dominant to the turnaround V, while the IV is a hypo gamma (pre-predominant) and preanchor to I.27 During the first half of Lee Allen’s tenor saxophone solo in Little Richard’s “Long Tall Sally” (1956), this secondary hierarchy is achieved by Allen’s glissando up to a prominent 5 just as the I arrives. While technically not a pedal since it does not extend beyond the I, this 5 is so salient that it enables us to hear it as the root of the Vs on either side, making the I subordinate to those two chords. (In Pat Boone’s sanitized 1956 cover of the song, there is no turnaround dominant V and thus no functional ambiguity.) All this said, we must reiterate that such situations are extremely rare: V–IV–I blue cadences are nearly always a straightforward dominantв†’tonic resolution softened by IV. As we engage larger and larger progressions, the potential for functional ambiguity increases dramatically. As we know, larger schemas tend to contain smaller schemas within them, so if we consider just one of the four functionally ambiguous three-chord schemas from above, , we should expect to hear that schema’s functional ambiguity as a latent effect of the following longer schemas, all of which can present ↓VII before IV before I: , , , , , , and the Jimi . Nevertheless, it would be extremely impractical for us to catalog every single possible permutation of functional ambiguity in all seventy-seven of our identified schemas (not to mention any other nonschematic long progressions), because even the most hierarchically predictable schemas can be made ambiguous under the right circumstances. In a sense, functional ambiguity is simply a property of all long progressions, and thus the very concept of functional ambiguity in this context becomes trivial, in exactly the same way that multivalence was not a specific enough criterion for creating a useful definition of harmonic ambiguity at the beginning of this chapter. In summary, we have conceptualized harmonic ambiguity as the hierarchical contradiction between either multiple simultaneous tonal centers or chordal functions (or both). In addition to centrically and functionally ambiguous effects themselves, scalar and schematic ambiguity are also possiblePage 261 → when they involve more than one center. We discussed in detail the process of hearing centric and functional effects, and we identified thirteen specific distinct types of musical factors that can contribute to their creation. The most common forms of centric ambiguity were termed wide (five semitones between competing centers) and narrow (three semitones), but we also encountered examples of four, two, and one semitone(s). We problematized the conventional wisdom that pentatonic scales are more inherently ambiguous than diatonic scales, and also problematized the distinction between centric ambiguity and reorientation, especially with regard to multiple competing centers within single harmonic phrases. Certain two-chord, three-chord, and slot loops were showed to be prone to schematic ambiguity, even sometimes when one or more of the projected schemas is incomplete. And we closed by examining a few examples of functional ambiguity that did not involve centric ambiguity. Ambiguity is a real effect of rock harmony. Yet the music is not an experiential free-for-all. A song enables a range of hearings, but not all hearings are equally viable. In this chapter we have attempted to explore the myriad possibilities of competing centric, scalar, schematic, and functional effects while at the same time pinpointing precisely when and why we might hear these effects. While our goal has been to present as accurate an account of this process as possible, there is no end to the caveats we could list. Any generalization of this size cannot help but whitewash many crucial details in hearing harmony, without even mentioning the degree to which individual listeners’ choices and backgrounds determine what the music sounds like. The distinctions between strongly ambiguous effects, weakly ambiguous effects, and unambiguous effects are helpful but not fixed. The relative intensity of all these effects is largely a reflection of who is doing the hearing. But so long as we are endeavoring to hear, we should endeavor to keep our ears open to the possibility of competing effects; this sort of competition can be one of the most intriguing characteristics of rock harmony.

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Conclusion Expressive Effects I consider that music is, by its very nature, essentially powerless to express anything at all, whether a feeling, an attitude of mind, a psychological mood, a phenomenon of nature, etc.В .В .В . [sic] Expression has never been an inherent property of music. That is by no means the purpose of its existence. If, as is nearly always the case, music appears to express something, this is only an illusion and not a reality. —Igor Stravinsky (1936, 91–92) Expression is the reason for music. Stravinsky’s point is that the expressiveness we hear in music is something we project onto it—not something inherent to it—an attitude with which we could feel a great deal of sympathy if not quite also one with which we might completely agree. In any case, the veracity of Stravinsky’s claim is irrelevant to the current proceedings; we are concerned here only with what we can hear, whether or not it reflects, in Stravinsky’s word, “reality.” If we did not find musical sounds expressive, we would not be so prolific in our creation—or voracious in our consumption—of them. Also irrelevant is whether or not we agree on what exactly a particular piece of music expresses; the undeniable fact is that we find music expresses something. Throughout this book we have laced the conversation with passing references to musical expression, from passing puns (the blurring of tonic harmonies in Puddle of Mudd’s “Blurry,” chapter 1), to the naming of harmonic structures based partly on those structures’ expressive connotations (the “steady” schema, chapter 3), to the head-on engagement with contradictory layers of narrative meaning (the potentially racist elements of Lynyrd Skynyrd’s “Sweet Home Alabama,” chapter 6). Writers about music relish moments when they can link music with its title or lyrics, because this act involves extracting music out of its purely sonic context and connecting it to the medium used by the writer herself: that of words. (Indeed, the present Page 263 →author has found it difficult to suppress his strong desire to talk about musical expression with each passing example.) In this concluding section, we shall finally indulge ourselves in rock harmony’s most important quality. Precisely because we find it is so important, musical expression is a difficult topic to tackle. Our personal and communal identities have become, to a great extent, intertwined with the music we listen to, so much so that occasionally we listen to particular styles solely because of what those styles say about us (to others and to ourselves). This is true not just of rock but of classical, jazz, and folk musics; each style and substyle has its own associations, its own identity politics, its own devotees and opponents. Music expresses something about us; to investigate musical expression is thus to investigate some of the ways we perceive ourselves and each other. In order to make it a useful description of a harmonic effect, “expression” will be limited here to instances wherein the harmony communicates something beyond itself, be it something as universal as an emotion or as specific as an event in a song’s story. This is how we used the term in chapter 6, when we talked about expression as being a type of musical information used in hearing centric and functional effects. Defining “expression” as extra-musical meaning helps to distinguish this harmonic effect from the four other large effects of function, schema, transformation, and ambiguity, so that, for instance, the functional label “tonic” can be used to signify a chord’s quality of stability without also necessarily implying that the chord expresses stability. To be sure, a chord can indeed express such a notion, as does the famous three-piano EM tonic triad concluding the Beatles’ “A Day in the Life” (and concluding the entire 1967 Sgt. Pepper’s Lonely Hearts Club Band album). But the quality of stability and the quality of the idea of stability are two different things: the former is a functional effect, the latter an expressive effect. While expression is a separate phenomenon from the other harmonic effects we have studied in this book, it is clearly related to the others. The Beatles’ epically stable triad is able to express stability only because it is stable. Hence, functional effects can be indicators of expressive effects. The same is true of schematic,

transformational, and ambiguous effects. When we a hear a schema, the situation is ripe for our hearing an expression of conformity, or of ironic conformity, or at least of familiarity. A transformational effect will sometimes be complemented by a quality of surprise or even rebellion; an ambiguous effect can occasionally accompany a theme of uncertainty or multiplicity in the lyrics. It goes without saying that it is impossible to generalize about these relationships on such an abstract level; the point here is that all the major harmonic effects we have identified can, and often do, relate directly to the meanings we hear in the music. Indeed, function, schema, Page 264 →transformation, and ambiguity are, in a very real sense, their own kinds of musical meaning, no less so than expression. Expression merely differs from the others in its pointing outward rather than inward. This said, there are some interesting cases where the seemingly clean division between musical and extra-musical meaning collapses, cases where the song is so harmonically self-conscious that it describes its chords as it unfolds. The simplest example must be 2002’s “One Chord Song” by Australian country artist Keith Urban, who uses the musical limitation of an unchanging catatonic I as fodder for some comic lyrics. Or take Sha Na Na’s performance in the 1978 film version of Grease of “Those Magic Changes,” the lyrics of which revolve entirely around the “magic [chord] changes” of the song’s looping I–↑VI–IV–V progression, an example of the king schema humorously outed as a harmonic clichГ© within the film’s 1960 setting. These sorts of songs chafe against our definition of expression but are rare enough to safely be considered exceptions proving the more general rule that harmonic expressive effects are usually about things other than the harmony. A more serious challenge to any discussion of musical expression is determining the extent to which a particular expressive effect must be aligned with a broader expressive agenda. There is little doubt that in the eerie G–G–Cв™Ї riff to their 1969 eponymous song, Black Sabbath are channeling diabolus in musica, the centuries-old associations of the tritone with the satanic. General rules of association are at the heart of musical semiotics, a branch of study dedicated to understanding how individual pieces of music create “signs” that communicate meaning in large part through community-shared connotations. (The work of Philip Tagg is the cornerstone of popular-music semiotics.1) No song is an island, for sure. Yet it seems clear that not all forms of musical expression conform to some repertory of shared signs. Very few tonics in rock music correspond to any obvious expression of stability, but the “Day in the Life” chord clearly does; that sonority’s meaning is not predicated on some generic associative convention that allows a tonic to be understand as a sign of stability. The issue here can be framed as one of context. In the circumscribed setting of the song and the album, the Beatles’ sonority expresses stability. But in a wider context—say, that of the Beatles music more generally—tonics do not usually signify in this manner, and therefore the “Day in the Life” chord has nothing to bounce off of; its meaning is muffled within the vast, nonreverberating space of the Beatles’ complete oeuvre. When we listen to any piece of rock music, we effortlessly switch between the most specific and most general expressive contexts. The key is to know where we stand at any given moment. Expressive effects can be projected by any size of harmonic object: an Page 265 →individual sonority, a short or long chordal progression, a tonal center. One might even consider tonal harmony itself, in toto, potentially expressive, especially if pit against alternative systems.2 An attempt at comprehensively assessing all the assorted kinds of harmonic expressive effects in the repertory would double the size of this book, and so we will not make such an attempt here. Nonetheless, there are two types that we would be derelict to ignore completely, those involving break-outs and pump-ups. Recall that a break-out normally entails modulation from one tonal center in the verse to another tonal center up three semitones in the chorus (occasionally by other intervals, or at other sections in a song), while pumping-up usually combines transposition and modulation upward by one or two semitones at some late point in a song or, sometimes, occurring throughout. A break-out is distinct from a pumpup in two ways: first, a break-out does not normally involve transposition, merely modulation; second, a pump-up does not normally move back to where it started, whereas a break-out does. While breaking-out and pumping-up are in themselves not expressive effects and can be used simply as a way to provide some harmonic variety (the pump-up near the end of Morrissey’s 1994 “I Am Hated for Loving You” is about as deadpan as they get), they often do line up with some extramusical aspect of the song. It is the latter, expressively charged variety of these transformations that is relevant here, and we will consider just a few more final tracks that exemplify

these. The primary expressive purpose of the break-out and the pump-up is to indicate an increase in the track’s emotional intensity. A textbook case of an expressive break-out is Eddie Money’s 1986 “Take Me Home Tonight” (backed by Ronnie Spector, formerly of the Ronettes): a loop on Bв™-in the verse (“I feel a hunger, it’s a hunger”) gives way to a journey loop on Dв™-at the chorus, where Money’s amorous plans are finally laid bare (“Take me home tonight”). A classic expressive pump-up appears in Whitney Houston’s 1992 “I Will Always Love You”: a transposition and modulation from A up to B is heard immediately after a brief silence and single drum hit. (This expressive move is added to the modulation-less original recorded by songwriter Dolly Parton in 1974.) In these types of situations, the transformations express expressiveness itself, as if to say, “I really mean it now, even more than before.” This is a double-edged sword: Lauren Hill deliberately avoids such obviousness in her cooled-down 1998 cover of Frankie Valli’s 1967 “Can’t Take My Eyes Off of You,” by removing the original’s oversized, three-semitone pump-up completely. Less commonly, break-outs and pump-ups can be used to differentiate places or things. In Elton John’s “Rocket Man (I Think It’s Going to be a Long, Long Time)” (1972), a break-out distinguishes between the narrator’s Page 266 →life problems in the verses on G (“She packed my bags last night, preflight”) and his epic, otherworldly flight through outer space in the choruses on Bв™-(“And I think it’s going to be a long, long time”). In Hank Snow’s 1962 cover of the original Australian patter song “I’ve Been Everywhere,” multiple pump-ups impart unique tonal centers for each of four lists of U.S. cities, conveying tonally the distances the narrator has traveled: Cв™Ї (“Reno, Chicago”), then D (“Boston, Charleston”), then Eв™-(“Louisville, Nashville”), and lastly E (“Pittsburgh, Parkersburg”). In their 1964 cover of “Louie Louie,” The Beach Boys use the pump-up not to distinguish between items identified in the lyrics but between more abstract musical idioms: they pay tribute to the two most important earlier recordings of “Louie Louie”—the 1957 original by Richard Berry and the Pharaohs, and the infamously unintelligible 1963 cover by the Kingsmen—by mimicking the original’s sound in their opening section, then pumping-up from center Gв™Ї to A for the middle section, where they imitate the Kingsmen, before pumping-down back to Gв™Ї for the Berry-like ending. The effect of pumpingdown is extremely rare in the repertory, but it is doubly odd in the Beach Boys’ track, because it represents a modulation and transposition back to the original pitch level, a technique that we cited as one of the main ways a pump-up is characteristically distinct from a break-out. It is perhaps when appearing in tandem that expressive break-outs and pump-ups are at their most interesting. In “Blame It on the Rain” (1989), Milli Vanilli break-out by the rare interval of a single semitone upward when moving from verse to pre-chorus, from center Bв™-(“You said you didn’t need her”) to center B (“you let her walk awayВ .В .В . blame it on the rain”), only to pump-up by that same amount from chorus to repeated chorus near the end of the song, up to center C. In “All I Need Is a Miracle” (1985), Mike + the Mechanics constantly change the tonal center by augmenting each verse-chorus break-out with a pump-up, resulting in a pattern of falling perfect fourths. The first verse’s F (“I said вЂgo if you wanna go’”) breaks-out to C in the first chorus (“all I need is a miracle”), which then goes back to a verse that has pumped-up to G (compared to the original F: “I never had any time”); the song then breaks-out to D at the next chorus (also heard as another pump-up when compared to the first chorus’s C), which then gives way to A (a pumped-up G) at the instrumental break (which is actually the music of the verse). Only Mike + the Mechanics’ final chorus fails to follow the miraculous pattern, instead simply going back to the previous chorus’s D (which is still a break-out as measured against the preceding instrumental verse’s A, but not a pump-up as measured against the D of the previous chorus). Both Milli Vanilli and Mike + the Mechanics invest a great deal of harmonic energy in trying to let us know just how much they mean what they sing. Page 267 →Our final example, for this brief discussion of expression as well as for the entire book, is the largerthan-life “God Gave Rock’n’roll to You,” originally recorded by the British band Argent in 1973 but famously reworked (with some new lyrics) as “God Gave Rock’n’roll to You II” by Kiss for the closing sequence of the 1991 film Bill and Ted’s Bogus Journey. Argent employs verse-chorus break-outs

from center Bв™-(“Love your friend and love your neighbor”) up a major second to C (“God gave rock’n’roll to you”), then sink down to A for a quiet bridge with a fake-out fadeout, before simultaneously breaking-out and pumping-up to D for the triumphant return of the chorus, a kind of harmonic Second Coming. The cover by Kiss largely follows the original, but with some important harmonic changes. Kiss transposes most of the song down a semitone, so that the verses start on center A and the choruses on B. Kiss also projects strong ambiguity in the verses by looping EM–AM (which is not in the original), operating as V–I on A but also I–IV on E; this ambiguity makes the chorus’s sturdy tonal center of B all the more powerful by comparison. But the really significant changes come in the middle of the song: rather than wait for the final choruses to pump-up (after the quiet bridge and false ending in the original), Kiss jumps the gun, pumping-up right as the second verse melts into its ensuing chorus, and not even to the expected B but rather to Eв™-, a shocking four semitones higher. The expressive highlight of the entire track, this giant leap requires the singers to noticeably strain their voices in order to hit the notes, the sound of their struggle heightening the already obvious expressive effects of the passage. Kiss collapses back down to B for the final choruses, likely because the strain of that vocal range for the entirety of the long, final fadeout would have proved too great. In any event, the pumpdown does represent another instance of a transformational effect, which in this context is still expressive of an increase in emotional intensity despite its downward motion, because of the cumulative rhetoric of the repetition. As if that were not enough, there is one more additional harmonic effect that contributes to Kiss’s expressive moment, although one so subtle that it will only be heard with knowledge of both performances: a pump-up between recordings. At the end of Argent’s track, the pump-up takes us to a highpoint of center D; in Kiss’s performance, the pump-up is to Eв™-, one semitone higher. For sure, hearing Kiss’s Eв™-in relation specifically to Argent’s D is not an obvious effect, but this pump-up is definitely something that one can hear; it is without question a potential harmonic effect. Absolute (perfect) pitch is not required (although it certainly helps); all we need to do is internalize Argent’s recording to the point where we can experience the difference in Kiss’s. (Playing or singing along helps as well.) The various break-outs and pump-ups of Kiss’s track, combined with expressive use of schemas—a combinationPage 268 → of thoroughly rock-ish and cadences with grand, baroque-ish gestures like the chorus’s stepwise descending line (not quite a sauntering schema, but certainly an elongated version of the slide, 1–ꜛ7–ꜛ6)—all make for an exemplary piece of popular-music expression. Moreover, our interpretation of Kiss’s cover in transformational relation to Argent’s original reflects a central message of this book: that there are potentially rewarding experiences to be gotten when attempting to hear the harmony (and disharmony) between the diverse voices of the rock era.

Harmony Heard Hearing rock harmony can be a complex experience. Even a seemingly simple loop like EM–AM or DM–CM–GM can create various effects of center and scale and schema and function, not to mention transformation and ambiguity and expression. Indeed, it is the short, repeating harmonic figures so characteristic of rock that can be the most baffling, although longer-range structures of course carry their own bags of tricks. In this book we have indulged our aural imaginations by listening closely, deeply, and broadly to a vast assortment of artists and styles in an attempt to squeeze out as much experience as possible from the fascinating harmonic practice of the rock era. In doing so, we have defied the instructions of several of the musicians under study, who by and large have taken a stance against any kind of appreciation of rock music that is self-conscious, that is facilitated by formal musical training, or—worst of all—that is perceived in any way as intellectual. But since defiance has been such a central theme to so many rock musicians, it seems that we are merely being good rock citizens in our revolt against the hegemonic dogma that the music be appreciated only in certain ways. To the potential criticism that we as hearers of rock harmony are both usurping and distorting the music for our own nefarious purposes, we might proudly say, “damn straight.” While empowering, this defiant attitude is at the same time hyperbole. To the charge of usurpation, we could respond that there is often no clear divide between rock insiders and rock outsiders, or between those who have the social authority to dictate our experiences and those who do not, and even if there were, there is no good reason for us, on purely logical or ethical or moral grounds, to advocate depriving certain groups of people the

right to aurally experience the music for themselves, in the manner they see fit. To the charge of distortion, we can point out that a central concern for us throughout this text has been the maintenance of a sensitivity to all the Page 269 →possibly relevant sonic details of the music, details that the musicians themselves (songwriters, performers, engineers, producers) put in, consciously or not. Our strategy of engagement with the music has thus really been one not so much of defiance but rather of simple disinterest with regard to stated authorial intentions, although even this is not entirely true, since we have many times taken into account what musicians have said about their work so long as it has deepened—not limited—our understanding of their work. Any distortion we might perpetrate will have been not a product of malicious intent but rather a consequence of our zealous immersion in the repertory. Much more than mere “distortion,” our engagement with the music has constituted a kind of inexorable renovation, a positive and at any rate inevitable change in what the music is resulting simply from its being heard by unique individuals with unique combinations of musical backgrounds, proclivities, and demands. While there is undoubtedly a sonic reality that lies outside the range of our individual interpretations, the music does not merely wait for us to come along and take notice of it. If we are honest about how we hear harmony, we must shoulder responsibility for the power we exert over our own musical experiences. We are the listeners, and therefore, to some extent, we are the music makers. A basic task of scholarship is to persuade its audience of the truth or significance of its claims through argumentation and evidence. A more specific task for this book would seem to be to convince skeptical music lovers that the entire enterprise of talking about rock harmony in a serious way—and indeed the act of hearing harmony itself—is a worthwhile endeavor. Does the intellectualization, the categorization, the verbalization of musical experience do violence to that experience? In all honesty, the more self-conscious we become as listeners, the less likely we will be to experience music as raw emotion, as spontaneous sonic expression of the human condition. Yet it is the opinion of this author that what we lose in rawness is more than made up for by what we gain in experiential depth and variety. We can of course still connect with music emotionally as educated listeners, but our awareness of the mechanics of our experiences will enable us to better understand which aspects of the music are the most important to us and to fellow listeners. This awareness will sharpen our ability to make informed choices about the kinds of musical experiences we want to have at any given moment. We are now well on our way toward a tonal theory for the rock era. Yet most of the necessary work still lies ahead of us. Beyond harmony, rock melody needs careful and extensive study; although we have engaged melody as it pertains to hearing harmony in certain ways, we have barely scratched its surface. Rock counterpoint—the interaction of harmony and melody—could Page 270 →also easily receive its own treatise. The magnitude of the work still remaining to be done is at once exhilarating and disheartening. We can only hope that by continuing to devote substantial, serious attention to this repertory, we will inch ever closer to a general understanding of how this music affects us in the ways it does. In any event, regardless of our personal goals and dispositions, it is an observable truth that rock music is bursting with chords. If we are not hearing what they have to say, we are missing a big part of the conversation.

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Appendix B Letter Notation Type of sonority (not exhaustive) power chord major triad

Examples E5 EM

E, B E, Gв™Ї, B

minor triad augmented triad

Em E+

E, G, B E, Gв™Ї, Bв™Ї

diminished triad 2-chord 4-chord major-minor triad major minor-seventh chord major major-seventh chord minor minor-seventh chord minor major-seventh chord half-diminished seventh chord fully-diminished seventh chord major flat-fifth minor-seventh chord 6-chord major minor-sixth chord minor major-sixth chord minor minor-sixth chord major-ninth chord minor minor-seventh major-ninth chord major major-seventh major-ninth chord major minor-seventh minor-ninth chord minor minor-seventh minor-ninth chord sharp-ninth chord (no fifth) major-ninth chord (no seventh)

Eo E, G, Bв™E2 E, Fв™Ї, B E4 E, A, B EM(m) E, G, Gв™Ї, B E7 E, Gв™Ї, B, D EM7 E, Gв™Ї, B, Dв™Ї Em7 E, G, B, D EmM7 E, G, B, Dв™Ї E(half)o7 E, G, Bв™-, D Eo7 E, G, Bв™-, Dв™E7(в™-5) E,Gв™Ї, Bв™-, D EM6 E, Gв™Ї, B, Cв™Ї EM(m6) E, Gв™Ї, B, C Em(6) E, G, B, Cв™Ї Em(m6) E, G, B, C E9 E, Gв™Ї, B, D, Fв™Ї Em9 E, G, B, D, Fв™Ї EM7(9) E, Gв™Ї, B, Dв™Ї, Fв™Ї E7(m9) E, Gв™Ї, B, D, F Em7(m9) E, G, B, D, F E7(в™Ї9)(-5) E, Gв™Ї, D, Fв™Їв™Ї(G) EM(9) or E9(-7) E, Gв™Ї, B, Fв™Ї

minor major-ninth chord (no seventh) Em(9) minor-eleventh chord Em11 major-eleventh chord (no third) E11(-3) Page 278 →sharp-eleventh chord E7(в™Ї11) major-thirteenth chord with sharp eleventh E13(в™Ї11)

E, G, B, Fв™Ї E, G, B, D, Fв™Ї, A E, B, D, Fв™Ї, A E, Gв™Ї, B, D, Fв™Ї, Aв™Ї E, Gв™Ї, B, D, Fв™Ї, Aв™Ї, Cв™Ї

Parenthetical tones are in addition to the rest of the chord, and are always indicated by full intervals as measured upward from root Roots are the assumed bass notes. Nonroot bass notes are indicated with a slash: e.g., “EM/B.” The bass note may be left out of the first half of the designation: e.g., “Em(m6)/D♯” rather than “Em(m6)(M7)/D♯”

2s and 4s are assumed to be perfect intervals; sixths are assumed to be major; sevenths are assumed to be minor; ninths, elevenths, and thirteenths are assumed to be major; seventh chords are assumed to feature major triads (hence E7); ninth chords are assumed to feature major minor-seventh chords (hence E9); these are all based on relative commonness in the repertory at large Numerals may replace the root letter: e.g., I5, VM(m), в™-II7(в™Ї9) Other ad hoc designations are to be added as needed (e.g., major-thirteenth chord with major seventh and sharp eleventh = EM7(9)(в™Ї11)(13) = E, Gв™Ї, B, Dв™Ї, Fв™Ї, Aв™Ї, Cв™Ї) Superscript designations indicate one note in addition to the root without precluding other possibilities; thirds are m or M; fifths are 5 or o or +; sixths are 6 or m6; sevenths are 7 or M7 or o7; ninths are 9 or в™-9 or в™Ї9

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Appendix C Diatonic Scale Degrees and Numerals Common diatonic scale degrees sharp/upper: в™Ї1 в™Ї2 књ›3 в™Ї4 в™Ї5 књ›6 књ›7 natural: flat/lower:

1

2 — 4 в™-2 књњ3

5 — — в™-5 књњ6 књњ7

Common diatonic numerals sharp: в™ЇI ↑III в™ЇIV ↑VI ↑VII natural: I II — IV V — — flat: в™-II ↓III в™-V ↓VI ↓VII Common scales with diatonic scale degrees major diatonic, or ionian: 1 2 књ›3 mixolydian: 1 2 књ›3 dorian: 1 2 књњ3 natural minor, or aeolian: 1 2 књњ3 pentatonic minor: 1 књњ3 pentatonic major: 1 2 књ›3

4 5 књ›6 4 5 књ›6 4 5 књ›6 4 5 књњ6 45 5 књ›6

књ›7 књњ7 књњ7 књњ7 књ›7

Common scales with diatonic numerals major diatonic, or ionian: I II ↑III IV V ↑VI ↑VII mixolydian: I II ↑III IV V ↑VI ↓VII dorian: I II ↓III IV V ↑VI ↓VII natural minor, or aeolian: I II ↓III IV V ↓VI ↓VII pentatonic minor: I ↓III IV V ↓VII pentatonic major: not normally the basis for harmonies The scales presented here are only those commonly heard in their entirety, even though they do not produce all the commonly heard scale degree and numerals (в™-2, в™Ї4/в™-5, в™ЇI/в™-II, and в™ЇIV/в™-V are normally chromatic or heard in partial scales) To produce more scale degrees or numerals, additional sharps, flats, or arrows can be added: e.g., в™Їв™Ї1, в™-в™II, књ›књ›6, ↓↓VII

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Appendix D Tonic and Predictive Functions alpha / tonic (centric 1; typically I) beta / pre-tonic dominant / hyper pre-tonic (7 and 2/књњ3; most commonly V, ↓VII, ↓III, ↑VII) lead dominant (књ›7 and 2/в™-2/в™Ї2; most commonly V, ↑VII) rogue dominant (књњ7 and 2/в™-2/в™Ї2/књњ3; most commonly ↓VII, ↓III, V) subdominant / hypo pre-tonic (6; most commonly IV, II, ↑VI, ↓VI, в™-II) upper subdominant (књ›6; most commonly IV, II, ↑VI) lower subdominant (књњ6; most commonly IV, II, ↓VI, в™-II) mediant / medial pre-tonic (књ›3 and књ›7; typically ↑III) gamma / pre-pretonic (scale-degree possibilities are numerous) pre-dominant hyper pre-dominant (dominant of a dominant) hypo pre-dominant (subdominant of a dominant) medial pre-dominant (mediant of a dominant) pre-subdominant hyper pre-subdominant (dominant of a subdominant) hypo pre-subdominant (subdominant of a subdominant) medial pre-subdominant (mediant of a subdominant) pre-mediant hyper pre-mediant (dominant of a mediant) hypo pre-mediant (subdominant of a mediant) medial pre-mediant (mediant of a mediant) delta / pre-prepretonic (voice-leading largely irrelevant at this point) pre-predominant pre-presubdominant pre-premediant epsilon / pre-preprepretonic (voice-leading largely irrelevant at this point) pre-prepredominant pre-prepresubdominant pre-prepremediant

Page 281 →

Appendix E Harmonic Schemas two-chord

other rotation I–в™-II I–II



I–↓III I–↑III

I–IV I–♯IV/в™-V

I–V

I–↓VI

I–↑VI

I–↓VII

I–↑VII three-chord









other rotations I–II–V V–I–II I–↓III–V V–I–↓III I–IV–V V–I–IV I–IV–↓VI ↓VI–I–IV I–IV–↓VII ↓VII–I–IV I–V–IV IV–I–V I–↓VI–IV IV–I–↓VI I–↓VI–V V–I–↓VI I–↓VI–↓VII ↓VII–I–↓VI I–↑VI–IV IV–I–↑VI I–↑VI–↓VII ↓VII–I–↑VI I–↓VII–IV IV–I–↓VII

Page 282 →four-slot

other rotations



I–↓III–↓VII–IV I–↑III–IV–V I–IV–I–V I–IV–II–V

IV–I–↓III–↓VII V–I–↑III–IV V–I–IV–I V–I–IV–II

↓VII–IV–I–↓III IV–V–I–↑III I–V–I–IV II–V–I–IV

bamba

I–IV–V–IV I–IV–↑VI–V I–IV–↓VII–IV

IV–I–IV–V V–↓I–IV–↑VI IV–I–IV–↓VII

V–IV–I–IV ↑VI–V–I–IV ↓VII–IV–I–IV



I–IV–↓VII–V I–V–II–IV

V–I–IV–↓VII IV–I–V–II

↓VII–V–I–IV II–IV–I–V

I–V–IV–V V–I–V–IV IV–V–I–V journey I–V–↑VI–IV IV–I–V–↑VI ↑VI–IV–I–V

I–V–↑VI–V V–I–V–↑VI ↑VI–V–I–V

I–V–↓VII–IV IV–I–V–↓VII ↓VII–IV–I–V zombie I–↓VI–↓III–↓VII ↓VII–I–↓VI–↓III ↓III–↓VII–I–↓VI steady I–↑VI–II–V V–I–↑VI–II II–V–I–↑VI king I–↑VI–IV–V V–I–↑VI–IV IV–V–I–↑VI

I–↑VI–V–IV IV–I–↑VI–V V–IV–I–↑VI

I–↓VII–IV–V V–I–↓VII–IV IV–V–I–↓VII

I–↓VII–IV–↓VII ↓VII–I–↓VII–IV IV–↓VII–I–↓VII walk I–↓VII–↓VI–V V–I–↓VII–↓VI ↓VI–V–I–↓VII watchtower I–↓VII–↓VI–↓VII ↓VII–I–↓VII–↓VI ↓VI–↓VII–I–↓VII pentatonic





I–↓III–IV I–↓III–↓VII I–IV–↓III I–V–↓VII I–↓VII–↓III I–↓VII–V I–↓III–IV–↓III

other rotations IV–I–↓III ↓VII–I–↓III ↓III–I–IV ↓VII–I–V ↓III–I–↓VII V–I–↓VII ↓III–I–↓III–IV IV–↓III–I–↓III



I–↓VII–↓III–IV

IV–I–↓VII–↓III ↓III–IV–I–↓VII

multipentascent I–↓III–IV–↓VI–↓VII etc. Page 283 → Meta-Schemas dip (descending from center): 1–ꜛ7–ꜜ7–ꜛ6 drop (descending from center): 1–ꜜ7–ꜛ6–ꜜ6–5 droop (descending from center): 1–ꜛ7–ꜜ7–ꜛ6–ꜜ6–5 shrink (short): књ›6–ꜜ6–5 slide (short, and descending from center): 1–ꜛ7–ꜛ6 slouch (short): 5–в™-5–4 slump (short): 2–в™-2–1 soar (short): 1–♯1–2 stretch (short): 5–♯5–ꜛ6 swell (short): 4–♯4–5 tease (up and down): 5–♯5–ꜛ6–ꜜ6–5 teeter (up and down): 5–ꜛ6–ꜜ7–ꜛ6–5 tour (up and down): 5–♯5–ꜛ6–ꜜ7–ꜛ6 twirl (up and down): 5–♯5–ꜛ6/4–♯4–5 Extended blue: I || IV–I || V–I crossing: IV–I || (IV or II)–V down’n’out: I5–↑IIIM–↑VIM || (II or IV)–↑VIM–II || (IIM or в™ЇIV)–V ease: I–IV–↓VII–↓III–↓VI || V in-mind: I–V–(I or ↑VI or IV)–IV || I–V–(I or IV)–I Jimi: saint: I–V || I–IV–I–V–I saunter: I–VM–↑VI–(↑IIIm or ↑IIIM)–IV–IM–V search: I–↑VI–I–↑VI || IV–V vaudeville:

Page 284 → Page 285 →

Notes Introduction 1. Popular music’s presumed plainness has also been touted as a virtue: songwriter Harlan Howard is often credited with calling country music “three chords and the truth” (Leamer 1997, 434). Critical theorist Theodor Adorno (2002 [1941]), on the other hand, in his critique of prerock popular music, acknowledged that this repertory comprises many more different chords than does Western classical music, but that the interchangeability of these chords is testament to their meaninglessness. 2. Following Moore 2001b, 1–4, this book will use the term “style” as opposed to “genre” in describing subcategories of rock-era popular music (rockabilly, glam, new jack swing, etc.). See also Moore 2001a. 3. See Berger 1999a, 1999b; Lilja 2009. 4. See Green 2002. 5. DeBellis 2003, 596; Dubiel 2004, 174. 6. It is worth mentioning that the same is true of any and every style of music, not just rock. Indeed, Western classical theorists have spent a considerable amount of its time cultivating ideas that require intensive formal study and that have little direct relevance to the wider population of classical listeners. And we should be okay with this. 7. Quoted in Miles 1997, 206. 8. On the topic of citation, I must point out that nearly all the scholarly references in this text are to music theory, despite my earlier assertion that this book’s theory is “philosophical-psychological.” The influence of scholarship in philosophy and psychology herein is strong if not often acknowledged explicitly; the landscape will be busy enough without inserting Peirce, Husserl, Longuet-Higgins, Deutsch, and a host of others into the scene. 9. See Snarrenberg 1997, 9–53. 10. Nietzsche 1968, 283. 11. Lilja 2009, 101–51, discusses distorted power chords at length, highlighting relevant issues of overtones and combination tones. 12. For more on sectional conventions in rock, see Covach 2005, Osborn 2013, de Clercq 2012, Summach 2012, and the 17/3 (2011) issue of the journal Music Theory Online. Page 286 →13. This book’s primary style of citing musical examples, that of using lyric snippets interlaced with chord symbols, was inspired by Everett 2009.

chapter 1 1. Letter notation actually varies widely, and in rock settings there is a tendency to assume a major triad for all chords unless otherwise indicated, so that “A” stands for “A major triad.” Such assumptions are very much in question in this book, so we will use “M” to specify major triads. 2. “Phrasing” here simply means the cohering of the music into small-scale chunks, based on gaps or changes in the instrumental and/or vocal lines; for instance, the brevity of the C7 relative to the surrounding sonorities creates a shorter bar of 2/4 right before B7. The “backbeat,” a regular emphasis on beats two and four in one bar of 4/4, normally determines a rock song’s beat tempo and meter; whenever we use the term “bar,” it will mean four beats measured against the main backbeat, unless stated otherwise. In certain kinds of heavy metal, the backbeat is sometimes understood as twice as slow as the beat, with a hit occurring on every third beat, but we will not follow that convention in this book; the backbeat will always be interpreted as the second and fourth beats. Some songs have more than one possible backbeat, but such matters are beyond our concerns in this text. 3. A Western classical musician would have written “AM64” instead of “AM/E.” The former “figured” notational style is alien to most rock musicians, and proves inadequate when labeling chords that feature dissonant basses.

4. Those readers trained in Western classical theory will recognize the C7 as an incorrectly spelled German augmented-sixth chord (C, E, G, Aв™Ї). We will use the “C7” designation because it is neater. The pitch class in question clearly operates as both Bв™-(within the sonority itself, out of time) and Aв™Ї (as part of a moving line, within time). 5. “Pitch-class intervals,” or “pc intervals,” refer to the distances in semitones between each pitch class in the chord. These distances can be measured on a piano or guitar by counting the number of keys or frets we travel, from one note up to the other. Guitar-tablature notation works exactly this way, with finger positions indicated by the interval above each open string. (The only difference is that in guitar tablature the intervals are measured between pitches, not pitch classes.) AM’s measurements are 4, 3, 5 (A to Cв™Ї, Cв™Ї to E, E to A), and Em’s are 3, 4, 5 (E to G, G to B, B to E). The arrangement of a chord’s pc intervals is traditionally referred to as the chord’s “quality,” but we will not be following this convention; rather, we will use “quality” more broadly, to describe any aural aspect of a harmony. 6. Readers who have already made it through this book at least once will recognize in the chorus of “Lucky” a transformation of the long version of the crossing schema (with repetition of IV–I) via numeric chord substitution (в™-VI for IV or II). All these technical terms will be developed in subsequent chapters. Page 287 →7. Harmonic “function” as a term originates with Riemann 1896 [1893], although Riemann’s use(s) of the term differed significantly from that here. See also Kopp 1995. 8. Scholars do not always treat the term “heptatonic” synonymously with “diatonic,” but for our own purposes the two terms are interchangeable. A tricky case is the so-called melodic-minor scale, which might not seem to qualify as diatonic under this definition of the word, since it features nine pitch classes when counting both its ascending from descending forms (e.g., E, Fв™Ї, G, A, B, Cв™Ї, Dв™Ї, E, D, C, B, A, G, Fв™Ї, E). Melodic minor, however, still contains only seven scale degrees, with two of them each offering two possible realizations at any given moment (C versus Cв™Ї, and D versus Dв™Ї). At any rate, the reality of melodic minor is controversial in itself, and we will not treat it as a standard rock scale. 9. Ken Stephenson (2002, 42–43 and 88–99) sees similar problems with the term “key” as applied to rock music, but still elects to employ it broadly, in combination with three harmonic “palettes” or “systems” that substitute for traditional major and minor scales. Walter Everett (2004a) has approached this issue by theorizing six distinct “tonal systems” for rock music, systems that resemble Daniel Harrison’s (2002) “key-articulation types” devised for the pitch systems of late nineteenth- and early twentieth-century classical music; Everett also keeps “key.” 10. In chapter 2, we will discuss the concept of functional strength, which speaks volumes about situations like this. By the end of “Hyper-Ballad” the lack of strong Bв™-tonics, combined with the prominence of Gm triads, eventually pushes the tonal center off Bв™-onto G. This type of swing between centers a minor third apart is quite common in rock; we will see many examples of this in chapter 6. 11. Note that our use of the term “dominant” versus “subdominant” in the “Lucky” has nothing whatsoever to do with the locations of the functions within the phrase. If the chorus’s B7 appeared where AM originally did and vice versa, and we still heard each chord projecting pre-tonic function, B7 would still be a dominant and AM a subdominant. 12. The key signatures in the notation should be thought of as “set signatures,” meaning that they merely indicate the primary set of notes used in a musical passage, not a key per se. 13. Depending on the context, the centric pitch class is traditionally written also as “8.” This convention blurs the distinction between scale-degree space and pitch space, a distinction that we will make an effort to keep clear. Since scale-degrees themselves, by definition, have no registral attributes, we will refer only to scale degrees 1 through 7 (with multiple versions available for each). (This said, we will still use numbers larger than 7 to indicate certain members of chords, such as 9, 11, and 13 for chordal ninth, eleventh, and thirteenth respectively, combined with a root letter: e.g., E9, E11, E13.) 14. In Western classical harmonic theory, the leading tone is a requirement for dominant function. In rock and jazz theory, on the other hand, dominants featuring the subtonic are a matter of course; see, among many other sources, Potter 1989, Moore 1995, and Tillekens 2002. Page 288 →15. Our severing scale degree 4 from subdominant function is likewise not totally without precedent. Kevin Swinden (2005, 254), inspired by Daniel Harrison (2002), suggests that 4 sometimes

expresses subdominant function (as it might when appearing as a chordal root) and other times dominant function (as it might when appearing as a chordal seventh of a dominant built on 5). 16. The Pumpkin’s Em triad is preceded by a dominant DM triad, which contributes to Em’s projection of two other effects: softening function (a term to be defined in the next chapter) and its own weak tonic function. This kind of functional multivalency will be briefly discussed later in this chapter, and will receive due consideration in chapter 6. 17. Daniel Harrison also hears great subdominant strength in 6. Harrison’s notion is expressed as a more general rule: his three functional “agents”—6 for subdominant, 7 for dominant, and 3 for tonic—are uniquely and “entirely dedicated to the function in question” (1994, 49). 18. In Harrison (1994, 90ff.), the realization of this kind of anticipated voice leading among scale degrees is termed “functional discharge.” 19. Hill’s version is different from the original 1967 recording by Frankie Valli. In the verses, Hill uses one Fв™Їm triad whereas Valli uses Fв™ЇM/E and then Fв™Їm/E (an example of we will call a “slouching” motion in chapter 4). However, Hill does maintain the original’s chords in her introduction. 20. See also Tymoczko 2003. 21. In the second bridge of “Glad All Over,” the raised note (Eв™Ї) is harmonized as an Aв™Ї5 (or Bв™-5), which functions as a dominant on new center Dв™Ї (Eв™-) and resolves to tonic Dв™ЇM (Eв™-M). In this way, the upward motion of the raised 2 actually encourages the tonal center itself to lift from D to Dв™Ї (or Eв™-). Such rising centric shifts are common in 1960s rock; chapter 5 will expand on these. 22. Even such exceptional augmented triads are sometimes offset by the simultaneous sounding of a major triad underneath, in which the natural 2 drags downward to 1 while в™Ї2 shoves upward to 3. This happens at the end of the bridge in Carl Perkins’ “Glad All Over” (1960), not the same song as Dave Clark’s, but possibly a source of inspiration for the title and the bridge-ending augmented harmonic gesture. See also Everett 2001, 80. 23. Bryan Ferry’s backing vocal line itself features both 6–5 and 6–1 anticipations. He moves from F down to E in anticipation of Am (before the Am chords actually occurs), then leaps up to A momentarily before coming back down to the earlier E: “[F] to wait [E] for the [A] bell [E] to ring.” Yet the solitary A sounds more like an embellishment of the F to E resolution, imitating the sound of a high “bell” being struck. 24. Our accepting that individual notes often anticipate travel between chords along multiple scale-degree paths of varying distances distinguishes the current theory from much other contemporary harmonic theory, which often focuses on chordal notes traveling along the most direct routes (e.g., Lerdahl’s (2001, 73–77) principle of the shortest path, Capuzzo’s (2004) parsimony, and Tymoczko’s (2011, 17–19) efficiency). Page 289 →25. Two seminal cognition-based writings on the nature of melodic hearing are Narmour 1990 and 1992. For an application of this kind of thinking to harmony, see Lerdahl 2001, 161–92. 26. There is actually an infinite number of possible scale-degree combinations beyond those we have already covered; scale degrees can always be raised and lowered another notch, so that we can have “doubly sharp 2,” “doubly flat 2,” “triply sharp 2,” “triply flat 2,” and so on. We will have no need for such abstract monstrosities in this book. 27. The в™Ї9 of this chord is notated literally as Cв™Ї in Example 1.7b, but traditionally it would be spelled as a flat tenth, Dв™-. 28. в™-2 is more common in pre-tonics with књњ6 than in pre-tonics with књ›7 or књњ7, which is to say they are more common in lower subdominants. An example can be heard in the FM–EM motions in the main sections of “Misirlou” by Dick Dale and His Del-Tones (1962): FM, with its root F as в™-2, and its chordal fifth C as књњ6, functions as lower subdominant to tonic EM, with its roots E as 1. 29. See, for instance, Kopp 2002. 30. It may be that књ›3 and књњ7 have never been combined in any pre-tonic ever. књњ3 combined with књ›7 would sound very much like (although not quite the same as) the в™Ї2 and књ›7 we heard in the lead dominant A+ from the Dave Clark Five’s “Glad All Over” (књњ3 and в™Ї2 are “enharmonic equivalents”). The difference between hearing this chord as an A+ versus an F+ has to do with various

factors, not the least of which is the root effect, an idea to be discussed in the next chapter. 31. Nirvana’s G might be analyzed a diatonic в™Ї2, but as such would probably shove upward to књ›3 (Gв™Ї) instead of maintaining itself through to the tonic’s chordal third as G-natural. When a scale degree has a natural form, as does 2, the sharp form tends to drive stepwise upward for resolution. By contrast, the flat form of the same scale degree will tend to drive stepwise downward, as в™-2 normally does to 1. These types of opposing tendencies are the main motivation for our distinguishing between sharp, natural, and flat degrees in the first place. 32. Our acknowledgment that diatonic and pentatonic scales correlate to white keys and open strings/black keys is not tantamount to offering anything approaching a physicality-based explanation as to why rock musicians tend to favor these scales. String orchestral music does not favor open-string pentatonicism, even though the open strings of violins, violas, cellos, and basses add up to C, D, E, G, and A. Correlation does not equal causation. There is obviously a relationship between the physical nature of instruments and the music composed for them, but this relationship is complex and not easily generalized. 33. Temperley 2011b explores rock’s “scalar shifts” in detail. See also Clement 2015. 34. For more on diatonicism versus chromaticism in rock, see Heetderks 2015. 35. Pentatonic versions of књњ6 and књ›6 arise when major and minor pentatonic scales start on 4; this phenomenon will be studied thoroughly in chapter 4’s discussion of pentatonic schemas. For a recent statistical argument for the existence of a blues scale, see Temperley and de Clercq 2013. Theirs they call the “pentatonic union scale”: 1, 2, књњ3, књ›3, 4, 5, 6, књњ7. Page 290 →36. See also Seeger (1958), who differentiates between “descriptive” versus “prescriptive” musical notations, although his point is different than that here. Benjamin Boretz (1977a, 1977b) frames this distinction as “descriptive” (or “explanatory”) theory versus “attributive” theory. See also Temperley 1999.

Chapter 2 1. While a secondary/applied dominant usually does not entirely fit into the prevailing diatonic scale, there is one possible exception: a major triad on књњ7 resolving to a major triad on књњ3 (e.g., with center E, DM–GM). This subtonic chord can be thought of as diatonic to a prevailing natural-minor scale (E aeolian). 2. Even though Williams’ dominant is G7, not GM, the secondary-dominant explanation holds. Socalled chordal “extensions” do not affect the analogy; the only true requirement is that the root, third, and fifth of each chord make a major triad. 3. The one function in Example 2.2a that may not really exist in the repertory is medial pre-mediant; the author has not found any cases of it, and he includes it here solely for the sake of logical completeness. 4. Henry Martin (1988) has a developed a notational style that designates the ultimate point of resolution (which he defines as a “tonicized chord” (14)) as “N,” with each preceding chord in order designated “N-1,” “N-2,” “N-3,” etc. backward through the harmonic progression. Martin’s nomenclature is based solely on chordal-root motions by fifth (and substitutions of these motions) and thus does not accommodate all the various chordal-root motions allowed under our theory. (For instance, Martin’s notation does not accommodate the chordal root relations by third that he finds at the deeper tonal levels in John Coltrane’s 1960 “Giant Steps.”) 5. The opposite to “sub” would be “super,” but using “superdominant” against “subdominant” would probably create so much confusion that it is not even worth trying. 6. For a multi-scalar numeric system, one based on all seven of the jazz modes, see Moore 1992; 2001b, 52–55; and 2012, 69–76. See also the discussion of Roman numerals in Lilja 2009, 56–61. 7. Trevor de Clercq and David Temperley (2011) find the most commonly occurring chords in its pool to be, in order: I, IV, V, ↓VII, ↑VI, ↓VI, II, ↓III, ↑III, в™ЇI/в™-II, ↑VII, and в™ЇIV/в™-V. De Clercq and Temperley’s findings are consistent with the assumptions about commonness underlying our own numeric notation, which is used in the previous sentence instead of the major-scale-standard notation employed by those authors. 8. A listener not experienced enough to aurally distinguish common chordal roots from uncommon ones

would presumably not hear the music in a way corresponding to these prefixes. This does not mean the notation cannot articulate such hearings, just that some of the motivation behind the symbols would be irrelevant. In that case, a numeric system based solely on the ionian system would be just as effective. Page 291 →9. Our numerals are also more flexible than the Arabic numerals of the otherwise-similar Nashville Number System, in which the major triad is treated as standard. 10. See also Lerdahl 2001, 227, for a similar function/numeral distinction. 11. See Everett 2004a, В§18; Stephenson 2002, 87–88; and Temperley 2011a, В§8.4. The chordal fifth in “With a Little Luck” is clearly audible when Paul McCartney arpeggiates the harmony in the electric piano part. Mark Spicer (2004, 38) traces the IV/5, which he calls the “rock dominant,” back to gospel music and Tin Pan Alley songs such as Rodgers and Hart’s 1938 “Who Are You?” 12. The “6” and “4” indicate the notes of the sonority by indicating the interval from the bass up to the other chord tones as measured in diatonic steps (with a unison as 1)—i.e., 6 from D up to B, and 4 from D up to G. “Cadential” refers to the typical phrasal context wherein these kinds of sonorities appear, which will be discussed in the next chapter. 13. E.g., Schenker 1954, 229. 14. Walter Everett (1997, 120–26) analyzes Simon’s GM/D in exactly this way. See also Kaminsky 1992, 41–42. 15. For a comprehensive discussion of how listeners derive chords from music in general, see Yeary 2011. 16. David Temperley (2007), following Allan Moore (1995), has gone as far to theorize rock melody as “divorced” from rock harmony based on the textural stratification inherent between vocal lines and polyphonic chords. As Drew Nobile (2015, 190) rightly points out, Temperley’s idea does not really entail “melodic-harmonic divorce” so much as “melodic-accompanimental stratification,” although Nobile still elects to use the former expression. 17. See also Swain 2002. 18. One could presumably say the same of jazz, although some jazz theorists view jazz harmonies primarily as triads with abundant nonharmonic tones (e.g., Strunk 1985 and Larson 2009). See also McGowan 2011. 19. To this author’s ear, Weill’s chord also contains the harsher M7—a IM7(9)(в™Ї11)(13)—while Paul’s contains the m7—a I13(в™Ї11). Both these examples are mentioned in the discussion of thirteenth chords in Everett 2009, 207–8. 20. Sometimes musicians use “sus2” and “sus,” the latter meaning “sus4.” 21. Technically, a note is “suspended” when it is held over from a previous chord. If it simply appears at the start of a chord, it is traditionally termed an “unprepared suspension.” 22. Mitchell’s use of nontriadic sonorities in “I Had a King,” in conjunction with her nonstandard guitar tunings that allow such sonorities to be played all on open strings, is explored in Sonenberg 2003, 43–51. See also Whitesell 2008 117–47. 23. We should also observe that a 2-chord, a 4-chord, and a three-note quartal chord can all potentially have the same pitch-class and scale-degree content. For instance, a chord containing A, B, and E could be a 2chord with root A (A, B, E), a 4-chord with root E (E, A, B), or a quartal chord with root B (B, E, A). Our hearing one version over the other is usually dictated by the bass, which tends to assert itself Page 292 →as the root. Hence, Mitchell’s harmony is A2, not E4 or a quartal B chord; Foreigner’s is G4, not C2 or a quartal D chord. 24. These and other types of chordal identity are theorized and illustrated with examples in Doll 2009 and 2013. Entity effects have already been theorized by none other than Heinrich Schenker; see Snarrenberg 1997, 43–8. 25. For example, Philip Tagg (2009, 280) does not transcribe the second IV. 26. “Retrogression” might originate with Allen McHose (1947); Paul Carter (2005) discusses at length retrogressions in rock. “Retrogression” has also been used by the present author in Doll 2007, where it was defined not as a reversal of another progression but as a kind of harmonic effect; the author has since abandoned hope of freeing the term of its historical baggage. 27. Everett 2004a, В§18, and 2009, 228–30. 28. “Love Hurts” is one of the examples of “scalar shifting” in Temperley 2011b. 29. IM and ↓VIM are almost “hexatonic poles” (Cohn 2007). A true hexatonic pole to IM would be ↓VIm, a combination resulting in the scale-degree space of 1, књњ3, књ›3, 5, књњ6, and в™-1—a

series of alternating semitones and minor thirds. 30. David Huron (2006, 225–27) theorizes deceptive motions as evoking two different types of expectations in listeners: “verdical” and “schematic.” The former are based on our prior familiarity with the song at hand, the latter on our familiarity with the generic conventions of the musical style. Huron states that in order to be deceived by a progression that we already know is coming, our schematic expectations must trump the verdical ones. 31. Zajonc 1968. Music theorist Elizabeth Margulis (2014, 95–116) points out that more recent cognitive research suggests that the feeling of rightness engendered by mere exposure is even more acute when the exposure is subconscious—when we are unaware it is happening—presumably because this makes it even easier for us to confuse hindsight for foresight.

Chapter 3 1. Significant discussions of rock harmonic formulas can also be found in Carter 2005; Everett 2008, and 2009, 214–301; Lilja 2009, 183–94; Moore 1992, and 2012, 76–85; Pedler 2003; Scott 2003; Stephenson 2002, 100–120; and Tagg 2009, 159–263. 2. The foundational work on musical schemas is that of Leonard Meyer (1973, 1989) and Robert Gjerdingen (2007). 3. This dual standard is roughly equivalent to psychologists’ distinction between prototypes and exemplars. See Gjerdingen 2007, 11–12. 4. Hypothetically, a numeric schema could also arise exclusively at a deeper level, where the adornment by other chords could be identified and reduced out through comparison of different incarnations, yielding a single deeper structure with its own unique schematic effect. But no such cases are known to the author. 5. “Loop” sometimes has a more restrictive definition than we are using here. Philip Tagg (2009, 173–240), for instance, defines a loop as comprising either three or Page 293 →four chords specifically; for two-chord loops, he uses the term “shuttle.” (Tagg’s shuttles actually do not fit entirely within our conception of a loop, because they include some one-chord repeating riffs that in this book do not qualify as progressions.) Tagg also restricts loops and shuttles to quick progressions that stay with “present-time experience,” while our loops here may last any amount of time. 6. Rock cadences of IV–I and ↓VII–I have been written about in detail by David Temperley (2011a) and Allan Moore (1995) respectively. A large discussion of rock cadences in general appears in Stephenson 2002, 53–72, and Nobile 2014, 76–87. 7. Earlier on, we could have also switched around I, V, and II to make “” just like No ordering of this progression, however (including II–I–V and I–V–II), is especially common or salient, and so we will not consider it a schema. But since the difference between a II and IV can be highly subjective (as we noted our discussion of numeric effects in chapter 2), several instances of might very well be interpreted instead, or additionally, as V–II–I, I–V–II, or II–V–I; the I–V–IV loop in the upcoming duet “When You Love Someone Like That” is a case in point. 8. See also Everett 2008, 154–56, and Biamonte 2010, 98–101. 9. The verses of the Beatles’ 1966 “Taxmen” are sometimes considered to be examples of a twelve-bar blues with a ↓VII–IV–I cadence. While that progression is indeed twelve bars long and cadences with ↓VII–IV–I, Trevor de Clercq (2012, 146–51) has shown that it is better understood as a sixteen-bar blues whose cadence (the nonstandard ↓III–I) arrives only in the very last verse; the ↓VII–IV–I cadence is really the result of ↓VII ornamenting the (noncadential) IV, which then resolves to I, instead of the ↓VII substituting for the normal cadential V. 10. The term “double-plagal” may have appeared first in Everett 1995. Synonymous terms include “extended plagal” (Steedman 1984) and “hyperplagal” (Wagner 2004). 11. See also Biamonte 2010, 101–4. 12. If the IV in a progression is a minor triad, it would offer the same scale-degree motion that serves as the roots of . But since IV is usually not a minor triad in , we did not bother to make a comparison between these two schemas.

13. Philip Tagg (2009, 280) calls a repeating I–IV–V progression with a doubly long V the “La Bamba loop.” (Tagg does not interpret the IV after the V as its own chord.) When this schema is projected by a minor I and a minor IV, Tagg calls it the “Che Guevara loop” after Carlos Puebla’s 1965 Guevara tribute song “Hasta Siempre, Comandante.” 14. The first IV of each loop is often difficult to hear because it is quick and because Brian Jones’ acoustic guitar is buried in the mix. It is more prominent in assorted live recordings from the period (and Brian Jones can be seen fingering the chord in video footage). 15. Scholar Allan Moore (2012, 240–41) similarly hears this progression in terms of a cognitive image schema, the “balance” schema. 16. Walter Everett (2009, 269) calls this the “Lazy River” progression, after the Hoagy Carmichael song. 17. The progression of “Be My Yoko Ono” may have been inspired by John Lennon’s Page 294 →1971 “Imagine,” which uses this schema starting on IV and ending on ↑IIIM, the latter chord sounding especially poignant in its placement immediately after the word “dreamer”: “[IV] You may [V] say I’m a [I] dreamer [↑IIIM].” Lennon’s own progression might have been influenced by “Soldier of Love,” which the Beatles covered and recorded live at the BBC in 1963. 18. Paul Carter (2005, 33ff.) also theorizes a “journey” progression (or “simple journey” progression), by which he means I–IV–V–I. He also defines a “reverse simple journey” (or “retrogressive simple journey”), meaning I–V–IV–I. These progressions, which we earlier identified as incarnations of the three-chord schemas and , are of course totally distinct from the journey schema defined in this book. 19. Although the ostensible subject of Paravonian’s routine is the chords to Pachelbel’s Canon in D (which we will mention again in the next chapter in relation to the “sauntering schema”), it also deals implicitly with the journey schema, as we will discuss later on. 20. This term was coined by journalist Marc Hirsh (2008, 2011), who admits that it is “dumb.” Hirsh actually defines the progression as ↑VI–IV–I–V (i.e., our journey schema), but acknowledges that the numerals I–↓VI–↓III–↓VII would provide a more accurate description. Musician John Mayer (2007) similarly links the schema to the likes of McLachlan and Osborne. See also Murphy 2014 for the schema’s use in film music. 21. For a quick historical survey of the lamento bass all the way through to present-day rock, see Ross 2010, 22–54.

Chapter 4 1. Walter Everett (2009, 262–64) expertly demonstrates how this idea of diatonic and chromatic additions to a pentatonic root line can work, starting from single notes that are doubled at the unison and octave, then moving to doublings at the perfect fifth (parallel power chords), then finishing with doublings at the major third (parallel major triads), all the while citing real songs that represent each stage. 2. See also Everett 2004a, В§17. 3. See also Capuzzo 2009a and Biamonte 2010, 104–8. 4. In response to the interview question “Did you put aeolian cadences in вЂIt Won’t Be Long’?” (the interviewer identified the wrong song), Lennon responded “To this day I don’t have any idea what they are. They sound like exotic birds” (original emphases, Lennon and Ono 1981, 74). London Times critic William Mann (1988, 28) is responsible for sparking the entire aeolian-cadence debate. Confusion over the term has infected even the most august critics: Dave Marsh somehow misinterprets the term to mean “a sustained C major chord” (2007, 19). 5. Ratt plays against these chords in an interesting way by offering a kind of backward root motion in a 4–ꜜ3–1 vocal melody: “[4, ↓III] Way [књњ3, IV] cool ju- [1, I] -nior”). 6. See also Everett 2004a, В§20. Page 295 →7. The inverted gesture, a “pentdescent” (likewise not a schema for us), can be heard in the introductory brass riff to Wilson Pickett’s 1965 “In the Midnight Hour”: ↓VII–V–IV–↓III–I. In “Knock on Wood,” the extra V at the end of the riff eventually

blossoms into a fully complete pentdescent by the end of the song, creating a kind of pentatonic rainbow of I–↓III–IV–V–↓VII–V–IV–↓III–I. Both “Midnight Hour” and “Knock on Wood” were cowritten by Stax Records producer, Booker T. & the M.G.’s [sic] guitarist, and Blues Brothers guitarist Steve “The Colonel” Cropper. 8. See Biamonte 2010, 104–8. 9. See also BГЎrdos 1975, 4–5; Kopp 1997, 264; and Van der Merwe 2004, 47–50. 10. In “Die Roboter” (1978), Kraftwerk gives us uncanny minor pentatonic scales on D, Bв™-, G, and A—possibly 1, књњ6, 4, and 5 respectively—which, fittingly for the subject matter, sound both familiar (1, 4, 5) and strange (књњ6) simultaneously. (Each of these scales only supports a single chord, but each scale is heard in its entirety melodically.) 11. The presence of a prominent IV in a pentatonic passage is of course no guarantee that we will hear a pentatonic transposition. In Beastie Boys’ 1986 “No Sleep Till Brooklyn,” the primary guitar riff (a knockoff of the earlier-cited riff from “I Love Rock’n’Roll”) moves through I and ↓III to rest on IV, then through V and ↓III back down to I; the pentatonicism here springs not from the prominent root 4 but rather entirely from 1, the two ↓III chords serving to embellish an underlying I–IV–V motion (the same as in “I Love Rock’n’Roll”). 12. See also the related discussion in Capuzzo 2009b, 186–89; Everett 2008, 150–51; and Everett 2009, 196–97 and 269–77. 13. The verses of “Sleep Walk” also occasionally offer a IV with a chordal major third instead of minor third; this king progression, I–↑VI–IVM–V, does not project a shrinking effect. 14. The stretching progressions of “Creep,” along with some of the song’s melodic phrases, bear a striking resemblance to those heard in the verses to the Hollies’ 1972 “The Air That I Breathe” (“[I5, 5] If I could make a wish, [↑IIIM, в™Ї5] I think I’d pass. [IVM, књ›6] Can’t think of [IVm, књњ6] anything I [I5, 5] need”). These resemblances led the composers of the Hollies’ track to sue for royalties, which they eventually won in the form of songwriting credits. 15. Several legal disputes have made the identification of the author of “The James Bond Theme” into a gnarly puzzle, although it is generally accepted that Monty Normal was the composer and John Barry was the arranger. 16. The earlier choruses of “Powerful Love” offer an interesting teasing progression of I5–↑IIIM–IVM–↓VI–(↓VII–)I5, with an extra ↓VII thrown in, momentarily disrupting the shrinking gesture of IVM–↓VI–I5 but adding a schematic effect of . 17. “The Girl from Ipanema” also features a dominant-functioning chord in the second half of the IV’s space, just before the resolution to I; this is sometimes a V7 (the seventh preserving 4) and sometimes a ↑VIIo (the diminished fifth preserving 4). 18. This more general arpeggiating figure is referred to as the “rogue riff” in Doll 2007, 170–207, and Doll 2011b. Page 296 →19. The remarkable historical impact of the “Louie Louie” riff, as recorded originally in 1957 by Richard Berry and later covered by the Kingsmen,” is chronicled in Doll 2011b and Doll 2014. 20. Our slide bears no relation to the SLIDE of neo-Riemannian theory (Lewin 1987, 178), which describes the motion between a major and minor triad whose chordal thirds are the same pitch class, for instance, Em–Eв™-M (the chordal third G persists). 21. Conversely, a verse-chorus effect can be generated without any expansion of the I; in Howlin’ Wolf’s “Evil” (1954), the onset of the refrain (“That’s [IV] evil”) creates a chorus effect for the latter eight measures of the schema, while the verse effect is relegated to the first four measures of I. 22. Particularly close attention to bridge harmonies can be found in de Clercq (2012, 74ff.). 23. The opposite possibility, with IV–I–IV–V as a loop in a bridge, is virtually (or actually) nonexistent. 24. The very first example in chapter 1, the chorus of Radiohead’s 1997 “Lucky,” can be heard as a variant of this form of the crossing, with в™-VI substituting for the final IV or II: IV–I–IV–I–IV–I–в™-VI–V. Although this progression appears not in a bridge but in a chorus, it is different enough from the simple bamba IV–I–IV–V that it will not likely project that additional schematic effect.

25. The first rock recording of “Hey Joe” was made in 1965 by the Leaves. The progression seems to have been in the air in the mid-1960s, also appearing in Love’s “7 and 7 Is” (1966) and Niela Miller’s unreleased “Baby, Please Don’t Go to Town” (1962). Some of the intricate history of “Hey Joe” is chronicled in Hicks 1999, 39–57. 26. In their 1978 cover “Take Me to the River,” Talking Heads reverse the order of ↓VII and IV, and seem to arrive at I early (their I chord is ambiguous at first, projecting numeric effects of both ↓III and I before settling on the latter): “Yeah, I wanna [↓VI] know, can’t you [↓III] tell me, am [IV] I in [↓VII] love to [I or ↑III] stay?” 27. Technically, the Romanesca would include only the saunter’s first six slots, not its ending V (Gjerdingen 2007, 25–43). 28. In Pachelbel’s piece, and in the Romanesca more generally, the fourth chord is sometimes a major triad I with књ›3 in the bass, which differs from a minor triad ↑III by only one note (IM/књ›3’s chordal root 1, instead of ↑IIIm’s chordal fifth књ›7). As for the “canon” in the title of Pachelbel’s piece, it describes the imitative melodies in the upper parts, not the repeating bass line or the harmonic progression. 29. McCartney used a related progression a year before his “Let It Be,” for the Beatles’ “Oh! Darling,” in which the journey opens the verses before giving way to IIs and Vs (“Oh, [I] darling, please be- [V] -lieve me. [↑VI] I’ll never do you no [IV] harm. Be- [II] -lieve me when I tell [V] you: [II] вЂI’ll never [V] do you no [I] harm’”). 30. Nicholas Stoia (2013) posits a “Trouble in Mind” scheme for prerock popular music and points out its connection to his “Key to the Highway” scheme. Stoia’s schemes include not just a harmonic component but also a melodic one; McCartney’s vocal melody in “Let It Be” bears some resemblance to that of the “Trouble in Mind” scheme. Page 297 →31. Charles’ “Georgia” offers phrasal pairs only in the beginning; other statements of the verse are singles, although the final one is extended, offering both a temporary resolution of anchor ↓VII7 (on the penultimate “mind”) and a final resolution of tonic I (on the final “mind”). 32. Definitions of the Gregory Walker/passamezzo moderno usually include IV in bars 3 and 4 (instead of I); e.g., Van der Merwe 1989, 198–204. See also Gombosi 1944. 33. “It Must be Jesus” itself is a reworking of the darkly religious folk song “There’s a Man Going ’round Taking Names,” recorded by many blues artists including Leadbelly and Josh White (both in the 1930s). 34. The music from this version of “The House of the Rising Sun” is set against the lyrics to “Amazing Grace” (also a saint-based song) in the 2001 recording of “Amazing Grace” by the Blind Boys of Alabama, a kind of live-performed mashup. 35. “Georgia” was composed in 1930 by celebrated songwriter Hoagy Carmichael, one year after the publication of “Down and Out.” Carmichael’s original 1930 recording exhibits a number of significant melodic and harmonic differences compared with Charles’ cover.

Chapter 5 1. According to Parker himself, the two-bar guitar riff of “Watch Your Step” was itself inspired in part by the one-bar Wurlitzer electric-piano riff of Ray’s Charles’ “What’d I Say” (1959). Both songs are centered on E, both follow the blue schema, both have Latin-type drum accompaniment, and both of their riffs are limited to the first, fourth, and fifth degrees of a minor pentatonic scale on a given chord. But it takes a bit more effort to hear the “Watch Your Step” riff as a transformation of the one in “What’d I Say” because their different lengths and melodic contours. (On the other hand, the E-centered riff that opens The Doors’ 1967 “Break On Through (To the Other Side)” is nearly identical to the “What’d I Say” riff when on its I (E).) Another riff to compare with all these is that of 1965’s “Come On Now” by the Kinks, who recorded and released their track several months before the Yardbirds. While the Kinks’ riff is an obvious Parker knockoff (probably by way of the Beatles), it is never transposed; the Kinks do offer blue cadences of V–IV–I, but the riff does not follow along. Additionally, “Come On Now” does not feature an

opening double hit of any kind; however, the Kinks were merely waiting a few months, because such an introduction appears in their “I Need You” (1965), the first event being a sliding guitar chord and the second event being the resulting feedback (itself probably copied from the opening of “I Feel Fine”). 2. Richard Wagner (1897) himself wrote on this concept. 3. “Transformation” is also a technical term in the linguistic generative theory of Noam Chomsky (e.g., 1965, 2002 [1957]). Chomsky’s transformations are in some ways comparable to those of Schenkerian theory; a Schenker-influenced, generative grammar for music is theorized in Lerdahl and Jackendoff 1983. 4. See Schenker 1979. Schenkerian levels, which blend harmony and melody, are Page 298 →not quite the same as our own harmonic levels, which contain only chords (but which can be influenced by melody). 5. Transformational theory, of the neo-Riemannian stripe, has been applied to rock music by Guy Capuzzo (2004), Kevin Holm-Hudson (2010), and Timothy Koozin (2011), among others. 6. In chapter 6, we will theorize a precedent as a kind of “parallel,” the only difference being that a parallel need not be transformed, only aurally prior and inviting comparison. 7. “Intertextuality” is a term applied sometimes to the relationship of a piece of music to others; the terms “stylistic intertextuality” and “strategic intertextuality” are also used to denote generic versus specific relatives (see Spicer 2009, following Hatten 1985). Our norms and precedents roughly correspond to these two brands of intertextuality, although there are also many differences we shall not go into here. 8. “Manish Boy” is the original Chess Records spelling of the title, but subsequent pressings list it as “Mannish Boy.” Waters’ track can also be heard as a sardonic answer song to Bo Diddley’s “I’m a Man” (1955), which is also a single-harmony song (riffing on I only) that likewise spells out the word “man.” Diddley’s song itself invokes (by way of its riff) the earlier “Hoochie Coochie Man.” 9. A famous case of both chordal extension and alteration is the “Hendrix chord,” a sonority regularly referred to as a sharp-ninth chord with no fifth, 7(в™Ї9)(-5). The tonic Is throughout the Jimi Hendrix Experience’s “Purple Haze” (1967) are examples.. See van der Bliek 2007. 10. A pentatonic effect starting on scale degree 2 constitutes a nonstandard transposition, beyond the versions on 1, 4, and 5. 11. Musicians for a long time have recognized this problem. Ethnomusicologist Mieczyslaw Kolinski (1957, 55) notes that “pentatonic scalesВ .В .В . have often been interpreted as gapped heptatonic [i.e., diatonic] scales; however, this is just as unjustifiable as to interpret, for example, a perfect fifth [a power chord] as an incomplete major or minor chord.” The same basic point applies to earlier styles of music as well. David Lewin (1998) writes that his impressions of incompleteness and ambiguity (two effects theorized in this book) when listening to the DM fugue subject from Johann Sebastian Bach’s WellTempered Clavier Book II are purely artifacts of applying an inappropriate scalar standard: seven-note versus six-note (the Guidonian hexachord). 12. See also Weisethaunet 2001, Wagner 2003, and Kubik 2008. 13. Relevant here are Guy Capuzzo’s (2009b) notions of “sectional tonality” and “sectional centricity.” 14. When there is no discernible increase in intensity, a chorus effect is usually based on the intermittent return of a lyrical refrain. Such is the case with Peggy Lee’s 1958 cover of “Fever,” in which the beginning of the chorus is signaled primarily by the refrain “you give me fever,” along with an anacrusis of percussion. 15. See also Spicer 2011 for a discussion of the original 1984 recording of “It’s My Life” by Talk Talk. The confusion over the arrival of No Doubt’s (pre-)chorus is mirrored by the confusion surrounding the exact pitch class of the second center: the pre-chorus and chorus’s center of Bв™-is consistently contested by Dв™-, primarily because of Page 299 →the progression Bв™-m–Eв™-m–Aв™-M–Dв™-M, which can be heard both as an easing fragment on Bв™(I–IV–↓VII–↓III) and as a steady schema on Dв™-. This kind of schematic ambiguity will be addressed in detail in chapter 6. 16. Pumping-up has been studied in depth by Dai Griffiths (2015), who dubs it “elevating modulation.” The phenomenon has also been called, among other things, “crowbar modulation”

(Kaminsky 1992), “truck driver’s modulation” (Everett 1995), “arranger’s modulation” (Ricci 2000), “shotgun modulation” (Sayrs 2003), and “gear-shift modulation” (Pedler 2007). 17. Madonna’s dropping schema starts with a preceding I (1), then doubles up on књњ7 with ↓III5 and ↓VII, then completes the gesture of књ›6–ꜜ6–5 with IVM–↓VI–I5. 18. Cherry’s recording opens with a lone, sung 5, which projects an entity effect of V more than в™-II.

Chapter 6 1. This image is a reproduction of the earliest known duckrabbit, an uncredited illustration printed in the German humor periodical Fliegende BlГ¤tter in 1892 (October 23, no. 2456, p. 147). (The joke is that, of all the animals, the duck and rabbit are the most closely related.) David Lewin (1986, 371) calls the ambiguous image a “dubbit.” 2. On the harmony of Steely Dan in general and the ambiguity of “Babylon Sisters” in particular, see Everett 2004b. 3. For example, see Biamonte 2010. 4. Nicholas MeeГ№s (2000, 2003) views these mirrored progressions of fourths and fifths as kinds of “harmonic vectors,” with falling-fourths progressions projecting a “вЂmodal’ effect” (2000, В§12). 5. Henry Martin (1998, 147 n. 8) calls the Beatles’ progression “modal” because it is an “вЂinversion’ of the [tonal] circle of fifths”; see also Martin 1988, 25, and Everett 2008, 155. The Beatles place an AM V right before the next iteration, which continues the fifths series from D. This V might be heard as a dominant that is prolonged by the ensuing series of falling fourths, or it could simply be a post-tonic; or it could be a pre-subdominant that resolves late to softening GM IV, with the briefer ↓III and ↓VI heard as embellishing a schematic V–IV–I progression. 6. Alf BjГ¶rnberg (2007, 275) notes the “juxtaposition of the terms modal and harmony” might seem “somewhat contradictory” to certain musicians because “[m]any chord sequences used in rock music are modal in the sense that they derive from melodic formulae.” Peter Manuel (1988, 183), writing on popular film songs in South Asia, uses “modal” in a similar vein when he states that “the conception of the melody is clearly modal, such that the chordal accompaniment functions in an ornamental rather than structural manner.” 7. One common situation in which multiple scales with different centers does not produce scalar ambiguity is when a minor pentatonic scale in the root-bass line is harmonized above by perfect fifths. The I–↓VII–↓III–IV–V power-chord riff of Blur’s Page 300 →1997 “woo-hoo” hit “Song 2” gives the entire minor pentatonic scale on F in the roots, while the chordal fifths give the same scale on C: C is never a contender for center, because the F scale, as the root-bass line, defines the entire progression. 8. Kofi Agawu goes so far as to suggest that musical ambiguity, from a scholarly perspective, is exclusively rational, that it is merely “an abstract phenomenonВ .В .В . [and] does not exist in concrete musical situations.” Agawu asserts that “theory-based analysis necessarily includes a mechanism for resolving ambiguities at all levels of structure” (1994, 107), and that the decision to abstain from employing this mechanism constitutes a failure on the part of analysts. For an ethnographic and philosophical (specifically phenomenological) look at competing harmonic interpretations offered by different rock listeners, see Berger 1999a and 1999b. 9. The casual notion of “information” employed here should not be confused with the more technical version featured in “information theory” (as in Meyer 1957). 10. See also Boone 1997, which points out information leading to harmonic ambiguity in the Grateful Dead’s “Dark Star” (1969). 11. Ken Stephenson (2002, 45–46) is probably the first scholar to publish a comparison of these two tracks. See also Tagg (2009, 222–26). 12. David Temperley (2011b) theorizes these four most common white-key scales as constituting a “supermode,” a larger scale that is missing only в™-2 and в™Ї4/в™-5. Ken Stephenson (2002, 41)

considers only ionian, mixolydian, and aeolian as standard (and not dorian). 13. Indeed, the notion of arpeggiating an imaginary chord is a potential Pandora’s box, with any two notes of any imaginable chord—the chordal sixth and eleventh of a V11(6), for instance—potentially serving as the starting and stopping points for scalar-decorated arpeggiation. In other words, there is also a danger here in indulging too much in our aural imaginations, to the point of hypothesizing aural absurdities. Again, as always, our guide will be our ears. 14. Buk 1998. 15. Another parallel worthy of a footnote is the two-bar verse loop to Boston’s “More Than a Feeling” (1976), which features the same basic DM–CM–GM progression but with durational emphasis shifted from GM to DM (which is a full bar) and with the GM metrically weaker than the CM (which arrives on the downbeat of the second bar). While this parallel clearly favors center D, the song’s chorus loops a GM–CM–Em–DM progression unambiguously centered on G. 16. See also Ballinger 1999, 74–81. 17. Fricke 1986, 33. See Hubbs 1996 for other biography/text/music analyses of Morrissey’s songs. 18. Allan Moore (1992, 77), following Jonathan Kramer (1988), also suggests just such a possibility regarding timbral information. Fred Lerdahl (1987) has written on the hierarchical possibilities of timbre by itself, independent of pitch. 19. In Flamenco music, the “Andalusian cadence” (AM–GM–FM–EM) is notorious for its wide centric ambiguity (just not by that name). See Fernandez 2005. 20. For example, see Everett 2004a, В§17. 21. On rare intervals, see Browne 1981. Page 301 →22. White-key sets feature one tritone, two minor seconds, three major thirds, four minor thirds, five major seconds, six perfect fourths. Black-key/open-string sets feature (in terms of diatonic intervals) no tritones, no minor seconds, one major third, two minor thirds, three major seconds, and four perfect fourths. 23. See Everett 2004a, В§17. 24. The harmonic ambiguity of “Dreams” is also a topic of discussion in Temperley 2001, 263–64; Stephenson 2002, 41–42; and Hough 2015. See Doll 2007, 85–87, and Clement 2013, 111–13, for two very different assessments of Temperley’s and Stephenson’s analyses. 25. The Aв™-–G–F arpeggiation can also be heard as the seventh and fifth of the Bв™-m7. As we previously mentioned, however, arpeggiations tend to be weaker when they do not involve the root of the chord, the defining note for any sonority. 26. Daft Punk’s 2013 “Lose Yourself to Dance” offers more or less the same progression transposed, with a root-bass line of Eв™-m11–Gв™-M7(9)–Bв™-m7–Aв™-6. In this case, however, the third root, Bв™-, is by far the strongest center, because of the slow harmonic pulse and various phrasal and textural elements, especially the guitar’s repeated Aв™-–F riff (suggesting the chordal minor seventh and perfect fifth of Bв™-m7) heard over every chord. 27. When we hear a long-range dominant V behind V–IV–I–V, it is analogous to hearing ↓VII–IV–I on 5 (IV = ↓VII of V; I = IV of V; V = I of V). The I of a V–IV–I–V, however, is almost by definition superordinate to the IV, so there is no real possibility of further functional ambiguity with the IV–I–V portion of the progression as there is with ; this is to say, the IV is clearly a pre-I and not a pre-V.

Conclusion 1. E.g., Tagg 1982, 1987, 1992, 2000, and Tagg and Clarida 2003. 2. A potential example of such a large-scale expressive effect is implicit in Kofi Agawu’s (2003, 8–10) postcolonial critique of the pervasive use of European-based tonal harmony by contemporary African musicians. Presumably (and not facetiously), once this view of tonal harmony is adopted, one could hear its “colonizing power” (as Agawu calls it) whenever encountering it in African music.

Page 302 → Page 303 →

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Index addition. See under transformation aeolian. See under scale alpha. See notation: letter (Greek) ambiguity defined as harmonic effect, 219 of center (see center: ambiguity of) of function (see function: ambiguity of) pentatonicism and, 241–43 of scale (see schema: ambiguity of) of schema (see schema: ambiguity of) anacrusis. See under meter analytical standards chords and, 7–8, 43–44, 55–56, 59–61, 68–69, 197–98, 200 scales and, 43–44, 55–56, 58–59, 126–27, 199–200, 287n8, 290n7, 298n11, 300n12 anchoring function, defined, 77–81 Andalusian cadence, 300n19 anticipation. See prediction, knowledge vs. applied dominant. See secondary dominant arpeggiation. See under centric and functional information arrow notation. See under notation articulation (category of centric and functional information), 227–30 augmented-sixth chord, 100, 184, 208, 286n4 augmented triad. See under triad authentic motion. See hyper function bamba. See schema: two-chord, bamba base. See under transformation: transformee beta. See notation: letter (Greek)

Biamonte, Nicole, viii, 293n8, 293n11, 294n3, 295n8, 299n3 black-key pentatonic scale. See scale: pentatonic, black-key/open-string blue note, 45–46, 184, 199–200 brackets (less-than and greater-than), 86, 139, 162, 170 breaking-out. See under transformation cadence Andalusian, 300n19 chain vs. loop vs. phrase vs. progression vs., 15, 85–86, 90–91 defined, 90 deceptive (see temporary resolution) partial, 90–92, 103, 159, 168, 180 temporary (see temporary resolution) whole, 90–91, 94, 97, 108, 150, 180, 186 Capuzzo, Guy, viii, 288n24, 294n3, 295n12, 298n5, 298n13 catatonic function, 19, 85, 87, 144, 165, 195, 200, 264, 298n8 center ambiguity of defined, 219–21 narrow, 239–41, 243–47, 249, 252, 261 strong vs. weak, 71, 230–32, 234, 237, 239, 241, 246–47, 252, 255, 261, 267 wide, 239, 241, 243–45, 247, 249–50, 261, 267, 300n19 Page 312 →creation of (see centric and functional information) definition, 20 modulation (see under transformation) reorientation (see under transformation) reorientation vs. ambiguity of, 230–31, 240–41, 252, 261 centric and functional information arpeggiation, 72–73, 87, 103, 123, 151–52, 155, 177, 228, 239–40, 246–47, 249–50, 295n18, 300n13, 301n25 duration, 225–27, 229, 232, 236–37, 247, 249–50, 257–58, 300n15

expression, 234–36, 239, 247–48 loudness, 233, 236–37 meter, 94–95, 106, 108, 116, 132, 134, 141, 159, 174–76, 193, 223–26, 228–29, 231–32, 236–37, 243, 249–50, 253, 257–59, 300n15 parallel, 98, 111, 136, 201, 233–35, 247, 256, 298n6, 300n15 pedal, 59, 148, 152, 227–30, 232, 234, 237, 248, 260 penultima, 144, 146, 159, 181, 231–32, 234–35, 257 phrasing, 225, 229, 231–32, 243, 253, 257–59, 301n26 repetition, 224–25, 229 scale, 225–26, 229–30, 232–34, 236, 238, 241–44, 248–50, 253, 299–300n7, 300n12 schema, 221–26, 228–30, 232–34, 236–238, 240, 243–44, 256, 258 texture, 225, 229–230, 238 chain. See function: functional chain chromaticism. See scale: chromatic correspondence (category of centric and functional information), 223–24, 226, 229–30, 232, 234–35, 264 deceptive resolution. See temporary resolution delaying function, 14–15, 74–76, 78, 80–82, 256–57 delta. See notation: letter (Greek) diatonicism. See scale: diatonic dominant definition, 26–28 lead vs. rogue, 37–39 See also hyper function; pre-tonic dorian. See under scale duckrabbit, 215, 219, 240, 299n1 duration. See under centric and functional information effect definition, 8 object or structure vs., 9, 70, 191 emphasis (category of centric and functional information), 224–25, 227, 229, 231–32

entity effect, 15, 17, 67, 70, 72–73, 80, 142, 152–53, 159, 161, 191, 200, 215, 218–19, 250, 292n24, 299n18. See also identity, chordal epsilon. See notation: letter (Greek) Everett, Walter, viii, 14, 73, 286n13, 287n9, 288n22, 291n11, 291n14, 291n19, 292n1, 293n8, 293n10, 293n16, 294nn1–2, 294n6, 295n12, 299n16, 299n2, 299n5, 300n20, 301n23 expectation. See prediction, knowledge vs. expression as centric and functional information (see under centric and functional information) as effect, 16, 38–39, 262–68, 301n2 extended schemas. See schema: extended false dominant. See secondary dominant false resolution. See temporary resolution Page 313 →fragment. See under transformation: transformee function ambiguity of, 219, 232, 235, 256–57, 267 creation of (see centric and functional information) defined as effect, 19–20 functional chain cadence vs. loop vs. phrase vs. progression vs., 15, 85–86, 90–91 defined, 14, 19, 49 functional strength, defined, 70–71 functional multivalence, 16 33, 48, 64, 111, 212, 218, 260, 288 four-slot schemas. See schema: four-slot gamma. See notation: letter (Greek) Greek letter notation. See notation: letter (Greek) harmony, defined, 8 harmonic level. See level (harmonic), defined harmonic phrase. See under phrasing harmonic progression, cadence vs. chain vs. loop vs. phrase vs., 15, 85–86, 90–91 harmonic rhythm. See pulse, harmonic

Harrison, Daniel, viii, 287n9, 288n15, 288n17–18 hearing, defined, 2, 5–6 hyper function, defined, 52–55 hypo function, defined, 52–55 identity, chordal defined, 15–19, 66–70 transformation and, 208–14 imagined chord tones, 60–62, 64, 86, 128, 139, 150, 156, 257, 300n13 imaginary transformee. See under transformation information. See types of centric and functional information interrupted resolution. See temporary resolution ionian. See under scale journey schema. See schema: four-slot, key, 7, 14, 21–22, 51, 57, 218–19, 287n9 key signature, 287n12 Lerdahl, Fred, vii, 288n24, 289n25, 291n10, 297n3, 300n18 letter effect, 15, 70, 118–19, 209, 211, 215, 218–19, 250. See also identity, chordal letter notation. See under notation level (harmonic), defined, 66–67, 70–72 locrian. See under scale loop cadence vs. chain vs. phrase vs. progression vs., 15, 85–86, 90–91 definition, 86 loudness as centric and functional information (see under centric and functional information) of individual chord tones, 12, 79, 210 lower subdominant effect. See under subdominant Lydian. See under scale major II. See under triad

major ↑III. See under triad major ↑VI. See under triad major ↑VII. See under triad major scale. See scale: ionian medial function, 14, 52, 54, 62–63, 82, 102, 128, 216, 290n3 mediant, 14, 39–44, 49–52, 54, 60, 62–63, 89, 203. See also medial function; pre-tonic meta-schema. See under schema Page 314 →meter anacrusis (as metric accent), 226, 237 as centric and functional information (see under centric and functional information) minor scale. See under scale minor V. See under triad mixolydian. See under scale modality, 16, 216–17, 241, 299nn4–6. See also scale modulation. See under transformation Moore, Allan, viii, 285n2, 287n14, 290n6, 291n16, 292n1, 293n6, 293n15, 300n18 natural minor. See scale: aeolian neighboring function, 15, 78–80, 82, 86–88, 105–6, 108, 163–64, 244, 260 neo-Riemannian theory, 190–91, 296n20, 298n5 Nobile, Drew, viii, 291n16, 293n6 nonchord tones, 66–71, 73, 85, 87, 190, 218, 220, 228, 237, 256 non-tonic I, 64–66 norm. See under transformation: transformee notation arrow (large up and down), 56–58 arrow (small up and down), 14, 36–37, 40 arrow (right), 74 diatonic vs. pentatonic vs. chromatic, 41–44, 46, 57–58 key signature, 287n12

letter (Roman), 13, 17–19, 21, 37, 55–56, 58–60, 70, 191, 198, 207, 209, 211, 286n1, 287n13 letter (Greek), 13, 15, 49, 54–55, 62–65, 71, 75, 82, 105–10, 113, 115, 121–23, 128–33, 135, 171, 206, 212, 235, 260 meta-schematic, 137, 139 Nashville number system, 291n9 numeric (Arabic) (see notation: scale degree) numeric (Roman), 55–60 root (see notation: numeric (Roman); root effect) scale degree, 14, 32, 36–40 staff, 13–14, 27, 58, 185, 207 standards and (see analytical standards) superscript (see notation: meta-schematic) tablature, 286n5 numerals. See under notation numeric effect, 69–70, 118–19, 150, 218–20, 246–47, 249, 293n7, 296n26, See also identity, chordal object, effect or quality vs., 9, 70, 191 objectivity, 10, 20, 191, 220, 228, 232, 238 open-string pentatonic scale. See scale: pentatonic, black-key/open-string parallel, as centric and functional information. See under centric and functional information passing function, 15, 77–80, 82, 100, 107–10, 112, 116, 120, 129, 151, 174, 213, 218, 223, 232, 233, 248, 257–59 pedal, as centric and functional information. See under centric and functional information pentascent, 133. See also schema: pentatonic, multipentascent pentatonicism. See scale: pentatonic; schema: pentatonic pentdescent, 245, 295n7 penultima, as functional information. See under centric and functional information phrasing as centric and functional information (see under centric and functional information) Page 315 →harmonic phrase defined (phrasal effect), 85–86

cadence vs. chain vs. loops vs. progression vs., 15, 85–86, 90–91 phrygian. See under scale pitch class, defined, 17, 70 plagal motion, 98–99, 293n10. See also hypo function positional effect (identity), 213. See also identity, chordal post-anchoring function, 15, 75, 77–80, 82, 175, 213, 232, 258. See also post-tonic post-tonic, 15, 75–77, 79–80, 89, 101, 103, 110–11, 113, 116–17, 121, 133, 137, 141, 149, 154, 223, 232, 258, 260, 299n5. See also post-anchoring function power chord, as a rock-defining sonority, 3, 12, 43, 60–61, 68, 198–99 precedent. See under transformation: transformee prediction, knowledge vs., 25–26, 81–82 pre-anchoring function, 15, 77–79, 81–82, 91, 110, 116–17, 121, 143–44, 149, 154, 175, 211, 231–32, 260 pre-dominant, defined, 50–51 pre-mediant, 50–52, 290n3 pre-subdominant, defined, 50–51 pre-tonic, defined, 25 progression, cadence vs. chain vs. loop vs. phrase vs., 15, 85–86, 90–91 pseudo-schema. See under schema pulse, harmonic on center, influence of, 226–27, 236, 301n26 definition, 67–68 differences in, 68, 94, 97, 116, 134, 141, 178, 245 on functions and levels, influence of, 94, 106, 116, 133, 141, 236 on nonchord tones, influence of, 67–68 on schemas, influence of 166 pumping-up. See under transformation quartal harmony, 69, 291–92n23 ragtime progression, 112, 148–49, 170–71, 184–86 reordering. See under transformation

reorientation. See under transformation repetition, as centric and functional information. See under centric and functional information retrogression, 73, 292n26 reversal. See under transformation Riemann, Hugo, 39, 62, 287n7 rock, defined, 2–3 rogue dominant. See under dominant Roman numerals. See notation: numeric (Roman) root effect, 15, 70, 193, 215, 218–19, 227, 289n30. See also identity, chordal rotation. See under transformation scale aeolian (natural minor), 21, 27, 33, 37, 45, 55–57, 96, 126, 129, 202–3, 216–17, 226, 236, 242–44, 248, 252–53, 290n1, 294n4, 300n12 ambiguity of, 16, 218–21, 230–32, 234–36, 238–39, 241–43, 260–61 as centric and functional information (see under centric and functional information) blues, 45, 289n35 chromaticism, defined (see scale: scalar effect, defined; notation: diatonic vs. pentatonic vs. chromatic) diatonic default, 44, 127 dorian, 22, 24, 37, 45, 56, 96, 126, 216, 226, 241–43, 248–50, 300n12 double harmonic major, 89 harmonic minor, 26–27, 226 heptatonic, 21, 287n7, 298n11 Page 316 →ionian (major), 21–22, 24, 26–27, 37, 45, 55–57, 76, 126, 155, 202–3, 219, 226, 290n8, 230–32, 241–44, 248, 252–53, 290n8, 300n12 lydian, 24, 45, 76, 88, 155, 226, 248–49 locrian, 45, 216, 226 jazz minor, 243–44 melodic minor, 26–27, 226, 243–44, 287n8 mixolydian, 22, 37, 45, 56, 76, 96, 126, 216, 226, 231–32, 242–44, 248, 300n12 notation (see notation: diatonic vs. pentatonic vs. chromatic)

pentatonic ambiguity and (see ambiguity: pentatonicism and) black-key/open-string, 43–46, 126–27, 133, 199, 226, 242, 289, n32, 301n22 effect, defined, 45 major vs. minor, 43–45, 127–28, 226, 242 transposition, 133–36, 184–85, 188, 199, 238, 289n35, 295n11, 297n1, 298n10 See also schema: pentatonic phrygian, 24, 45, 88–89, 216, 226 scalar effect, defined, 45–46, 58, 221 white-key (diatonic), 45, 58, 126, 199, 202, 216, 226, 229, 242, 244, 252, 289n32, 300n12, 301n22 schema ambiguity of, 16, 88, 94, 120, 122, 219–21, 230–32, 234–36, 238–41, 243–57, 260–61, 267, 298–99n15 as centric and functional information (see under centric and functional information) definition, 15, 83–86, 221 extended blue, 78, 92, 94, 98, 105, 134, 162–67, 178, 186, 188, 194–97, 207, 213–14, 259–60, 293n9, 297n1 crossing, 92, 106, 167–70, 186, 286n6, 296n24 down’n’out, 176–77, 179–80, 185–87 ease, 171–72, 186, 253–55, 298–99n15 in-mind, 118, 177–80, 185–87, 296nn29–30 Jimi, 162, 173–74, 186, 206, 253, 260, 296n25 saint, 180–86, 192, 297n34 saunter, 174–76, 186, 268, 294n19, 296nn27–28 search, 166–67, 186 vaudeville, 127, 162, 170–71, 173, 176–77, 184, 186, 253 four-slot , 121–22, 127, 173–74, 217, 253–54, 260 , 114–15, 184, 293–94n17 , 104–5, 127, 163, 179–80, 185–6, 254

, 121, 254 bamba, 71–73, 76, 78, 99, 106–7, 127, 132, 152–53, 167–69, 293n13, 296nn23–24 , 115, 206, 254 , 98, 106–8, 127, 152, 260 , 111, 127, 254 , 120–21, 254 , 79–80, 105–6, 127 journey, 101, 115–21, 123, 153, 175, 177–79, 186, 202, 206, 252–53, 265, 294nn18–20, 296n29 , 109–10 , 110, 127, 156, 254, 260 zombie, 118–20, 123, 174, 252–53 steady, 111–14, 121, Page 317 →148–50, 153, 170–71, 184–87, 193, 212, 253–54, 262, 299 king, 101–2, 112–115, 121, 143, 149, 153, 166, 170, 176, 186, 193, 206–7, 212, 252, 264, 295n13 , 115, 206–7 , 110–11, 127, 260 , 106–7, 127, 260 walk, 122–23, 155, 159, 172, 193, 255 watchtower, 99–100, 108–9, 123 harmonic phrase and, 85, 124, 166 meta-schema ambiguity of, 255 defined, 137–39 dip (1–ꜛ7–ꜜ7–ꜛ6), 155–57, 159, 162, 184 droop (1–ꜛ7–ꜜ7–ꜛ6–ꜜ6–5), 155, 157–59, 162, 169, 247 drop (1–ꜜ7–ꜛ6–ꜜ6–5), 136, 151, 155, 159–62, 164, 169, 181–85, 206, 299n17 naming and notation, 139 shrink (књ›6–ꜜ6–5), 117, 141–46, 148, 150, 157, 159, 161–62, 167, 169–70, 183–85, 295n13, 295n16

slide (1–ꜛ7–ꜛ6), 110, 116–17, 151, 153–55, 159, 162, 167, 171, 174, 183–86, 244, 268, 296n20 slouch (5–в™-5–4), 76, 146–49, 162, 171, 186, 213, 288n19 slump (2–в™-2–1), 150–51, 162, 171 soar (short): 1–♯1–2), 149–51, 162, 185–86, 193, 212 stretch (short): 5–♯5–ꜛ6), 76, 114, 137–41, 143, 145–46, 151, 154, 162, 171, 176, 179, 181–85, 190, 255, 295n14 swell (4–♯4–5), 144–46, 149, 162, 167, 169, 177, 183–85, 255 tease (5–♯5–ꜛ6–ꜜ6–5), 143–46, 151, 160, 162, 183–84, 295n16 teeter (5–ꜛ6–ꜜ7–ꜛ6–5), 108, 151–53, 155, 162, 193 tour (5–♯5–ꜛ6–ꜜ7–ꜛ6), 140–41, 148, 160, 162 twirl (5–♯5–ꜛ6/4–♯4–5), 145–46, 160, 162 pentascent (see pentascent) pentatonic , 74, 129–34, 136, 199, 213, 228, 248–50, 295n11 , 129–32, 135–36, 223, 230, 234, 245 , 129, 131–32, 136, 233, 249 , 98, 128–29, 132, 136, 249–50 , 129, 131–32, 136, 245 , 128–29, 132, 136, 245, 252, 249 , 132, 136 , 124, 132–33, 136, 260 multipentascent, 133–36, 160–61, 184–85, 238 pentdescent (see pentdescent) pseudo-schema, 237–38, 249–50, 255–56 three-chord , 92–93, 104, 113, 163, 177, 186, 217, 244, 252–53, 255, 293n7 , 103–4, 127, 249–50 , 71–73, 76–77, 88, 92–94, 96, 104, 114–15, 127, 164, 166, 176, 186, 218, 246–49, 252, 254, 257–59, 293n13, 294n18, 295n11 , 103–4, 136, 161, 249–50, 295n16, 299n17

, 96, 100, 104, 107–8, 127, 245, 249–50, 253, 257–59, 293n12 Page 318 →, 64, 71–73, 78, 94–99, 104–6, 115, 125, 127, 129, 163, 165–66, 177–78, 188, 193–94, 207, 212–13, 218, 221, 223, 228–32, 249, 253–54, 257–60, 293n7, 294n18, 297n1, 299n5, 301n27 , 102–4, 137, 186–87 , 100, 104, 123, 163, 246, 252 , 88, 99–100, 103–4, 109, 125, 135–36, 153, 165, 174, 193, 237, 246–48, 252, 265, 268, 293n12, 295n16 , 101–2, 104, 165 , 100–1, 104, 246 , 74–75, 96–99, 104, 108, 111, 121, 125, 127, 173–74, 206–7, 217, 221, 223, 228–29, 231–32, 245, 249, 253, 257, 259–60, 268, 293n9, 301n27 two-chord , 39, 88–89, 123, 207–8, 246, 252, 289n28 88, 149, 201, 246–48, 252 , 74, 87, 91, 120, 126, 133, 136, 184, 233, 243–45, 252–53, 293n9 , 40–41, 62, 89, 236 , 22, 72–73, 86, 91, 94–96, 98, 102, 105–8, 111, 127, 132–34, 140–41, 163–64, 166, 168–70, 173–74, 177–78, 186, 192, 197, 213, 218–19, 232, 240–41, 243–44, 252–53, 256–59, 267, 286n6, 293n6 , 59, 89, 91 , 22, 71–72, 87, 91–97, 103–6, 110–11, 113, 115–16, 123, 127, 129, 159, 162–66, 173, 176–78, 180, 185–86, 194, 197, 207–8, 213, 218–19, 232, 240–41, 243–44, 252–53, 258–59, 267 74, 76, 87–88, 103, 109, 136, 236 , 74, 87–88, 102, 109–10, 140, 153, 167, 243–44, 253 , 74–75, 86–87, 91, 96, 98, 101, 107–9, 111, 127, 129, 131–32, 174, 201, 207, 246–47, 252, 257, 259, 293n6 , 89–90, 98, 246, 252 Schenkerian theory, 8, 66, 190, 228, 292n24, 297n3, 297–98n4 secondary dominant, 14, 51–52, 64–66, 290n1. See also pre-dominant; pre-mediant; pre-subdominant staff. See under notation Stephenson, Ken, viii, 287n9, 291n11, 292n1, 293n6, 300nn11–12, 301n24

section (musical), defined, 13, 285n12 softening function, 14–15, 73–76, 78–79, 82, 93–95, 104, 106, 108, 115–16, 129, 132, 163, 171, 188, 207, 213, 218, 223, 231–32, 257, 260, 288n16, 299n5 Spicer, Mark, viii, 291n11, 298n7, 298n15 stability, defined, 19–20 subdominant definition, 28–29 lower vs. upper, 36–37 See also hypo function; pre-tonic subjectivity, 10, 20, 67, 70, 191, 220, 232–33, 238, 293n7 substitution. See under transformation subtraction. See under transformation superscript. See notation: meta-schematic “Sweet Home Alabama,” 16, 222–37, 239 tablature. See under notation Tagg, Philip, viii, 264, 292n25, 292n1, 292–93n5, 293n13, 300n11 temporary resolution, 32, 80–82, 90–91, 117, 149, 186, 211, 297n31 Page 319 →texture as centric and functional information (see under centric and functional information) on entity effects and nonchord tones, influence of, 67–68, 218 on phrasal effects, influence of, 85 Temperley, David, viii, 289n33, 289n35, 290n36, 290n7, 291n11, 291n16, 292n28, 293n6, 300n12, 301n24 three-chord schema. See schema: three-chord timbre on center and function, influence of, 238, 300n18 on entity effects and nonchord tones, influence of, 67–68 on phrasal effects, influence of, 85 pitch vs., 12 tonal center. See center tonic, defined, 20

types of centric and functional information. See centric and functional information transcription, 12–13, 62 transformation addition, 16, 196, 207, 213–14, 255 breaking-out, 16, 202–6, 214, 237–38, 246–47, 249, 252–53, 255–56, 265–67 breaking-out vs. pumping-up, 265 definition, 188–191 modulation, 93, 165, 201–5, 208, 211, 230, 237–38, 240, 247, 252–53, 255–56, 265–68, 299n16 (see also transformation: pumping-up) pumping-up, 16, 164, 204–6, 214, 265–67, 299n16 reordering, 16, 206–7, 214 reorientation, 16, 201–3, 211, 214, 230–31, 233, 240–41, 252, 261 reorientation vs. centric ambiguity, 230–31, 240–41, 252, 261 reversal, 16, 206, 214 rotation, 16, 206, 214, 252–54 substitution coloristic, 209–14 defined, 207–9 functional, 211–14 hierarchical, 213–14 numeric, 210–214, 286n6, 296n24 schematic, 124, 166, 183, 201, 293n9 subtraction, 16, 207, 213–14, 244 transformee base, 16, 193–98, 200, 207–8, 214 defined, 16, 190–91 fragment, 16, 195–96, 199, 214 norm, 16, 192–200, 206, 208, 213–14, 93n9, 298n7 precedent, 16, 191–96, 198, 200–1, 206, 208, 214, 233, 298nn6–7 real vs. imaginary, 190–92, 195–97, 214

whole, 16, 195–97, 214 transposition, defined as transformation, 200–1 modulation and, see transformation: pumping-up of pentatonic scales, see scale: pentatonic: transposition transformee. See under transformation transposition. See under transformation triad augmented, 33–34, 39, 59, 138–142, 144, 158, 168, 184, 288n22, 289n30 diminished, 28, 59, 141–44, 146, 148–49, 151, 155–57, 185–86, 295n17 major II, 51–52, 76, 88, 112, 144–49, 169–71, 176–77, 183–86, 213–14, 217, 246–49 major ↑III, 114–15, 137–46, 148–49, 170–71, 174–77, 179, 183–86, 293–94n17, 295n14, 295n16, 296n28 major ↑VI, 112, 148–50, 170–71, 176–77, 184–86, 193 major ↑VII, 39, 90 Page 320 → V, 27–29, 32, 37–38, 61, 129, 152–53, 157–58, 193, 216, 257 notation, 59, 139, 286n1 (see also notation) as a rock-defining sonority, 3, 43, 60–61, 68, 198–200, 291n9, 291n18 See also analytical standards: chords and twelve-bar blues. See schema: extended: blue two-chord schema. See schema: two-chord voice leading, defined, 30 “Werewolves of London,” 16, 222–36 white-key diatonic scale. See scale: white-key (diatonic) whole. See under transformation: transformee