Piano tuning: Its significance in music education
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PIANO TUNING: ITS SIGNIFICANCE IN MUSIC EDUCATION
A Thesis Presented to the Faculty of the School of Music University of Southern California
In Partial Fulfillment of the Requirements for the Degree Master of Music
by Abraham Epstein August 1950
UMI Number: EP61872
All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion.
Dissertation Publishing
UMI EP61872 Published by ProQuest LLC (2014). Copyright in the Dissertation held by the Author. Microform Edition © ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code
ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 4 8 1 0 6 - 1346
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T h i s thesis, w r itte n by
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A B M M M .M E S m 'W
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u n d e r the g u id a n c e o f h $ ,§ ... F a c u l t y C o m m itte e , an d a p p r o v e d
by a l l
its
m em bers, has
been
presented to a n d accepted by the C o u n c il on G r a d u a t e S tu d y a n d R e s ea rch in p a r t i a l f u l f i l l m e n t o f the re q u ire m e n ts f o r the degree o f
msvm or Mtraic
Faculty Committ
ii AGKNOWLIDDGKMKNTS
To the faculty of the University of Southern Cali fornia for directing my every effort and encouraging my work toward completion. To the various manufacturers of musical instruments and their technical staff, who have given me so freely of their time and knowledge. To the various piano tuning associations whose publi cations and national conventions have been both enlightening and enjoyable*
TABLE OF CONTENTS CHAPTER
PAGE
I. THE PROBLEM AND DEFINITION OF TERMS USED . . . . The problem
1
...........
1
Statement of the problem
. . . . . .
Importance of the study
................
2
.................
6
Definitions of terras used
...
1
Piano t u n i n g ............................
6
Piano repairing...........................
6
Organization of the remaining chapters
...
II. QUALIFICATIONS FOR PIANO TUNERS ...............
6 3
Aptitude: What it takes to be a successful piano tuner and technician
.................
$
Concerning the hearing senses ............
9
Concerning the touch senses ..............
9
Concerning the sight senses ..............
9
Concerning mechanical ability
. . . . . .
Concerning physical ability .............
10 .
Regardless of your a b i l i t y ............... Testing
..................................
10 10 10
Tests for tone discrimination.............
10
Vocationally speaking . .....................
11
The piano tuners workshop . . . . . ;
...
11
...
13
III. FUNDAMENTAL KNOWLEDGE (THEORY) NECESSARY FOR UNDERSTANDING THE SCIENCE OF PIANO TUNING
iv CHAPTER
PAGE
Identifying and recordingkeys, notes, and tones^
13
Numerical m e t h o d ...........................
13
Pitch method (using staff names) ............
14
Vibrational method (also called the Cycle method)
...................
14
Cents m e t h o d ............................... The fundamentals of music Vocationally speaking III.
.• ................
17 19
........................
20
THE EVOLUTION AND DEVELOPMENT OF THE PIANO . . .
21
Piano classification........................
21
The piano
belongsto the percussion family •
21
The piano
belongsto the string family . . .
21
The piano
belongsto the wind family • • • •
22
The piano
belongsto the organ family
...
22
The piano virtually belongs to all families.
23
History of the keyboard instruments
........
In the beginning.........................
23 23
O r g a n s ............................. . •
23
Combinations of instruments (claviorgan)
24
C. 5^0 to the end of the thirteenth century.
26
The m o n o c h o r d ..........................
26
The p o l y c h o r d ..........................
27
The clavicytherian......................
23
Fourteenth to the Sixteenth Century
....
29
CHAPTER
PAGE Fifteenth century developments . . . ........
34
Sixteenth century keyboard instruments . . . .
35
.......................
37
Bells (carillons)
Seventeenth and eighteenth century ..........
3$
The clavichord...........................
41
The h a r p s i c h o r d .........................
46
The eighteenth century ......................
50
The clutsam keyboard ......................
51
Friction rods (Nail piano) ................
52
Clavicylinder
...........................
52
The p i a n o - f o r t e .........................
52
i
The nineteenth century and the p i a n o ........
54
Characteristics of the p e r i o d ............
54
The philosophy of the times in relation to the piano
. . .............
55
The pianoforte...........................
56
Principal keyboard composers ..............
60
Twentieth century
.....
Vocationally speaking V.
PIANO CONSTRUCTION
.
................
6l
..................
62
................
63
The c a s e ...................................
63
The frame
.................................
63
The back p l a t e ...........................
63
The tuning pin b l o c k .....................
63
vi CHAPTER
PAGE
The resonating b o a r d ...............
64
The sound b o a r d .......................
64
Batons (belly bars, bridges) ............
65
R i b s ...................................
65
The action and k e y b o a r d ..................
65
....................
66
The strings
VI.
. . •
• . . .
The trap action (pedals).................
67
The quality of construction..............
68
STUDY OF PIANO ACOUSTICS AND STUDY OF STRING VIBRATION..................................... Sound and acoustical s c i e n c e .........
70 70
Definition of s o u n d .......................
70
Audio frequencies
70
....................... ................
70
The velocity of sound in a i r ..............
70
Sound— musical tones or noise ..............
71
Characteristics of sound
71
Propagation of sound waves
..................
Production of s o u n d .......................
73
Transference of sound .....................
7$
Resonance.................................
79
Sympathetic vibrations
79
....................
The effect of temperature and humidity on pianos and other musical instruments Orchestral trends'^...........
..............
80 $4
vii CHAPTER VII.
PAGE
PIANO T U N I N G ...........................
86
Definition of tuning .......................
86
Methods of tuning
................
86
The diatonic scale and the human ear . . . . .
90
Building a new scale from the C scale
93
....
Tuning the piano the Equal Tempered Scale
. .
Setting the bearings..................
97
Laying the b e a r i n g s .........
9&
Beat r a t e .............
9&
Testing the bearings..................... ..
99
....................
99
General h i n t s ........................... ..
103
Tuning hammer technique
VIII.
95
SUMMARY, CONCLUSION AND RECOMMENDATIONS
BIBLIOGRAPHY
....
.....................................
APPENDIX......................................... ..
105 108 113
LIST OF ILLUSTRATIONS ILLUSTRATION
PAGE
No. 1 .......................................
114
No. 2 . . . .
115
. ........................... . .
No. 3 ........................................
•
11^
No. 4,
The
Diatonic S c a l e ................
117
No. 5,
The
Piano-forte Family T r e e .......
11$
No. 6,
The
Piano-forte Family T r e e ......
121
No. 7,
The
Case C o m p o n e n t s ..............
122
No. $,
The
Frame Components..............
123
No. 9,
The
Resonating Board and Its Components.
12A
No. 10, The Action and Keyboard Components; Standard Drop Action (Spinet Pianos)
....
No. 11, The Action and Keyboard Components
• •
12$ 126
No. 12, The Action and Keyboard Components; Standard Action(UprightPianos)
............
127
No. 13, The Action and Keyboard Components; Standard Grand Action
•
12$
No. 14, The StringComponents.................
129
No. 15, The Trap Action Components
130
. . . . . .
No. 16, The Trap Action Components (Grand Piano Pedal Actio n) ............................. No. 17, . . .
131
...............
132
No. 1 $ , ...................
.
No. 19,
132 132
,>
■
•
No% 2 0 .....................................
133
ix ILLUSTRATION
PAGE
No. 2 1 .....................................
134
No. 2 2 ...........
134
No. 2 3 ...........
134
No. 2 4 .........
135
No..2 5 ...........................
135
No. 2 6 .....................................
135
No. 2 7 .....................................
136
No. 2 g .....................................
136
CHAPTER I \ THU; PROBLEM AND DEFINITION OF TERMS USED The lush years of our post war prosperity have creat ed in the minds of most people* a desire for the better things of life*
The economic conditions of a country de
termine how well its citizens are fed, clothed, housed, and entertained*
In short, economic conditions determine the
standard of living for the nation*
The educational system,
provided by the government, for the benefit of its people, determines, or better still, guides these same people in their choice and conception of fThowM to make best use of their abilities, time, and money.
The cultural level of
people is raised through proper training.
=
The piano is basically the expression of a cultured society.
The piano because of its place in the American
home is an important factor in cultural education.
It has
become an instrument of beauty, in design and compactness, blending gracefully with the atmosphere of any environment. The sound effects of this useful instrument have also been heightened in a degree comparable to its richness of appear ance. I. Statement of the problem.
THE PROBLEM It was the purpose of this
2 study (1) to reveal to the student of music and the piano, an enlightened and interesting understanding of the mechan-ics of the instrument;
(2) to consider the importance and
effectiveness of piano tuning as a medium for music educa tion;
(3) to trace the history of the piano from antiquity
to the present time;
(4) to exhaust all sources of informa
tion in an attempt to secure a completeness of subject matter;
(5) to stimulate interest and growth in the field
of piano mechanics for both the amateur and the professional musician; (6) to attempt a clarification of the existing confusion among various authorities# Importance of the study# its place in many homes#
The piano is again finding
It is only of late that the
physical obstacles of size and mechanism relative to the piano have been overcome by scientific research.
Stream
lining and sound production have been satisfactorily fused in order to create the modern "Grand" and "Spinet type" or "Small piano#"
Because of its size, this useful and beauti
ful instrument has again found its way into today1s smaller, more compact homes#
In America for many years, a home was
never considered completely furnished until a piano adorned the living room#
It served as the center piece around
which all other furnishings were grouped.
It was quite pro
per and fitting that the musical instrument should be so honored because it offered innumerable hours of pleasure and
3 relaxation, and served as a unifying force, bringing into close harmony the respective members of the household as a family group. Pianos, being composed of material items, can be turned out in mass production.
The number of qualified
piano tuners and repairmen, however, is insufficient for the instruments now being played.
The National Piano Manufac
turers1 Association of America, Inc., has made the following figures available. From data obtained from the United States Uensus of Manufactures and from the records of the National Piano Manufacturers1 Association a total of approximately 10.000.000 pianos have been manufactured in the United States from the turn of the century to date. A portion of this total was of course exported; on the other hand, there were imports. Probably one-half, i.e., about 5,000,000 of these 10.000.000 instruments are in use today or are in such condition as to be economically restorable to use. Any decrease in their numbers is more than counter-balanced by the production of new pianos in today’s active piano industry. The prewar demand for pianos was high, with an even greater present postwar demand. A piano tuner-technician in active work, can service at the most about fifteen pianos per week or about 750 instruments per year, of a diverse variety of types and conditions. It is a ready deduction from the above that there should be at least 6700 piano technicians available in the United States today and in the foreseeable future, to properly service the nation’s pianos. This is a conser vative estimate; the actual requirement may be as high as 10,000 qualified technicians. The tuners’ societies, however (the American Society of Piano Technicians and the National Association of
4 Piano Tuners) reported last year that there were avail able only about 3,000 piano technicians for outside ser vice work (i.e., outside piano factories). They further reported that tne average age of these available techni cians, was about 56 years. Actuarial statistics show that only 1,600 of these present technicians will be available ten years hence. Based on such figures, there will be a shortage of tuner-technicians, ranging from about 3,700 at present to about 5,100 ten years hence. The present piano techniciansf training schools operating under the auspices of the National Piano Manu facturers Association have a training capacity of slight ly more than 200 per year. Their output, at the most, will relieve conditions only to the extent of reducing the shortage ten years hence to about 3,100. In the interim, acute shortage will continue.^ Piano tuning schools were not in existence until recently.
The most recent addition to this field is the
mail order course of study. were created, not taught.
In the past piano technicians The father-to-son relationship
existed strongly in the piano factories. of training has its merits.
The factory type
The old guard, that is the
most reliable and experienced tuners, will boast of their factory training, and rightly so.
It is not the product
of the factory school, but with the factory as a school, that this writer objects. Webster defines the term "factory*1 as "a building or collection of buildings, usually with its equipment or The Tuner-Technician Training Program of the Na tional Piano Manufacturers* Association of America. Inc. A revised report covering the aims and accomplishments of the NPMA Manpower training committee. Published May 1, 1947, at 505 Arch Street, Philadelphia 6, Pennsylvania.
plant, appropriated to the manufacture of goods."
It is
reasonable to assume that production costs and efficiency are the determining factors in a factory.
In the same
light, it is also reasonable to assume that the point of saturation is quickly reached where the training of new hands is required.
Schooling on company time is expensive
for the company, and therefore not encouraged.
Only a
limited few have fought their way into the sanctuary of the factory for expert training and guidance.
The rest of the
willing aspirants have found their way into so-called tuning and repair schools, mail order type and the others.
The
official trade magazines run many articles concerning the plight of these unfortunate youths who have sought their training with these schools.
Many factors are responsible.
The manufacturers have sold thousands of new pianos.
There
are still many thousands of old pianos begging for atten tion.
The man who starts his training now will still reap
the benefits of these times. The solution of this problem lies in well organized schools of instruction.
The purpose of this study is to
investigate such an organized system of instruction. Aside, and distinctly apart, from the vocational aspect of the piano-tuning and repair business there is ample reason for all music students to study piano tuning and its related arts.
Music is favored with a definite
and well defined place in the school curriculum*
Music sub
jects like piano study, theory, acoustics, history and others will be richly enhanced by delving into the inner workings of a piano.
The piano is the basis of all melodic and har
monic playing.
Piano students should have a working know
ledge of the mechanics and history of the piano to better express themselves in playing performance.
Piano tuning is
excellent ear training for pitch discrimination.
Music
theory can be better understood through its association with the principles of music acoustics. II. Piano timing.
DEFINITIONS OF TERMS USED The act of placing a piano in tune
according to the accepted principles of equal temperament as conceived by Johann Sebastian Bach. Piano repairing.
The act of placing a piano in
proper mechanical order so that each key mechanism responds properly to the repeated touch of the player. III.
ORGANIZATION OF THE REMAINING CHAPTERS
The remainder of this thesis is organized as follows: Chapter II, "Aptitude" is a discussion on what it takes to become a fine piano tuner and mechanic.
Chapter III,
"Fundamental Musical Knowledge (theory) necessary for Piano
7 Tuning” covers the various systems of key notation on the piano and suggests fundamental theory practices*
Chapter
IV, ,fPiano History and its involution” traces the growth of the piano from infancy to the present day*
(An attempt is
made to restrict the wordology to that which may be compre hended by high school students*)
Chapter V, ”Piano Con
struction” delves into the physical aspects of the piano as classified by the writer into six (6) distinct parts. Chapter VI, "Science of Piano Acoustics and the study of String Vibration” is a technical study of acoustics as it bears upon the piano.
An attempt has been made to inves
tigate every available field of research to amass the necessary information.
Chapter VII, "Piano Tuning” using
the tools of the trade, the author proceeds to take the reader step by step through the intricate maze of the tun ing techniques.
Chapter VIII, "Summary, Conclusion, and
Recommendations" gives the results of the findings and makes recommendations for further advanced fields of study.
CHAPTER II QUALIFICATIONS FOR PIANO TUNERS In this chapter the writer tries to point out the qualities and qualifications that are necessary in order to succeed as a piano tuner and repairman.
To accomplish
this purpose the various aspects of abilities as related to the hearing, touch, and sight senses as well as the mechani cal and physical abilities are discussed.
A sample test
for tone discrimination is outlined in detail.
The chapter
closes with a discussion which the writer titles, tfThe Piano Tuners Workshop.”
In it the various apsects concerning
the tuner at work is elaborated upon. I.
APTITUDE:
WHAT IT TAKES TO BE A SUCCESSFUL
PIANO TUNER AND TECHNICIAN Piano tuning is an art which requires, however, no special previous training.
The finest tuners of today may
have had absolutely no musical background before starting their training in tuning and repairing. In the past it was customary for the son to enter the profession of the father, regardless of desire or apti tude.
Fortunately, this is not true today. In the past, it was also customary to take one’s
training at a piano factory.
Inasmuch as this is not feas
9 ible for many (the practice being strictly limited to a select few), this thesis may serve as a guide for students interested in adding to their, qualifications, facilities, and powers far in excess of that which is available strict ly by the factory apprenticeship system.
Piano tuning and
repair as presented herein will benefit the music student even though he has no intentions of pursuing the subject as a vocational endeavor* Concerning the hearing senses*
If you can distin
guish between high pitch and low pitch sounds, such as the difference between the deep bass voice of the bass violin and the high piercing notes of the violin, you may consider yourself capable of completing this course assured of a reasonable degree of success. Concerning the touch senses.
The vibrational sense
as related to touch is a great aid to piano tuning.
In
Switzerland, deaf children are taught to experience and hear music by sense of touch.
Chapter VIII, "Piano Tuning,"
delves further into this aspect of the work. It is possible to tune a piano completely by visual means if the tuner uses the "Stroboconn."
With this de
vice the tuner can "see" if his tones are in tune. Concerning the sight senses*
The sightless piano
10 tuners now in the field have proven that lack of seeing facilities is of no particular hinderance. Concerning mechanical ability.
The inability to
drive a nail into the wall successfully is not an indication of failure so far as mechanical aptitude is concerned.
It
takes much practice, as any reliable carpenter or mechanic knows• Concerning physical ability.
To properly tune and
repair a piano requires a fairly agile person.
It is nec
essary to be able to bend the body at the waist and the knees, to sit, and to stand for prolonged periods of time. Regardless of your ability.
A bit of ear training
along the line as laid down in the following tests will help sharpen your tone perception.
Secure the aid of someone
who is in a position to aid and judge your efforts. II. TESTING Tests for tone discrimination. play a tone somewhere on the keyboard.
1.
Using one piano,
Sing back this tone,
or play it back on another instrument, or the same instru ment. 2.
Using one piano, play broken octaves and demon
strate in like manner using your voice.
Ex. C f —
C^#
IX 3*
Using one piano, play other intervals*
strate in like manner using your voice. 4*
Ex. C f —
Sing or hum. a tune (any tune) *
Demon Gf.
wAmerica” is an
ideal tune. 5.
Take either the trSeashore Musical Aptitude11 test
and/or some other reliable musical ability and mechanical ability tests. Practice the above until some progress is made. There is no such thing as inability to learn tone discrimin ation. III.
VOCATIONALLY SPEAKING
The Piano Tuners Workshop. take him into a variety of places.
The piano tuners work may In homes the pianos are
usually in the living room or the music room. clean and interesting. lating. for.
The work is
Meeting different people is stimu
Expert work is greatly appreciated and well paid Musicians are critical as well as helpful.
The
piano repairman is in business for himself and is, therefore, his own boss. The following reprint from the "Accordian World11 is most applicable at this time: Every man is more musically inclined than he thinks because he: Has drums in his ears, fiddles away his time, trumpets his achievements, plays on your heart strings, horns in on your business, beats his gums, walks with
12 rhythm, talks with tempo, has melody in his voice, sings the blues when hefs downhearted, has harmony in his ideals, croons lullabies to his kids, loves to sing his own praises, is an artist in executing the old song and dance, is often sharp, sometimes flat and at his best when he can B natural*
CHAPTER III FUNDAMENTAL MUSICAL KNOWLEDGE (THEORY) NECESSARY FOR UNDERSTANDING THE SCIENCE OF PIANO TUNING I.
IDENTIFYING AND RECORDING KEYS, NOTES, AND TONES The Dick Tracy comic strip made the average reading
public conscious of the fact that there are eighty-eight keys on a full size piano*
This number includes both the
black and the white keys.
Dividing the keyboard total
by the number twelve (because there are twelve keys to the octave, Ex. c-c#-d-d#-e-f-f#-g*-g#-a-a#-b), we find that there are exactly seven octaves plus four tones, or seven octaves plus a minor third, or seven and one-third octaves -in the keyboard* Example•
12 x 7 *
Numerical method*
#4
&4 4 4 a
Numbering the keys successively
starting from the left hand side (bass or lowest tone side) offers a clear way of knowing exactly which key is being re ferred to*
The piano manufacturers have made a practice
of stamping these numbers on each key, behind the front or name board*
(See Illustration No. 1.) >
14 Pitch method (Using staff names).
Numbering the
keys in agreement with the well known and accepted staff notation, correlates the keyboard with staff notation. (See Illustration No. 2.) Vibrational method (also called the Cycle method)• Many musicians are familiar with the term "440" "Double vibration per second," and know that this particular tone is used as a standard for tuning orchestral instruments. The violinist tunes his "A" string when the conductor re quests the oboe player to sound his "A" on the oboe.
Often
times a timing bar (a metal bar resting freely over a sound box, pretuned to the tone of "A", and struck with a rubber or felt covered mallet), is substituted for the same pur pose . Kach tone audible to the human ear has been assigned a scientifically recorded vibrational number.
The range of
sound audible to the human ear consists of from sixteen double vibrations per second (lowest, deepest sound) to twenty-thousand double vibrations per second (highest, thin nest sound).
This is the scientists point of view.
Some authorities claim that the range of hearable sounds lie between twenty-seven and thirty-two thousand cycles per second. The American Standards Association claims that the
15 lowest musical tone distinctly recognizable as a musical sound has a frequency of twenty-seven and one-half cycles per second (c.p.s.). recognizable one
The highest musical tone, distinctly
as a musical sound, has a frequency of forty-
thousand eighty-six and nine thousandths cycles per
second*
This is the range of the standard eighty-eight
note piano, when the piano is tuned to ”A 440” double vibra tions per second (cycles per. second)• It is ter
a well known fact that some people, as a mat
of fact, most people, can hear up to thirty-two thousand
cycles per second.
The point in question is whether or not
these same people are hearing the fundamental tones or har monics of these same fundamental tones. Dogs and other animals are able to hear tones higher in compass than is possible for human beings.
These higher
tones have been classified as tones in the "sonic and ultra sonic” range. The human ear can hear at least a range of ten octaves.
The standard eighty-eight note piano consists of
seven octaves plus a minor third.
(See Illustration No. 3*)
Observation will disclose that by simply adding any tone once again to itself it is possible to get the same tone pitched an octave higher.
By subtraction we get the
same tone pitched an octave lower.
16 Example: c1 = 261.63 \ 261.64 ♦ 261.64 = 523.251 c2 s 523.251. The relation between the key note and the octave is commonly known as 1 : 2*
Illustration No. 4 contains the
cycles per second of the first thirteen tones on the piano. It might be interesting at this time to make mention of the fact that the piano is tuned according to the equal tempered scale and therefore an octave being twelve tones away is the 12th root of the octave ratio of 1 : 2 or more correct 1 : 1.0594631 (correct to seven places in the decimal).Another way of expressing
this ratio is this:,
approximately 6 4 .8 9 or 101 : 107^. In order to find the vibrational frequency of an equal tempered semitone above any other tone, we must mul tiply, using this factor 1.0|>94631. Example;
We know that A (49) has 440 c.p.s.; to find A# or Bb (50)— an equal semitone away (tempered) we must multiply 440 x 1.0594631 « 4 6 6 .I64 c.p.s. or, to find G# or Ab (4&) we mustdivide 440 * 1.0594631 = 415.305 c.p.s.i
Further discussion on piano tuning will be found in Chapter VIII. William Braid White, "Piano Tuning and Allied Arts," pp. 60. ”
17 Gents method*
In the Gents method each musical semi
tone oi* the equal tempered scale is divided into 100 cents or hundredths. ' Since there are 12 semitones in an octave the cents method assumes an octave contains 1200 cents. From one equal tempered semitone to another is a distance of 100 cents.
Example; from
c to e# is 100 cents
c# to d is 100 cents This distance being calculated as 100 cents regardless of the frequencies used. Since the frequency ratio of the Equal Tempered semitone is the 12th root of 2»1 . . . 1.0594631, the frequency ratio of the cents is in consequence the 1200th root of 2=1 . . . 1.000577& (approx.) or nearly 1730 : 1731.2 The cents method will be useful to us only when we employ an electric device like the Stroboconn for tuning pianos.
The trained ear will notice a 3 cents difference
in pitch, but anything less, either 2 cents or 1 cent, is impossible to detect by the human ear. The most widely used logarithmic method of finding musical steps or distances is the system of Cents that Alexander J. Ellis devised in London in 1&90. The following are its most important features: (1) The well-tempered (piano) octave is the measuring frame work. Each of its twelve equal semitones is sub divided into 100 cents, or hundredths... The non-tempered
2
Ibid., p. 250.
13 perfect fifth would measure 702, and the perfect fourth, 493 cents* (2) The logarithm of a cent is *00025, since it de rives from the twelfth part of an octave, which in itself has the ratio 2 ; 1 as a shortcut, the following table of cents and logarithms may be welcome; cents 100 200 300 400
500 600 700
300 900 1000 1100 1200
log .025 ♦050 ♦075 .100 .1 2 5
♦151 .176 .201 .226 .251
cents 10 20 30 40 5° 60 7° 30 90
log .0025 .0050 •0075 .0100 .0125 .0151 .0176 ♦0201 .0226
cents 1 2 3 4 5 6 7 3 9
log .0 0 0 2 5
.00050 .00075 .00100 .0 0 12 5 .0 0 1 5 1 .0 0 1 7 6
.00201 .00226
.2 7 6
.301
(3) To find the cents equivalent to a certain the easiest way is to reach for a table of logarithms: (a) look up the logarithms of each number; (b) subtract them; (c) compare the difference with the short cut table, computing the hundreds, tens, and units, and you have the desired cents. If there is no table of logarithms at hand, you avail yourself of the auxiliary number 3477 (which is easy to memorize, since the total of its digits is 7/7/7); then you multiply the difference in the two vibra tion numbers by 3477, and divide this product by their sum. The ratio 431 ; 441 gives 431-441 = 40 40 x 3477 = 139,030 431 / 441 = 922 139,030 ♦ 922 a 151 cents This result is a good example of the superiority of the cent system. The ratio 431 : 441 does not convey any clear picture of the distance between the two notes in question. But the number 151, cent equivalent of this ratio, shows impressively that the distance is midway between a minor and a major second; it is a three-quartertone.
19 With the aid of this practical method it is easy to win a clear and graphic picture of all the scales occurring in oriental music.! The cents method is a device or system whereby dis tances rather than intervals are discovered* In case the triple of the larger vibration number exceeds the quadruple of the smaller one, multiply the greater number by three and the smaller number by four before starting the operation indicated above, and you finally add 498 (the perfect, not the equal-tempered fourth) to the result* If on the contrary the propor tion of the two vibration numbers is greater than two to three, multiply the greater number by two, and the smaller number by three, before starting the operation indicated above, and you finally add 702 (the perfect fifth) to the result*2 This matter will be discussed further in Chapter VIII on Piano Tuning. II. .THE FUNDAMENTALS OF MUSIC Basic minimums of musical knowledge needed to under stand music should consist of the following:
(1) The rela
tionship of the octave, fifth, fourth, third, second and unison.
(2) The component parts of the triad and chord,
both major and minor. scales.
(3) The construction of the various
Most any elementary theory, or musical catechism
book will provide the necessary fundamentals of music. Curt Sachs, Our Musical Heritage (New York: Prentice-Hall, 1948), pp. 33^l5T ^ Curt Sachs, The Rise of Music in the Ancient World (New York: W.W. Norton Company, 1943), pp. 23-29.
20 It is most Important that the reader possess a work ing musical theory knowledge if he, or she, is to understand the complexities of temperament tuning.*1 It is highly recommended that each person who is unable to play the piano, start taking lessons on the instru ment at once if he plans to become a piano tuner*
Accom
plished pianists could benefit much by studying a string instrument, since this study will develop intonation and pitch* III.
VOCATIONALLY SPEAKING
A complete knowledge of the mechanics of the piano from the standpoint of the piano repair man will help even the concert pianist to become a better and finer performer on the instrument.
CHAPTER IV THE EVOLUTION AND DEVELOPMENT OF THE PIANO I.
PIANO CLASSIFICATION
The piano, as we all know, is classified in musical circles under the title of "percussion instrument*”
Var
ious exponents of today have severaly criticized this point of view* The piano belongs to the percussion family*
In de
fense of those people holding the opinion that the piano is a percussion instrument, we need only point in pride to manfs first attempts at communication by use of drums beaten with the bare hand or with crude mallets*
These people classify
the piano according to its means of reproduction*
This
consists of a keyboard and hammers which strike against strings* The piano belongs to the string family *
These
people hold the point of view that the piano belongs to the string family*
They believe also that the system of segre
gating instruments according to families is outmoded and utterly without rhyme or reason in attempting to catalog all the instruments in existence known to man.
Dr. Curt
Sachs and Dr. Erich M. von Hombostel are the foremost ex ponents of the newest system for classification of musical
22 instruments.
The determining factor in their system-is,
how the sound is produced and what is the primary source of vibration.
The piano as an instrument belongs to the
"chordophone" group of instruments.
This is the same group
into which all stringed instruments fall, be they bowed, plucked, or hammered.
The piano being in the general form
of the "board zither" type of instrument is therefore sub classified as such.i The piano belongs to the wind family.
Although the
brass and woodwind players have never voiced their plea that the piano be included in their domain, they, too, could find legitimate claim.
The piano, composed of so many di
versified materials,' uses the principle of a resonating board and a sound box.
Historically speaking, primitive
man used a long horn to amplify musical sounds.
Shall we
stretch our imagination to give the wind players their due on the bases of its material and amplification? The piano belongs to the organ family.
Various
authorities claim that the organ preceded the development of the piano. 2
^
Curt Sachs, The History of Musical Instruments (flew Yo**k: W.W. Norton and Co., 1940), PP* 463-4* 2 Alfred James Hipkins, Piano History (Novello, bwer and Co., 1&26-1903), p. 47*
23 Praetorius (1571-1621) says, thus the clavicordium Is the fundamental of all keyboard instrument^ such as organs, clavicymbels, symphonies (Spinets or Virginals), and etc #3 These people voice the same argument as is voiced by the percussion people: means of reproduction; keyed action. The piano virtually belongs to all families.
With
so many groups claiming recognition for the development of the piano, it is no wonder that the paths of development have crossed and recrossed in so many diverse ways.
From
the point of view of material used in the piano, method of tone production, and better still, the blending quality of the piano with the other instruments, it could very easily belong to all the musical families# II.
HISTORY OF THE KEYBOARD INSTRUMENTS A.
IN THE BEGINNING
Organs. These were first mentioned in the Bible# Our generation knows that the term organ as used in the Bible did not stand for today1s counterpart nor anything even vaguely resembling the same. Cainfs descendent, Jubal, is said to be "the father of all such as handle the harp and the organ.” Genesis
4 :21.^ ^
Ibid#. p. 5 6 #
4
Curt Sachs, 0 £. cit•, pp# 25 and 106.
24 The first organs were called "water organs.”
Water
was not used to make the pipes speak, but was a controlling device, similar to the diving bell principle.
Water com
pressed the air, a valve opened, and released the air which then went into the pipe or pipes. In the ancient Mediterranean world, the organ was considered an outdoor instrument. purposes.
It was used for secular
For the Christians in Rome, however, the organ
had disagreeable connotations since it was played at their persecutions.
The Hebrew and Christian religions themselves
outlawed this instrument from their church services.
It
was not until 500 A.D. that it again came into use through the efforts of the ecclesiastics who desired to use this instrument as tone regulators (standards of pitch) when teaching boys to sing the Gregorian chants.
Later on it
was used for-vocal accompaniments in the church services. Before the thirteenth century, it had no keys. J.S. Bach played a German ”pedal-klavizimbel.” This instrument had a set of pedals for the feet which re sembled our m o d e m organ.
Organists of his day used it as
a practice piano.5 Combinations of instruments (claviorgan).
5
Ibid.. p. 378
Sachs
25 says that the, Claviorgan is the name generally given to a combina tion in one instrument of a small organ with a stringed keyboard* Instrument either a spinet, a harpsichord, a clavichord or, later, a piano* One should be skeptical, however, when this term occurs in old sources, . . • Consequently, a claviorgan was not a combination, but could be paired with a harpsichord or another stringed keyboard instrument. 5 *
In the Groves Dictionary of Music and Musicians, we find the following statement which contradicts many of the so-called positive statements concerning the origination of the
first keyboard* The statement is as follows: We are without definite information as to the origin of the keyboard. A primitive keyboard is exhibited in the Hydraulus• There is reason to believe that the little portable organ or regal may at first have had a keyboard derived from the T-shaped keys of the Hurdy Gurdy.y Barnes, in his
containing keys which
book, described the
same organas
had a width of from three to five
inches, and the organist had to strike the key with the clenched fist, the organist was therefore called an ,Torgan beater.ft^ Willi Apel says that reports concerning the size of the organ keys are most probably erroneous.
^
The need to
Ibid., p. 342.
7 H.C. Colles, Groves Dictionary of Music and Musi cians (New York: The Macmillan Co., 1938), Vol. Ill, p. 1$. ^ Barnes, The Contemporary American Organ (New York: J. Fischer and Brother, 1930), p. 13*
26 play upon them with the fist is probably also an over exaggeration.
"Organs of the 9th and 10th centuries A.D.
had a number (6 -1 0 ) of large keys, called ’linguae1 (tongues), which were pulled out and pushed in.f,9 It is most unfortunate that learned s cholars are not able to place their finger on exact dates and places, but perhaps this, too, has its merits.
When the first key
board was used, or in what shape or form, is probably the least important item necessary for understanding the later development of the instrument.
There are many who will
argue this point, but for our purposes we must leave it where it is, until such time as more progress is made along these lines.
It is probably more important to know that
differences of opinion do exist. B.
C. 560 TO THE END OF THE THIRTEENTH CENTURY
The monochord.
Credit is erroneously given to
Pythagoras (c. 580-500 B.C.), an Egyptian seer, for the development of the monochord.
Such is the fate of promin
ent people in any era. Many people consider the monochord as' being the fore runner of the m o d e m piano.
A very logical conclusion may
9 Willi Apel, Harvard Dictionary of Music (Cam bridge, Massachusetts: Harvard University Press, 1947), p. 3§7*
27 be inferred if one thinks solely of a string which has been made secure at each end and supported above a sound box by two bridges.
The monochord is such a device, consisting
of one stretched cord (membrane— string) over two wedges, one at each end (called bridges).
A one-stringed violin
is similar in design, with the exception of the curved soundbox;
The monochord has a rectangular type of box.
Striking the string with a mallet, plucking it by hand, or smoothing the string with a horse hair bow will set the cord in motion. tions.
The waves so produced are known as vibra
These waves are amplified by a resonance box under
neath the strings. Acoustical experiments are best demonstrated with the monochord.
To change the pitch stop the string at
various places along its length, move the bridge, or fur ther stretch or loosen the tension of the string.
The
Greek and K0man church used the monochord for choral music in the same way as the modern orchestra today uses the tuning-bar
primarily to sound the pitch.
Uurt Sachs
claims that ,fthe actual monochord with only one string and without keys was used as a musical instrument before 1 1 0 0 . The polychord.
-*-0
This was invented shortly afterward
. cit.,
Curt Sachs, ojd
p. 270.
and was simply the addition of more strings to the monochord with a correspondingly larger resonating box*
Guido
de Arrezo, in approximately 1000 A.D., paved the way for future development, by adding balanced lever devices (keys) and a tangent to strike the stretched membrane.
In this
guise he instigated the creation of the "clavichord." In the same manner and at approximately the same time the addition of a balanced lever device and a quill to pluck the stretched membrane (string) created what was commonly known as the "harpsichord." banks of keys.
The harpsichord often had two
The value of each instrument was hotly
debated in the sixteenth century. It is generally agreed
that the "thirteenth century
is the traditional date for the application of a keyboard to a stringed instrument . " H The clavicytherian.
The addition of more strings
and consequently more keys resulted in a larger keyboard instrument which was given the name of clavicytherian. It is in the form of an upright spinet and contained enough keys to form the diatonic scale.
The Germans accepted
and improved upon this instrument.1 2 11 Phillip James. Larly Keyboard Instruments (London Peter Davies, Ltd., 1930;, p. 12 Newton Price, Development of Keyboard Instruments (Unpublished master's thesis, University of California, Los Angeles, California, September, 1942), p. 5*
29 C.
FOURTEENTH TO THE SIXTEENTH CENTURY (THE RENAISSANCE PERIOD) It would be going beyond the compass of this study
to describe the cultural history of the period up to the fourteenth century. history book.
We refer the reader to any ancient
It might be added that the scope of this
study does not permit extensive description of the times in any one period, but an attempt will be made to give enough information concerning the activities of the peoples of each era to orientate the reader with the flhowff and "why" of the society of the period, and its effect upon the development of the keyboard instruments* The fourteenth century is marked by great literary activity with such names as Petrarch, Dante, Boccaccio, and Chaucer. The most important painter of the period is Florentine Giotto. It was also a period of trouble in the Church, resulting in a dual papacy (Avignon and Rome) between 137$ and 141$* Two additional historical events belong to the fourteenth: the ffHundred yearsT Warft between France and England (1337-1453) and the Great Plague of the black death (1349)• Italy shares musical leadership with France in the ars nova. The music of the fourteenth century was referred to as the ars nova ("the new artTt) by contemporaries to dis tinguish it from the older practices of the thirteenth century which they referred to as ars antiqua ("the old art" ) #13 This period was noted chiefly for its religious
Miller, An Outline History of Music (New York: Barnes and Noble, Inc., 1947), p. 27*
30 pilgrimages; Chaucer wrote "Canterbury Tales”; it was a period of wars fought for the independence of countries and sovereign rulers; universities were established in many countries; war with Kngland; clocks were constructed on mathematical principles; it was a period of inquisitiveness— adventurers and s cholars were desirous of looking into the distant future.
The people, however, were still bonded to
the service of the Lords,
For the mass of humanity,
freedom as we know it was unknown; most people knew only poverty, hunger, and despair. In the fourteenth century the first indication of reading music in a vertical fashion— that is, reading music in an up-and-down procedure— has been given.
People were
desirous of reading and playing more than one note at a time; this is the progression of music from chord to chord. Before this, music was read and performed in a horizontal fashion, note to note in a horizontal (contrapuntal) pat tern.
Where there were two lines of music it was necessary
for two musicians to read and perform each line of music individually.
This may be compared to the reading of news
print in a paper or book.
It must be remembered that our
ftmodern system of notation dates back to the early seventeenth century.”^4
14
There were many systems of notation previous
Apel, ££. cit.% p. 494.
31 to this period. The music of the Ars Nova portrayed the following characteristics: (1) Predominance of secular music in the ars nova is attributed to trouble in the Church. (2) New polyphonic forms were added to the old ones. (3) Imi tation and canon were employed rather extensively for the first time. (4) An important characteristic of the ars nova was the development of a new rhythmic freedom. Tempus imperfectum (duple time) now predom inated over tempus perfectum (triple time). Strict adherence to the rhythmic modes disappeared, along with the monotonous, short, recurrent patterns char acteristic of the ars antiqua music. (5) There was a predominance of two-part writing (especially in Italy). Three and four part polyphone was used mainly in France and England. (6 ) Melodic style was generally more florid. This was especially true in Italy. (7 ) Har monic style was characterized by a more extensive use of thirds and by a bold treatment of dissonance. There was little parallelism. Instruments like the dulcimer, monochord, and psal tery were satisfactory instruments for this era, in that they could reproduce two or more tones at one time. The monochord, is an instrument consisting of a long box of thin wood, with a bridge fixed at each end, and an intermediate movable bridge, over which is stretched a wire or catgut string. This was the pro totype of the clavichord and the piano.^ The psaltery, in triangular, square, curved or harp like form was either carried with a ribbon around the neck, or, when used was placed on some piece of furni ture. Its strings were operated by means of a plectrum, which was fastened by rings to the hand of the perform er. The psaltery was the prototype of the spinet and harpsichord. 17 15
Miller, op. cit.. p. 27.
16 Morris Steinert-, Keyed and Stringed Instruments (New York: C.F. Tretbar, 1893), p. 6 5 . 17
Ibid.. pp. 67-S.
32 The dulcimer, is a trapeze shaped instrument of* not more than three feet in greatest width, composed of a wooden framing, enclosing a wrestplank for the tuning pins around which the strings are wound at one end and a soundboard, ornamented with two or more sound holes and carrying two bridges, between which are the lengths of wire intended to vibrate with a hitch-pin block for the attachment of the other end of the strings* Two, three, four and sometimes five strings of fine brass or iron wire are grouped for each note* The dulcimer laid upon a table or frame is struck with hammers, the heads of which are clothed on either side with hard and soft leather to produce the forte and piano effects. The tone, harsh in the loud playing, is always confused, as there is no damping contrivance to stop the continuance of sounds when not required*i£ The
dulcimer is the prototype of the pianoforte. Whereas the psaltery and the spinet had a silvery
sweet, gentle tone, the dulcimer had a louder, but harsher tone.
The German name for the dulcimer is "hackbrett”
(butcher’s board for chopping meat).
The plectrum prin
ciple of keyboard instruments of bnglish descent are the spinet, harpsichord, virginal. spinetta are of Italian descent.
The clavieymbalo and The clavecin and epin-
ette are of French descent, and the flugel and psaltery are of German descent.
Keyboard instruments of this period
had black naturals and white sharps. In 1351 A.D. at Augsburg, the drawing of music wire (iron wire) was first developed.
It marked a great step
forward in the development of keyboard instruments.^9 18
Ibid.. pp. 70-71.
19
Ibid.. p. 69.
'
It was now possible to build instruments which would pro duce a bigger tone*
Of course this meant correspondingly
heavier construction all over to support the pull of the stretched strings*
It brought with it many new complica
tions which were not overcome until the eighteenth and nineteenth centuries* As early as the fourteenth century these new instru ments started to appear*
There were three different
shapes of jack instruments: The harpsichord of trapeze form, the clavichord of oblong or rectangular form, frequently called spinet or virginal, and the upright harpsichord or clavicytherium. It must be remembered that the long harpsichords were often described as spinets or virginals from their plectra or their use by young ladies, but the table shaped ones known commonly by the latin names were never called harpsichords*20 It must be remembered that these newer instruments were not called spinet, harpsichord and clavichord until many years later.
There has been much discussion concerning
the origin of the name ftvirginal,f.
Some historians attri
bute it to the Virgin Queen tilizabeth*
Some point out
that she reigned from the year 155 # on, a date which finds itself in the sixteenth century* both sides of the picture:
Helen Kaufmann, presents
34 The spinet and virginal were early varieties of the harpsichord• The latter, a great favorite of Queen Elizabeth, was supposedly so called in deference to that Virgin Queen, but since the virginal was a lap instru ment used by young girls to accompany their songs, it may have derived its name from them . 21 This writer finds that exact dates of demarcation concerning music, instruments, and other worldly occurrances is sometimes impossible because research proceeds upon the bases of discoveries— either of physical, material things, or of written records, usually in the form of letters.
In
neither case is it possible to honestly vindicate onefs selection of a date.
Ambiguous writing upon the part of
one authority, or transcribed mistakes upon the part of the - second authority, or insincere writing of letters, perhaps intended as jests between two people may often be construed by people in later centuries to have quite another meaning than the original writer's intention. D.
FIFTEENTH CENTURY DEVELOPMENTS
During the fifteenth century keyboard instruments were still being experimented upon by many people, but many of the above mentioned instruments were being used, per fected, and discarded.
Although musical developments
during this century were mostly in the vocal field, char-
21 Helen Kaufmann, The Little Guide to Music Appreciation (New York: Grosset and Dunlap, 1947), P# 111.
35 acteristics of the instrumental style were as follows:
*
A growing awareness of the fact that musical instru ments have certain special properties eventually led to an independent instrumental style. The presence of any one, or a combination* of the following pro perties eventually led to an independent instrumental style. The presence of any, or a combination, of the following properties .implies the use of instrumental idiom as opposed to vocal idiom: (1) Angularity of melodic line, the use of skips, (2) Wide range of melodic line, (3) Long, sustained notes, long phrases, (4) Sharp rhythm, strong accents, syncopation, (5) A freer treatment of dissonance than practiced in vocal music, (6 ) Rapid, repeated notes and figures, {7 ) Rapid scales, (8 ) Freely added parts and chords filled in (called Freistimmigkeit), particularly in lute and keyboard music, (9) Melodic ornamentation, including figuration (repeated figures or patterns on each note of the basic melody), embellishment (mordents, turns, trills, etc.) and coloration (free melismatic material added to the basic notes of the melody). The latter is not exclusively instrumental.22 In the Rules of the Minnesingers, by Eberhard Cersne,
A.D. 1404, mention of the harpsichord is made under the name of the clavicymbalum.
Instruments like the clavichord,
the monochord, and other musical instruments are also mentioned, as being in use at that time. 23 E.
SIXTEENTH CENTURY KEYBOARD INSTRUMENTS
The sixteenth century is called the "Golden Age ' ' of Polyphone."
22
Artists and painters like Da Vinci and
Miller, op. cit.. p. 50. Steinert, op.~cit.. p. 6 9 #
36 Michelangelo; literary people like Shakespeare, Spenser, Bacon, and Johnson; musicians like Lassus, Willaert, Arcadelt, and Palestrina, served to make this truly the expression of the Renaissance*
The church, particularly
the Protestant church in its reforms, as led by Luther, served to direct the musical events of the century. 24 The harpsichord, virginal, spinet, clavichord, and the organ were in use during this period. It is interesting to observe that keyboard instru ments were used only in the Western civilizations.
The
Far Eastern countries like Arabia and its neighbors had no use for the piano. no chords.
Their music was linear; they used
It might be added that the piano in its present
day stage of development cannot duplicate the quarter-tone type of music used in many of these eastern countries.^5 In the sixteenth century composers like Tallis, Byrd, and Bull wrote music for the various instruments of the day, but it was not until the seventeenth century that great strides were made.
The shift from vocal music to
instrumental music was affected*
It is known as the
period of "firsts”— firsts in inventions, politics, thought,
^
Miller, o£. cit., p. 3 6 .
25 Curt Bachs, in his lectures in the summer of 1949 delivered at the University of southern California.
37 science, and economics# Louis XIV becomes the first absolute monarch, the first king to overcome the power of the feudal lords, to conceive ruling as a profession, to assume total authority which strengthens the nation yet leads it into costly wars. And wars are different now* The armies are no longer composed of levies, servants fighting at the command of feudal masters. They are mercenaries, and they demand their pay. aide by side with all of this, Newton is giving to the world the scientific method, the law of gravitation, deductive reasoning; Galileo is working with the new telescope, John Locke is proposing a society ordered according to natural: man’s right to life, liberty-and property. 26 The baroque spirit pervades the music of the period in the same ways it pervades the arts. It is manifest in large-scale productions, spectacular music, contrasts, and an over-all grandeur. 27 Montiverdi in Italy and Purcell in England are the biggest musical figures of the times. At this point it is possible to mention several developments not heretofore commonly known to the general public, or alluded to in history books about the piano. Bells (Carillons)•
The use of mechanical appli
ances to aid in the playing of music developed as the need arose.
Sometimes inventive genius lay dormant until the
26 Paul Grabbe, The Story of Orchestral Music and its Times (New York: Grosset and"Dunlap, 1942), pp. 4 -6 . 27
Miller, ££. cit.„ p. 6 7 .
public demanded such developments.
The piano keyboard
found its application even to the gigantic bells in mon asteries.
At first these bells, or chimes, were struck
by hand with hammers, then they were attached with cords to cog wheels having appropriate notches, so that certain combinations of tones would sound automatically.
The next
step was probably the use of cylinders containing nails which activated the bells through their hammers in complete series of tunes, much like our present day "music boxes. 11 In the sixteenth century the keyboard was adapted to the use of bell playing.
In the seventeenth century a foot
keyboard was added.2**
F.
SEVENTEENTH AND EIGHTEENTH CENTURY: THE BAROQUE PERIOD, 1600-1750
Dr. Miller describes the general historical back ground of this period as follows: The century and a half between 1600 and 1750 was a period of colonization. The first half of the seven teenth century was dominated in Germany by religious, political wars known as the "Thirty Years’ War" (l6 lo1643). The second half of the seventeenth century was dominated by the culture of Louis XIV of France (16431715), and his lavish court at Versailles. The prin cipal names in science are Newton, Harvey, Galileo, Bacon, and Leibnitz. The leading philosophers of the period are Descartes, Pascal, and Spinoza. In the field
2^
Curt Sachs, op.y cit.. p. 378.
of literature there is an important array of £nglish names: Milton, Dryden, Defoe, Addison, Swift, Pope, and Samuel Johnson. In France the principal literary names are Corneille, Racine, and Moliere. The great names of baroque painting are Rembrandt, Rubens, Van Dyck, El Greco, and Velasques. The meaning of Baroque. The painting, architecture, and music of this period are in general characterized by a certain spirit of theatricalism, of grandiose concepts, and by a rather heavy elaboration of design and signifi cance of effect. Baroque spirit in general began in Itqly as a result of the Catholic Counter Reformation which sought to impress the world and to re-establish the influence of the Church. Baroque style in the arts and music soon spread over all Europe and dominated the spirit of cultural creations. 29 The important musical names, were as follows, Monte verdi, Scarlatti, both Alesandro and Domenico, Corelli, Vivaldi, Lully, Couperin, Rameau, Purcell, Schein, Seheidt, Schutz, Froberger, Praetorius, Buxtehude, and Pachelbel. The big names of the period were J.S. Bach and Handel. Bach’s field was church and instrumental music while Handel’s forte was chiefly opera and oratorio. The principal musical usage of the piano was in figured bass style.
It was common practice in this era
for the composer to sit at the piano and accompany the in strumentalists as they extemporized upon his music with chords.
This writer wonders whether the critics of m o d e m
jazz music are acquainted with the similarity between the practices of the two groups of musicians.
40 In those days it was the usual thing for a composer to sit at the harpsichord when his piece was performed, occasionally lifting one hand to beat time for the other musicians, while with the other playing chords that held them to the desired rhythm. He frequently omitted to write out the individual parts, and for himself jotted down only a set of figures as symbols for the chords he intended to use in playing the bass part. This was called a "figured bass," in Italian "basso continuo." The players were obliged to improvise on that bass, and he filled in the gaps when their ingenuity failed. Re sourcefulness in inventing embellishments to cover empty places on the spur of the moment was one measure of a composer’s skill, and since it was impossible to produce a sustained note on the harpsichord, those em bellishments consisted of runs and trills and rapid figures. 30 Music for the harpsichord consisted mostly of pieces to be used outside of church functions.
It was mostly
secular in nature— dance suites consisting of movements in allemande, courante, sarabande, and gigue tempi.
Dance
pieces like the gavotte, bourree, menuet, loure, air rigaudon, and passepied, were the latest vogue.
Domenico
Scarlatti wrote virtuoso pieces called sonatas and suites. Variation forms like the partita, chaconne, passacaglia, and the ground, were favorite types. were used for many piano works*
Descriptive titles
Toccata’s, prelude’s and
fantasia’s were more miscellaneous forms used. To the piano tuner J.S. Bach’s most important work, his Well-Tempered Clavier containing 48 preludes and fugues on each of the twelve major and minor keys, is all important, 30
Kaufmann, ojp. cit.. p. 110.
41 for it is in this work that he sets forth the illustrating material for the inception of the system of equal tempered tuning.31 The clavichord.
The seventeenth century was the
greatest period of use for the clavichord.
It was used by
such men as J.S Bach and C.P.E. Bach. This instrument could not play loud (sustained); it had no forte.32
its producer of tones were small tangents
of brass (string touching devices) which remained in con tact with the strings and did not rebound. History has it that the clavichord was derived from the ancient monochord, a one-string instrument used for scientific testing purposes.
A later development saw
its introduction as a musical instrument by the minstrels and bards who used it to accompany themselves for s tory telling or singing.
Eventually, through several successive
stages of development, several moveable bridges were added to the instrument from below the strings. Back in the fifteenth century these bridges had been attached to levers and they then assumed the character istics of small tangents which could stop the string when 31
Miller, op. cit., pp. 91-4*
32 T. Cambell Young, Making of Musical Instruments (London: Oxford University Press, 1939), p. 2.
42 the levers to which they were attached were pressed down at the opposite end.
These tangents had a dual purpose,
first they struck the strings to produce the sound, second they automatically stopped the strings at predetermined positions, thereby shortening the strings and determining their pitch.
However, at this stage of development, the
instrument assumed-the name clavichord, actually it was a monochord with keys. The tone was very tiny, but very charming.
The
instrument was housed in a shallow box without benefit of stand or legs.
It was very small in size because one string
was used in such a manner as to produce two or three dif ferent sounds. The clavichord . . . had strings for the lower or natural keys only, the semitones on the upper keys being produced by tangents directed toward the strings of the lower. Thus G sharp was obtained by striking the G string at a shorter length. D - sharp and E in a like manner also. About the year 1725 Daniel Faber, or Grailsheim, gave the semitone its own string, and the instruments so made were distinguished as "bundfreiTt from the older "gebunden,'” which was a system" of Getting. The early history of the clavichord previous to the fifteenth century, together with that of the chromatic keyboard, rests in profound obscurity. Welcker describes the oldest clavichord he had met with as bearing the date 1520, having four octaves, but the notes D sharp and G sharp were wanting. Glavichords had, even with the last improvements, a soft, hesitating tone . 33
33
. cit.,
Steinert, ojd
p. 6 7 .
43 Bundfrei clavichords were larger in size because each key worked in conjunction with a separate string*
The
invention was not successful from the standpoint of size and price. The clavichord, being portable, was used by many of the classical and romantic musicians as practice pianos in their youth.
It is probably because of this feature
that Handel could practice in the attic late at night.
The
well-known picture by Margaret Isabel Dicksee in the Compton Pictured Encyclopedia shows the boy discovered practicing on the clavichord with legs attached. Pressing the key harder or easier with the finger made it possible to control the shading of the sounds.
It
lent itself best to expressive interpretation of the music being played.
The strings had no dampers to stop the sing
ing of the strings, so the tone lasted.
The tangent stuck
to the string as long as the key was held down, thus the string vibrated only in the length determined by the tangent. The rest of the string was usually damped by a piece of tape interwoven between one end of the strings when the instru ment was manufactured.
Because of its construction the
clavichord player could also make the string vibrate in
34 tfThe Story of the Piano and its Ancestors,11 Compton Pictured Encyclopedia and Fact Index (Chicago: Compton and Company, 1939), P» 111#
44 much the same manner as the violinist does when he employs his finger to create a vibrato. The advantages for commercial success of this instru ment were many.
There were few strings, it had a small
resonant body, it was easy to tune, it was inexpensive and it was portable.
The player could, and often did, rest
it on a high table and play from a standing position. legs were later added as an accessory.
Four
This brought about
the playing from a lower position such as having the player assume a sitting position on either a chair, stool or bench. The keys were very short when compared with the piano. This made for a light, quick finger action. One of the most striking features of all older clavi chords was the shortness of the keys. They projected only three centimeters beyond the semitones, while the keys of m o d e m pianos project five centimeters. This seems to have been due to the mechanical action required, the weight of the front of the key needing to balance exactly the weight of the rear. A player using modern fingering would stumble against the semitones on such a keyboard. The shortness of the keys necessitated the awkward fingering of the sixteenth and seventeenth cen turies; the players used the second and third fingers when they ascended, and the first and second fingers when they went down, while the thumb and the fourth finger were seldom engaged. This fingering was already fami liar to players of the. portative organ, in which the keyboard was situated at right angles to the player. 35 The disadvantages, of course, were not in evidence until composers wrote coincident seconds.
35 P. 332.
Sachs, History of Ancient Instruments, op. cit..
45 J.S. Bach was its most prolific composer and per former.
It was also he who introduced the thumb into key
board use.
Bachrs competitors were George Philip Telemann,
and Domenico Scarlatti. In the seventeenth century it (the clavichord) fell into disuse everywhere except in Germany, where it con tinued in use as a vehicle of expressiveness and sensi tivity. 36 Among the many instruments now reposing in museums, it may be noted that no provisions were made, by the original builders, for a music rack.
The lid, when in open position,
revealed at first either a papered or painted surface. Later when expensive mahagonies and other fine woods were used they served as beautiful displays unto themselves. J.S. Bach is perhaps the only great composer to think in terms of the clavichord.
The composers of the
eighteenth century, like Haydn and Mozart wrote exclusively for the piano.
Here again differences of opinion exist
among historians since Steinert claims that Mozart’s traveling spinet is really a clavichord.. Bach’s style was characteristically suited to the clavier instruments, or is it not proper to say that his style was determined by the physical characteristics of the instrument.
^
He wrote 15 two-part inventions, 15
’Harvard Dictionary, op. cit., p. 157»
46 symphonies, 6 partitas, 6 English suites, 6 French suites, 4£ preludes and fugues, the Goldberg Variations, and a host of miscellaneous pieces, all for the harpsichord, or clavier instruments* The clavichord yielded to the piano in the nineteenth century. The harpsichord.
The harpsichord saw its greatest
use in the seventeenth century, and was often built with two manuals or sets of keys.
The tone was produced by the
action of a jack (quill, leather or brass tonguej, which pro truded far enough to pluck the string in order to produce the sound. century.
The foot pedal was invented in the seventeenth The compass of the instrument ranged about four
or five octaves.
There were from one to four strings per
note, with some of the strings tuned an octave or two higher. Many erroneous classifications have been made due to the various names given to this instrument in different countries.
Dr. Gurt Sachs makes the following classification:
English French Italian
37
Grand Form
Square Form
harpsichord clavecin clavicembalo
virginal or spinet epinette
Sachs, op. c i t p. 335*
47 The harpsichord, developed in the sixteenth century, found its greatest usage beside the clavichord in the seventeenth century.
It was based on the mechanical prin
ciple of a plucked, rather than a struck, string.
Opposite
the key mechanism, upon which the player used his fingers, was attached a jack, into which, at the upper extremity, was attached a pointed quill insert which projected out from the jack.
This was sturdy and strong, and was fastened in
such manner that when the player depressed the key, it would pluck the string, and, being elastic, would fall back immediately into position of rest.
The musical consequence
resulted in a tone that lasted* for a longer period of time than the modern piano, with damper removed.
The tone was
clear and clean, and stops built into the piano altered the quality of loud and soft* During the seventeenth century the building of a second keyboard above the first came into existence. These early keyboard instruments were tuned to the meantone temperament.
The white keys were tuned as they are today,
but the black keys were timed as leading tones.
The harp
sichord could not transpose beyond a fifth above or a fifth below.
The second keyboard was, therefore, a transposing
one, and made possible the synchronizing of the fifth and fourth from above the tones of the lower keyboard.
When
equal tempered tuning came into vogue, the second keyboard
48 was pitched and tuned like the first keyboard, thereby becoming a color keyboard*
Because the second set of
quills plucked the string at a different place on the string it produced a slightly different vibration which acted to enrich the tone*
Changing the partials within an instru
ment will produce this effect.
The stops on the harpsichord
shortened the strings so that octave tones would sound* It must be remembered that Haydn, Mozart, and Beet hoven did not write music for the harpsichord but for the piano-forte.
This was not quite the same piano-forte
which we use today, however.
Erard invented the double
repeating action in 1 8 2 3 , after these aforementioned masters passed on.
His is the action of the modern piano,
and is not the same instrument just referred to. Before Erard, but immediately after the inception of both the clavichord and the harpsichord (with its various names as used in different countries), Bartolommeo Cristofori in 1709 (Curt Bachs), 1710 (Steinway and Co.), 1711 (M. Emett Wilson), invented the hammer action and applied it to the dulcimer. cerning the true date.
(Various authorities disagree con Steinert attributes 1709 as the date
on page 9 0 , and 1711 as the date on page 7 2 *) This new instrument, now by means of the hammer mechanism, could control the strength of the stroke on the key, making loud and soft as well as all shades between
49 possible*
The Viennese pianoforte of Stein and Streicher
gave performers an instrument of even, light and facile touch.
Mozart played this piano.
Uzerny wrote and execut
ed his velocity compositions on this type of piano.
It is
no small wonder that a piano with a shallow key dip should lend itself so admirably to fast, agile playing,
ftor any
wonder that the Viennese people preferred the harpsichord and the Streicher piano, to the heavier, more ponderous, and voluminous toned piano of the eighteenth century. The harpsichord had a key dip of three millimeters, while the modern piano has a key dip of seven-sixteenths of an inch.3$
Steinert attributed this lightness of touch to
the change in position of the hammer with the rising and falling of the key. Johann Andreas Stein, born at Heidesheira, 172# . . . As a pianoforte builder he justly deserves the name of "Father of the German School," for the reason while Silbermann adopted the action used by Gristofori, the real inventor of the pianoforte, Stein favored an action totally different and more simple. The Stein escapement differs from GristoforiTs and the English action, in the fact that the axis of the hammer changes its position with the rising of the key, the hopper (Ausloser), be coming a fixture at the back of the key. From this dif ference a radical change of touch took place, and an ex treme lightness became the characteristic of the Stein action, as developed by Andreas Streicher, of Vienna, Stein’s son-in-law, who, in 1794, improved and finally established the great renown of the Viennese pianos. ______
JV
*
Sachs,
39
Steinert, op. ,cit.. pp. S6-7.
Lectures summer of 1949, op. cit.
50 The spinet is a keyed instrument with plectra or jacks. It was used in the sixteenth, seventeenth and eighteenth centuries. It may be described as a small harpsichord or Virginal, with one string to each note. It is said to be the invention of the Venetian, Banchiere Spinetti, in 1603. It derives the name "Spinetta" from this maker. It is in shape the same as the clavichord and has the same keyboard. The jack action is derived from the psaltery plectrum, while the tangent of the clavichord comes from the monochord bridge. All instru ments of the spinet, harpsichord, virginal and clavicyrabalo family were on the plectrum principle, and there fore were incapable of dynamic modification of tone by difference of touch. The strings were set in vibration by points of quill or hard leather, elevated on wooden uprights known as jacks, and twitching or plucking them as the depression of the keys caused the points to pass upward. G.
THE EIGHTEENTH CENTURY (1750-1320, CLASSICAL PERIOD)
This century Is a brilliant period, magnificent in splendor, and refined in taste.
Elegance, especially in the courts
of the princes and kings is something to be seen, but not enjoyed.
For the rich lords there was wine and song, for
the poor there was taxes, bread and water.
Voices like
Voltaire shout out into the wilderness in a plea for liber alism. Classical music is an accurate reflection of the age. At first the temper of the times is one of breadth, magnificence, and great vitality. This is mirrored in the elaborateness and splendor of Italian opera, in the exuberant yet easy-flowing forcefulness of Handel, and in the sweep and grandeur of Johann Sebastian Bach. After the century’s half-way mark is reached a different mood
40
Steinert, op. cit., p. 63.
51 appears, and in the music of the times we note the change* Mozart, Haydn and other composers of the period reflect a society which has embarked upon an age of reason with order, clarity, precision as its chief ideals; an age, too, when court life has become sated with luxurious display and has turned to elegrance, refinement, and so phistication. But oper$ is only one aspect of the musical vitality in this prolific age* In another field composers are laboring in relative obscurity. They are perfecting instrumental music, and it is mainly their efforts that will be remembered later on. To understand this other side of music it is impor tant to remember that in the eighteenth century nonoperatte music exists chiefly by the grace of wealthy noblemen, each with his princely court and court musicians. Even the most vital creative spirits of the age— Bach and Handel, Mozart and Haydn, Corelli and Scarlatti and Rameau— are dependent on the generous but often petty and tyrannical bounty of these mastery composers must conform to princely taste. In the first half of the cen tury they must be boldly picturesque, express a massive luxuriance touching the epic; in the second, they must adopt a style that is lighthearted but not frivolous, intelligent yet not too deep. Their music must be clear, symmetrical, well-mannered. It must embody the spirit which later generations will describe as classicism. Strict etiquette must be observed in music no less than in dress and manners, and all expression of strong feeling is officially taboo. 41 The eighteenth century saw many developments in the progress of the piano.
Some of the lesser devious paths
which this progress took follows below* The clutsam keyboard♦
This was a curved and concave
keyboard, which was an expedient device taking into account the fact that the arm moved in an arc and should do so when playing the piano*42 41
Grabbe, o£. cit., pp. 21-24.
^ Percy Scholes, The Oxford Companion to Music (New York: Oxford University Press, 1947, 7th ed.), p. 495*
52 Friction Rods (Nail Piano). In 1733, Charles Clagget in London obtained a patent for a piano with metal rods or tuning forks, instead of strings, with a special "Celestina stop" which consisted of"an endless fillet (rubrd with resin dissolved in spirits of wine) producing the sounds on these bars as it does on the strings." Three years later, in 1791, a drawing teacher in Bernburg, Saxony, transformed in a similar way the nail violin with a rubbirg wheel into a "nail piano".^ Clavicylinder. About the same time, the famous physicist Ernst Friedrich Chladni in Halle, the father of modern acoustics, constructed instruments of thin glass rods rubbed length wise by the fingers and transferring their longitudinal vibrations to iron rods which resounded in a "soft and aethereal" way. The inventor called it "Euphones". In 1799, he replaced the rubbing fingers by piano keys and a rubbing cylinder and called this keyboard instru ment "Clavicylinder" There were other musical devices using water glasses plus a keyboard in the eighteenth century,
^his design did
not last long, but gave way to the "Harmonium" type of key board instruments.
This instrument was basically a metal
reed type of instrument using bellows and a keyboard.^5 The Piano-forte.
The addition of a hammer action
to the harpsichord helped create the modern piano action, and subsequently the modern piano-forte.
43
Sachs, op. cit., p. 403*
^
hoc, cit.
45
Ibid., pp. 404-5*
Greatest credit
53 for this discovery in 1711 is given to Bartolommeo Cristofori, an Italian*
Cristofori’s invention came about at the
same time that the orchestras in Rome innovated the cres cendo or decrescendo over passages of several notes in suc cession (not to be confused with the organ swelling type of crescendo)• An authentic piano-forte made by Bartolomeo may be seen at the Metropolitan Museum of Art in New York City* It is most strange that even though Cristofori’s invention came as a result of the times, he could not interest the Italians in his invention*
The Germans took
over his ideas for the next two decades and also in turn discarded same.
The German piano could not compete in size
and price with the clavichord; it being much heavier and larger.
An attempt to produce a cheap piano did not meet
with success.
It was not until after the seven years war
(1756-1763) that the Saxon piano-makers emigrated to England where ‘they were welcomed with open arms.
Firms like Kirch-
mann, changed its name to Kirckman, along with others.
John
Broadwood was the first of these people to lead the movement away from the ideals of the harpsichord and clavichord to thinking in terms of the piano.
Johann Christian Bach
(1 7 3 5 _17 £3 ) was a brilliant exponent of the piano.
He gave
the world’s first piano recital in I76 & in London and thereby established the position of the piano as an instrument unto
54 itself. H.
THE NINETEENTH CENTURY AND THE PIANO
Having traced the development of the keyboard instru ments up to the nineteenth century, we find that the piano was in its last stage of development and there awaited the world to make use of it.
The time was ripe.
Interest in
the piano became so great that all other forms of musical expression were shunted into the background.
To understand
the reasons for this amazing occurrence one must examine the characteristics of the period, its history, culture, economics, politics and ideology.
Its writers, painters,
architects, scholars, and musicians. Characteristics of the period.
The nineteenth cen
tury was highlighted by the industrial revolution in industry. The period was characterized by the invention of the railway, the steamboat, electric lights, and so on.
The individual
in seeking independence, sought to be self-sufficient, free in thought and independent in movement.
Artists, painters,
poets, and musicians left the services of Church and State to produce their works free from coercion and the dictates of society.
The artistic circle was able to indulge in
producing ”Art for Arts 1 sake.” In consequence, as the romantic, or revolutionary
55 elements of civilization broke loose from the shackles and bondage of the upper ruling class, the growing spirit of Nationalism served to free suppressed ideas and peoples to such an extent that the era became one of confusion, or simplification depending upon onefs point of view.
Per
haps the French Revolution and the Civil War pointed the way for the mass of people. The philosophy of the times in relation to the piano. The period was a melting pot of ideas which found room for all types of expression. and deeds.
It was a hodge-podge of thought
Music was the center of the arts.
Within this
center as its chief exponent, was pure instrumental
m u s i c . 46
And within the framework of this instrumental music, the piano was the most versatile.
A tremendous amount of music
was conceived during the nineteenth century for this instru ment.
Composers and performers like Liszt used the piano
to dispH^r an intensly developed artistic and powerful vir tuoso style.
In the article on ”Piano Playing and Piano
Literature” by Leslie H0dgson in the International Cyclopedia of Music and Musicians, the following quotation expresses the reason for the output of the so recently developed piano, which had just emerged into full bloom during the romantic 46 Alfred Kinstein, Music in the Romantic Lra (New York: W.W. Norton and Co., -Inc., 1947) > P* ^3•
56 period: The first pianists, with their uncompromising in sistence upon clarity had permitted but sparing use of the damper pedal* Beethoven was first to recognize the artistic possibilities of greater recourse to i b * ^ The Pianoforte, forte
It islittle wonder that the piano
came into its own in the
nineteenth century.
The use
ar^d full acceptance of this instrument, over the harpsichord and clavichord was as natural as the change of seasons from summer to winter, or the cycle of day and night of the earth* As
the pianoforte was capable of a maximum of flexibility
between loud and soft, crescendo and decrescendo, as well as all imperceptible shades inbetween, thus it became more in keeping with the music of the times.
Further, the piano
could sustain its tones, or sound them in short, staccato, or choppy manner.
Thus, the history of its growth has been
a long and interesting one. .The successful inventor is to
knows that if his invention
meetwith success, it must fill the needs of the pub
lic for which it is intended.
It took many centuries to
develop the keyboard instruments into their final form, liach step in its development came only when the need for it became necessary. It was not, however, always universally acceptedt as is witnessed in Italy and Germany where the harpsichord found even greater usage after Cristophere Bartholemew
57 invented the modern pianoforte hammer action in 1 7 0 9 * The Germany too, were slow to accept the piano* When Johann Andreas Stein died in 1792 he left his factory to his daughter Nanetta.
She married Mr. Streicher and in
1794 they moved the factory to Vienna, where they manufac tured the Streicher piano*
Beethoven, who was a close
friend of Nanetta, did not write his sonatas for the Streicher piano*
They were not possible on this piano.
The key
board was too light fingered, and the key dip was entirely too shallow for him.
He needed a stronger, more solid feel
ing instrument.47 it might be added that Beethoven was tremendously interested in the manufacture of pianos.
He
shared his enthusiasm with J.S. Bach who preceded him in this field.
As a result of this interest he was the recipi
ent of many pianos which he bestowed his uncanny genius on.43 In the Steinert collection of keyed instruments there exists a concert grand of 6 | octaves "Bearing the sounding board the following inscription: ’Nanette Streicher nee Stein, Wien, iBlb’. " ^
This particular concert grand was loaned to
Beethoven during his stay at Baden.
47
Curt Sachs, lectures, summer of 1949*
43
Pauline Alderman, lectures, summer of 1949*
49 Morris Steinert, Keyed and Stringed jfastruments (New York: Charles Tretbar, steinway Hall, 1$93), p. 55* >
53 It was not until the nineteenth century that the piano actually replaced the harpsichord and the clavichord* More inventions were added to the piano in this century than at any other time*
Several of these were: (1) the
instrument was made heavier and thicker;
(2 ) the sound
board became thicker, this added quality and sonority to the tone, so vitally necessary in this period;
(3 ) the
range of the instrument was increased to include up to eighty-eight keys;
(4 ) the pitch was raised to conform with
the piercing and penetrating quality so necessary for loud performances;
(5 ) steel bars were added to support the
frame since the pressure exerted by the string tensions would split any construction solely of wood. Alphaeus Babcock added the first all cast steel frame. The strings were thus attached to the pins on the plate at one end, and attached to the pin block at the other end. Some strings being of double length simply went around a pin on the plate and were attached to two pins at the pin block end.
The pin block, being of cross-grained sections of wood
glued to each other with holes to receive the tuning pins, was securely fastened to the steel plate with steel bolts. Steinert says that Uonrad Meyer of Philadelphia is the invent or of the iron ^
f r a m e . 50
Actually, when iron was introduced
Ihid.. p. $1 . s
59 into the construction of the piano, the piano industry had new vistas opened for it. The pioneers of the powerful western piano were John Broadwood in London, Sebastien Erard in Paris, and John Isaac Hawkins in Philadelphia. Broadwood was the first builder to cut the ties with the clavichord and the harp sichord in the outer shape as well as the inner construc tion, In 1800 Hawkins invented the earliest metal braces between the wrestplank with the pegs and the soundboard in order to counteract the thicker strings of the time with their over-increasing tension. In 1821, Erard created the modern fully reliable action with the double escapement or automatic backfall, of hammers to a posi tion midway between rest and stroke, which allowed for a ready repetition of tones. In 1825 Alphaeus Babcock in Boston designed the earliest full cast-iron frame to take the tension of the strings entirely off the sound board and the outer case. At last this same Babcock de vised, in I 83O, the so-called over-strung scale. In this modern arrangement, the bass strings stretch diagon ally across, and a little above, the higher strings. This allows them to profit from the better resounding middle of the soundboard instead of being left to the in effectual margin, and it also allows them to arouse better the sympathetic co-vibrations of the higher strings and thus increase the intensity of partials. Indeed the modern piano originated in the three decades from 1800 to I83 O .5 1 Successive developments in double escapement im proved the instrument still further.
Beethoven employed
the early 19 th century pianoforte for his creative endeavors. Before the invention of cross stringing just explained, the piano had a clarity of
of tone which made
possible the hearing
single tones, in scale or chromatic
passages which ishot
possible with the overstrung piano.
Due to the sympathetic
Curt Sachs, Our Musical Heritage (New York: Prentice-Hall, Inc., 194&) PP* 319-20.
60
vibrations which the overstrung piano produces, its enriched tone lends itself to modern compositions* The nineteenth century romantics expanded the harmonic range of music.
They produced beautiful tone colors, used
chromaticism, altered the sevenths, used ninth chords, and modulation as a part of the musical structure within a piece rather than always between pieces of music to connect it. Clarity of tone was superceded by warmth of color and rich ness of tone.
The piano had reached the stage of development
where it could supply all of the necessary qualities needed to satisfy the desires of the romantics. Principal keyboard composers.
The principal com
posers of the period who contributed materially to the key board music were: 1.
Beethoven, who expanded the classical forms,
particularly the sonata-allegro form, and who was cast in the role of connecting link between the classic and the ro mantic period; 2.
Schubert, whose music reflects the influences
of both the classics and the romantics; 3.
Schumann, the true romanticist;
4«
Mendelssohn, who combined the classic harmony
with the romantic use of melody and tone color, best known for his piano music, particularly his forty-eight Songs
61 without Words; 5*
Chopin, who was exclusively a piano composer;
6*
Franz Liszt, the great piano virtuoso of his day;
7.
Johannes Brahms, the neo-classicist.
and,
Brahms brought the romantic period to its end, and with him the nineteenth century passed on.
I.
TWENTIETH CENTURY
The modern period from 1900 to the present includes the Impressionistic period from 1885-1914*
4jLke modern per
iod unlimited in concepts and resourcefulness, has made tremendous strides as is witnessed by its tall skyscraper buildings, suspension bridges, and atom bombs.
Various
styles and ideologies have helped form a broad understand ing of freedom and internationalism.
Even after two great
world wars the problem of living peacefully with one’s neighbor has not been settled.
The world has reared expres
sion in the shape of impressionism, realism atonality, poly tonality and jazz.
It is too early to write the history of
the times as the perspectus is too close to our day. The history of developments in the piano however, continues.
Twentieth century technicians are working on the
following developments, many of which are already with us
62 today:
the aluminum piano plate which will take the 13-
ton string tension, yet reduce the overall weight of the piano; the introduction of the spinet or small piano; the development of the portable piano; the designs for a key board resembling the accordian in size and action; the use of hexagon steel core wire for the strings; the improvement of touch and tone through a balanced even tension scale; direct hammer blow action, pipe organ type tone chamber in the case; the Story and Clark electrically amplified piano; the Moor-Bechstein double keyboard piano, and the quartertone piano. Vocationally speaking.
No greater satisfaction can
be derived than from seeing and examining old piano master pieces, whether they are restored to playing condition or left in their original state of discovery. Artists, performers, and imitators of musical sound should make every effort to understand the period of the times in which certain music was written.
It is also for
them to decide whether modern day practices of vibrato, sensuality, and expression are applicable or desirable in the performance of these same compositions.
CHAPTER V PIANO CONSTRUCTION The ease*
This consists of* the exterior framework
which is made of solid mahogany, oak, black walnut, maple or other hardwood*
Some people are now upholstering the
wood with imitation leatherette and mirrored glass* is noreason why some other material could Thegrand piano shape is formed
There
not be used*
by bending wood with steam
and metal pressers* The cases of good pianos are so accurately designed and made, that there is a very slight difference in the levels taken before and after an instrument has been strung and drawn up to the required pitch. It is an elastic framing that is sought for, rather than one abso lutely rigid; flexible enough to permit the sympathetic molecular vibration of the wood and metal, while provid ing the stiffness of thrust and resistance required for the necessary strength of the structure.^ The frame (Including the back plate and pin block)• ■k# The back plate*
This is usually made of steel,
aluminum, or cast iron, and in the older pianos, of wood, which unites the case and other parts.
It supports the
entire pull of the strings. The tuning pin block*
This is made of various
layers of hard wood (beech and wainscott wood) glued tor
gether with the grains in the wood crossing each other. ^ Alfred James Hipkins. "Piano History” (Boston: Novello, i*iwer and Co. fl&63-1903), P. 14
64 This intensely strong block is capable of setting up tremen dous frictional resistance to the pull of the strings.
In
the grand piano, this block is found in frort* above the key board, and in the upright piano, it is found at the extreme top of the piano. block.
The tuning pins are hammered into this
Holes are bored in the pin block.
The tuning pins
being a bit oversize are hammered into the block.
The pins
have extremely fine grooves threaded around their circum ferences. The resonating board (Including the soundboard, batons. and ribs)• A.
The sound board (or belly board)•
This section of
fir wood or Rumanian pine, well seasoned, is a flat, wide surfaced elastic table, consisting of uniform grained lengths of wood, varying from 3/& of an inch to 5/16 of an inch in thickness (usually thicker in the center and thinner at the edges).
It vibrates freely at the edges in order to amplify
the tone when a string is set into motion.
(Slender strings
have little contact with the air and need a thicker wood to resonate their tones.)
The soundboard is never screwed or
nailed to the frame of the piano, instead it is glued in with the tapered side facing the strings.
As Young says,
"Sound travels along the grain six times more quickly than across it . " 2 2 T. Campbell Young, "Making Musical Instruments" (New York: Oxford Press, 1939), p. o.
65 Batons (belly bars, bridges).
These are an inch
thick, are glued in such a manner as to maintain the arched design of the sound board (belly board) and to assist in the formation of nodes (points of rest or concentration) where crossing lines of vibration meet.
These batons are
made of hard wood* The strings in their passages across the bridges ac quire side-bearing by means of suitably driven pins. These bridges are glued to the sound-board and secured from the back thereof by means of screws. 3 C. Ribs.
The ribs are found on the underside of the
sound board (the flat side)•
fhey are made of spruce or
pine and are glued across the grain of the wood, parallel to each other.
These ribs develop the sympathetic resonance
of the instrument. The action and keyboard.
This consists of the sum
total of parts as comes in one unit in a grand piano, and two units in an upright piano. are called:
In this case the two parts
1) The action, which includes the repeating
action, the hammer heads and dampers to stop the sound; and 2) The keyboard, which includes the keys, levers, ivories, and ebonies. The action parts consist of Maple wDod from Canada
3 William Braid White, "Piano Tuning and Allied Arts” (Boston: Boston Tuners supply, 1946), p. 121.
66 and hornbeam wood from France. wood*
Each is hard, close-grained
Plastics are being substituted for many action parts*
The wooden head of the hammer is covered with compressed sheep’s wool, cut from one piece*
The hammer shanks are
made of light wood such as pear, hickory, white beech, or cedar*
uedar is the most elastic wood but fractures the
easiest.
The damper key, of felt stops the singing of a
string after it is no longer wanted.
Lime wood is used in
the keys, because this wood warps the least of all woods* The key is covered with ivory, ebony, or any other substitute* The keyboard is usually forty-eight inches in length, and six inches deep.
The white keys are six inches in length and
13/16 inches wide. the front board.
They are usually 7/S of an inch above The
black keys are four inches long and
7/16 to J inch wide, and extend j inch above the white keys. The strings*
There are approximately 233 strings
depending upon the number of keys (the average piano has SS keys), and the number of strings used per key.
Usually
three strings for the center section and the treble section, made of cast steel wire, two strings in the bass section and one string in the deep bass section, known as overspun wound strings.
These are heavy in order to compensate for their
lack of length.
Overspun with copper, the bass strings
are usually strung above the treble section.
67 Bradwoods normal tension in 1362 was 150 lbs. tension avoirdupois for each string of steel wire. (The new pianos have a greater strain per string.) (Middle C assumed as a mean tension for the whole scale.) Steinway pianos bear a strain of 60,000 lbs. (nearly 27 tons). It is probably true to say that these strings of cast steel wire, represent the strongest elastic material in exist ence; we may form some idea of their strength when we realize that a two-foot length of the thinnest wire used (thickness thirteen and one-half gauge) would support, without breaking a weight, of something like twenty stone. (This is two hundred and eighty pounds.)/^ The trap action (pedals)•
The trap action consists
of all the pedals and parts which the player uses to regulate the intensity of tone.
The pedals serve two functions:
1) to sustain the tone(commonly referred
to as the loud or
right foot pedal); and 2) to soften the tone.
The latter is
accomplished by one or more of the following three methods: 1) the insertion of a wool pad between the hammer head and the string; 2) shortening the distance, the hammer head has to travel to reach the string; and 3) shifting the keyboard so that the hammer head strikes only two out of the three strings. As you will notice inany case, the action taken amounts to putting the
pedal either on or off.
There is no
graduated degree of control when using the sustaining pedal and an infinitesimal amount of control when using the soft pedal.
Halfway shifting of the keyboard (method 3) tends ^
Hipkins, op, cit,.. p. 12.
6£ to produce a fuzzy tone as the hammer head grooves are un duly upset,
(This particular method is mostly used on the
grand piano style and some very few upright pianos,) The quality of construction.
This is usually gov
erned by the salesprice and the manufacturer’s respect for his name and product.
Most pianos in use today, with rare
exceptions, are not the products of any one concern.
Var
ious specialists make one or more parts of the piano and sell them to assembly houses.
There are some concerns,
however, which build pianos from start to finish in their own plant.
On the whole, action parts are standardized.
It is difficult to indicate preference for one type of construction over another.
Unless pianos are kept in re
pair and in perfect tuning, played upon often, and not subjected to extreme humidity and temperature changes, they deteriorate in due time. The repairman will determine for himself which type of piano he likes to work on best.
He will also determine
which type of piano costs the most to repair.
To cite an
example: pianos with brass flanges are difficult and expen sive to repair. For reference in selecting instruments, f,The Purchas e r ’s Guide to the Music Industry” is a magazine published to inform and protect the public.
It is a yearly magazine
69 compiled and edited
by the publishers of the Music Trades
and Musical America at 113 W. 57th Street, New York 19, New York. It might be argued that when a piano increases with age, the gum and other volatile matter that have existed in the wood have now evaporated and dried up, thus freeing the wood, especially that wood in the sound-board, to vibrate with more freedom.
some people claim that a certain amount
of wear on the hammer heads tends to give the piano a cer tain charm of tone quality.
Others say that were the action
parts on an old piano changed every several years, that piano would be much better than a new one. A new
piano,on
the
other hand, it is claimed, or
one that has been used just enough to take the roughness out of it, is better than an old piano.
Unlike a fiddle, which
grows more mellow and beautiful with use, the action parts on a piano warp and deteriorate. All pianos, new or old, should always be kept in good condition and in perfect tuning. with every seasonal change in the year.
This means a tuning
CHAPTER VI STUDY OF PIANO ACOUSTICS AND STUDY OF STRING VIBRATION A*
SOUND AND ACOUSTICAL SCIENCE
The nature of sound becomes exceedingly important when discussing piano tuning, since the action of a piano creates sound waves* Definition of sound*
Sound is defined as a distur
bance in a material medium caused by the vibration of any body at a certain definite frequency* Audio frequencies*
This is a term used to designate
the range of frequencies audible to the human ear.
The
range audible to the human ear is strictly a controversial subject among physicists* Propagation of sound waves*
Sound travels through
a material (elastic) medium, such as air, water, wood, or steel, in the form of compressional or longitudinal waves, by means of compressions and rarefactions*
A longitudinal
wave is defined as one in which the to and fro vibrations of the particles of the medium takes place along the line of propagation of the wave. The velocity of sound in air.
Sound travels 1090
feet per second when the temperature of the air is 0 °
71 centigrade or 32° farenheit (freezing point of distilled water.
The speed of sound rises with increasing tempera
ture by two feet per second for each degree centigrade rise, so that at room temperature (20^ centigrade) the velocity is 1130 feet per second* Sound— musical tones or noise? the point of view of the listener*
This depends upon
Sounds producing repe
titious vibrations wherein each cycle is like the last one with regard to frequency, amplitude, and wave form for a single tone are usually classified as musical sounds*
When
the shape and amplitude of the individual wave lengths are discordant (different) the sounds produced are considered noise* (Jharacteristics of sound *
These are determined by
three factors: pitch, intensity, and timbre* A* Pitch is determined by the frequency of the vibra tions, produced by the vibrating body*
The ratio of pitch
to frequency is direct; as the rate of vibration (frequency) increases the pitch of the sound is raised. B.
Intensity is determined by the amplitude of the
vibrations (volume, loudness, pressure of compressions and rarefactions).
Intensity is measured by a sound level
meter, or the acoustimeter. f,decibel.,,
The unit of measurement is the
The threshold of audibility is registered as
72 zero decibels.
A quiet church or breathing through the nose
registers ten decibels, or one bel.
Full volume of* a mod
ern home radio or an average factory registers sixty decibels. The threshold of pianful feeling, thunder, artillery firing, unmuffled airplane engine, equals one hundred and ten deci bels.
The relative energy at this point will equal the
number, 1 0 0 ,0 0 0 ,0 0 0 ,0 0 0 , whereas, at the threshold of audi bility the relative energy will equal the number 1 . Mature has wisely arranged our hearing so that our ears compensate for extremely loud sounds by not respond ing to them as well as to very faint sounds. For in stance, if one violin is playing in a room, a certain sound level is obtained. To make violin music in that room sound twice as loud to the ear, you would need closer to ten violins than two violins. It has been found by subjective tests that every time you wish to double the apparent noise level, you must multiply the sound energy by 10. Therefore, to go from 10 decibels to 100 decibels calls for an increase in the sound energy of 1,000,000,000 times. To make a notice able reduction in the noise level, it is necessary, therefore, to absorb an enormous amount of sound energy. 2 The decibel is really a ratio based on the sound level being measured and upon a pre-set zero degree level.
The
decibel can not be thought of as in ther terms of one inch, one pound, or any other such unit of measurement.
Robert R. Buntaine, tTA Story of Sound,” Bulletin Nn. 120. 10-45-10M (Chicago: Burgess-Manning Company), pp. 9 and' l6 . 2
Ibid., p. 16.
73 C.
Timbre is determined by the number and prominence
of overtones.
Timbre is the quality of tone.
Overtones
are integral multiples of the lowest frequency being pro duced,
The lowest frequency is called the fundamental tone.
Multiples of the fundamental tone are called overtones, harmonics, or partials# Production of sound.
The following illustrations
will tend to show how sound is produced: A, The Pendulum,
The three items above may be illus
trated by the use of a swinging pendulum.
If a pendulum
is suspended and allowed to move (oscillate) freely all three characteristics may be observed. 1. Pitch.
The to-and-fro motion (from A to C
and G to A, see Illustration-No. 1) is what is meant by vibration.
This pendulum will travel very slowly
but the speed of this motion serves to explain the term frequency.
In Illustration No. 17, the number
of times per second that the swinging pendulum com pletes its swing from A to C and back to A is the frequency in cycles per second# 2. Intensity.
Amplitude, which determines in
tensity, is the maximum displacement of a vibrating body from its mid-point.
Again referring to Illus
tration 17, amplitude is the distance from A to B
or from B to C.
The slowly vibrating pendulum will
produce no audible sound because its frequency is too low to be heard by the human ear. 3.
Timbre.
Since there is no audible sound
there can be no overtones. B.
Vibrating strings*
The theory of sound may be
further illustrated by using strings.
A monochord of the
manufactured type should be used if available, however, one may be improvised, or a cello may be substituted. It may be seen that if the string is allowed to vibrate its full length the pitch of the tone and the speed or fre quency of vibration will be., low.
See Illustration No. 1&.
By placing a bridge at the midpoint of the string (C in Illus tration No. 3) the pitch will be an octave higher.
It is
thus shown that the length of the string is inversely pro portional to the frequency of vibration.
If the string
used in the above experiment is one of the plain steel var iety it should now be replaced by one of the heavier wound strings and with the same tension (weight) applied the sound or tone produced will be lower.
If the diameter of the
second string is twice that of the first the tone produced by the latter will be one octave lower.
(See Illustration.
No. 19.) It can be further shown that by applying more tension
75 to the string a higher pitched tone will result*
If the
weight is increased four times, the frequency will be doubled* Finally, if two strings of the same length and dia meter but of different material (steel and brass) are both brought to equal tension it will be found that the tones pro duced will“~be different* From the above demonstrations the following laws gov erning frequency and vibrating strings are derived: 1. Frequency of vibration of a string varies in versely as the length. 2. Frequency varies inversely as the diameter. 3* Frequency is directly proportional to the square root of the stretching weights. 4* Frequency is inversely proportional to the square root of the density. Continuing with the deraonstrations of the monochord, we can show that the string vibrates in segments as well as in the whole, thus producing complex vibrations.
If the
string is stretched to a tension which will produce 1 3 0 .# 1 3 vibrations per second, the pitch C (2nd space, bass clef, piano tuned to A-440) will sound.
By lightly stopping the
string at the exact center and again starting the string vibration, a tone one octave higher will sound. will be middle C (321*626 vibrations)•
This tone
By touching the
76 string one-third of the way from either end, the number of vibrations will how be 392 *4 vibrations per second. tones are called harmonics, partials, or modes.
These
By divid
ing the string further into fourths, fifths, et cetera, enough of the harmonic series can be produced to explain harmonics graphically.
The number of these harmonics will
determine the quality of the tone.
Three theoretical
complex sound waves are shown in Illustration 20 to show how the number of harmonics affect a resultant composite wave . The sound waves in Illustration Wo. 20 are reproduced as they would appear on an "Oscilloscope".
(An oscillo
scope shows sound waves on a screen, making it possible to study wave frequency, phase and shape.) wave represents the sound actually heard.
The resultant Th© red lines
drawn through the waves show how the resultant wave is de rived.
If all the portions of the waves above the reference
line are added together and subtracted from the sum of all the portions below the red line, the result will be the distance above or below the reference line for the resultant wave.
For example in a, the distance from 1 to 2 is sub
tracted from the distance from 3 to 4*
The difference
will equal 5 to 6 . In case C above, the distances 1 to 2, and 7 bo 8 are added together, then the distances 3 to 4 , and 5 to 6
77 are added.
These are subtracted from the first sum and the
result is the distance from 9 to 1 0 . Of great importance to the piano tuner is an under standing of what occurs when two tones of the same frequency are sounded together and when two tones of slightly differ ent frequencies are played.
When the frequencies are the
same, the sound waves reinforce each other as in Illustra tion No. 4*
If> however, the two frequencies are different
by a few vibrations, beats are produced.
Beats are regular
pulsations which occur in a regular sequence.
Following
each of the pulsations there is a short period of silence. These alternate beats and periods of silence are caused by interference of the two sound waves ((see Illustration No. 21 ) . Illustration No. 6 shows what happens when two sound waves of slightly different frequencies are sounded together. When the compressions and rarefactions coincide, the loud ness and, therefore, the amplitude increases.
When the
compressions and rarefactions are out of step they tend to oppose each other and reduce the amplitude of the resultant wave (see Illustration No. 22). When the compressions and rarefactions are completely out of step, as at a in Illustration No. 6 , silence results. At b, they are exactly in step producing maximum loudness. The number of beats which will occur per second will correspond to the difference between the frequencies of the
73 two sounds.
In the case of the two tones in Illustration
No. 6 the difference between 425 c.p.s. and 420 c.p.s. is five.
How the piano tuner makes use of beats will be dis
cussed in the section on piano tuning. Transference of sound♦
It was previously stated
that waves produced by the vibrating body must be transmit ted through a medium to produce an auditory sensation. For discussion purposes let us assume that our medium is air.
If a tuning fork is struck and allowed to vibrate
it will force the molecules of air surrounding it to move to and fro in the exact manner of the vibrating prongs.
These
molecules of air in turn strike against the molecules they are in contact with and thus the impulse is passed on from molecule to molecule until it reaches the ear drum.
It
should be explained here that it is not the air itself which is disturbed and transferred from one point to another but that each individual molecule passes on the impulse to its neighbor.
This transference of sound can be illustrated
by constructing a chute just wide enough to accommodate a billiard ball or some similar ball and a foot or more in length.
By placing in the chute a half dozen balls to repre
sent molecules we would have a set-up somewhat like that shown in Illustration No. 23. If a ball A is struck a sharp blow it will transfer
79 the impulse to ball B. and so on.
Ball B passes it on to C, G to D,
It will be seen that each individual ball will
not have moved any great distance, only large enough to pass on the impulse.
As each molecule strikes its neighbor we
have a "compression11 (as when A strikes B) .
Then while B
is striking C there is an expansion between A and B.
Thus,
we see that like the vibrating body sound waves are com posed of compressions and expansions.
In acoustics these
expansions are called "rarefactions" (See Illustration No. 2/j.) . Resonance.
If the tuning fork in the preceding
illustration is vibrating in the air the two prongs set into vibrations comparatively few molecules of air.
Now
place the heel of the fork against a wooden table or box, the tones will be much louder. phenomenon, "resonance".
This brings forth a new
In this case the vibrations are
transmitted through the heel of the fork to the table top setting it into vibration.
The large table top can now
set into vibration the larger number of air molecules adja cent to it.
Wood is set into vibration quite easily,
therefore sound boards in pianos are always made of wood. Sympathetic Vibrations.
If a second tuning fork is
used it can be hoswn how sound waves can set a body into
80
vibration.
This is called "sympathetic vibration"; (see Il
lustration No* 2 5 . If tuning fork A is struck, its vibrations will set the adjacent air molecules into vibration.
The air wave in
turn will set fork B into vibration, if they are of the same frequency. B.
THE EFFECT OF TEMPERATURE AND HUMIDITY ON PIANOS AND OTHER MUSICAL INSTRUMENTS The factors which generally cause pianos to go out
of tune are: 1*
Excessive use, or abuse, as well as lack of use.
Proper use under ordinary playing conditions demands that the performer use varying shades of "piano" and "forte". The "time" factor involved will, in due course, obligate the strings to lose tension and change pitch.
Fading of
tone quality and elasticity of both the hammer heads and strings will result.
The hammer head will harden, espec
ially under a condition of "no use", and thereby cause the partials coming from the strings to be different.
The
result: one piano out of tune. 2.
Atmospheric conditions such as climatic changes
which result in loss of physical properties by material things.
All scientific studies are based on experiments
conducted under ideal conditions.
Sound experiments are
£1 usually conducted in air conditioned and temperature con trolled rooms*
All manner of devices are employed to
further insure ideal testing conditions*
For example,
rooms are soundproofed and all testing equipment is kept in perfect shape.
Even though adverse and unfavorable condi
tions like noise, etc., is being tested, the testing labor atory maintains ideal testing status. The results of many findings are incorporated by manufacturers into their products.
It is correct to sur
mise that the manufactured product will last a lifetime and yet soon after the consumer takes possession, the arti cle starts to come apart. best of products?
What is it that undermines the
Can it be constant use, or abuse, or
are other detrimental factors present? We may assume that in the natural course of events, man made products must show their fair share of disinte gration due to either proper or improper use.
It is the
latter half of the question with which we are concerned. What are these detrimental factors? are they the products of nature?
Are they man made, or Any musical instrument,
whether it is composed of steel, wood, brass, plastic, or other material, or any combination of same will undergo physical changes due to sudden changes in the atmospheric conditions.
In the case of combinations of materials
82 affected, physical changes call for an entirely new set of scientific rules.
Because of the unequal co-efficients of
expansion and contraction between various materials, new sets of scientific rules are necessary when two or more dis similar materials are used together.
It is because of
these combinations of materials that great confusion and disagreements between respective authorities have resulted. The following is a result of this writer’s findings. Physical changes in musical instruments are most easily recognized in the products of these same instruments, the product being sound, or in particular, pitch and tone. The basic principles affecting various known ele ments are as follows: 1.
Metal is affected by temperature changes (hot or
cold), but unaffected by humidity (moisture content). 2.
Wood is affected by humidity, but unaffected by
temperature changes. Temperature is the degree of heat or cold. expands metal while cold contracts it.
Heat
Humidity is the
amount of moisfcure in the air, wet or dry.
Excessive
moisture expands wood, and dry air (no moisture) contracts it. It is because the above definitions are seldom made that so much confusion exists over the effects of climatic changes and their influence5'upon "pitch11.
S3 Assuming that the cast iron plate in the piano should be strong enough to resist the pull of the various compon ents, namely the soundboard and the strings, what happens when the humidity rises to put the piano out of tune?
The
metal strings are not affected by humidity, but are influ enced by the soundboard.
The wood soundboard absorbs
moisture and swells against the strings, causing the strings to go sharp.
In as much as the pressure exerted does not
affect the strings in an equal manner, the piano will there fore go out of tune.
Dr. William Braid White, in a bulletin
entitled ffYour Piano" published by Walton Laboratories Inc., in Irvington, New Jersey (no page numbers) , writes: Now, let us consider for a moment the atmospheric conditions likely to prevail in the room or hall in which this piano is used. In most of the United States, such a room is almost certain to be too humid (moist) in sum mer, or not humid enough in the winter. In the summer if there is a great deal of rain, and the temperature is high, the atmosphere inside the rooms of houses will con tain from 75$ to $0$ moisture most of the time. During this time of the year, the soundboard of a piano will greedily soak up the moisture so that the wood of which it is made will swell, and because it is rigidly fastened within the case of the piano, it will be obliged to strain itself against the strings, there being no other direction in which the swelling of the wood can be taken up and compensated. This means that during these months the strings will be put under additional tension, the piano will go sharp in pitch, and of course out of tune . 3 Since moisture also affects the pin block which is
^ Dr. Wm. Braid White, "Your Piano" (Irvington, New Jersey: Walton La bo rat or ies^, Inc.), no page numbers.
$ 4-
made of wood, it proceeds to swell-, consequently gripping the pins tighter, sometimes twisting them slightly. From these principles we may conclude that, where pianos are concerned, dry heat will not affect wood, except to restore it to a natural state, but wet heat (moisture) will expand wood and consequently force a piano to go sharp* The rise, or fall, in pitch will never be the same for all instruments, and not quite the same for each note on a piano.
The we 11-trained instrumentalist will be able
to compensate for some of his poor intonation due to atmos pheric changes, but the pianist cannot hope to pull out a tuning hammer and alter the pitch of the piano during a per formance. Orchestral trends.
We find orchestral directors
requesting higher and higher tuning pitches for pianos, when this instrument is expected to play with the orchestra. This is perhaps understandable when one considers that the pitch of the orchestra will rise, when all the instruments are completely warmed up.
Generally speaking orchestras
sound more brilliant when the pitch is higher.
Good
orchestra people warm up their instruments before checking the tuning with either the tuning bar, oboe, or piano. Orchestral people play diatonically, altering their tones, depending upon which way they are playing the scales,
35 either up or down.
The piano is an equally tempered in
strument, consequently it is playing in between exact tones. Most orchestral players, therefore, temper their tones, when playing with a piano. It is important to the tuner and the musician to know these highly debated principles, as a successful per formance either in playing or tuning will depend upon how expertly the tuner or player understands and can anticipate climatic changes.
CHAPTER VII
PIANO Definition of tuning.
TUNING Tuning is the process of ad
justing the strings of the piano so that one can play scales upon it* Methods of tuning instruments*
1*
The Cyclic
Principle was used as far back as the fifteenth century, B.C. in many civilizations like Egypt, china, and Babylonia* This method of tuning string instruments was referred to as the "Up and Down Bystem."
Actually the first string was
tuned to a tone which was half way between the singer’s highest and lowest tone.
The balance of the strings were
tuned up and down from this tone in fourths and fifths. Not as a cycle of fifths, but asacontinual cycle, rising and falling (see Illustration No* 26).
In China the Ch’in
was tuned to this system. 2.
The Equipartition Principle was used, as depicted
on Egyptian and Sumerian Art works of pipes of the last two thousand years B.C.
The tone holds in the pipes were placed
equally apart from each other.
For wind blown instruments
this system proved to be a poor one since few true tones could be sounded.
Players tried to improve their pitch in
many ways, as playing with lip slurs and by re-tooling the tone holes of the instruments (re-shaping the angle, width, and length of the hole, but never making a new hole in a more desirable place).
When this same system was used on
string instruments with equidistant frets, it resulted in a more useful arrangement.
The strings could be stopped at
different lengths more quickly and much more accurately. However, this system also had its discrepancies. True, twelve equal parts were in some measure satis factory since they allowed for just octaves (1 2 :6 ), fifths (1 2 :8 ), fourths (1 2 :9 ). and minor thirds (1 2 :1 0 ), but the other stops, such as (1 2 :1 1 ) or (1 2 :7 ) were musically unsatisfactory.^ 3.
The Divisive Principle was used by radical lut-
anists who discarded the poorly placed frets (Equipartition Principle) for a system that provided for increased dis tances between tone holes.
They kept the intervals of the
octave (1 :2 ) and the fifth (2 :3 ) and the fourth (3 :4 ) and added the major third (4 :5 ) and the minor third (5 :6 ) rela tionships.
Faults of this system were, that the major
third was smaller and the semitone larger, while the whole tone came in two different sizes when compared with the cyclic system. The equivalents in cents for the intervals derived from the two systems (Cyclic and Divisive): One perfect fifth One perfect fourth Two Major thirds (Cyclic) (Divisive) Two minor thirds c d
702 49$ 408 386
316 294
Curt Sachs, The Rise of Music in the Western World (New York: Norton Company, 1943), p* 75*
Two whole tones
c d c d
Two semitones
204 132 112 902
The Divisive System is pretty much like our system of today (Equal Temperament System) with the exception that we temper (alter) all our tones but the octave*
Even with
the octave, there is a tendency to stretch it in order to satisfy a certain type of critical ear . 3 4.
The Mean-Tone Principle was one of the first
attempts at developing a scale for the twelve tone to the octave keyboard in the sixteenth century.
Mr. White4 gives
the following s cale comparing Mean-Tone, Just, and Equal Temperament in cents. B
C
c
D
E
F
G
A
0
193
366
503
696
669
1033
1200
0
193
366
49#
702
£34
1033
1200
0
200
400
500
700
900
1100
1200
Cents from C Mean-tone Cents from C Just Cents from C Equal Tempered
The Mean-tone principle was so-called because it strove to find an equal division between a major tone
and a
minor tone of the diatonic scale. 2
Ifeid*, p* 76.
3Ibid.. pp. 72-77.
^ William B. White, Piano Tuning andAllied Arts (Boston: Tuners Supply Company, 1 9 4 6 )", P* 233.
39 Frequency ratio between pairs of tones (diatonic scale): C-D D-E E-F F-G G-A A-B B-C
Whole tone Whole tone Half tone Whole tone Whole tone Whole tone Half tone
3.9
9 :1 0
15:16 3:9 9:10 3:9 1 5 :1 6
major minor major minor major
The most effective attack was made at the point where the difference between the Major Tone (3:9) and the Minor Tone (9:10) of the justly intoned diatonic scale first emerges. It was proposed to tune so that the two incom patible ratios, the difference between which is the Comma of Didymus (3/9 ♦ 9/10 ■ 30/31), should be fused into one ratio, the mean between them. This was the Mean Wholetone or Mean Tone . 5 5.
The Justly Intoned Principle, William Braid White
defines as follows: Just: intonation: An intonation realizing all the tones required by the diatonic and the chromatic scales, exactly in their correct ratios, so that any interval or combination of tones (chord) may be had without distor tion. Just intonation is not attainable with the ordin ary keyboard of twelve semitones to the octave. 5 Diatonic: The name given to the fundamental scale of music. It is most easily identified as a succession of seven white keys on the piano keyboard, C, D, E, F, G, A, B, with its eight or octave C, from which a second series may be begun.y Chromatic Scale: The name usually given to any suc cession of tones taken at intervals of a semitone. The
5
Ibid.. p. 2 3 7 .
6
Ibid.. p. 2 6 3 .
7
Ibid.. p. 2 5 4 .’
90 name arose out of the fact that in early musical nota tions, notes intended to represent sharps or flats of tones were printed or written in red. Hence they were called the "chromatic” or colored notes.g Our chromatic and diatonic scales are modified Greek scales or modes.
Pythagoras, a Greek mathematician, dis
covered the cycle of fifths system by measuring the lengths of strings.
Mathematically the intervals are perfect..
Violinists, slide trombonists and singers, when unaccompan ied, use the Justly Intoned Principle because the human ear and mind will atune itself to a new key-feeling with each and every different song.
Equal tempered instruments like
the brass (with the exception of the bugle), woodwinds, and piano cannot play the Justly Intoned diatonic, chromatic scale• The diatonic scale and the human ear.
To understand
the system of Equal Temperament it is most important to understand the construction of the diatonic scale, thus proving the need for a tempered scale. It has been pointed out in previous units that the pitch of a tone depends upon the frequency of vibrations. It is, therefore, safe to say that all musical sounds or tones must have definite ratios with one another.
This
will be seen clearly if we construct a diatonic scale. 8
Ibid.. p. 251. *
91 By using the monochord we can see that if we divide the string
in half we get
of 1:2 or,
if we refer to a tone of definite frequency,
the
first tone
being C-123 we can calculate C2 as 2 5 6 .
di
viding the
string into thirds we evoke the next closest
relationship, the fifth.
octaves.
Thus we have the ratio
By
When we calculate this ratio we
find that with a tone which is a fifth above another fixed tone, the upper tone will have lj times as many vibrations per second as the lower tone. 2:3.
Thus our ratio is 1:1| or
By using the method of Pythagoras, we can construct
a diatonic (just or untempered) scale. the scale of C.
Let us do so with
If we take a series of consecutive fifths
upward from C, we can arrive at such a scale.
For conveni
ence we will take the first fifth downward from C.
By
bringing down the tones from staff A and B to staff G in Illustration 1 (transposing the pitch of the tone), we will form the diatonic scale of C.
(See illustration No. 27.)
Let us say that C equals 12$ C.P.S. 1. Calculate the first 5th (C to G) 2:3 » 123: G 2G » 3&4 G » 192 C.P.S.
or
2:3 = :G:C (123) 3/2 x 123/1 = 192 G - 192C.P.S.
2. Now the 5th (G to D) 2:3 - 192:x 2x « 576 x = 233 = D -233 C.P.S. Dropping this one octave divide 233 by 2, and D a 144 C.P.S.
92 3. The third 5th (D to A) 2:3 = 2 £B: x 2x - £64 & = 432 Dropping this one octave, divide 432 by 2: A s 216 C.P.S. 4. A to E 2 : 3 = 2 l 6 :x 2x a 64 £
x - 324
E - 324 C.P.S.
Dropping this one octave divide 324 by 2:
E s 162 C.P.S.
5. E to B 2:3 = I62:x 2 x = 4&6 x - 243 B * 243 C.P.S. 6 * In order to calculate C.P.S. for F we must observe that this step is taken one fifth downward from c. (If we took B upward, a perfect 5th would be B to F#.) So we must calculate from C to F downward. The ratio proportion is set up thus:
2:3 * x:1 2 £ 3x = 256 x - £5.33
F * 35.33 C.P.S.
Shifting the F up one octave: 1 :2 = £5*33: x
x s 170.66 7. C 126
D 144
C.P.S.
Now we have the scale equalities: E 162
F 1 7 0 .6
G
A
B
192
216
243
C
256
The ratios between C and each of the other tones in the above scale are as follows: C C C C
to to to to
C1/1 D9/S E5/4 F4/3
C to C to C to C to
G 3/2 A 5/3 B 15/8 C2 2/1
93 The method of figuring the above ratios can be seen from the example below: If C = 128 and D = 144 C.P.S,, then 128/144 reduced is 8/9
D:C » 9:3
Now by using the above ratios between each pair of tones we derive the following: C to D
9:3
D
toE 9/3 * 5/4 * 9/10 or 9:10
E
to F 5/4 4 4/3 = 15/16 or 15:16
F
toG 4/3 4 3/2 a 8/9 or 8:9
G
toA 3/2 * 5/3 = 9/10 or 9:10
A
toB 5/3 415/3 - 8/9 or 8:9
B to C 15/3 4 2/1 a 15/16 or 15:16 In analyzing the above we observe.that there are two different sized whole tones (steps) i.e., the interval from C to D is 8:9 while from D to E is 9:10. Building a new scale from the C scale.
Taking a
tone from the above C scale we can build a new scale using the original process (that of taking a series of fifths)• For example, taking the 5th of the scale we have G = 192 C.P.S. Now we have the following equalities: G 19 2
A
B 216
C 243
D 2 7 3 .3
E 288
F
# 324
G 364.5
334
Now if we build a scale on G by using the ratios be tween adjacent tones we have the following equalities: G 192
A
B
C
216
240
256
D 285.5
E 321.17
F# 3 5 6 .8
G 330.6
94 Now we compare the two scales: G 192 192
\
A
B
C
D
E
F#
G
216
243
273+
283
324
364 *
384
216
240
256
235*
32U
356 *
380*
It can be seen that the two scales built by tuning perfect fifths, or by using the ratios of different tones are per fectly legitimate scales, even though they differ in the vibrational numbers from each other*
Further differences
in vibrational numbers are encountered when we compare many different scales with each other. 6.
The ftqual Tempered Principle.
Since the piano
must be tuned so that we can play in all keys without offend ing our ears (even if mathematics be slighted), we must find a system of tuning which will satisfy musicians and permit harmonious playing of melody and harmony. iiiqual Temperament most satisfies this need.
The system of As the name im
plies this system is an adjustment between the twelve equal semitones.
In this case the ratio of the semitone is the
twelfth root of the octave ratio 1:2 or more correctly 1:1.0594631*
Thus the frequency of any tone lying a semi
tone above any other is obtained by multiplying its fre quency by this factor. This factor is then the basis of the equal tempered scale of twelve equal steps to the octave.
A different type
of unit is used also to calculate the distances*
This unit
95 is called the Cent, and is too small to be heard by the human ear, but can very well be recorded by the Conn strobo scope.
The cent or 1/100 part of the semitone, or 1/1200
of an octave is the smallest unit.
The distance from one
semitone to the next is always 100 cents and 1200 cents equals one octave. We can build a tempered scale of 12 semitones by start ing with A » 440, by using the factor 1.0594631♦ 440 (A) 4 6 6 .1 6 4
493.383
x 1 .0 5 9 4 6 3 1 X above t»
tt
523.251
f» n n it r?
5 5 4 .3 6 5
587.330
622.254 659.255
6 9 8 .4 5 6
tt
739.989 783.991 330.609
tt tt
= =
4 6 6 .1 6 4
493.883 5 2 3 .2 5 1
554.365 587.330 622.254 659.255 6 9 8 .4 5 6
739.989 783.991 830.609 879.999
(A#) (B) (C) (c#) (D) (J£b) (E) (F) (F#) (G) (G#) (A)
The reason that the figures do not come out to 880 for the octave is that we make the answers correct to three de cimal places.
This slight error is too small to matter
greatly. Tuning the piano.the ttqual Tempered Scale.
In our
discussion of beats we found that two tones of different frequencies, when sounded together, would cause beats.
The
number of beats heard will depend upon the interval between the two tones.
Tuning is accomplished by comparing the two
tones with each other.
The intervals usually used in set-
96 ting the temperament are the fourths and fifths.
We learned
that the number of beats which would occur would be equal to the difference between the frequencies of the two tones, for example, if we tune C 261.62 to the correct frequency and we wish to tune the fourth tone below the C which would be G, we could calculate the frequency of the tone G by use of the ratio of 3:4*
This would give us a frequency of 196.21 C.P.S.
3:4 = X:261.62
or 4X » 7 6 4 .6 6
or X ■ 196.21
Now, in order to find the number of beats which would sound, we would subtract the two frequencies: 261.62 - 196.21 z 65.41.
This large number of beats per second will, of
course, be too many for the human ear to hear.
However,
each tone will have its harmonics (partials) and we can make use of these harmonics in tuning in the following manner: In the interval C to G, which we have above, we find that the 3rd harmonic of C will be of the same frequency as the 4th harmonic of G.
c -c - g g -
g - d -
1 2
3
g 4
If we alter the C (or) the G, beats will arise between these two harmonics, and
since they will bealtered
the human ear willbe capable of hearing will help us to count these beats,
onlyslightly,
this difference and
essentially this is what
happens while in the process of actually tuning a piano. example:
G * 196.21 C.P.S."* C * 261.62 C.F.S.
97 3rd harmonic 4th harmonic
of C » 261,62 x 3 or of G = 196,21 x 4 or
7^4*36 7 8 4 .8 4
Now if we alter the G by two beats or make its fre quency equal to 194•21 C.P.S. we would have the following equations: 3 rd harmonic 4th harmonic
of G ■ 261.62 x 3 or of G x 194*21 x 4 or
7 &4 *86
776.84 £ .0 2
(number of audible beats)
In the above example the beat rate is still too fast to be of value, but it serves to illustrate how the harmonics of two tones could be used.
If we had used 195*96 for ~B and
carried out the above calculation, we would have arrived at 7 8 3 .#4 C.P.S. for the 4th harmonic.
Subtracting this from
734*&6, we would get 1.02 C.P.S., which we could readily hear. This slow beat is the one that usually is used for tuning.9 Setting the bearings.
Laying the bearings consists
of setting up twelve evenly divided semitones which comprise an octave.
Before this can be done, one must explain fur
ther the reason for altering tones in order to accomplish this end.
If one starts tuning from the first A (Al) on the
piano and tunes upward in perfect fifths, each in the ratio of 2:3 and ends up with the highest A seven octaves higher, he will end up with a different figure than if he had taken a 9
Ibid.. pp. 55-56.
98 series of octaves from A (A^) . Calculation:
Al equals 2 7 .5 0 C.P.S. and we calculate a series of 5ths we arrive at 3 5 6 9 * cycles roughly.
Ex. 2:3 ■ G:C (27 .50) 3/2 x 27.50 * 41*25 3/2 x 4 1 .2 5 = etc.
.Calculating a series of octaves we arrive at 3520 C.P.S. We can see thus that with the frequency obtained by taking the fifths upward we end up 49 C.P.S. sharper Ex. 3569 3520 49 C.P.S. Laving the bearings:
In laying the bearings, we
take a series of alternating fourths and fifths.
All tones
must be lowered (flatted), with the exception of the C which is tuned exact and the first J?‘ which is raised (made sharp) . (See Illustration No. 28.) Beat rate.
Beat rate per second to the nearest 0.5
between two altered tones in the temperament (vibrations per sec.) . C C C G D A S
to to to to to to to
10
C 0. F .6 G .9 D .7 A 1. B 1.3 B 1.1
Ibid.. pp. 88-89
B to F# F# to C# 0# to G# G# to D# D# to A# A# to F
.8 .6 1. .7 1. .8nn AU
99 Testing the bearings.
Having determined and set our
temperament, we must now perform tests to check our work: a.
The most obvious test consists of slowly replay
ing the tones in our temperament, b.
Checking by playing major and minor thirds chro
matically up and down the scale.
Major thirds should have a
bright sound, while minor thirds should have a dark sound. c.
Testing sixths, major sixths are wide, therefore,
they are bright; minor sixths are narrow, therefore, they are dark. d.
Test by playing chromatic triads, chords both
major and minor, augmented and diminished.
All similar
triads should have the same tone color regardless of the position in the scale. e.
Play chords with the seventh tone added.
f.
The last F in the temperament series should blend
and coincide with the first F. should also coincide with the
The next to the last tone (A#) tuned at the beginning of
the series. g.
There should be amoticeable absence of beats (or
pulsations)• not exceed 1.1 h.
The beat rate between two altered tones should C.P.S.
Tune with the Stroboconn to check work.
Tuning hammer technique.
There are eighteen steps to
100 be followed in learning how to tune pianos: 1.
The first step is to learn how to manipulate a
tuning hammer.
The tuning hammer consists of a steel rod
to which is usually attached a 2J inch star head. of its shape it is misnamed ’’hammer*1. as a wrench.
Because
Actually it is used
When using the hammer, one should never pull
downward, that is, push the hammer either against or away from the pin block. bend it.
The object is to turn the pin, not
A pin that has been bent in tuning will soon slip
back, thereby returning the string to its old position. The recommended hammer handle length is about twelve inches.
The hammer should be worked preferably with the
left hand.
The hammer should be held almost straight up
or, better still, slightly inclining towards the bass side, and then gently pushed in the desired direction, when used on an upright piano. When used on the grand piano, the hammer should be manipulated by the right hand because of the peculiar con struction of the instrument.
The highest treble strings
however should be tuned by the left hand.
The string must
always be pulled evenly throughout its entire length. Kest the arm whenever possible while in the process of tuning.
In this manner it is possible to always maintain
exact control of the amount of leverage being exerted upon the string by the tuning hammer.
101 2.
The second step is to learn how to m
tuning fork. ing
forks.
One should
have on hand a
When this is impossible one
another piano which is in tune. use
fork may
may makeuse of-
Most professional tuners
only one fork either the C or the A a* tuning
completesetof tun
fork.
be intensified
in many manners.A
fork should be hit against some soft object like wood, the knee, the arm bone, or it can be plucked by the fingers• To amplify the resonance place on any solid wooden object, the teeth, or any other handy resonance box material*
Where
there is quite a bit of outside noise it may be necessary to place the ear close to the fork to hear it.
A fork should
never be struck upon a metal or hard object. The following standards of pitch have been accepted at one time or another; In 1739 at Leipsic, Bach declared the Philosophers C2 = 472
Pitch.
In the years that followed, many degradations were accepted.
The highest pitch ever, was in 1&59 when they
established nOpera Pitch” in England:
C2 = 5 4 6 .
In 1&£5 Vienna ratified a French standard which is now known as International Pitch: C2 = 517* In 1917 the American Federation of Musicians adopted Concert Pitch: A 3- » 440 and
s 523.2
In 1920 the United States adopted this as the official
pitch. 3.
The third step is learning to match one piano
string to the pitch of the tuning fork by the use of the ham mer.
Using wedges, block out two strings from the group of
three under consideration.
It is important to bear in mind
that excessive turning of a tuning pin will wear out the wood fibers of the tuning block to the extent that the string will not stay in tune.
Change the strings under considera
tion quite often. 4.
The fourth step is to match the remaining two
strings with the one already tuned.
Remove one wedge at a
time and match the free string with the one in tune. to eliminate all beats.
Strive
Make the tone sound flat and dull,
and yet clear and clean. 5.
The fifth step is to learn how to tune octaves,
matching the higher or lower octave with the string already tuned. 6.
Tune perfect unaltered fifths.
7.
Tune perfect unaltered fourths.
3.
Tune thirds and sixths, both major and minor—
the thirds should be bright in major and dark in minor. 9*
Tune seconds.
10.
Tune semitones.
11.
Then set a temperament.
12.
Test a temperament.
103 13.
Tune chromatically in octaves all tones above
the temperament, testing so the fourth and the fifth, which have already been tuned in the octave, are true. treme upper tones are difficult to hear.
The ex
It is necessary
to pluck the strings individually with one’s finger or with an ivory pick. 14*
Having tuned two or more octaves, use the same
tests that were used in testing the temperament. 15.
Play some familiar tune (e.g., America, Drink
to me only) in all twelve scale keys. lb.
Play chromatically grand octaves starting from
lowest D in the temperament. 17.
Tune the lower half of the piano.
The lower tones,
are difficult, therefore it is necessary to depress a key a major 3rd (12th)
above the tone which is being used as a
standard to tune atone an octave lower.
This
key is depressed
in order that the damper will be raised from the string al lowing it to vibrate sympathetically. Example:
C32.70 Tune this tone
C 6 5 .41 This is already Tuned
E 32.40 Hold this tone down 18.
Check lower and upper half, as well as the tem
perament using all tests previously mentioned. General hints.
These are just general hints concern-
104 ing the proper care and upkeep of the piano: 1. Keep the piano away from hot steam pipes, st'oves, registers or radiators* 2. Maintain an even temperature for the piano if possible, avoiding direct drafts and sudden changes from hot to cold. 3. An electric light fastened to the interior of the piano-prevents mildew, excess dampness, swelling wood, and warping. 4. Keep the case and keyboard clean and free from dust and debris. 5. Clean the interior of the piano frequently by using soft damp rags and soft dust brushes for the pur poses. 6. The strings of the piano being metal, may rust. Black lead or chalk placed on a soft rag and lightly rubbed over the strings should remove rust and corrosion.11
War Department Technical Bulletin, TB 2&-1, The Care and maintenance of special services equipment (Hnited States Government, August, 1944), pp. 13-14.
CHAPTER VIII
SUMMARY, CONCLUSION AND RECOMMENDATIONS It has been this author’s privilege to discuss the piano, an instrument which is as common as the automobile, and just as much misunderstood by its users#
It is almost
unbelievable, that people who spend so much time behind the steering wheel of an automobile know so very little about the construction of that vehicle. A professional examination usually discovers some minor defect which the driver could easily have repaired himself had he studied the mechanics of the car as well as the operation of same.
Most people neglect their cars,
very seldom is the underside of a car kept spotlessly clean, for instance. Mechanics, be it electrical, automotive, piano, or any one of a number of other types, is equally simple when properly learned.
It was not the purpose of this study to
make each person who reads this thesis, an expert on piano tuning.
Only years of experience and study may do that.
It was rather the purpose of this study (1) to inform the general public about the piano, (2) to stimulate and guide those who seek to make piano tuning and repair a vocation, (3) to instill confidence in the musician who desires to keep his, or her, piano in playing condition between regular
106 visits of a professional piano tuner and repairman, (4 ) to simplify the maze of technicalities, complexities and in consistencies in the literature of this instrument, and (5 ) to present a clear and concise history of the piano. In order.to achieve these purposes and aims, the following information was presented: 1. Aspects of musical and physical abilities neces sary for the piano tuner. 2 . Fundamental musical knowledge necessary for under
standing the science of piano tuning. 3* Piano history and its evolution. 4* Piano construction. The science of piano acoustics and study of string vibration. 6 . The science of piano tuning.
This thesis is not primarily concerned with problems of piano repairing, yet the reader will note how the problems of tuning continually border upon problems of construction and repair.
Piano repair, hew ever, is a very extensive study
in itself and the student who wishes.to become an expert should next proceed to a study of this field as well. Further extension beyond the scope of this study,
'
should lead to the study of: (1 ) piano repairing, (2 ) musi cal instrument repairing (wooding, brass, percussion, and string instruments) , and (3 f ) industrial arts courses in
107 woodworking, metal, and plastics, (4 ) and, as a further con clusion, it is the belief of the writer that piano tuning should be taught in