Writings on Music, Volume II: A Proposal to Perform Musick and Related Writings, 1685-1706 [1 ed.] 0754668452, 9780754668459

Table of contents :
Contents
List of Figures
Series Editor’s Preface
Acknowledgements
Abbreviations
Introduction
1 Correspondence with John Wallis (1685–6)
2 ‘The Use of the Musical Canon’ (?1686–8)
3 A Proposal to Perform Musick (1688)
4 ‘The Practicall Theory of Musick’ (1702)
5 ‘The Division of a Monochord’ (?1702–6)
6 ‘The Theory of Musick Reduced’ (1705)
7 Correspondence with Hans Sloane (1705–6)
Select Bibliography
Index

Citation preview

Thomas Salmon: Writings on Music

Music Theory in Britain, 1500–1700: Critical Editions Series Editor Jessie Ann Owens, University of California, Davis, USA This series represents the first systematic attempt to present the entire range of theoretical writing about music by English, Scottish, Welsh and Irish writers from 1500 to 1700 in modern critical editions. These editions, which use original spelling and follow currently accepted practices for the publication of early modern texts, aim to situate the work in the larger historical context and provide a view of musical practices. Also published in this series: A New Way of Making Fowre Parts in Counterpoint by Thomas Campion and Rules how to Compose by Giovanni Coprario Edited by Christopher R. Wilson Synopsis of Vocal Musick by A.B. Philo-Mus. Edited by Rebecca Herissone A Briefe and Short Instruction of the Art of Musicke by Elway Bevin Edited by Denis Collins A Briefe Introduction to the Skill of Song by William Bathe Edited by Kevin C. Karnes John Birchensha: Writings on Music Edited by Christopher D.S. Field and Benjamin Wardhaugh ‘The Temple of Music’ by Robert Fludd Peter Hauge

Thomas Salmon: Writings on Music Volume II: A Proposal to Perform Musick and Related Writings, 1685–1706

ARDHA GH Benjamin Wardhaugh Wolfson College, University of Oxford, UK

ROUTLEDGE

Routledge Taylor & Francis Group

LONDON AND NEW YORK

First published 2013 by Ashgate Publishing Published 2016 by Routledge 2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN 711 Third Avenue, New York, NY 10017, USA Routledge is an imprint of the Taylor & Francis Group, an informa business

Copyright © 2013 Benjamin Wardhaugh Benjamin Wardhaugh has asserted his right under the Copyright, Designs and Patents Act, 1988, to be identified as the author of this work. Bach musicological font © Yo Tomita All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. British Library Cataloguing in Publication Data Salmon, Thomas, 1648-1706. Thomas Salmon : writings on music. Volume II, A proposal to perform musick and related writings, 1685-1706. – (Music theory in Britain, 1500-1700) 1. Musical pitch. 2. Musical pitch – Early works to 1800. 3. Salmon, Thomas, 1648-1706 – Criticism and interpretation – History – 17th century. 4. Salmon, Thomas, 1648-1706 – Criticism and interpretation – History – 18th century. I. Title II. Series III. Wardhaugh, Benjamin, 1979 780.1'092-dc23 Library of Congress Cataloging-in-Publication Data Thomas Salmon : writings on music / [editorial noes by] Benjamin Wardhaugh. v. cm. – (Music theory in Britain, 1500-1700. Critical editions) Includes bibliographical references and index. Contents: Volume I. An essay to the advancement of musick and the ensuing controversy, 1672 3 – Volume II. A proposal to perform musick and related writings, 1685-1706. ISBN 978-0-7546-6844-2 (v. 1 : hardcover) – ISBN 978-0-7546-6845-9 (v. 2 : hardcover) 1. Salmon, Thomas, 1648-1706 – Criticism and interpretation. 2. Locke, Matthew, 1621 or 2-1677 – Criticism and interpretation. 3. Music theory – Early works to 1800. 4. Musical intervals and scales – Early works to 1800. 5. Musical notation – Early works to 1800. 6. Musical temperament – Early works to 1800. I. Wardhaugh, Benjamin, 1979- II. Salmon, Thomas, 1648-1706. III. Locke, Matthew, 1621 or 2-1677. MT6.T46 2012 780.1'48--dc23  2012006246 ISBN 9780754668442 (hbk) Vol. I ISBN 9780754668459 (hbk) Vol. II ISBN 9781409465034 (hbk) Two vol. set

Contents List of Figures vii Series Editor’s Preface ix Acknowledgementsxi Abbreviationsxiii Introduction Correspondence and Publication: 1674–89 Correspondence with John Wallis, 1685–6 A Proposal to Perform Musick (1688) ‘The Service of God & Man’: Theologian and Historian: 1690–1706 Final Musical Work: 1702–6 ‘My Harmonicall Canon’: Salmon and Wallis on Tuning ‘Two Viols were Mathematically set out’: Musical Experiments Amateurs, Professionals and ‘Mechanicks’ ‘Then is the Theory of Musick Settled’: Salmon’s Legacy Editorial Policy

1 1 2 3 5 9 12 18 22 27 29

1

Correspondence with John Wallis (1685–6)   Editorial Note   Letter 1   Letter 2  

43 43 45 47

2

‘The Use of the Musical Canon’ (?1686–8)   Editorial Note   Text  

51 51 56

3

A Proposal to Perform Musick (1688)   Editorial Note   Text  

79 79 85

4

‘The Practicall Theory of Musick’ (1702)   Editorial Note   Text  

125 125 129

5

‘The Division of a Monochord’ (?1702–6)   Editorial Note   Text

145 145 148

vi

Thomas Salmon: Writings on Music

6

‘The Theory of Musick Reduced’ (1705)   Editorial Note   Text  

161 161 166

7

Correspondence with Hans Sloane (1705–6)   Editorial Note   Text  

173 173 175

Select Bibliography   179 Index185

List of Figures 0.1

The syntonic diatonic scale

13

1.1

Salmon’s letter to John Wallis, December 1865. Bodleian Library, MS Eng. Lett. C 130, fol. 27r. Reproduced by permission of the Bodleian Library, University of Oxford.

44

2.1 2.2 3.1 3.2 3.3 3.4 4.1 4.2 4.3 4.4

5.1

The first page of ‘The Use of the Musical Canon’.  Bodleian Library, MS Mus. Sch. d375*, fol. 32r. Reproduced by permission of the Bodleian Library, University of Oxford. A possible reconstruction of the diagram accompanying ‘The Use of the Musical Canon’.   The first plate for A Proposal. British Library, shelfmark 557*.e.25.(4.). Reproduced by permission of the British Library. The second plate for A Proposal. British Library, shelfmark 557*.e.25.(4.). Reproduced by permission of the British Library. The third plate for A Proposal. British Library, shelfmark 557*.e.25.(4.). Reproduced by permission of the British Library. The fourth plate for A Proposal. British Library, shelfmark 557*.e.25.(4.). Reproduced by permission of the British Library. A page of ‘The Practicall Theory’, showing Salmon’s hand in a marginal addition to the text. British Library, Add. MS 4919, fol. 4v. Reproduced by permission of the British Library. The first ‘scheme’ for ‘The Practical Theory’. British Library, Add. MS 4919, fol. 6r. Reproduced by permission of the British Library.   The second ‘scheme’ for ‘The Practical Theory’. British Library, Add. MS 4919, fol. 6r. Reproduced by permission of the British Library.   The ‘Scheme of proportions’ for ‘The Practical Theory’. British Library, Add. MS 4919, fols 10v, 11r. Reproduced by permission of the British Library.   The first page of ‘The Division of a Monochord’. Cambridge University Library, Add. MS 3970, fol. 2r. Reproduced by kind permission of the Syndics of Cambridge University Library.

55 73 104 105 106 107

128 131 132 136

146

viii

Thomas Salmon: Writings on Music

5.2

A possible reconstruction of the first ‘scheme’ for ‘The Division of a Monochord’.  

6.1

The first diagram for ‘The Theory of Musick Reduced’; p. 2041. Reproduced by kind permission of the Royal Society of London.   167 The second diagram for ‘The Theory of Musick Reduced’; foldout. Reproduced by kind permission of the Royal Society of London.   169

6.2 7.1

157

Salmon’s second letter to Hans Sloane, January 1706. British Library, MS Sloane 4040, fol. 109r. Reproduced by permission of the British Library.   174

Series Editor’s Preface The purpose of this series is to provide critical editions of music theory in Britain (primarily England, but Scotland, Ireland and Wales also) from 1500 to 1700. By ‘theory’ is meant all sorts of writing about music, from textbooks aimed at the beginner to treatises written for a more sophisticated audience. These foundational texts have immense value in revealing attitudes, ways of thinking and even vocabulary crucial for understanding and analysing music. They reveal beliefs about the power of music, its function in society and its role in education, and they furnish valuable information about performance practice and about the context of performance. They are a window into musical culture every bit as important as the music itself. The editions in this series present the text in its original form. That is, they retain original spelling, capitalization and punctuation, as well as certain salient features of the type, for example the choice of font. A textual commentary in each volume offers an explication of difficult or unfamiliar terminology as well as suggested corrections of printing errors; the introduction situates the work and its author in a larger historical context. Jessie Ann Owens Professor of Music Dean of Humanities, Arts and Cultural Studies University of California, Davis, USA

Taylor & Francis Taylor & Francis Group http://taylorandfrancis.com

Acknowledgements It is a pleasure to acknowledge the kindness of Jessie Ann Owens, the editor of this series of volumes, in suggesting this project and providing support and guidance at various stages. I am also grateful to the staff of Ashgate Publishing, in particular Heidi Bishop, Laura Macy and Pam Bertram for their work on the book. All Souls College, Oxford, has supported me throughout the period of work on this book, and I have great pleasure, too, in recording my gratitude to that institution. David Cram, Christopher D.S. Field, Jessie Ann Owens and Minji Kim read drafts of this volume and saved me from a multitude of egregious errors. Dr Field has once again been extraordinarily generous with time and advice; his numerous contributions to the substance of this volume are individually noted. Dr Philip Beeley has provided advice on a number of matters, and has been generous with time and information in responding to arcane requests connected with John Wallis. A number of other individuals have supplied information and clarification about points of detail, as well as practical help in the form of access to books and manuscripts, in particular Alastair Fraser at Durham Cathedral Library, Katie Flanagan at Eton College Library, Peter Sewell at Indiana University Library, David E. Schoonover at the University of Iowa, David Hunter at the University of Texas at Austin, Manuel Erviti at the University of California, Berkeley, and James Collett-White and the staff at the Bedfordshire and Luton Archives and Records Service. Faults which remain are of course my responsibility alone. I am grateful to the Bodleian Library, University of Oxford, the British Library, the Syndics of Cambridge University Library and the Royal Society for permission to reproduce the illustrations in this volume.

Taylor & Francis Taylor & Francis Group http://taylorandfrancis.com

Abbreviations BDECM  Andrew Ashbee and D. Lasocki (eds), A Biographical Dictionary of English Court Musicians, 1485–1714 (Aldershot, 1998). ‘The Division of a Monochord’ Cambridge University Library, Add. MS 3970, fols 1–11: ‘The Division of a Monochord’ (see Chapter 5). DNB  Leslie Stephen and Sidney Lee (eds), The Dictionary of National Biography (63 vols, London, 1885–1900). ECCO  Eighteenth-Century Collections Online: galenet.galegroup.com/servlet/ ECCO. EEBO  Early English Books Online: eebo.chadwyck.com. Essay  Thomas Salmon, An essay to the advancement of musick … (London, 1672). ESTC  The English Short Title Catalogue: estc.bl.uk. GMW  Andrew Barker (ed.), Greek Musical Writings II: harmonic and acoustic theory (Cambridge, 1989). Grove Music Online  Stanley Sadie (ed.), The New Grove Dictionary of Music and Musicians (29 vols, London, 2nd edition, 2001; online edition, 2007–10, at www.oxfordmusiconline.com). ODNB  H.C.G. Matthew and Brian Harrison (eds), Oxford Dictionary of National Biography: from the earliest times to the year 2000 (60 vols, Oxford, 2004; online edition, 2008, at www.oxforddnb.com). OED  Oxford English Dictionary (Oxford, 3rd edition, 2010; online edition, 2010, at www.oed.com). ‘The Practicall Theory’  British Library, MS Add. 4919, fols 1–11: ‘The Practicall Theory of Musick […]’ (see Chapter 4). Proposal  Thomas Salmon, A proposal to perform musick, in perfect and mathematical proportions … (London, 1688) (see Chapter 3). ‘Remarks’ John Wallis, ‘Remarks on the Proposal to perform musick, in perfect and mathematical proportions’, in Proposal, pp. 29–41. ‘The theory of musick reduced’  ‘The theory of musick reduced to arithmetical and geometrical proportions, by the Reverend Mr Tho. Salmon’, Philosophical Transactions, 24 (1705): 2072–7, 2069 (see Chapter 6). ‘The Use of the Musical Canon’  Bodleian Library, MS Mus. Sch. d375*, fols 32–40: ‘The Use of the Musical Canon’ (see Chapter 2). Vindication  Thomas Salmon, A vindication of an essay … (London, 1672).

Taylor & Francis Taylor & Francis Group http://taylorandfrancis.com

Introduction This volume presents Thomas Salmon’s 1688 Proposal to perform musick and his writings and correspondence related to it. This material dates from the mid-1680s to the end of Salmon’s life in 1706, and is concerned almost exclusively with musical pitch, a subject which had played only quite a minor role in Salmon’s Essay and the ensuing controversy in 1672–3. Though there are some substantial gaps in the preservation of the sources, this material shows fairly clearly the evolution of Salmon’s thinking as well as providing some evidence for the network of personal relationships on which it depended. Most of these texts are of a rather different kind from the Essay and Vindication, and several of them were intended for a relatively small readership, at least in the form in which we have them. This introduction discusses Salmon’s life from 1674 to 1706 (his earlier life has been described in the introduction to Volume I of this edition). It sets within this biographical context the production of his various writings – musical and non-musical, manuscript and printed – during that period. It also addresses three particular topics which are crucial for understanding his musical work: the details of Salmon’s idiosyncratic system of musical tuning and its relationship to the work on the same subject by John Wallis, with whom Salmon corresponded and exchanged ideas; Salmon’s ideas about musical experiments and their possible sources; and the intersection of theory and practice in Salmon’s distinctive approach to the study of music. The introduction thus attempts to provide a context for what is, with all its idiosyncrasies, a distinctive and important body of work on the mathematics of musical pitch from Restoration England. Correspondence and Publication: 1674–89 Salmon moved to Mepsal by April 1674 to take up his duties in the parish.1 These need not necessarily have been more onerous, or more fatal to his musical hobby, than his previous activities in London (where he may have been assisting at his mother’s school, and he was allegedly already involved in ‘the cure of souls’ by mid-1672),2 but the fact is that we do not hear from Salmon again in print until 1688, when he produced his Proposal to perform musick, in perfect and mathematical proportions. (One exception: his name appeared on the list of subscribers for Mace’s Musick’s monument in 1676.)3 If he maintained contact with John Birchensha, his teacher, or John Carr, the printer who had, initially, embraced his notational reform with some enthusiasm, such contact has left no trace. The simplest explanation is that he to some extent laid aside his musical interests during his first years in Mepsal, taking them up again in the 1680s.

2

Thomas Salmon: Writings on Music

He did not altogether lose contact with John Wallis during that time, however. During March 1675 there was some correspondence at least between Wallis and the Salmon family concerning a possible marriage between an unnamed ‘gentlewoman’ and Wallis’s eldest son.4 The surviving material – letters from Wallis to Salmon’s mother and sister-in-law; an implied letter to Salmon himself is lost – is tantalising rather than securely informative, and the gentlewoman may have been a student at the Salmon school rather than anyone more closely connected with the Salmon family. But this exchange does suggest that the two families were linked socially as well as intellectually. The younger John Wallis, a year or so younger than Salmon, attended Trinity College, Oxford, in the 1660s, and would therefore quite probably have known Salmon.5 In the event he married an Elizabeth Harris in 1681;6 there seems to be no way of knowing whether this was the ‘gentlewoman’ of Wallis’s letter. Several years of silence follow, during which Katherine Salmon bore nine more children. In 1685 Salmon was licensed to preach at Mepsal, which presumably affected the detail of his activities there.7 But if his duties to parish and family were growing, they did not prevent the pursuit of his first love. By the end of the same year he had taken up music again, visiting instrument-makers in London, observing closely the performances of James Paisible (‘Mr Peasable’) on the bass violin, producing and several times ‘rectifying’ (as he put it) a quantitative description of the musical scale, and renewing his musical correspondence with John Wallis. Correspondence with John Wallis, 1685–6 The only certain evidence which survives for Salmon’s musical activities between 1674 and 1688 takes the form of two letters: one from Salmon in late 1685, and Wallis’s reply early in January 1686.8 These letters (see Chapter 1) refer to a previous exchange of documents (‘I have long agoe received your letters & my papers’, wrote Salmon), and Salmon’s tone suggests a fairly well-established correspondence. Their contents are frustratingly slight, and do not allow us to say very much about the stage which Salmon’s ideas about tuning had reached. Nor do they really allow us to determine how much factual content Wallis had imparted to Salmon, or how far Salmon’s mathematical work on the musical scale depended upon Wallis’s advice or correction, but when Salmon asserted that ‘I have […] rectified my Harmonicall Canon the third time’ (emphasis added) he implied that he was exercising some intellectual independence. It was in this letter of 1685, though, that Salmon made the only comment we have which bears directly on his mathematical competence; he asked for Wallis’s help in understanding why the operation of multiplying ratios worked as it does: I have much occasion to add and subduct intervals; this is very evident to mee when I measure my strings geometrically, but if I go to do it by [Gassendi’s] way of numbers […] I find it always come right, but I cannot see the reason of it […].9

Introduction

3

It is difficult to reconcile this passage with Salmon’s apparent confidence in his other writings – and even elsewhere in this letter – as a mathematical theorist of music. Faced with a description – to add two ratios, multiply corresponding terms; to subtract, multiply non-corresponding terms – he could carry out what was described, but did not see why it worked. It is possible that he had become confused because of the unusual way he used ratios to describe musical intervals, speaking of cutting off a certain proportion – a ninth, say, or a tenth – of a string in order to produce a new pitch. If two such operations were performed consecutively it would not be obvious how the two proportions were to be combined.10 But this does not go very far to rescue Salmon’s reputation as a mathematician. The passage leaves the distinct impression that at this stage his conceptual grasp of the operations on mathematical ratios which underlay his approach to musical tuning was very weak. It casts a shadow over much of Salmon’s later writing; indeed, his later writings tend to suggest that his conceptual grasp of ratio calculations remained weak even if his confidence in carrying them out reached quite a high level. From this period may also date the manuscript text ‘The Use of the Musical Canon’.11 Bound with the Bodleian Library’s copy of ‘The Musicall Compass’ (see below, p. 12 and in the introduction to Chapter 2), this text seems unmistakably to reflect Salmon’s ideas: it discusses a scale virtually identical to his and sets out in detail the placement of frets on a viol with and without separate frets for each string. It may perhaps be identified with ‘the Arithmetical and Geometrical parts of Musick’,12 to which he referred in his Proposal. At the same time it shows what seems to be the clear influence of Wallis on his thinking, reinforcing the impression that it may date from the period in the 1680s when Salmon and Wallis were corresponding about musical matters. The manuscript is in the hand of James Sherard (1666–1738), apothecary, botanist, and amateur composer and violinist, and seems to reflect a somewhat confused source or set of sources, with one section appearing in two different versions, and the word ‘Finis’ inscribed partway through the text. The details of this somewhat puzzling text are discussed in the introduction to Chapter 2; in this edition I have chosen to place it tentatively earlier than the Proposal, and therefore to consider it as evidence for Salmon’s musical thinking during the period of his correspondence with Wallis prior to the publication of the Proposal. A Proposal to Perform Musick (1688) In the two years following his suriviving exchange with Wallis, Salmon’s ideas about musical tuning, and his confidence in expressing them, grew to the point where he felt able to work them up into the form of a book. A / PROPOSAL / TO / Perform Musick, / IN / Perfect and Mathematical Proportions. / CONTAINING, / I. The State of MUSICK in General. / II. The

4

Thomas Salmon: Writings on Music Principles of PRESENT PRACTICE; according to which are, / III. The Tables of PROPORTIONS, calculated for the Viol, and capable of being Accommodated to all sorts of Musick. / By Thomas Salmon, Rector of Mepsal in the County of BEDFORD.

He had told Wallis in 1685 that he had ‘no thoughts of proposing or publishing any thing, till I find some practicall success in what I have already done’, and the appearance of this publication is therefore presumably evidence that his discussions with practitioners had been encouraging, at the very least. This book had a good deal in common with the Essay of 1672, despite the change in subject matter. Salmon was once again engaged in telling those better qualified than himself how to do their jobs, and he once again adopted a positive, didactic tone which could almost have been calculated to offend those it was supposed to persuade. The substance of the Proposal was a mathematical description of the musical scale (of which more later), and the suggestion that it be realised in practice using a system of interchangeable fingerboards, to be attached to one’s viol as needed. Each fingerboard would do for a pair of scales: on C with sharp third, sixth and seventh or on A with flat third, sixth and seventh, for example. (Salmon was always clear in his writings on pitch that only two forms of scale were in widespread use; to avoid circumlocution I will sometimes adopt the terms ‘major’ and ‘minor’, which he did not use.) Diagrams were provided at the back of the book, from which a suitably-skilled person could construct eight different fingerboards; just how they were to be attached to the instrument was never made completely clear (see pp. 26–27 below), though a later text had them sliding in and out ‘as you pull out and thrust in the Drawer of a Table’.13 Their principal idiosyncrasy was not so much where they placed the frets as that they provided a separate set of frets, potentially positioned quite independently, for each string: an arrangement which could not be achieved using lengths of gut tied around the viol’s neck.14 Like the Essay, too, the Proposal came with the approbation of certain (supposedly) relevant professionals; this time it was ‘both the Mathematick Professors of the University of Oxford’, namely John Wallis and Edward Bernard, the Savilian Professors of Geometry and of Astronomy. It comes as no real surprise – and it would have come as no real surprise to anyone who had followed the Essay controversy – that Salmon was able to enlist Wallis as a supporter; whatever the details of the relationship between the two men, Wallis’s public stance was always supportive of Salmon and his work. Edward Bernard (1638–96) made no other appearance in Salmon’s life; his contact with him seems to have been limited to providing this approbation of the Proposal. As well as Professor of Astronomy, he was also an Arabist and a Greek scholar, and he assisted John Fell, Bishop and Vice-Chancellor of Oxford, on more than one occasion with learned publications; he assisted, in particular, with the publication of the brief treatise on ancient Greek musical theory by Edmund Chilmead (1610–54) in 1672.15 That he was prepared to look over Salmon’s work and write a (very) brief letter of approval is therefore less surprising than it might at first appear. He had nothing more to say about

Introduction

5

the Proposal than that he wished ‘that the use of the Masters of that Art may not hinder the best Method to obtain it’,16 a comment which may have been a glance at Matthew Locke’s opposition to Salmon’s Essay, but which was silent on whether Salmon’s Proposal really represented ‘the best Method’ for anything. It is difficult to see this as better than lukewarm, but, for all that, it was an endorsement from a writer who knew something about the subject. Wallis’s remarks were very much more voluminous, and, although he expressed general approval of Salmon’s scheme, he did not hesitate to suggest improvements to it, or to point out places where Salmon had, in his view, got the details wrong, although he concealed the worst blunders behind a decent veil as ‘particulars, which seem either not so clearly, or not so cautiously expressed’.17 His most important suggestions will be discussed below (pp. 16–17). It is perhaps a consequence of the troubled times in which it appeared for sale that the Proposal does not seem to have made anything like the impact of the Essay. We have practically no contemporary responses to the book apart from those of Wallis and Bernard. Matthew Locke was dead by this time, and no musician saw fit to take up the cudgels for a fresh bout against Salmon. Likewise, I know of no copy of the Proposal with substantive annotations.18 John Lawrence, the bookseller named on the title page, does not seem to have made enormous efforts to sell the book. Very many of his publications contained lists of his other books offered for sale, but the Proposal featured in these on only six, apparently random, occasions, all between 1694 and 1705.19 (These advertisements did not state the price of the Proposal, and neither did the ‘Term Catalogue’; on two occasions in the eighteenth century (1764 and 1765) copies were listed for sale priced at one shilling, and this may have been the book’s original price.20) This sequence of advertisements began more than six years after the book was printed, and it suggests that a stock of unsold copies was beginning to be an irritation to Lawrence. He never succeeded in ridding himself of them; M. Lawrence took over shop and stock from 1714 and advertised the Proposal for sale in another book in 1716;21 subsequently shop and stock passed to Richard Ford, and his printed list of stock in 1726 also included the Proposal (whose title he got wrong).22 After 38 years the first (and only) print run had still not sold out. ‘The Service of God & Man’: Theologian and Historian: 1690–1706 After the appearance of his Proposal our evidence about Salmon’s life continues to be patchy. We have a pair of letters between Wallis and Salmon in 1690 concerning an attempt to place ‘two young Gentlewomen’ at one of the Salmon schools.23 The school – that of Salmon’s sister Sarah Cruttenden – in fact turned out to have closed, suggesting that Wallis was no longer particularly well informed about the Salmons’ activities. In the same letter Wallis desired Salmon to request assistance with a new edition of his mathematical works from ‘Mr Samuel Morland’ (my

6

Thomas Salmon: Writings on Music

emphasis): not the well-known inventor and diplomat, who had been a knight and a baronet since 1660, but very possibly his eldest son, with whom Salmon must therefore have been in touch.24 We also have a few pieces of information about Salmon’s parish of Mepsal. The will of one Sarah Emery led to the creation of a Charity of Elizabeth Emery for education in March 1692, and the founding of a school at the church in 1698. The school still exists (as Meppershall VA Lower School), and its early years are quite well documented. Copies of the school’s ‘Orders’ survive in Salmon’s hand, as do end-of-term reports of the children’s attainments and an account book which names teachers and pupils. This material gives the impression of Salmon as overseeing the institution reasonably closely, and the school seems to have thrived in a modest way, with two regular ‘dames’ and three other occasional teachers, and a total of 38 pupils from 14 families over the eight years from its foundation to Salmon’s death. They learned their catechism and prayers, and the dames taught the girls to read, sew, knit and spin. The 12 boys who attended in this period were supposed to learn to ‘read write and cast account’, according to the ‘Orders’, but the records are silent about any such teaching, raising the possibility that it was provided not by a paid master but by Salmon himself.25 During this period Salmon was spending at least a small portion of his time in London, and references in his writings to contact with London musicians and instrument-builders hint that he was, at times, travelling to London as frequently as he could in pursuit of his musical projects (and resenting the limitations of the ‘little village’ of Mepsal).26 In May 1690 he was briefly at Warwick House, that is ‘Lord Commissioner Maynards house in Holborn London’, as Wallis put it addressing the letter mentioned above.27 As with so much else about Salmon’s life we cannot say what his connection was with Sir John Maynard, commissioner of the great seal. More concretely, Salmon published four books on non-musical subjects during the last decade of his life. In 1699 he was involved with the production of The catechism of the Church of England.28 This brief work of 35 duodecimo pages comprised, in part, the catechism from the Book of Common Prayer, lightly edited and re-formatted; Salmon’s contribution was ‘a short explication’, in fact longer than the catechism itself, ‘containing the grounds and reasons of the Christian religion’, consisting of notes which he himself had found useful in catechesis.29 A final-page advertisement indicated that the printer, Brabazon Aylmer, specialised in books intended (ideally) to be bought in bulk and given away (‘cheaper to those who are so Charitable to give away Numbers’); the cover price of the Catechism was three pence.30 In 1701 Salmon produced a potentially much more explosive work, entering upon the controversial subject of infant baptism with A discourse concerning the baptism and education of children.31 This was a more substantial book, a quarto of 62 pages, and its printer, Benjamin Tooke, one of the most eminent of the time: he had been the king’s printer in Dublin and would be printer to Dean Swift and to the queen.32 The infant baptism controversy had as one of its participants

Introduction

7

John Wallis, and we naturally wonder whether Wallis had a hand in this book.33 Once again there seems no clear evidence to support this possibility. The book was dedicated to ‘Ralph Freeman, Esq: of Aspeden-Hall in Hertfordshire’; presumably a neighbour, this may perhaps have been the Ralph Freeman who was MP for Reigate in 1679 and 1681.34 Believing that a new and comprehensive Poor Law might soon be devised, Salmon proposed specific measures to be incorporated into it, which would have set up a ‘free school’ in every parish, supplied with a ‘School-Dame’ and a Committee of Directors and funded from the Poors Bill.35 This was set out and explained in the last few pages; the bulk of the book was taken up with what amounted to (and could have originated as) a sermon on the subject of the baptism and religious instruction of children, intended as far as possible to support the proposal by indicating the importance and likely result of such early training. Salmon characteristically seems not quite in control of the material in this book, which continually threatens to lose itself in discursive asides. Works of this character provide an opportunity to say slightly more about Salmon’s doctrinal opinions, and indeed to gain somewhat more of a sense of his character; A discourse concerning baptism shows him as an optimist somewhat disappointed by human nature. I know [the Golden Rule] is written in my Conscience; and since we are all the off-spring of God, Acts 17.28 (as the Heathen Poet says, and the Apostle with a Divine Authority confirms it) I believe that the Rule is written in the Consciences of all Men in the World.36

Yet: [T]he confusion of a Child’s blushes, plainly discovers a shame that Falshood should get the victory over Truth […]. This Depravation encreases with their Years; and though afterwards they are more capable of knowing God, yet they are by their Lusts more estranged from him. The commanding Habits of Sin, the settled Resolutions of accustomed Wickedness, give us many Examples to what a height it will at last advance. Many wholly cast off their Natural Reverence of a Deity, or else think God to be altogether such an one as themselves[.]37

It is not altogether encouraging to reflect on the experiences (as teacher, rector or father?) which this passage seems to describe; the book as a whole is, perhaps, Salmon’s most human piece of writing. At the same time, A discourse concerning baptism makes it quite clear that by this stage Salmon had repudiated any connection with nonconformity; he devoted its several final pages to showing the ‘unreasonableness’ of certain characteristic behaviours of ‘some Dissenting Congregations’, and to urging their members to ‘lay aside their Prejudices, and forsake the separate Congregations’,

8

Thomas Salmon: Writings on Music Which certainly would be better for them to do, than to endeavour to overthrow a Church which God establish’d by his Martyrs; which cannot be suppos’d to contain any thing sinful in it, since the Divine Providence did so eminently appear in its Settlement.38

Dense with quotations not just of Scripture but of the Articles of the Church of England, the book does much to display its orthodoxy,39 and – barring what would seem an improbable degree of noisy hypocrisy – seems to settle the question of Salmon’s own commitment to the established church. It points in the same direction, of course, that he must presumably have taken the oaths to William and Mary in 1689, and to Anne in 1702; despite the fact that two of his close relatives had refused the oaths in 1662 and one of his own sons did so in 1702. Likewise the slighter Catechism, in which Salmon (voluntarily) put his name to a statement and a defence of Christian doctrine entirely along the lines laid down in the Book of Common Prayer. There followed two further non-musical books, which present something more of a puzzle. An historical account of St. George for England, and the original of the most noble Order of the Garter appeared in 1704.40 There are two versions; one is unillustrated; the other adds three illustrations and has a title page which draws attention to them: ‘Illustrated with CUTTS’.41 The texts of the two versions are, I believe, otherwise identical, down to errata slip and final advertisement.42 An historical account of St. George is a distinctly peculiar work. Salmon’s argument was that the true St George was one George of Ostia, papal legate to England in the eighth century and chiefly responsible for the re-establishment of Christianity in Britain. The story of an early Alexandrian martyr he dismissed as a very elaborate fiction based originally on the mistaken insertion of an Arian martyr (George of Cappadocia) of the fourth century into the liturgical calendar of the orthodox, later deliberately cultivated by ‘a Party of Monks’43 for nefarious reasons of their own, and fused with a fraudulent story about an angel appearing as a crusader. As well as an allegory for several of the triumphs of the true faith, including the defeat of the Arian heresy, the story of George and the dragon was therefore the story of British Christianity triumphant over paganism but – until now – obscured by popish fables. The Order of the Garter could thus be assured of a history not just factual but British. It is evident from the range and density of citations – quotations in Latin, Greek and French, and some fairly close reading of modern sources: Sir Henry Spelman, and Peter Heylyn’s 1631 eulogy on St George44 – that all of this had cost Salmon some pains, but it seems to exemplify his habit of well-intentioned engagement in complex matters beyond his competence. It is difficult to escape the feeling that, whatever the attractions of a project which enabled him to display his loyalty so clearly, his judgement was at fault when he took it on. Finally in 1706, the last year of Salmon’s life, he plundered some of the same sources used for An historical account of St. George to produce Historical collections, relating the originals, conversions, and revolutions of the inhabitants of Great Britain to the Norman conquest.45 Some copies have a title page which

Introduction

9

names no author, but most have one on which ‘Thomas Salmon, M. A. Rector of Mepsall, in the County of Bedford’ is named. (The texts are otherwise identical.46) The text received what was described as a ‘second edition’ – really a reissue with a new title page and preface – in 1725 under the editorship of Salmon’s son Thomas, with the title The history of Great Britain and Ireland.47 Compared with the rest of Salmon’s output these are lengthy books: An historical account of St. George fills about 240 pages in total, Historical collections 475, both in octavo. And they survive in very many more copies: ESTC lists a total of 33 (of which four are unillustrated) of An historical account of St. George and 45 of the Historical collections (of which five have the anonymous title page); this should be compared with the 14 known copies of the Proposal.48 In his lifetime they may have done more for his visibility than his musical work. Each book lies well outside the range of interests which are elsewhere recorded for Salmon, although it is easy enough to imagine his own curiosity and enthusiasm taking him in these new directions. And either – particularly the fairly pedestrian compilation which is the Historical collections – would sit very much more easily in a list of the works of the younger Thomas Salmon (1679–1767), who would begin to make a name for himself as a historical writer in the 1720s.49 Yet both state clearly on their title pages that they are by the rector of Mepsal, and the second edition of the Historical collections goes so far as to distinguish the contribution of the son from that of the father. The Historical collections, too, were referred to in a letter of Salmon to Hans Sloane, apparently confirming that he was their author and mentioning that they were ‘false printed, by reason of my absence’ (i.e. from London).50 It is tempting to speculate, nonetheless, that the younger Thomas Salmon, in his twenties at the time, had an unacknowledged role in the writing of these two books; but this, or the reasons for such a deception, is beyond proof or disproof. Final Musical Work: 1702–6 Between the appearance of An historical account of St. George and that of the Historical collections came Salmon’s final burst of (recorded) musical activity. We have a manuscript dated 1702, ‘The Practicall Theory of Musick’, which seems to show him revisiting the ideas explored in his Proposal and taking them in new directions.51 This manuscript is not in Salmon’s hand (which is known to us from his surviving letters: see Figures 1.1 and 7.1 on pp. 44 and 174), but it contains diagrams and corrections which are. The most natural conclusion therefore seems to be that the text was copied by someone within Salmon’s household – perhaps one of his children – and revised by its author. Although it began as a fair copy, the alterations and corrections – although they do not remedy all of the errors made by the copyist – turned it into something rather less presentable. This manuscript does clearly tell us that nearly 15 years after the printing of the Proposal Salmon was still wrestling with the problems of tuning and its realisation which he had considered there. As with the period of silence after the appearance

10

Thomas Salmon: Writings on Music

of the Vindication in 1672, we have no evidence which would tell us whether or not Salmon had continued to work on musical matters during the years which intervened. If there was further correspondence with John Wallis, who seems to have been at the very least an important sounding board for Salmon’s musical ideas in the 1670s and 1680s, it has not survived. A different mathematical professor, however, seems now to have made an appearance in Salmon’s intellectual life: although we cannot know when or how Salmon first made contact with Isaac Newton, there is good evidence that by this period he had done so. That evidence takes the form of another, undated, manuscript treatise, ‘The Division of a Monochord’, which is now to be found bound together with some of Newton’s own writings in Cambridge University Library.52 Again, the hand is unknown, and the path which has led the document to its present location cannot be reconstructed with any certainty. But it seems a fair supposition that the manuscript was not just owned by Newton but read by him, even if it was sent to him unsolicited. The text seems to me to represent a further development of the ideas in ‘The Practicall Theory’ of 1702.53 Three other facts provide very slight support for the possibility of Newton’s interest in Salmon’s writings. First, copies of Salmon’s Proposal and Catechism appear in the library of Newton’s Cambridge college, Trinity; these are rare books, the latter exceedingly so, although only the first was published during the time that Newton was living at Trinity, and indeed only the first appears to have belonged to Newton.54 Second, Salmon’s sudden and rather inexplicable interest in the Arian heresy in An historical account of St. George is suggestive, given that Newton’s private beliefs were anti-Trinitarian; but Newton’s (necessary) secrecy on such matters makes it very hard to see that this can be more than coincidence.55 Finally, not long after Newton became President of the Royal Society in November 1703, Salmon appeared, unexplained, at two meetings of the Society in June and July 1705.56 On the first occasion he displayed a fingerboard; on the second he organised a demonstration performance with instruments which had been modified to his mathematical specifications. This second appearance at the Society was surely Salmon’s finest hour. For much of his life he had pressed for the importance of experimental knowledge in a musical context, and he was at last, in his fifties, offered the chance to display his musical ideas in the most prestigious experimental setting Great Britain offered. We might expect the appearance of a non-Fellow (who was also not a natural philosopher) at meetings of the Society to have been preceded, as in the case of another musician, John Birchensha, 40 years earlier, by a letter or even a treatise sent to the Society by the postulant, by a recommendation from a Fellow, or possibly even by the formation of a committee to examine the individual’s claims.57 In this case no such initial approach is recorded in the ‘Journal Book’ of the Society’s meetings, nor does any letter of introduction or self-recommendatory treatise survive in its archive, leaving us at a loss to know how Salmon first came to the Society’s attention, and providing at least a suspicion that the personal interest of its president may have been involved.58

Introduction

11

These pieces of evidence are suggestive, but against them it must be noted that no correspondence survives between Newton and Salmon, nor is Newton known from other sources to have interested himself in the mathematical theory of music at this stage in his life.59 Newton’s copy of the Proposal shows no sign of serious study; it bears no annotations, and the only evidence that Newton read it at all is a single folded-down leaf which may have been meant as an aidememoire concerning Isaac Vossius’s De poematum cantio.60 He may have been an interested and active supporter of Salmon’s work; he may merely have been the recipient of a treatise and a book which he did not really want. After the performance before the Royal Society, Salmon moved quite fast to ensure that posterity would know of the event, sending an account of the demonstration to (presumably) the Secretary of the Royal Society and editor of the Philosophical Transactions, Hans Sloane. This was duly published in the Transactions, and we have two letters from Salmon to Sloane in December and January 1705–6 in which he commented on the appearance of the paper in print and asked for help in finding a patron to enable the continuation of his musical work.61 Whether or not it was Newton who had brought Salmon to the Royal Society’s attention, Salmon’s belief at this point was that his existing (or former) supporters could not be relied upon to fund his further exploits, and his experience at meetings of the Society had not left him feeling able to approach any Fellow directly in his search for patronage. His second surviving letter to Sloane mentioned ‘a full consort’ and ‘an advancement into the Enharmonick Musick’ as two possibilities for further practical work. One final piece of evidence sheds light on Salmon’s plans during 1706. On 5 March the Court of Aldermen in London received a petition: The Consideracion of Mr Thomas Salmons Peticion, for this Courts leave, to hold A Consort of Musick in perfect and Mathematical Proporcions within this City is by this Court Adjourned to another Day.62

Unfortunately this is absolutely the whole of our information about Salmon’s approach to the Aldermen, whose permission he would have needed, as a nonmember of the Worshipful Company of Musicians, to stage a public musical performance in the City of London. The petition itself does not seem to survive among the Court’s papers,63 nor did the promised consideration of it on ‘another Day’ ever take place. Presumably the new performance was intended to achieve something that the demonstration at the Royal Society had not, perhaps the larger group of performers or the ‘advance’ into the Greek enharmonic mode he mentioned to Sloane, but he could have been thinking more straightforwardly of a larger audience. Presumably, too, money had been found with which to stage this new performance, but of its source we know nothing. Salmon died later in 1706. A slab in the church at Mepsal records his death on 1 August;64 he was buried two days later, and his will was proved on the thirteenth of that month.65

12

Thomas Salmon: Writings on Music

In relation to this chronology of Salmon’s life we should briefly note a printed pamphlet which seems to bear similarities to Salmon’s thought, but which cannot be shown with any certainty to be his work.66 It bears the title ‘The Musicall Compass’ and comprises three engraved pages each containing a small amount of text and a number of diagrams – ‘design’d to shew How the Eight Notes circulate in their perpetuall order’ – and four pages of verse explaining basic musical concepts and notation, separately titled ‘Of the Gamut’. This, too, describes the ‘circulation’ of the octave. The whole was ‘Printed for J. gillibrand at the Golden Ball in St. Paul’s Church Yard, 1684’. Although it is tempting to suppose that anything which refers to the ‘circulation’ of the octave at this date must be connected with Thomas Salmon, these must have been a complex and expensive set of engravings to commission, and it would seem unlike Salmon to go to so much trouble and fail to mention the pamphlet elsewhere. (In fact, I know of no seventeenth-century reference in print to this pamphlet, from him or from anyone else.)67 Thus, nothing like certainty can be attained; given such small quantities of text it is impossible to identify Salmon’s tone or his ideas with any real confidence. Nor, in any event, would this material add very much to our knowledge of Salmon’s musical thought. After much hesitation it has seemed wiser to exclude this pamphlet from this edition of Salmon’s musical writings, where its presence might give rise to an impression of more than is known. ‘My Harmonicall Canon’: Salmon and Wallis on Tuning This account of Thomas Salmon’s life and writings between 1674 and 1706 is arguably all the context that is needed in order to understand the texts edited in this volume. Certainly it would be unwise to attempt a complete analysis of their contents here, which would (I hope) date faster than the edition itself. Nonetheless, there are other elements of the content of and context for Salmon’s elusive ideas about musical pitch and how to study it, which it seems valuable to present in the second half of this introduction. Looming very large indeed is Salmon’s relationship with John Wallis, for the consideration of which we must first review some of the details of what each man had to say about the mathematics of the musical scale. A particular mathematical description of the musical scale had been presented by musical theorists from the late fifteenth century onwards; it matched in form though not in function what Ptolemy called the ‘syntonic diatonic’, and was sometimes known by that name in the sixteenth and seventeenth centuries, but more recent writers have generally called it the ‘just scale’ or the ‘just intonation’.68 The essential feature of this mathematical construction is that it uses two different sizes of whole tone – ‘major’ and ‘minor’, with ratios 9 : 8 and 10 : 9 – in order to create a scale in which most of the fifths, fourths, thirds and sixths are ‘pure’ in the sense that they correspond to string-length ratios which use simple whole numbers. Thus, conceived in terms of pure ratios of string lengths, it could look, for example, like this:

Introduction

Figure 0.1

13

The syntonic diatonic scale

Salmon in fact discussed two different forms of the syntonic diatonic scale, identical except for the division of the major third (when the scale is in white notes) C–E, where the major tone may either precede or follow the minor tone. I will call these the ‘C’ form and the ‘D’ form, depending on whether the major tone of 9 : 8 is placed upon C (as in Figure 0.1) or upon D. Among mathematical theorists of music, on the whole, the C form seems perhaps to have been described more frequently, as for instance by Kepler in the seventeenth century and by Alexander Malcolm and Leonhard Euler in the eighteenth. But many gave both, as for instance did Mersenne, and – perhaps through inadvertence – Salmon himself in his Vindication.69 In ‘The Use of the Musical Canon’, he advocated using the C form for major keys and the D form for minor keys (as had Francis North in his 1677 Philosophical Essay, though North’s subsequent division of tones into semitones was entirely unlike Salmon’s).70 In the Proposal he described only the D form, to be used for all keys. Wallis specifically suggested using the C form instead in his ‘Remarks’; he adopted it in all of his own musical writings.71 The C form seems to have become Salmon’s settled preference thereafter; he used it in ‘The Practicall Theory’, ‘The Division of a Monochord’ and ‘The theory of musick reduced’. (He was unswayed, it seems, by William Holder’s advocacy of the D form in 1694.72) The syntonic diatonic scale (or scales) seems to have been of more frequent interest to mathematically-minded theorists than to practitioners, although it should not be dismissed out of hand as exclusively a theorists’ construction.73 If Salmon is likely to have seen it in the writings of Descartes and Mersenne,74 he certainly also knew the discussion of it in Simpson’s Compendium (a book which he had cited in his Essay).75 Salmon was in fact one of a large group of writers, many of whom were practitioners, concerned to describe intonation which would be ‘just’ in the sense that both (most) fifths and (most) major thirds would have their mathematically pure sizes, a concern which leads naturally to two different sizes of whole tone and therefore to something like the syntonic diatonic scale, if not to the rigidity and elaboration of a scheme like Salmon’s. Patrizio Barbieri has assembled evidence that violinists and woodwind players cultivated intonation approximating to just (syntonic) or meantone norms and even extended it to quarter-notes, particularly in the Italy of Corelli’s time.76 Likewise David D. Boyden has shown that

14

Thomas Salmon: Writings on Music evidence from the writings of 18th-century violinists, particularly Geminiani and Tartini, points to a kind of just intonation flexibly applied to successive intervals with adjustments when necessary both melodically and harmonically on each of the four strings, tuned in pure 5ths, as points of reference.77

This will be important when we assess Salmon’s report of his observations of James Paisible’s intonation. Nonetheless, a rather rigid scheme of the kind which Salmon presented – a mathematically-determined scale rather than a flexible principle that certain intervals should, where possible, be tuned so as not to ‘beat’ – does raise problems if it is supposed to be used in practice. One is its two different sizes of whole tone, ‘a feature that tends to go against the grain of musical common sense’, as Mark Lindley puts it.78 Another is that the detailed mathematical placement of the chromatic notes of the scale which Salmon envisaged made no concessions at all to the fact that it might sometimes be desirable to use those notes harmonically: so, for instance, in his C major the ratio between D and F# was 85 : 64 – not the pure major third which was made so important elsewhere in his construction of the scale. Further, any change of keynote would require some pitches to be re-tuned. The characteristic just mentioned – that chromatic pitches did not in general form consonant intervals, in this scale, with diatonic pitches (or with one another) – meant that even basic pitch relationships like the structure of the tonic triad could not be relied upon without such re-tuning. Salmon only once considered the question of re-tuning, in a brief passage in ‘The Division of a Monochord’; where we might have expected some consideration of a less mathematically unbending placement of chromatic notes, so as to produce at least a few more consonances in the new key (his example was in effect a modulation from G major to A major), he merely asserted that the infelicities of the new key ‘may well be granted’ (that is, ignored).79 He seems to have had in mind music where modulation was limited in range; although there was much seventeenth-century music for which this was a fair assumption, it is not hard to point to examples where a tonally restricted scheme such as Salmon’s would not produce satisfactory results. In England, the works of Henry Purcell furnish abundant examples.80 Salmon believed that the syntonic diatonic scale, in the idiosyncratic and elaborate form which he favoured, was a correct mathematical description of the musical scale as it should be, and as it – at least sometimes – was in practice. He had three different kinds of evidence for this. First was the testimony of various writers whose opinions he respected, including Descartes and Mersenne, coupled with the appearance of the syntonic diatonic scale in Ptolemy’s Harmonics, a fact which connected it with his developing interest in restoring the lost effectiveness of ancient Greek music. The second was his observation of the intonation practice of James Paisible (see pp. 25–26 below) together with, eventually, the fact that when his experimental instruments were tried out at the Royal Society ‘the most complete harmony was

Introduction

15

heard’. This was powerful evidence that his modifications to musical instruments were proceeding along the right lines. Salmon’s writings are not forthcoming about the existence of modified instruments earlier than 1705, but we should probably assume that he possessed a viol with some system of interchangeable fingerboards (made by Richard Meares?) by the time the Proposal was printed, and that he found its sound sufficiently satisfactory to encourage his further work on the mathematics of tuning. Finally there was the evidence provided by the scale’s mathematical characteristics. The requirement of pure fifths and pure major thirds led quite naturally to that scale. Indeed, once pure thirds were adopted there were only a few possibilities for their division into tones: the traditional tone of 9 : 8 produced as its complement the minor tone of 10 : 9 and thus the syntonic diatonic scale; the only obvious alternative was to divide the third into two equal parts, but this produced a complex ratio that had no place in a system of pure intervals (though it was of course used in practice in the meantone temperament).81 From the mathematical point of view, the coherence of the scale could be further supported by a method of construction which made it at least appear mathematically natural. The process rested on an operation which I will call ‘arithmetical division’ of ratios (that term was used in the early modern period, but not wholly consistently). In its simplest form this operation (which was found in several of the ancient sources on music theory) would take the ratio a : c and split it into two ratios a : b and b : c by placing b, the intermediate term, at the mean, the average, of a and c. Algebra was beyond the ken of most musical writers, and the operation was typically described using examples, in which the trick was to double both terms of the original ratio, making it obvious where to place a middle term between them. The ratio of the octave, 2 : 1, for instance, is equivalent to 4 : 2. The middle term of 4 and 2 is 3, and we can therefore divide the ratio 4 : 2 into ratios 4 : 3 and 3 : 2. As it happens, these can very satisfactorily be assigned to the perfect fourth and perfect fifth, which (necessarily) add up to an octave.82 The process can be continued. If 3 : 2, the ratio of the fifth, is treated in the same way, it is transformed into 6 : 4 and split into 6 : 5 and 5 : 4, ratios which can be assigned to the minor third and major third. Next, the major third, 5 : 4, can be transformed into 10 : 8 and split into 10 : 9 and 9 : 8, the ratios of the minor and major tones. This, together with a semitone defined as the difference between a perfect fourth and a major third, was sufficient to assign ratios to each step of the diatonic scale and thus to each consonant or dissonant interval within it. But the process can evidently be continued, and its continuation can be made to provide precise values for the positions of the chromatic notes of the scale; in his later writings Salmon invariably proceeded to divide both the major and the minor tone using the same arithmetical procedure. The minor tone’s ratio, 10 : 9, was divided into 20 : 19 and 19 : 18; the major tone’s, 9 : 8, into 18 : 17 and 17 : 16. Any of these four ratios might serve as a chromatic semitone at need, and together with the diatonic

16

Thomas Salmon: Writings on Music

semitone (16 : 15) this resulted in a 12-note chromatic scale with five different sizes of semitone.83 Salmon’s 1688 Proposal contained a somewhat vague account of a chromatic scale of this form – tones were divided into major and minor semitones in his diagrams, but the procedure was only hinted at in the text – but his manuscript writings gave more details, and his 1705 paper in the Transactions gave a very clear account of the subject. A scale of this particular kind was not unique to Salmon. One was described in 1667 by Christopher Simpson, in a passage concerned to establish the proper positions of ‘greater’ and ‘lesser’ semitones by a purely geometrical procedure, and we must surely count the Compendium among Salmon’s inspirations for his own exploration of the subject. Simpson’s placement of the semitones matched Salmon’s in that the smaller always stood below the larger, and one of Salmon’s lost manuscript diagrams may have been rather similar in form to a diagram of Simpson’s.84 But Salmon adopted different terminology – ‘major hemitone’ for Simpson’s ‘greater semitone’ – and he never named Simpson as a source for his mathematical ideas. More importantly, Simpson incorporated into his account various elements – some information from Boethius concerning a division of the tone into nine ‘commas’, and a brief discussion, citing related matter from Kircher, of the difficulty of dividing a tone into two equal parts – which made no appearance in Salmon’s work.85 Indeed, Simpson was apparently synthesising a geometrical account of the division of tones into semitones (in which tones themselves had two different sizes) with the division of the whole octave into 53 (roughly) equal ‘commas’ reported by Boethius (in which all tones were the same size), and this led him to be somewhat vague about the details of his construction of semitones. Thus he described the greater and lesser semitones as arising from the division of a major tone, but when he came to specify their positions in the scale he implied that they could be the constituents of any tone, and that the lesser semitone could also be identified with the diatonic (16 : 15) semitone.86 Although it is quite possible that Simpson’s book was one of Salmon’s first glimpses of a system of unequal tones and unequal semitones, and contains information which he could certainly have used, there can be no question, I believe, of a detailed dependence upon it for Salmon’s much more precise account of the matter. John Wallis represents a very different case. He, too, published descriptions of a scale of unequal semitones, similar to Salmon’s (though not identical; see p. 17 below for the details) in papers in the Philosophical Transactions in 1698.87 We know that Salmon and Wallis discussed musical matters with one another, and there seem grounds to suspect that the invention in fact originated with Wallis. We have Salmon’s own admission in 1685 that he found ratio operations conceptually difficult; and we have his practice in the Proposal and elsewhere of giving mathematical conclusions without their demonstrations, a practice which he excused as a concession to the reader but which could equally signal the limits of his competence.88 And, once, he explicitly disclaimed originality for the theory of tuning which he presented.89 All of this points, if not unambiguously, to a role

Introduction

17

for Wallis in the development of what was presented under Salmon’s name in the Proposal. Two more detailed points bear on this possibility. First, the construction of the musical intervals as above, by repeated arithmetical division of ratios, was arbitrary, in that only some ratios were subjected to the division process: the fifth but not the fourth, the major third but not the minor. The exhaustive division of every interval into smaller parts would produce a whole clutch of new ratios, not at all easy to fit into the musical scale or to relate to specific intervals used in musical practice. Salmon and Wallis both mentioned this issue; they both, in particular, mentioned the possibility of dividing the perfect fourth arithmetically in order to produce intervals with ratios 8 : 7 and 7 : 6, intervals which Wallis seems to have considered to hold more musical interest than did Salmon.90 Second, the arithmetical division of intervals necessarily placed the larger subdivision above the smaller, a feature which made the major triad and its appearance in the major scale hard to account for mathematically.91 Salmon never addressed this issue explicitly, and in nearly all of his writings simply stuck to a scheme of arithmetical division of ratios which left, arguably, a gap between his account of the derivation of intervals and his choice of a particular order for those intervals in the scale. Wallis, however, adopted a different solution. Briefly: Wallis replaced arithmetical division of ratios by a different procedure, harmonic division.92 This can be described in a variety of ways. It divides the ratio a : c at b in such a way that the ratio a – b : b – c is equal to a : c itself. Or, equivalently, the point of division, b, has the property that its reciprocal is equal to the mean of the reciprocals of a and c. Or, using algebra, b = 2ac/(a + c). Written in these ways it is not obvious what the merit or the musical use of such a monster could be; in fact it divides any ratio into the same pair of new ratios as arithmetical division, but puts them in the opposite order.93 For the octave, for example, the ratio 2 : 1 is divided into 3 : 2 and 4 : 3, a fifth below a fourth. For the fifth, the ratio 3 : 2 is divided into 5 : 4 and 6 : 5, a major third below a minor third. Adopting this procedure allowed Wallis to describe the construction of the diatonic major scale somewhat more naturally than Salmon. When it came to the chromatic pitches it led him to place the larger semitone below the smaller whenever a tone was divided, the opposite of Salmon’s procedure in the Proposal.94 In his remarks in the Proposal, Wallis urged Salmon to reconsider, and he seems eventually to have been successful; in 1705 Salmon’s procedure for placing the chromatic notes became identical to Wallis’s. Thus it seems that the impulse to extend the principles of the syntonic diatonic scale to the construction of a chromatic scale may have been Salmon’s, although nearly all the printed descriptions of such a scale bear the stamp of Wallis’s particular way of doing so. Meanwhile, the result of having not just two possible forms of the diatonic scale but also two different strategies for dividing tones into semitones was a superficially confusing diversity of chromatic scales, which may on occasion have baffled both Salmon himself as well as the readers of his manuscript writings.

18

Thomas Salmon: Writings on Music

‘Two Viols were Mathematically set out’: Musical Experiments One context for Salmon’s work on the mathematics of music was provided by a small number of texts which explored broadly similar problems by broadly similar means: the writings of Mersenne and Descartes which we know he read, Meibom’s Auctores, which he had certainly seen, and the works of Kepler and perhaps Galilei which he may well have consulted.95 And of course there were writers closer to home: Brouncker’s printed commentary on Descartes, John Birchensha’s Pythagorean approach to the musical scale, Wallis’s edition of Ptolemy, with its long appendix, Chilmead’s brief essay on ancient music, Francis North’s Essay and William Holder’s Treatise.96 At the impressionistic level, a cumulative effect of these writings would certainly have been the belief that the mathematical, historical and natural philosophical study of music was intellectually respectable; it was, as Henry Oldenburg once wrote to Robert Boyle, ‘worthy of Philosophers’.97 In detail, Salmon’s account of the diatonic scale and its construction certainly derived from recent models – immediately from Wallis – but beyond them stood sources ranging from Euclid to Zarlino. At times Salmon was keen to represent his work as classical restoration, musical humanism in a pure form with little dependence on writers more recent than Ptolemy.98 Elsewhere the authority of the moderns was explicitly invoked;99 and on the evidence we have, Salmon’s acquaintance with ancient theorists cannot be shown to have amounted to more than half a dozen or so passages, typically cited in seventeenth-century Latin translations. Salmon himself never seems to have come to a lasting decision about the most satisfactory way to present his work’s textual dependencies. This is one of the main puzzles Salmon presents for the historian. Indeed, a very great deal of factual information in this tradition of musical writing seems to have passed Salmon by. A whole tradition of writing about the nature of sound was apparently of no interest to him; he never mentioned any specific explanation, mechanical or otherwise, for the phenomena of consonance.100 Equally, he seems to have been uninterested in the problems – popular, not to say ubiquitous, with other theorists – of ranking the consonances in order of their harmoniousness, or the difficult status of the perfect fourth as consonance, dissonance, or some sort of hybrid. For the purpose of understanding Thomas Salmon it would therefore be, in some respects, useless to look in detail at the texts which form the most obvious background to his work. Quite a different area of dependence, though, and quite a different context, is provided by Salmon’s pervasive and distinctive interest in experiment, something which takes somewhat more work to locate in his sources. This was little less than an obsession for him; his statement in 1685 – ‘Except wee can introduce the expression of purer proportions into our performances, the study of them may bee pleasant but it cannot bee usefull’ – might be taken as the programme for nearly all his musical activity in the second half of his life, when ‘demonstrating’ his ideas by practical as well as mathematical means became a more and more frequent

Introduction

19

concern.101 Yet the concept of a musical experiment is not a self-evident one, and it is arguably here that Salmon’s chief claim to originality as a thinker must lie. Historians of science know a good deal about how those who wrote about experiments in the early modern world provided the illusion of witnessing for their readers, how they made the experiment room ‘real’ using specific literary ‘technologies’.102 The role of sound and of the hearing in this is unclear. For very many experiments it is clearly absent, and I am not aware of any studies which examine descriptions of aural sensations as a specific feature of experimental reports from this period. Certainly Salmon, even if he had read quite widely in natural philosophy, would not have had a very great deal of material to hand on the philosophical use of the hearing. Conceivably the medical practice of auscultation might have provided one model, but a further complication is that Salmon explicitly stated that he considered the musical hearing a separate faculty from the ordinary hearing.103 We must therefore look to specifically musical experiments for the possible sources of his ideas about what that faculty could do for experimental knowledge. Ptolemy’s musical experiments, performed in the second century, could have been known to Salmon through Wallis’s 1682 edition and translation of the Harmonics.104 Briefly, Ptolemy was interested to do what he could to reconcile a rationalising study of music as mathematical structure (the ‘Pythagorean’ approach) with a pragmatic approach based on experience (the ‘Aristoxenian’ approach). One of his tools for achieving this was the detailed study of the relationship between the lengths of strings and the pitches and intervals they produced. Ptolemy described in meticulous detail an experimental set-up for performing such investigations, the thrust of which was to check the aural results of a pre-existing structure of ratios (thus, not to set up intervals by ear and then check to what ratios they corresponded). Ptolemy described experimental set-ups involving both single strings and a more complex device, the helikōn, the relative lengths of whose multiple strings could be accurately fixed by geometrical means. In both cases, elaborate mechanical precautions aimed to guarantee the exact lengths of the strings: a bridge, for instance, with a circular profile producing just one precisely-controlled point of contact with the string. This has been described, and with justification, as a ‘scientific method’ of investigation, in which very precisely quantitative theoretical results were checked against their real-world results using apparatus whose accuracy it would have been virtually impossible to improve upon with the technologies available at the time. What is important for Ptolemy as a possible source for Salmon is that the experiments amounted to ‘checks’ of pre-existing theoretical results: sophisticated and precise checks, certainly, but checks which ultimately threw the burden of judgement onto the ear and the musical sense to say whether a particular interval or set of intervals was acceptable, harmonious or musically useful. A series of experiments which began with the Minim friar and scientific correspondent Marin Mersenne in the 1630s, and was transmitted through the

20

Thomas Salmon: Writings on Music

French atomist Pierre Gassendi to the Royal Society of London, was rather different in character.105 Mersenne took a string whose characteristics he knew: a very long string, analogous to a musical string but whose vibrations were slow enough that they could actually be counted. Apparently by trial and error, he found a way of setting up this string – 67.5 feet of (sheep’s) gut, under a tension of half a pound – so that its vibrations occurred once per second. Altering its tension, he displayed the quantitative relationship between that parameter and the string’s vibrational frequency. He next both shortened the string so that it produced an audible, identifiable pitch, and manipulated its length so as to show the relationship between that and the string’s frequency.106 Using the relationships established between the string’s length and tension and its frequency, he could deduce its frequency when it was producing a pitch, even though its vibrations were then much too fast to count. He thus established the frequency of vibration corresponding to a particular musical pitch; he was the first to do so, and published his results in 1636.107 Gassendi repeated broadly the same sequence of experiments, as did his English follower Walter Charleton, and the Royal Society did likewise in 1664, producing the result that a string producing G sol re ut was vibrating 272 times per second.108 Very different from Ptolemy’s work, these trials actually produced quantitative knowledge by methods which included the use of the ear, rather than employing the ear in a check on knowledge already possessed. The Royal Society, indeed, struggled to find the proper role for the ear, using terms like ‘guess’ and suggesting that the results be somehow checked using a pipe, a harpsichord or a bass viol, not apparently realising that no such check would get them away from an eventual reliance on the judgement of the (musical) ear. The Society went on to perform something like a much cruder version of Ptolemy’s checks, setting up certain ratios of string lengths and verifying that they indeed produced the intervals they were supposed to. More interestingly, they briefly reversed the procedure, setting up a musical interval by ear and measuring its ratio. This novel approach they, sadly, did not pursue.109 We know that Salmon had read Gassendi’s Manuductio, or part of it, by 1685; we have no direct evidence that he had ever perused any of Mersenne’s musical works (although he would have been strangely remiss if he had not); the atomist Charleton might have been beyond his intellectual horizons, but it is not unlikely that Wallis had passed him the details of the Royal Society’s work (the Philosophical Transactions did not begin publication until the year after the Society’s long-string experiments). He could therefore very well have been aware of these experiments in one or more of their different versions. A third, somewhat different, type of musical experiment may also have been known to Salmon in the form of a brass device constructed by Robert Hooke and inspired by the work of Francis North. This is not the place to rehearse the history of this device and of the ideas underlying it;110 suffice it to say that Hooke displayed it to the Royal Society on one occasion in 1681.111 (Although no report appeared in the Transactions it is once again possible that a description of the

Introduction

21

device was passed to Salmon by Wallis.) It consisted of a brass wheel with teeth, which, when the wheel rotated, struck ‘an edge’ so as to make a sound. When the wheel rotated fast enough those strokes were heard as a pitch. In Hooke’s hands this was a device for verifying the relationship between interval and frequency ratio; he did not, as far as we know, use it to establish the frequency of particular pitches. Here the variable which could be controlled was the frequency, or rather relative frequency, of strokes, not the length or tension of vibrating strings; but in other respects this provided a model of musical experiment broadly similar to Ptolemy’s, using a mechanical device to produce sounds whose mathematical characteristics were known, in order to check their musical characteristics aurally. Salmon thus had available to him two main models of musical experiment. One was that of Mersenne, in which quantitative knowledge was derived from procedures involving the manipulation of vibrating strings and in which the direct involvement of the ear was limited, perhaps to estimating the pitch of a sound produced by a string, or to judging that that pitch was a unison to a certain pitch played on a musical instrument. The other was that of Ptolemy, in which the faculty of musical judgement was called upon to assess sounds produced by (potentially) a very precise mechanical apparatus and a pre-existing mathematical description of musical intervals or scales. Each of these kinds of musical experiment had recent precedents at the Royal Society as well as being described in printed books which Salmon had certainly seen. He chose the second model, that of Ptolemy. For Salmon, the way to prove the excellence of a musical proposal was through a public demonstration in which performers and hearers could judge the musical excellence of the results.112 Thus, in the Proposal he repeatedly apologised for providing mathematical results without demonstrations, but it seems fairly clear that the demonstration he believed most worthwhile was the experience of hearing his tuning; to that end, he provided the reader with as many tools as he could to facilitate such an experience. In the 1680s Salmon apparently also hoped that trials of a different kind would be carried out by his associates in London. In 1685 he left with ‘some of the most eminent Musicians’ the results of his calculations of fret positions, ‘to make triall of’. This seems to imply building or modifying musical instruments, and thus the desired ‘agreement … between their practise & my reasons’ would (perhaps) be the agreement specifically of instrument-building practice with Salmon’s ‘reasons’: a matter of detailed physical measurement rather than anything involving actually playing or listening to the instruments.113 Salmon’s envisaged ‘checks’ or ‘demonstrations’ of his mathematical description of music were thus both more musically complex and less quantitatively precise than anything to be found in Ptolemy’s work. What he had in mind was always something approaching the whole musical experience of the reader. In the case of the Essay Salmon’s intention seems to have been that the reader would learn or re-learn music from scratch using Salmon’s clefs, would learn and perform pieces using them, and would judge the success of the Essay’s ideas by the satisfaction

22

Thomas Salmon: Writings on Music

of that experience of music. For the Proposal, similarly, the reader would ideally obtain an instrument or instruments designed or modified to Salmon’s specifications, and make exclusive use of such instruments henceforth. In both cases Salmon’s ideas were meant to pervade and perhaps to dominate the musical experience of the acquiescent individual henceforth; the proof offered for their excellence was that that individual would find musical life more satisfying as a result. This being the case, we may wonder whether the kind of experimental situation which the Royal Society could provide really had anything to offer to Salmon. Before 1705 we have no reason to suppose that he thought it did. Yet, when the opportunity became available, Salmon was able to find a compromise between his idea of demonstration and the Society’s, putting together a performance using professional musicians and professionally-built instruments modified to his specifications. Although this was hardly the holistic experience of his musical ideas that he had envisaged, it did provide the opportunity for him to elicit the testimony from the distinguished performers that ‘all the Stops … [were] perfect’, a testimony which, together with the actual sound of the performance, was presented to the audience of assembled Fellows as evidence for the excellence of Salmon’s musical scheme.114 The Fellows were not musical experts, although a fair proportion of them would have had some experience of musical performance.115 Salmon therefore felt it necessary to hammer his points home in his subsequent paper in the Transactions, where he to some extent defeated the point of the live demonstration by bringing out his standard mathematical explanations of his scheme and merely asserting that when it was realised ‘the most complete harmony’ had been heard.116 For those who had had that experience, little was added; for those who had not, such an assertion could hardly have sufficed as a substitute. Arguably, Salmon’s distinctive type of musical experiment – and his choice of Ptolemy rather than Mersenne as a model – simply made his work a poor fit for what the Royal Society had to offer. Amateurs, Professionals and ‘Mechanicks’ It will be clear already that Salmon’s approach to music theory contrasted quite sharply with that of John Wallis. Where Wallis edited classical texts, wrote and made mathematical discoveries apparently in pen-and-paper mode, pursuing music as a textual activity, Salmon took almost the opposite line, firmly convinced that what he was doing was mathematics but apparently at least as interested in the practical and the personal as in the details of paper calculation, and always keen to derive from theoretical considerations conclusions which would – at least in his opinion – be of practical benefit to musicians. For Wallis, indeed, the syntonic diatonic scale was a description of what musical practice must surely be, despite the assertions of practitioners to the contrary; for Salmon, contemporary practice was something to be discovered, engaged with and then changed, by means which included conversation with practitioners and direct observation of

Introduction

23

their instruments and their fingers. In this respect his musical project took him into social and cultural areas that were generally beyond Wallis’s ken.117 Wallis himself acknowledged that Salmon knew more of practice and practitioners than he;118 Salmon clearly had a knack for persuading leading figures in the London musical scene – James Paisible, Richard Meares, the Steffkin brothers, Gasparo Visconti – to take an interest in his ideas and to help him promote them. How successful he really was at convincing them his proposals were more than the idle whims of a country clergyman is hard to judge. For all we know, some of the ‘eminent musicians in London’ whom he approached in 1685 may have wanted nothing to do with him and his ideas; some must certainly have remembered the controversy with Locke 13 years earlier. Again, Salmon apparently felt his contact with the musical world of the capital was unfortunately restricted once he was living at Mepsal; if that left him free to make sometimes fantastic assertions to which few practitioners, surely, could have been induced to assent, it is clear that on occasion they could still lend vital support to his musical project. The first of Salmon’s informants from the world of musical practice was of course himself. He could be astute: in his first surviving letter to Wallis he noted that for some keynotes the open strings of the viol needed to be detuned from pure interval relationships with one another in order to produce the syntonic diatonic scale, producing a knock-on effect on the positions of frets on those strings. Salmon’s acknowledged struggles were with the mathematical description of those effects. Again, his writings on pitch sometimes convey the sense – less strongly than in the Essay – that Salmon was writing about his personal experiences as a performer. To Wallis, for example, he wrote ‘I shall perform the Musick more perfect & with better assurance, than any violin does’ (my emphasis).119 If this is correct, it might help to explain his almost exclusive focus on fretted stringed instruments in his writings on pitch.120 Salmon’s acquaintance with various London musicians had been much on display in his writings on notation reform, but in the second half of his life his tendency was more frequently to be vague about the details. On one crucial occasion, though, Salmon observed that players moved their frets when changing ‘from one suit of Lessons to another’,121 and the evidence of ‘The Use of the Musical Canon’ is that he took that not just as general support for his scheme to regularise those changes but as detailed evidence concerning which compromises might be feasible and which not. Here is one moment when the close observation of practice informed Salmon’s writings about pitch, and in some detail, but it is not clear that this was a regular occurrence, and he did not trouble to record the names of the individuals who had helped him. The only visible continuity in this respect with the era of the Essay was provided by the Steffkin family.122 Theodore Steffkin was named as an informant in both the Essay and the Proposal, but had in fact left England in May 1673 and died in Cologne later that year.123 His two sons, Frederick William (1646–1709) and Christian Leopold (d. 1714) appeared 33 years later in Salmon’s demonstration

24

Thomas Salmon: Writings on Music

performance before the Royal Society. Frederick William was evidently the elder; he was an almost exact contemporary of Salmon.124 At the Restoration he was granted a joint place with his father in Charles II’s Private Musick, and after his father’s death continued to hold that place until 1705. He placed an advertisement in the London Gazette in December 1703 offering ‘to set the frets of viols brought to his house at the lower end of Basinghall Street in perfect proportions, and to give the necessary directions for correct performance’.125 This must surely refer to Salmon’s system of ‘perfect proportions’, and Frederick Steffkin may have had his authorisation or encouragement for this offer. The fact that this was 15 years after the publication of the Proposal suggests that he might have been prompted by seeing one of Salmon’s more recent, unpublished, writings on pitch, or even that ‘The Practicall Theory’ might have been written with this commercial use of its information in mind. Certainly it indicates some sympathy on his part to Salmon’s ideas well before the performance at the Royal Society. Yet Frederick was not a viol maker, and he cannot presumably have done more for any respondents to this advertisement than set gut frets or make marks on fingerboards, following Salmon’s instructions. Frederick’s seniority relative to the others involved suggests that he may also have acted as Salmon’s ‘fixer’ for the demonstration performance at Gresham College. Finally in 1705, Salmon apparently felt authorised to say that ‘all the Stops were owned by them [sc. the Steffkin brothers], to be perfect’,126 a remark which might perhaps be related to Frederick Steffkin having personally ‘set the frets’ of the instruments used. Like Frederick, Christian Steffkin was presumably taught the viol by his father. He married Bridget Fletcher on 12 May 1681 at All Hallows, London Wall, but nothing seems to be known for certain about his professional activities until July 1689, when he joined his brother as a member of the Private Musick of William and Mary; he continued to serve as a court musician throughout Queen Anne’s reign. He was buried at St Clement Danes on 2 December 1714; he was survived by his wife and several young children (their daughter Althea was christened at St Paul’s, Covent Garden, on 6 August 1708, in a record which names Christian as ‘Leopold Christian Stefkin’).127 Five months later the Daily Courant announced a benefit concert to be given on 5 May 1715 at Stationers’ Hall for his widow and children. Gasparo Visconti, the third performer named at Salmon’s musical experiment in 1705, was among the first of a wave of Italian violinists to visit Britain in the eighteenth century, where his arrival closely coincided with the beginning of a vogue for Corelli’s music. He had, indeed, studied in Rome as ‘Corelli’s Scholar’ for five years before arriving in England.128 He appeared at a concert in the York buildings on 2 November 1702, aged only 19, and was soon being engaged to perform some of the sonatas of Corelli between the acts of plays at the Theatre Royal, Drury Lane. Visconti was married to a daughter of Christian Steffkin, Ebenezer (also known as Cristina), on 22 April 1704, and it was presumably through this family connection that he came to be involved in Salmon’s experimental performance the

Introduction

25

following year. Not long after the baptism of their child Annunciata Maria on 14 September 1706, the family seems to have left London and settled in Cremona, Visconti’s home town.129 Ebenezer/Cristina was a viol player herself, and there survives in the Museo Stradivariano a paper pattern for a cello neck, a fingerboard pattern and a wood template, bearing inscriptions indicating that they were measured from Christina Visconti’s viol, which was made in 1707.130 As more than one scholar has noticed, this raises the tantalising possibility that, through Christina Visconti, Salmon’s system of tuning might have been transmitted to Stradivari himself. Stewart Pollens has examined the evidence in detail; after detailed consideration of the measurements of the patterns and the characteristics of Salmon’s scale, his conclusion is that From the evidence provided by Stradivari’s fingerboard pattern MS no. 256, Cristina Visconti née Stefkins does not appear to have been a convert to the fretting system that Thomas Salmon demonstrated before the Royal Society with the aid of the Stefkins brothers and her husband in London in 1705 and subsequently published in the Philosophical Transactions of the Royal Society of London.131

Another individual named during Salmon’s explorations of pitch was James Paisible. Salmon reported in 1685 that Mr Peasable the best player of a Base in London uses no frets, his hand is more unsteady, his only advantage is that Hee observs the Major & Minor Tones by the direction of ‹an› excellent ear.132

James (Jacques) Paisible (c.1656–1721) first arrived in England in 1673 and worked at court from 1677–88; he returned to England from 1693 to his death. He was known as a player of the recorder and other instruments, and as a composer; he was much associated with the stage. Salmon’s description of him as a highly distinguished string player – particularly at this early date – is therefore noteworthy; most references to him as a string player date from his second period in England, when he played the bass violin or cello in the band at the Drury Lane and Haymarket theatres.133 As it happens, we have measurements of a bass violin belonging to Paisible, among James Talbot’s notes about musical instruments, made in the 1690s. Though fairly small, it was apparently tuned g–c–F–B'@, a tone lower than a modern cello.134 The passage quoted is enigmatic. There is no strong reason to doubt that Salmon heard what he said he heard – see pp. 13–14 above, with note 76, on practitioners’ interest in just intonation – but the question is how he knew, or thought he knew. The confident claim that ‘Hee observs the Major & Minor Tones’ gives the impression of quantitative measurement, but it is difficult to imagine how this could have taken place (some experiment involving marking the fingerboard of the instrument would have been possible in principle, but

26

Thomas Salmon: Writings on Music

hardly seems likely). Possibly Salmon believed he could recognise by ear when the major and minor tones of just intonation were being realised correctly; but it is not clear from his other writings that Salmon really had this kind of confidence in his own aural abilities. It seems most likely that it was simply Paisible’s assertion (and his ‘excellent ear’) which convinced Salmon that he was hearing major and minor tones, and that he was therefore in much the same position vis-à-vis Paisible as the Fellows of the Royal Society would be when faced with his experimental performance 20 years later: he could assent to the excellence of what he heard, but had to take its mathematical characteristics on trust. There can be no doubt, though, that Salmon was convinced, and many years later he would repeat that ‘a good ear & well practis’d hand’ could produce on the violin ‘Notes […] more perfect than can be expres’d upon our common fretted instruments’.135 Whatever Salmon experienced in his meeting with Paisible, he was able elsewhere to speak of setting ‘the Mechanicks to work’ on his designs for modified musical instruments, and actually to obtain such modified instruments in 1705.136 He was aware that he was systematising an existing set of practical compromises, including slanting the frets so as to provide a better set of consonances in some situations, or shifting them slightly before beginning a piece in a new key,137 and in his manuscripts he gave some very detailed consideration to the question of just which compromises were desirable in which keys, as well as to the possibility of providing a single fingerboard which would work at least reasonably well for most or all of the keys in common use. In the Proposal he provided, as a final concession to those too idle to change their fingerboards at every change of key, such a compromise set of frets.138 But the thrust of the Proposal, as of most of his writings on pitch, was towards a level of mathematical precision which seems at odds with any such spirit of practical compromise, and which demanded specially modified instruments for its realisation. His writings give only a few clues to the various stages through which the design and development of his system of fingerboards passed.139 The crucial period seems to have been 1685–7. By December 1685 Salmon had apparently formulated his basic idea of having detachable, interchangeable keyboards for different keys. It is not clear that he had made a decision about how many would be required, and it seems that at this stage practical realisation was not very far advanced; he does not seem to have found a viol-maker who would carry it out. By the time he was writing the Proposal, during 1687, the situation had moved on, with one passage (p. 17) implying that Salmon himself had played on a viol with one of his special fingerboards, and found it ‘very convenient’. Evidently someone (perhaps Richard Meares) had found a way to make the system work, which may not have been at all straightforward. Salmon described changing only the ‘upper part’ of the fingerboard, and his diagrams showed only the section from the nut to just above the seventh fret; presumably the remainder of the fingerboard remained (firmly) in place all the time. Meares’s advertisement of March 1689 (see p. 80) implies that he was prepared at least to consider carrying out the necessary

Introduction

27

alterations to viols or lutes. These would have been quite drastic, involving the removal of part or all of the original fingerboard, and the new set of fingerboards would have had to be very carefully tailor-made to fit the individual instrument. To the disadvantages of expense and inconvenience which Salmon mentioned in the Proposal should be added a third, perhaps more serious: the risk of ruining an instrument if the alterations were botched, or failed to please.140 In 1702 Salmon provided a description of how the fingerboards fitted to the instrument: ‘They are taken out and put in upon the Neck of the Viol, with as much ease, as you pull out and thrust in the Drawer of a Table.’141 There seems no reason to suppose that this was an innovation at this stage, so it can probably also stand as a description of the system in use from 1687, possibly of Meares’s devising. Throughout this whole period, Wallis’s alternative suggestion – individual frets sliding in grooves, with coloured marks to show their different places142 – was available for Salmon to consider, but apparently he never believed it worth pursuing in practice, although ‘The Use of the Musical Canon’ seems to show him considering the details of such a set of marks. (Possibly his reservations concerned the obvious question of how to prevent the frets slipping during performance.) As with the support of the bookseller Carr for Salmon’s proposed reform of musical notation, without which he could never have seriously proposed his scheme for widespread adoption, the support of Meares and possibly of other ‘mechanics’ with the skills to build and modify musical instruments was crucial to Salmon’s work on musical tuning as he conceived it. Despite their low profile in his surviving writings, we should remember that it was through such individuals – as well as his networks of learned and scientific contacts, and of performers – that his proposals made, or attempted, the leap from paper to practice. ‘Then is the Theory of Musick Settled’: Salmon’s Legacy Thomas Salmon’s legacy is hard to assess, although I hope that this edition provides those who are interested with most of what they need in order to make such an assessment. By contrast with the noise generated by the Essay controversy, Salmon’s Proposal seems to have passed practically without comment in print, and the same is true of his experimental performance in 1705 and his death in 1706. Neither his scale nor his idea of musical experiment was taken up by others, and his personal willingness to bridge the widening divide between the study of music’s effect on the human person and that of its mathematical characteristics was shared by only a few individuals later in eighteenth-century England. A handful of musical ‘experiments’ took place at the Academy of Sciences in Paris, attempting (apparently successfully) to cure individuals of fever using music. These attempts at music therapy may have had something in common with what Salmon intended to do, but they cannot be called the norm; and indeed for Salmon the effect of music on the human person was nearly always a matter of pleasure rather than of any more dramatic control or cure.143

28

Thomas Salmon: Writings on Music

Alexander Malcolm mentioned Salmon’s proposed scale, citing his paper in the Philosophical Transactions and repeating – probably unwittingly, since he did not mention the Proposal or any other source – Wallis’s suggestion about the placement of semitones: observe, that he places the lesser Semit. lowest, which I place uppermost; and when I had examined what Difference this would produce, I found the Advantage would rather be in the Way I have chosen.

He went on to cite Simpson (see above, p. 16) in Salmon’s support, but concluded that ‘there will be no Reason found why it should be as Mr. Simpson says, rather than the other Way’.144 Burney did not mention the Proposal, and indeed gave the impression that he was unaware of its existence, omitting Salmon’s name from his list of those in England who had ‘thought harmony and the philosophy of sound objects of their most profound meditations and researches’.145 Hawkins consigned the book to a (lengthy) footnote to his several pages on the Essay, summarising its contents, lambasting its ‘vulgar and affected’ style, and passing the rather curious judgement that Salmon’s proposal was ‘not mathematical’ because it did not adopt an equal division of the octave: It is difficult to discover in what sense proportions thus adjusted can be termed mathematical. All men know that it has been the labour of mathematicians for many ages to effect an equal division of the octave […] it may therefore be inferred that no proportions strictly mathematical can be found by which a division, such as the author pretends to have discovered, can be effected.    After all, this proposal is not mathematical, but simply practical[.]146

His account of Salmon’s paper in the Transactions was less openly dismissive, but Hawkins made his scepticism plain about what Salmon had achieved. The result of this experiment was a conviction, at least of the author, that the harmony resulting from his division was the most complete that had ever been heard, and that by it the true theory of music was demonstrated, and the practice of it brought to the greatest perfection.147

In the twentieth century Salmon has been placed successively in the contexts of notation reform, developing tonal theory, or a broader musical humanism; Robert Lawrence provides a useful summary.148 Salmon’s significance as a theorist of musical pitch is, if anything, even more elusive than his significance as a proponent of notational reform. In the earlier case his impact in his own lifetime depended on his proposals being attacked by Matthew Locke; in the present case it depends upon the fact that he achieved contact with John Wallis and Isaac Newton, with the Steffkin brothers and Richard Meares, and that ultimately he was allowed

Introduction

29

to appear before the Royal Society, writing himself into its Journal Book and its Transactions as one of the very few music theorists the Society chose to take seriously. If he had disciples they are all but invisible to us. His legacy, therefore, is a coherent body of work which, although it had in the long run no effect on how musical instruments were tuned, was during its author’s lifetime a fairly visible, even an important, part of the discussion about how they might be tuned, and, perhaps more significantly, about how musical knowledge might be conceived, achieved and disseminated. Editorial Policy For the Proposal and for ‘The theory of musick reduced’ there is a single original edition; I have detected no variants among the main texts in the copies I have inspected. The texts presented are thus those of the first and only editions, reproducing their spelling, punctuation, capitalisation, italics, paragraph breaks, indentation and blank lines. Pagination is recorded in square brackets; running heads, where present, are recorded in the footnotes. The following are ignored: minor irregularities of spacing, including occasional cases of spaces omitted between words or after abbreviations such as l. or p.; horizontal rules at ends of chapters and occasionally elsewhere; catchwords, except where they are incorrect. The printers deployed italic punctuation marks somewhat haphazardly; I have regularised to the convention that punctuation is italicised when it forms part of an italicised phrase, passage or quotation, and not elsewhere. Italic forms of the letters u and v are occasionally transposed in the originals, and I have silently regularised to modern spelling in the handful of cases involved. For the manuscript texts edited in this volume the following policies have been adopted:149 insertions are placed in ‹angle brackets›; deletions, including illegible deletions (Salmon could be quite thorough about rendering deleted matter unreadable) are recorded in footnotes, but very small illegible deletions are disregarded; abbreviations involving the thorn or the notation ~ (for omitted m, n, or ti) are silently expanded, as are the following common abbreviations: wch, wth, 2d, 3d, Sr; where other letters or punctuation are supplied editorially, they are placed in [square brackets]; where a word has been altered from an illegible earlier state, this is disregarded; spaces are silently supplied in terms like Alamire (A la mi re); editorial judgement has been used, where needed, to distinguish between upper and lower case for initial L and S, to distinguish between capital I and J, and to determine whether or not certain marks are intended as commas;

30

Thomas Salmon: Writings on Music

indentation and the use of blank lines largely follow the sources, but are not always clear in them; it has seemed preferable, for reasons of clarity, to impose a somewhat greater degree of uniformity than to attempt a ‘type-facsimile’; for the same reason chapter headings, which appear in all three main manuscript texts, are printed in a larger type and centred on the line, while subheadings, which occur in ‘The Practicall Theory’ and particularly ‘The Use of the Musical Canon’, are centred and printed in italics. Sub-subheadings, which occur in this last text, are simply printed in italics. The sources make such visual distinctions inconsistently. The following are not transcribed: endorsements in later hands; and catchwords, except where they are incorrect. In all of the original texts – printed and manuscript – fractions appear vertically (see Figure 6.1 for examples); here they are printed diagonally, thus: 3/4. In the endnotes to each text I have endeavoured to gloss rare words or unusual meanings of words, to provide translations for foreign quotations, and most particularly to elucidate points where the modern reader might otherwise be uncertain of Salmon’s meaning, whether that is the result of confusion on Salmon’s part or not. I have tried to limit the amount of interpretation contained in the notes. Readers of this volume will doubtless come from a variety of disciplinary backgrounds, and their patience is craved for those notes which are of less interest to them than to others. Notes 1 See the Introduction to Volume I of this edition, pp. 4–5. 2 Matthew Locke, The present practice of musick vindicated (London, 1673), p. 22 (Locke’s remarks are dated 24 July 1672). 3 Thomas Mace, Musick’s monument, or, a remembrancer of the best practical musick, both divine, and civil, that has ever been known, to have been in the world. […] (London, 1676), sig. c2v. Salmon is one of four subscribers listed for Bedfordshire. 4 Oxford, Bodleian Library, MS. Add. D. 105, fol. 47r: Wallis to Martha Woodcock, 13 February 1674/5 and Wallis to ‘Mrs Salmon at Hackney’, 15 March 1674/5. I am grateful to Philip Beeley for drawing these letters to my attention. 5 John Wallis, ‘Dr. Wallis’s account of some passages of his own life’, in Thomas Hearne (ed.), Peter Langtoft’s chronicle (2 vols: Oxford, 1725), pp. cxl–clxx, at p. clx. 6 Wallis, ‘Dr. Wallis’s account’, p. clxi. The International Genealogical Index (www. familysearch.org) places the marriage at ‘Perkinham’, Bedfordshire, and assigns it to 1675. Perkinham – modern Pertenhall – is about 20 miles from Mepsal. 7 Information from The Clergy of the Church of England Database (www. theclergydatabase.org.uk): Salmon was licensed to preach on 17 September 1685. See the Introduction to Volume I of this edition, note 43. 8 Oxford, Bodleian Library, MS Eng. Lett. C 130, fols 27–8: Salmon to Wallis, 31 December 1685; Wallis to Salmon, 7 January 1686. See Chapter 1 of this volume. 9 Oxford, Bodleian Library, MS Eng. Lett. C 130, fol. 27r.

Introduction

31

10 For example, taking the open string as A, we reach B by reducing its length by 1/9. We reach C by reducing its new length by 1/16. The resulting string is shorter than the one with which we began by 1/6 (see Proposal, p. 9). How to get 1/6 by ‘adding’ – in any sense – 1/9 and 1/16 is not obvious, and a description like Gassendi’s does not help. In fact, we must consider not the parts which are removed but the parts which remain: if the original string is one unit long and we reduce it first to 8/9 of its original length and then to 15/16 of 8/9, it follows without much trouble that what results is a string 5/6 units long. It seems plausible that it was calculations of this kind which had confused Salmon and that, consulting Gassendi, he had not been able to understand why his instructions for adding and subtracting ratios matched the results of Salmon’s measurements on the neck of a viol. 11 Oxford, Bodleian Library, MS Mus. Sch. d375*, fols. 32r–40r: ‘The Use of the Musical Canon’. 12 Proposal, p. 28. 13 ‘The theory of musick reduced’, foldout after p. 2077. 14 See ‘The Division of a Monochord’, fol. 8r: ‘frets tied cross the neck of the instruments’. 15 Hugh de Quehen, ‘Bernard, Edward (1638–1697), mathematician and Arabist’ in ODNB; Αρατου Σολεως Φαινόμηνα καὶ Διοσημεῖα. Θεωνος Σχόλια. … Accesserunt annotationes in Eratosthenem et hymnos Dionysii (Oxford, 1672), pp. 47–69; Benjamin Wardhaugh, ‘Edmund Chilmead Revisited: musical scholarship in early seventeenth-century Oxford’, in Scott Mandelbrote (ed.), The Peterhouse Partbooks: music and culture in Cambridge in the 1630s (forthcoming). 16 Proposal, p. 42. 17 Proposal, p. 29. 18 The copies in Cambridge University Library and the library of Trinity College, Cambridge, which I have seen, bear no annotations whatever; neither does one of the copies held by the Bodleian Library (shelfmark 4o P 37 Art; for the other see pp. 82–3 below). The copies in Durham Cathedral Library and Eton College Library also apparently bear no annotations; I am grateful to Alastair Fraser and Katie Flanagan at those libraries for this information. 19 The advertisements appeared in John Pechey, The London dispensatory […] (1694); Thomas James, A vindication of that part of Spira’s despair revived which is challenged by the Anabaptists […] (1695); William Shewen/‘Trepidantium Malleus’, William Penn and the Quakers either imposters or apostates […] (two variants, 1696); Samuel Morland, Hydrostaticks […] (1697); Edmund Calamy, A funeral sermon preached upon occasion of the decease of the eminently pious Mrs. Elizabeth Williams […] (1698); George Lawson, Theo-Politica (1705). 20 See note 16 on p. 84: Payne gave the price as 1s both times; the other copies appeared in bound volumes together with other items, priced at 6s and 5s respectively. Similarly, a volume containing the Proposal together with 12 other pamphlets, in Durham Cathedral Chapter Library, bears the price 2s. 6d; I am grateful to Alastair Fraser for information about this copy. 21 Isaac Watts, Hymns and spiritual songs (London, fifth edn, 1716), sig. Q5v. Plomer’s Dictionary has no information on M. Lawrence, who may have been John’s widow. 22 A catalogue of books, printed for Richard Ford, at the Angel in the Poultry, near Stocks-Market [London, 1726?], p. 2 (quartos, item 4): ‘A Proposal to perform

32

Thomas Salmon: Writings on Music

Musick in perfect and mathematical Propositions [sic]. By Thomas Salmon’. 23 Oxford, Bodleian Library, MS. Add. D 105, fols 92–3: Wallis to Salmon, 15 May 1690; Salmon to Wallis, 16 May 1690. I am grateful to Philip Beeley for drawing these letters to my attention. 24 On Samuel Morland Jr. (1663–1716) see Alan Marshall, ‘Morland, Sir Samuel, first baronet (1625–1695), natural philosopher and diplomat’ in ODNB. For Salmon’s connection with the Morlands (his niece married a nephew of Sir Samuel), see the Introduction to Volume I of this edition, p. 4. 25 F.A. Blaydes (ed.), Bedfordshire Notes and Queries (Bedford, 1882–93), vol. 3, p. 57 quotes Sarah Emery’s will (in part); the relevant provision was that after the death of her sister Elizabeth her estate was to be placed in trust ‘for the schooling poor children’ in Ampthill and Meppershall. Bedfordshire and Luton Archives and Records Service holds the Orders (rules) and account book (1698–1705) for the school (reference P29/25/1). See also see ‘Parishes: Meppershall’, in William Page (ed.), A History of the County of Bedford: Volume 2 (London, 1908), pp. 288–93 (www.british-history.ac.uk/report.aspx?compid=62650) and ‘Parishes: Ampthill’, in William Page (ed.), A History of the County of Bedford: Volume 3 (London, 1912), pp. 268–75 (www.british-history.ac.uk/report.aspx?compid=4242). The Victoria County History reports that a register book of the parish contains ‘a copy of Latin elegiac verses, composed about 1706 by a former rector, giving a vivid idea of the charms of the house two centuries ago’ (‘Parishes: Meppershall’, p. 288); in fact these verses date from 1709, after Salmon’s death. The poems appear in item P29/1/7 in the Bedford and Luton Archive. I am grateful to James Collett-White at that archive for information and help concerning this material. 26 London, British Library, MS Sloane 4040, fol. 104r: Salmon to Sloane, 4 December 1705. 27 Oxford, Bodleian Library, MS. Add. D 105, fol. 92. Salmon’s other surviving letters, from 1684 and 1705–6, are all dated from Mepsal. 28 The catechism of the Church of England divided into five parts; I. The Christian covenant. II. The Christian faith. III. The Christian practice. IV. The Christian prayer. V. The Christian sacraments. With a short explication, containing the grounds and reasons of the Christian religion. By Thomas Salmon, M.A. Rector of Mepsal, in the county of Bedford (London, 1699). 29 Only three copies survive, which may indicate that the initial print run was small; they are held in: Cambridge, Trinity College, The Wren Library; Oxford, All Souls College, The Codrington Library; and Washington, DC, Folger Shakespeare Library. The ESTC wrongly reports a second copy at All Souls, and a copy at Indiana University; I am grateful to Peter Sewell for information about the alleged Indiana copy. 30 See sig. B6v. The Catechism exists in at least two variants. I have compared the EEBO facsimile (of the copy in the Codrington Library) with the copy in the Wren Library; the latter corrects certain errors in the text (two missing spaces on fol. A2r, migh for might on p. 15, the catchword on p. 14 is wrongly changed to roman from italic) while introducing a handful of irregularities of its own (fol. A2 is labelled 2A, p. 21 is numbered 12), and has a different final advertisement leaf. 31 A discourse concerning the baptism and education of children, as the best means to advance the religion and prosperity of the nation. Whereunto are annexed proposals

Introduction

33

for the settlement of free-schools in all parishes, for education of the children of the poor. By Thomas Salmon, M.A. rector of Mepsal, in the counties of Bedford and Hertford (London, 1701). Six copies survive, in (according to the ESTC): Liverpool, Liverpool University Library; London, the British Library; Oxford, Christ Church Library, Leicester; the University of Leicester Library; Los Angeles, University of California, William Andrews Clark Memorial Library; and New York, the Union Theological Seminary Library. The remarks which follow are based only on the British Library’s copy (there is no facsimile in ECCO). 32 Henry R. Plomer, A Dictionary of the Booksellers and Printers who were at Work in England, Scotland and Ireland from 1668 to 1725 (Oxford, 1922), p. 293. 33 John Wallis, A defense of infant-baptism. In answer to a letter (here recited) from an anti-pædo-baptist (Oxford, 1697). 34 See C.E. Challis, ‘Freeman, Sir Ralph (d. 1667), government official and author’ in ODNB; Salmon stated that Freeman had ‘with Faithfulness serv’d your Country in Parliament’ and apparently believed he was in a position to ‘convey’ the proposal to Parliament: Salmon, A discourse concerning … baptism, sig. A2r, A3r, A2v. 35 Salmon, A discourse concerning … baptism, pp. 59–62. Salmon noted (sig. A2v) that ‘We have now before us the greatest Opportunity that ever was, for accomplishing this Design; His Majesty having graciously Proposed to his Parliament to take the Poor into their Consideration, and the Parliament having Resolv’d to bring all their Concerns into one General Bill’. 36 Salmon, A discourse concerning … baptism, p. 34. 37 Salmon, A discourse concerning … baptism, pp. 36, 37. 38 Salmon, A discourse concerning … baptism, pp. 55–8, quotes pp. 56, 57. 39 Salmon’s remarks about the nature of the soul (pp. 28–9) seem, perhaps, incautious, but I do not think they represent conscious heterodoxy. 40 A historical account of St. George for England, and the original of the most noble order of the Garter. By Thomas Salmon, M.A. rector of Mepsall in the county of Bedford (London, 1704). Janeway, probably the son of the ‘fanatically Protestant’ Richard Janeway senior, was another occasional associate of Dunton’s: see Plomer, Dictionary, p. 170. 41 The ‘cutts’ comprise portraits of Queen Anne (frontispiece) and of Edward III (facing p. 60), and a picture of St George’s Chapel in Windsor Castle (facing p. 112). In the version which has them the title page begins thus: A new historical account of St. George for England, and the original of the most noble order of the Garter. Illustrated with cutts. It continues as in the unillustrated version. 42 I have inspected only the online facsimiles provided by ECCO, of the copies from the University of Texas (unillustrated) and the British Library (illustrated). On these I have performed limited spot-checks; I have not collated the texts exhaustively for variants. The only difference I have found is that the illustrated copy begins with the list of contents to part 1, the errata, and the list of contents to part 2, while the unillustrated copy moves the contents list for part 2 of the book to a position immediately before part 2 itself. This may of course be an irregularity of binding specific to this copy. 43 Salmon, An historical account of St. George, part 2, p. 4. 44 Salmon, An historical account of St. George, part 2, p. 22 and passim; Henry Spelman, Concilia, decreta, leges, constitutiones, in re ecclesiarum orbis Britannici (London, 1639); Peter Heylyn, The historie of that most famous saint and souldier

34

45

46 47

48 49

50 51

52

53 54

55

Thomas Salmon: Writings on Music of Christ Iesus; St. George of Cappadocia asserted from the fictions, in the middle ages of the Church; and opposition, of the present. The institution of the most noble order of St. George, named the Garter. […] (London, 1631). Historical collections, relating the originals, conversions, and revolutions of the inhabitants of Great Britain to the Norman conquest, in a continued discourse. The collections are chiefly made out of Caesar and Tacitus, Bede, and the Saxon annals, Mr. Camden, and Archbishop Usher; the two bishops of Worcester, Stillingfleet and Lloyd. The english authors are cited in their own words, and the rest carefully translated (London, 1706). Despite the imprint date, Salmon was able to send Hans Sloane a copy of the book in December 1705, remarking that he had ‘carried [it] to the press in the summer’ (London, British Library, MS Sloane 4040, fol. 104r). Wyat seems to have been another member of the nonconformist world: see Plomer, Dictionary, p. 322. Again, this is based on spot-checks, not exhaustive collation, of the ECCO facsimiles of two copies in the British Library. The history of Great Britain and Ireland; from the first discovery of these islands to the Norman conquest. Wherein the relations given us by Cæsar, Tacitus, Bede and the Saxon annals are faithfully rendred into English. And the antiquities of the Britains, Picts, Romans, Scots, Saxons, Danes and Normans, collected from Mr. Camden, Arch-Bishop Usher, the bishops Stillingfleet and Lloyd, and other antiquaries, are reduced into one uniform, methodical discourse; with reflections upon the whole. By Thomas Salmon, M.A. late rector of Mepsal in Bedfordshire. The second edition. With a preface, wherein the partiality of Mons. Rapin, and some other republican historians, is demonstrated. By Mr. Salmon, author of the modern history (London, 1725). I have not attempted to verify the ESTC’s holdings report for these two books. The works of Thomas Salmon, Jr. included A compleat collection of state-tryals, in four volumes (1719), The review of the history of England (1722), Modern history, or, The present state of all nations (31 volumes: 1724–38), and many other historical and geographical works. See Volume I of this edition, p. 5. London, British Library, MS Sloane 4040, fol. 104r. London, British Library, MS Add. 4919, fols. 1–11: ‘The Practicall Theory / of Musick / To perform Musick in perfect proportions / and / To set out the proportions upon the Viol / so that they may fall right / upon the frets. / 1702’. See Chapter 4, this volume. Cambridge, Cambridge University Library, Add. MS 3970, fols. 1–11: ‘The Division of a Monochord’. See Chapter 5, this volume. On Newton and Salmon see also Penelope M. Gouk, Music, Science and Natural Magic in Seventeenth-Century England (New Haven and London, 1999), pp. 231–2. See the introductions to Chapters 4 and 5 below. Class numbers NQ.16.77[7] (Proposal) and C.32.12[1] (Catechism). The copy of The Catechism (class number C.32.12(1)) was, according to a bookplate in the volume of religious and political writings in which it appears, left to the college by Thomas Smith (c. 1657–1714), chorister, scholar and graduate of Trinity, fellow from 1679 and vice-master from 1712. (Information from The Clergy of the Church of England Database.) On Newton’s Arianism see T.C. Pfizenmaier, ‘Was Isaac Newton an Arian?’, Journal of the History of Ideas, 58 (1997): 57–80. It should be pointed out that Salmon’s

Introduction

56 57 58 59

60 61

62

63

64

35

Catechism and Baptism contain no hint at all that Trinitarian formulae might make him uncomfortable; indeed rather the reverse: see for example Catechism, p. 19, or Baptism, p. 44: ‘The Baptismal words, in the Name of the Father, and of the Son, and of the Holy ghost, are the most substantial Creed: That therefore is the greatest Heresy, which is a contradiction to it.’ London, Royal Society, Journal Book Original, vol. 10, pp. 109–10. See Christopher D.S. Field and Benjamin Wardhaugh (eds), John Birchensha: writings on music (Farnham, 2009), pp. 12, 15–18. See Leta Miller and Albert Cohen, Music in the Royal Society of London (Detroit, 1987). One manuscript provides evidence of a different kind of interest in musical theory for Newton; arguably this could have provided a point of contact with Salmon, but relevant evidence is lacking. See James E. McGuire and Piyo M. Rattansi, ‘Newton and the “Pipes of Pan”’, Notes and Records of the Royal Society, 21 (1966): 108– 43. On Newton and music more generally see Gouk, Music, Science, and Natural Magic, chapter 7; and Penelope M. Gouk, ‘The Harmonic Roots of Newtonian Science’, in John Fauvel, Raymond Flood, Michael Shortland and Robin Wilson (eds), Let Newton Be! a new perspective on his life and works (Oxford, 1988), pp. 101–25. Cambridge, Trinity College Library, class number NQ16.77(7). The folded leaf is the top of p. 30; the previous leaves, including some of the diagrams, were folded down together with this leaf. ‘The theory of musick reduced to arithmetical and geometrical proportions, by the Reverend Mr Tho. Salmon’, Philosophical Transactions, 24 (1705): 2072–7, 2069; London, British Library, MS Sloane 4040, fols. 103–4, 108–9: Thomas Salmon to Hans Sloane, 4 December 1705 and 8 January 1706. London Metropolitan Archive, COL/CA/01/01/114 (olim REPS/110): Repertories of the Court of Aldermen, 6 November 1705 – 28 October 1706, fol. 86v: 5 March 1706. The court’s original rough minutes for 1704–1706 are in COL/CA/02/02/008 and the fair copy minutes (7 February 1706 – 27 March 1716) in COL/CA/02/01/004; both record that Salmon’s petition was ‘adjourned’ on 5 March 1706. See also Penelope M. Gouk, ‘Music in the Natural Philosophy of the Early Royal Society’ (unpublished Ph.D. thesis, London, 1982), p. 245 and J. Harley, Music in Purcell’s London: the social background (London, 1968), pp. 164–5. Specifically, the repertories do not mention the subject again during the period to the end of July 1706; neither do the rough minutes or the fair copy minutes. There is nothing relating to the matter in either of the London Metropolitan Archive’s two boxes of relevant material relating to the Court of Aldermen for this period, namely COL/CA/05/01/007: ‘Papers’, 1705–1706 and COL/CA/05/02/003: ‘Miscellaneous petitions’, late seventeenth century to 1790s, R–Y. The absence of Salmon’s petition from this last box suggests that it may have been mislaid (or discarded) at an early date. Blaydes, Bedfordshire Notes and Queries, vol. 3, p. 374: ‘Hoc etiam situs est THOMAE SALMON A.M. per triginta et tres annos hujus Ecclesiae Rector, vitâ defunctus primo die Augusti 1706. Cujus propitiatio Christus. Vir haud vulgari dignas praeconio Qui vero hoc tantum inscribi voluit.’ According to F.W. Kuhlicke, ‘The Salmons of Meppershall’, Bedfordshire Magazine, 1/5 (1948): 177–80, at p. 179, there is also a brass plate, now mural, with slightly different wording: ‘Hic

36

65

66

67 68

69 70 71

72

Thomas Salmon: Writings on Music etiam situs est Thomas Salmon A.M. / Per triginta et tres annos huius ecclesiæ Rector / Vita defunctus primo die Augusti MDCCVI / Cuius Animæ Propitiatio Christus / Vir haud Vulgari Dignus præconio / Qui Vero Solum inscribi voluit.’ Prerogative Court of Canterbury PROB 11/490: will of Thomas Salmon, proved 13 August 1706; Meppershall Parish Register, transcription of 1948/2003 supplied by Bedfordshire and Luton Archives and Records Service, p. C48. The New Grove places his burial on 16 August, but this seems to be a mistake; the ecclesiastical records place his notional death on 1 October, which was in fact the day his successor at Mepsal was instituted: ‘Salmon, Thomas’, in Grove Music Online; The Clergy of the Church of England Database. The two extant copies are in the Bodleian Library (shelfmark [MS] Mus. Sch. D.375*, fols 28–31) and the British Library (shelfmark 557*.e.25.(3* and 6)). The British Library catalogues the two parts of the pamphlet – engravings and text – separately, and they there appear in a bound volume separated from one another by other material, but the Bodleian’s catalogue considers them a single item; Jessie Ann Owens concurs, and so do I. See Jessie Ann Owens, ‘You Can Tell a Book by Its Cover: reflections on format in English music “theory”’, in Russell Eugene Murray, Susan Forscher Weiss and Cynthia J. Cyrus (eds), Music Education in the Middle Ages and the Renaissance (Bloomington, 2010), pp. 347–85, at 370; and Jessie Ann Owens, ‘“el foglio rigato” Revisited: prepared paper in musical composition’, in M. Jennifer Bloxam, Gioia Filocamo and Leofranc Holford-Strevens (eds), Uno gentile et subtile ingenio: studies in Renaissance music in honour of Bonnie J. Blackburn (Brepols, 2009), pp. 53–61, at p. 58, with n. 28. See also Rebecca Herissone, Music Theory in Seventeenth-century England (Oxford, 2000), front cover, p. 85 and 97 for illustrations of the ‘Compass’ and passim for a discussion of its contents. Elsewhere (Benjamin Wardhaugh, Music, Experiment and Mathematics in England, 1653–1705 (Farnham, 2008), p. 170 with n. 88) I have incorrectly described ‘The Musicall Compass’ as also containing a volvelle in the British Library’s copy. The device in question is in fact a stray part from Ambrose Warren’s Tonometer (London, 1725); see p. 21, where the volvelle is described. Specifically, full-text searches in EEBO, ECCO, and the Burney Collection of newspapers (find.galegroup.com/bncn) do not turn up any uses of the phrase ‘musical[l] compass’. See J. Murray Barbour, Tuning and Temperament: a historical survey (East Lansing, 1951; New York, 2004), pp. 89–105, citing Bartolomeus Ramis de Pareja, Musica practica (Bologna, 1482) and Gioseffo Zarlino, Istitutioni harmoniche (Venice, 1558); see also Wardhaugh, Music, Experiment, and Mathematics, pp. 13–15. Barbour, Tuning and Temperament, pp. 89–102; Vindication, p. 15 (with n. 40 in this edition). [Francis North], A philosophical essay of musick directed to a friend (London, 1677), p. 26. Wallis, ‘Remarks’, p. 37; John Wallis, ‘Appendix de veterum harmonica ad hodiernam comparata’, in Claudii Ptolemaei harmonicorum libri tres (Oxford, 1682), pp. 281–328, at p. 324; John Wallis, ‘A letter of Dr. John Wallis to Samuel Pepys Esquire, relating to some supposed imperfections in an organ’, Philosophical Transactions, 20 (1698): 249–56, at p. 253. William Holder, A treatise of the natural grounds, and principles of harmony (London, 1694), p. 155 and facing foldout.

Introduction

37

73 My assertion to that effect in Music, Experiment and Mathematics, p. 14, is incorrect. I am grateful to Christopher D.S. Field for the substance of some of the remarks which follow. 74 H. Floris Cohen, Quantifying Music: the science of music at the first stage of the scientific revolution, 1580–1650 (Dordrecht, 1984), pp. 100–110 (Mersenne), 167– 8 (Descartes). 75 Christopher Simpson, A compendium of practical musick in five parts (London, 1667), pp. 102–7. 76 Patrizio Barbieri, ‘Violin Intonation: a historical survey’, Early Music, 19 (1991): 69–88; Patrizio Barbieri, ‘Violin and Woodwinds Intonation, 1650–1900’ in his Enharmonic Instruments and Music 1470­–1900 (Latina, 2008). See also David D. Boyden, ‘Prelleur, Geminiani and Just Intonation’, Journal of the American Musicological Society, 4 (1951): 202–19. 77 Mark Lindley, ‘Just [pure] intonation’ in Grove Music Online; see also Mark Lindley, Lutes, Viols and Temperaments (Cambridge, 1984), passim. 78 Lindley, ‘Just [pure] intonation’. 79 ‘The Division of a Monochord’, fol. 10v. 80 Christopher D.S. Field has drawn my attention to the fact that in Purcell’s Sonnata’s of III parts: two viollins and a basse: to the organ or harpsechord (1683) it is generally agreed that a viol was the preferred instrument for the ‘basse’ part, as specified in Playford’s advertisement in Choice ayres (1684). He points out that in Sonata V (A minor) the third fret has to serve for both d sharp and e flat on the c string, and for both A sharp and B flat on the G string; in Sonata VI (C major) the first fret has to serve for both c sharp and d flat on the c string, and for both G sharp and A flat on the G string, while the fourth fret has to serve for g sharp and a flat on the e string. 81 See Wallis, ‘Appendix’, p. 179. 82 Wallis, ‘Appendix’, pp. 178–80; see also Holder, A treatise of … harmony, passim. 83 As Stewart Pollens has pointed out, some features of the system of fretting that resulted are shared with Silvestro Ganassi’s instructions for fretting the viola da gamba, published in 1543. It seems next to impossible that this text was known to Salmon. See Stewart Pollens, ‘A Viola Da Gamba Temperament Preserved By Antonio Stradivari’, Eighteenth Century Music, 3 (2006): 125–32, at p. 132, citing Silvestro Ganassi, Regula rubertina: Lettione seconda pur della prattica di sonare il violone d’arco da tasti (Venice, 1543). 84 See Figure 5.2, and Simpson, Compendium, p. 106. 85 Boethius, De institutione musica III, chapter 8. See Barbour, Tuning and Temperament, p. 123. 86 Simpson, Compendium, pp. 104, 108. 87 John Wallis, ‘A question in musick lately proposed to Dr. Wallis, concerning the division of the monochord, or section of the musical canon: with his answer to it’, Philosophical Transactions, 20 (1698): 80–84; John Wallis, ‘A letter … to Samuel Pepys’. 88 Proposal, sig. a4r. 89 Proposal, p. 14. 90 Wallis, ‘Appendix’, p. 180; Wallis, ‘Remarks’, p. 40; ‘The Division of a Monochord’, pp. 5–6. 91 This is easy to see if we consider the division being performed on an actual string; as Simpson put it (Compendium, p. 107), ‘every equal division of a line or string,

38

92 93 94 95

96

97

98 99 100 101 102 103 104

105 106 107

Thomas Salmon: Writings on Music doth still produce a greater Interval of sound, as it approaches nearer to the Bridge’. Alternatively, in numbers, we begin with two strings whose lengths are 4 units and 2 units and which therefore produce pitches an octave apart, let us say A and a. A middle string with length 3 units produces a ratio of 4 : 3, a fourth, with the longer, lower string and 3 : 2, a fifth, with the shorter, higher string. It therefore corresponds to D. This is the point which Wallis made at ‘Remarks’, pp. 39–40; he used the possibly unhelpful term ‘musical division’ for what I have called a ‘harmonic division’. See John Birchensha on ‘mediations’ in his ‘Compendious Discourse’, fols. 20r–20v: Writings on Music, p. 157. Proposal, p. 15. Marcus Meibom, Antiquæ musicæ auctores septem (Amsterdam, 1652); Johannes Kepler, Harmonices mundi libri quinque (Linz, 1619); Vincenzo Galilei, Discorso intorno alle opere de Gioseffo Zarlino et altri importanti particolari attenenti alla musica (Venice, 1589; facs. edn Milan, 1933). Galilei is the most doubtful of these, since we have no evidence that Salmon read Italian. René Descartes, Renatus Des-Cartes excellent Compendium of musick, ed. and trans. anon. [trans. Walter Charleton, ed. William Brouncker] (London, 1653); for Chilmead see note 15 above. Salmon referred to Kircher early in the Proposal as a publisher of ancient notation but actually cited Chilmead (and in fact the reprint of Kircher’s bogus specimen of ancient musical notation was added to Chilmead’s treatise by its editor, Bernard); he did not ask the reader to believe that he had consulted Kircher’s Musurgia itself. Henry Oldenburg, Correspondence, ed. A. Rupert Hall and Marie Boas Hall (13 vols, Madison and London, 1965–77), vol. 2, p. 555 (Henry Oldenburg to Robert Boyle, 10 October 1665): ‘the Inquiry about Sounds is worthy of Philosophers […]’. See chapter 2 of ‘The Division of a Monochord’: ‘The Proportions set out according to a Scheme of the Grecian Musick’. See Proposal, pp. 2–3. See Cohen, Quantifying Music, esp. chapters 3 and 4; and Wardhaugh, Music, Experiment, and Mathematics, esp. pp. 16–19. Bodleian MS Eng. Lett. C 130, fol. 27r. See for example S. Shapin, ‘Pump and Circumstance: Robert Boyle’s literary technology’, Social Studies of Science, 14 (1984): 481–520. Essay, pp. 2–3. Another translation existed but is less likely to have been available to Salmon: Antonius Gogava, Aristoxeni musici antiquiss[imi] Harmonicorum elementorum libri III. Cl. Ptolomaei Harmonicorum, seu de musica lib. III. Aristotelis De obiecto auditus fragmentum ex Porphyrij commentarijs / omnia nunc primum Latine conscripta & edita ab Ant. Gogauino grauiensi (Venice, 1562). For what follows see Andrew Barker, Scientific Method in Ptolemy’s ‘Harmonics’ (Cambridge, 2000). See Wardhaugh, Music, Experiment and Mathematics, pp. 98–110. Marin Mersenne, Harmonie universelle (Paris, 1636), ‘Livre troisième des mouvemens & du son des chordes’, prop. 6, p. 169. The pitch was G re sol and the frequency was 168 cycles per second, implying (not credibly) A = c. 377. Mersenne seems to have made a mistake somewhere in his procedure.

Introduction

39

108 Pierre Gassendi, Syntagma philosophiae epicuri (The Hague, 1649), part 2, ‘Physica’, sectio I, Liber VI, caput X: ‘De sono’, in Pierre Gassendi, Opera omnia (6 vols, Lyon, 1658, facs. edn Stuttgart, 1964), vol. 1, pp. 414–22 at pp. 418–19; Pierre Gassendi, Manuductio ad theoriam seu partem speculativam musicae, in Gassendi, Opera omnia, vol. 5, pp. 633–58, trans. as Initiation à la théorie de la musique, texte de la ‘Manuductio’ traduit et annoté par Gaston Guieu (Aix-en-Provence, 1992), pp. 5, 38–9; Walter Charleton, Physiologia Epicuro–Gassendo–Charletoniana: or a fabrick of science natural, upon the hypothesis of atoms (London, 1654), pp. 222–3; Thomas Birch, A history of the Royal Society of London (4 vols, London, 1756–7), vol. 1, p. 446. 109 Birch, History, vol. 1, pp. 451–6. See Gouk, ‘Music in the Natural Philosophy of the Early Royal Society’, passim. 110 See Wardhaugh, Music, Experiment and Mathematics, pp. 107–10, where the views of Jamie Kassler and Penelope Gouk are cited, but note Kassler’s remarks in her review of that book in Isis, 100 (2009): 915–16. 111 Birch, History, vol. 4, p. 96. 112 See the introduction to Volume I of this edition, pp. 19–22. 113 Oxford, Bodleian Library, MS Eng. Lett. C 130, fol. 27r. 114 ‘The theory of musick reduced’, p. 2069. 115 See Gouk, ‘Music in the Natural Philosophy’, passim. 116 Gouk, ‘Music in the Natural Philosophy’. 117 For Wallis’s forays into contact with practitioners see in particular ‘Dr. Wallis’s letter to the publisher, concerning a new musical discovery; written from Oxford, March 14. 1676/7’, Philosophical Transactions, 12 (1677): 839–42 and ‘A letter … to Samuel Pepys’. He was not above gathering data about vibrational nodes from practitioners and on one occasion having a sort of consultation with an organ builder, but it does not really seem that these activities played any very substantial role in his musical work or writings. See the introduction to David Cram and Benjamin Wardhaugh, John Wallis: writings on music (Farnham, forthcoming). 118 Wallis, ‘Remarks’, p. 33. 119 Oxford, Bodleian Library, MS Eng. Lett. C 130, fol. 27r. 120 See Proposal, p. 22 and ‘The Division of a Monochord’, fol. 8v. 121 Proposal, p. 28. 122 I am indebted to Christopher D.S. Field for much of the substance and wording of these remarks on the Steffkin brothers and on Visconti. 123 Essay, p. 82, Proposal, p. 22. Theodore Steffkin accompanied Charles II’s plenipotentiaries to the Congress of Cologne that followed the Third Anglo-Dutch War. 124 His birth-date can be deduced from the assertion in Tim Crawford, ‘Constantijn Huygens and the “Engelsche Viool”’, Chelys, 18 (1989): 41–60, n. 73, that he was ‘aged sixteen-and-a-half’ in November 1662. 125 London Gazette, 20 December 1703. 126 ‘The theory of musick reduced’, p. 2072. 127 Andrew Ashbee in BDECM names him Christian Leopold; see also Christopher D.S. Field, ‘Steffkin, Theodore’, in Grove Music Online. 128 See the advertisement, signed ‘Gasparini’, attesting to the reliability of John Walsh’s Corelli editions in the Post Man, 29 September–2 October 1705 and Daily Courant, 1 October 1705, and William C. Smith, A Bibliography of the Musical Works Published by John Walsh during the Years 1695–1702 (London, 1948), pp. 57–8.

40

Thomas Salmon: Writings on Music

129 See Carlo Chiesa, ‘The Viola da Gamba in Cremona’, in Susan Orlando (ed.), The Italian Viola da Gamba (Limoges and Turin, 2002), pp. 87–95, at p. 94; and Walter Hill, ‘Visconti, Gasparo’, in Grove Music Online; also Raffaello Monterosso, ‘Gasparo Visconti, Violista Cremonese del Secolo XVIII’, Studien zur Musikwissenschaft 25 (1962): 378–90. 130 Stewart Pollens, Stradivari (Cambridge University Press, 2010), pp. 153–60 and especially 155–6 with his figures 6.4, 6.5, citing Museo Stradivariano nos. 308, 256, 258. 131 Pollens, Stradivari, p. 160. See also Pollens, ‘A Viola Da Gamba Temperament’, and Myrna Herzog, ‘Stradivari’s Viols’, Galpin Society Journal, 57 (2004): 183–94 at 189–91, where she draws the same general conclusion; but note Pollens’ remarks about Herzog’s work on this matter in his Stradivari, notes 22, 24, 25, 27 on p. 314. The Museo internazionale e biblioteca della musica di Bologna possesses an undated manuscript entitled ‘Teoria della Musica ridotta a proporzioni aritmetiche e geometriche, del Sig. Tomaso Salmon’ (catalogue number E.42, olim Cod. 058:2.: see badigit.comune.bologna.it/cmbm/scripts/gaspari/scheda.asp?id=2162 and Gaetano Gaspari, Catalogo della Biblioteca del Liceo Musicale di Bologna (5 vols, Bologna: 1890–1943), vol. 1, p. 254). The catalogue confirms what the title clearly suggests, namely that this is a translation into Italian of Salmon’s ‘The theory of musick reduced’. This item, which came to my attention too late to be considered in detail in this edition, might perhaps shed some light on the possible transmission into Italy of Salmon’s tuning system in the early eighteenth century, whether by Christina Visconti or by another route. 132 Oxford, Bodleian Library, MS Eng. Lett. C 130, fol. 27r. 133 David Lasocki, ‘Paisible [Peasable], James [Paisible, Jacques]’, in Grove Music Online and Lasocki’s article on Paisible in BDECM; Christopher D.S. Field, personal communication. 134 Christopher D.S. Field, personal communication. Talbot’s notes are now in Oxford, Christ Church, Mus. MS 1187. See also Robert Donington, ‘James Talbot’s Manuscript: Bowed strings’, Galpin Society Journal, 3 (1950): 27–45, reprinted in Chelys, 6 (1975–6): 43–60; Peter Trevelyan, ‘A Quartet of String Instruments by William Baker of Oxford’, Galpin Society Journal, 49 (1996): 65–76; Brenda Neece, ‘The Cello in Britain: a technical and social history’, Galpin Society Journal, 56 (2003): 77–115. 135 For example, ‘The Division of a Monochord’, fol. 8r. 136 London, British Library, Sloane MS 4040, fol. 104r. 137 A lucid modern discussion of the placing of frets for different tunings, including the possibilities of splitting or slanting them, is given by Elizabeth Liddle in Alison Crum and Sonia Jackson, Play the Viol (Oxford, 1989), pp. 155–64. 138 Proposal, pp. 25–7. 139 I am indebted to Christopher D.S. Field for the substance of the remarks which follow. 140 See Proposal, pp. 25. 141 ‘The theory of musick reduced’, foldout. 142 ‘Remarks’, p. 41. 143 The first article (Histoire de l’académie royale des sciences (1707), pp. 7–8) reports on the success of a musical concert used to help cure a musician ill with a delirium of fever. The second article (Histoire (1708), pp. 22–3) contains a similar report

Introduction

144 145 146 147 148 149

41

concerning a dancer with fever cured by familiar airs played on a violin. For the broader context of these articles, see Albert Cohen, Music in the French Royal Academy of Sciences: a study in the evolution of musical thought (Princeton, 1981), pp. 20–21. Alexander Malcolm, A treatise of musick, speculative, practical, and historical (Edinburgh, 1721), pp. 305, 306. Charles Burney, A general history of music, from the earliest ages to the present period (4 vols, London, 1776–89), vol. 3, pp. 474–5. Sir John Hawkins, A general history of the science and practice of music (5 vols, London, 1776), vol. 4, p. 423. Hawkins, A general history of the science and practice of music, vol. 4, pp. 444–5, quote p. 445. R.E. Lawrence, ‘The Music Treatises of Thomas Salmon (1648 [sic]–1706)’ (unpublished M.A. thesis, University of Calgary, 1991), pp. 8–16. I follow, very broadly, the wise advice of Michael Hunter in Editing Early Modern Texts: an introduction to principles and practice (Basingstoke, 2007).

Taylor & Francis Taylor & Francis Group http://taylorandfrancis.com

Chapter 1

Correspondence with John Wallis (1685–6) Editorial Note Two letters preserved in the Bodleian Library (MS Eng. Lett. C 130, fols 27–8) are all that survive of a correspondence between Salmon and Wallis which, it is implied, included at least two earlier letters from Wallis and one from Salmon. Salmon had apparently conveyed ‘papers’ to Wallis, which may have been in effect a draft of the Proposal or of part of it; Wallis had returned these and supplied Salmon with some information about the possibility of using moveable frets. Evidently work on what would become the Proposal was well under way, and some of what Wallis would write in his ‘Remarks’ in 1688 had already been formulated. Salmon wrote to Wallis from Mepsal on 31 December 1685; Wallis replied on 7 January, writing his draft (no fair copy is known to survive, so we cannot in fact be certain that Salmon ever received this letter) on the inside cover of Salmon’s letter and directing his answer via ‘Mr John Hos[…] on snow-hill, London’, whom I cannot identify with any confidence. One possibility is Sir John Hoskins (1634–1705), one of the founding Fellows of the Royal Society and its president in 1682–3, and a close friend of Francis North, but by the date of this letter he was not plain ‘Mr’ but a baronet. Each letter is in the hand of its author; the sheet on which both were written has been folded once to form two leaves of approximately 300mm × 195mm; it bears the remains of the seal which Salmon used. The contents of these letters are discussed in the Introduction. Salmon was already thinking in terms of a system of fingerboards which could be exchanged when the keynote changed, the system he would present in the Proposal. Wallis was already advocating the different mechanical system which he would advocate in his ‘Remarks’ on the Proposal: individually moveable frets which could slide up and down the fingerboard, perhaps in grooves. At this stage the tuning system under discussion was simply the syntonic diatonic scale. Salmon’s contact with ‘eminent musicians’ in London was evidently already begun: see pp. 23–6 for a discussion. Some had apparently agreed to try out (in some sense) his ‘harmonicall canon’; whatever form that trial took, the results cannot have been discouraging, since Salmon’s ideas about tuning would be printed less than two years later.

44

Figure 1.1

Thomas Salmon: Writings on Music

Salmon’s letter to John Wallis, December 1865. Bodleian Library, MS Eng. Lett. C 130, fol. 27r. Reproduced by permission of the Bodleian Library, University of Oxford.

Correspondence with John Wallis (1685–6)

45

Letter 1 [fol. 28v]a To the Reverend Dr Wallis at his house   in     Oxfordb [fol. 27r]  

Mepsall Decemb[er] 31. 1685

Honoured Sir I have long agoe received your letters & my papers; and should bee very much at a loss for an excuse, why I have no sooner made an acknowledgment of your care & trouble, but that in reality I thought better to stay, till I had something more to begg an information of, than only to confess my obligations for what you had already communicated. I have no thoughts of proposing or publishing any thing, till I find some practicall success in what I have already done; for except wee can introduce the expression of purer proportions into our performances, the study of them may bee pleasant, but it cannot bee usefull. I have therefore rectified my Harmonicall Canon1 the third time (which, if it had not been out of shame for having so c often alter’d, I had now sent you) and thence calculated, where the frets upon every key2 must bee most properly situated: This I have left in the hands of some of the most eminent Musicans in London to make triall of, & to see what agreement there is between their practise & my reasons.3 For the matter of fact is undeniable; every good master upon the change of his key, moves his frets some higher, some lower; if therefore mine bee sett out beforehand, it saves much of the trouble, & puts it into the capacity of the meanest learners. Wee4 are already agreed upon some phænomena: viz, that the treble of the viol ‹D la sol re› must bee tuned d not a true fourth to A la mi re the second string ‹but a little sharper›;5 & my reason took place, because there were two major tones in it, insteed of a major & minor Tone with the Hemitone:6 wee are also agreed that the third fret under the Sixth string must incline to the nut, because from D to F, the string open to the said fret, is not a true lesser third, but a minor tone & an Hemitone[.]7 Though this ‹& other things› doee very much t’wards rectifying an

a   i.e. the outside of the original wrapper. The address is written sideways across the page. b   There follows an only partly legible annotation in what may be a different hand: Chr[d?]ec 4. c   Deleted: man[y]. d   Deleted: a true fourt[h]. e   Altered from: does.

Thomas Salmon: Writings on Music

46

instrument, yet it must bee confess[’d]a that there cannot bee a perfect accomodation because of the different b ‹demands of› Major Tones & Minor Tones upon the same fret: Yet setting the Key exactly right, and taking care of the principall cords to the Key, makes it quite another thing, than when all is left at randome. Thus much for the present. But I would have a fingerboard made for every Key; & I am of the opinion, when the ancients plaid upon different Keys or Modes, they had different pipes & instruments; if this were true in them, or however if wee do it, c every note shall bee rendred in the utmost perfection. I know the adapted scale8 took no notice of the mathematicall proportions, but I don’t doubt, if the ancientd Musitians e had as good ears as the modern,f they did observ them practically. Mr Peasable the best player of a Base in London9 uses no frets, his hand is more unsteady, his only advantage is that Hee observs the Major & Minor Tones by the direction of ‹an› excellent ear.10 Thus the frets must bee crooked, but the ear will direct the finger into the notch:11 I dont fear but if I can get a Mechanick to make mee a sett of fingerboards, to bee taken off & put on according to occasion, I shall perform the Musick more perfect & with better assurance, than any violin does. I would fain proceed to a tuning & fingerboard for the genuine Chromatick Musick, by an adapted scale in that sort of Musick:12 I don’t know what success I shall have, because since the restoration of Musick,13 there has been nothing designed in such a Key, as to have g the third from it, two intervals of two Hemitones, & then [fol. 27v] the Fourth gradually ascending by the intervall of a Semiditonus &c14 but I am sure by my canonicall way I shall express the same sounds, & as pure, as they did. when I have thus prepared my materials,h I must gett the help of some Practicall composer to give form & air to them; for I reckon the experiment will bee contemnd except it has also the life of the modern Musick: If you meet with any thing that may either correct or direct mee in this designe, I shall acknowledge your assistance, as I have ever done.15 But one thing I must entreat an account of from you, which I know not how to come at, except you please to undertake the trouble of informing mee: It is the reason of the Arithmeticall operations in Gassendus’s introduction to speculative Musick:16 I have much occasion to add and subduct intervals; this is i very evident to mee when I measure my strings geometrically, but if I go to do it by his way of numbers, multiplying the greater by the greater, the lesser by the lesser, for addition; then multiplying the greater by the lesser for subduction, &c I find it always come right, but I cannot see the reason of it, nor does Hee attempt to give it.17 I have revieued the a

    c   d   e   f   g   h   i   b

Edge of paper is damaged. Deleted: ?aforement[ioned]. Deleted: ?if. Altered from: antients. Deleted: ?had. Altered from: moderns. Deleted: ?three. Altered from: materiall. Illegible deletion.

Correspondence with John Wallis (1685–6)

47

Epigram before Bacchius,18 from whence I think it plain, that Dionisius lived in the time of Constantine, but Bacchius before him; At the beginning of it Bacchius is said to have discoursed of Tones, Modes &c then Τούτῳ συνῳδὰ Διονύσιος γράφων,a Dionisius writing things consentaneous to him sets forth Constantine as a Lover of Musick. So that Bacchius seems to bee some renowned foregoing Author, & very probably the Father of Justine the eminent Martyr & Philosopher. Thus, Sir, having begg’d pardon for so frequently19 troubling you I have nothing more at present, but ‹to present› my most humble servise to your Lady & family, remaining Y[ou]r Most Obliged & Faithfull Servant Thomas Salmon. Letter 2 [fol. 28r]b For Mr Thomas Salmon, of Mepsal, to be left with Mr John Hos.c on d snow-hill, London.20 Oxford Jan. 7. 1685/6. Sir, Yours of December 31. I received this morning. To play all Keys on the same finger-board, so as to have all the proportions exact; is not to be done without movable Frets. As I signified in my last. If for every Key, & every pitch, you have different finger-boards; it may be done. Or, without this, if you have movable frets, to slide up & down; not allways to go quite cross, from side to side; but, for every string; its own. which may be directed by lines drawn with ink, in their proper places, to shew where, in each case, the fret is to be sett.21 The case of Bacchêus may, for ought I know be as you say. But then he must be a great deal elder then Constantines hand.e As to that of Gassendus; f the Book is not at hand, & so I canot speak dire[ct]lyg to it. But, as to the thing itself, it is easy. what they commonly ca[ll]h the Addition of Proportions (& so, of Intervals,) is indeed a work of Multiplication; & what they call Subduction, is Division. If AD be the double of AB, a

    c   d   e   f   g   h   b

Initial gamma altered from an illegible earlier state. i.e. the inside of the wrapper of Salmon’s letter. An illegible letter follows Hos., perhaps indicating either Hoskins or Hosier. Illegible deletion. This word is practically illegible. Deleted: ?I. Paper is damaged. Paper is damaged.

Thomas Salmon: Writings on Music

48

(and therefore an Eighth22 to it) and AF the like to AD; then is AF the double of the double (that is, the Quadruple) of AB. (which is expressed by multiplying the Exponents or Denominators23 of such proportions; 2 × 2 = 4. two multiplyed by two is equal to four; or, the double of the double is the Quadruple.) If AH be the Double of AE, & this the Triple of AB; then is AH the Double of the Triple (that is, the sextuple) of AB. (That is, 3 × 2 = 6, or 3/1 × 2/1 = 6/1.) If AC be the sesquialter of AB, a (or as 3 to 2:) b and AD the sesquitertian of AC (or as 4 to 3:) then is AD the sesquitertian of the sesquialter, of AB; 4/3 × 3/2 = 2. That is, c four thirds of three halves of AB; that is, the double of AB. (which is the same as when we say, in the musicians language, If AC be a fifth to AB, and AD a fourth of AC; then is AD an Eighth to AB; for a Fifth and a Fourth, makes an Eighth; because 4/3 × 3/2 = 2.) Contrarywise, if ‹from› our Eighth we take a Fourth, there remains a Fift[h]; or if we take a fifth, there remains a Fourth. That is, if 2 = 4/3 × 3/2 be divided by 4/3, the Quotient is 3/2; If divided by 3/2, the Quotient is 4/3[:] /3 × 3/2 = 3 × 4/2 × 3 = 2.d /3 ) 4/3 × 3/2 ( 3/2. 3 /2 ) 4/3 × [3/2]e ( 4/3.24 4 4

Now, in common Arithmetick, in the Multiplication of Fractions, we are to multiply the Numerator by the Numerator, & the Denominator25 by the Denominator. /3 × 3/2 = 4 × 3/3 × 2 = 12/6 = 2.

4

But, in Division of Fractions, we are to multiply the denominator by the Numerator, & the Numerator by the Denominator.26 4

/3 ) 2/1 ( 3 × 2/4 × 1 = 6/4 = 3/2f /2 ) 2/1 ( 2 × 2/3 × 1 = 4/3

3

This, I hope, may suffice to satisfy your demand, from Sir your friend to serve you John Wallis.   Deleted: and.   Illegible deletion. c   Deleted: 4. d   Line breaks are editorial. In this first equation the second element seems to have been altered from 3/2 × 4/3. e   Paper is damaged. f   Line break is editorial. a

b

Correspondence with John Wallis (1685–6)

49

Notes 1 This ‘Harmonicall Canon’ (κανον) might have been a rule marked with the positions of different pitches, with or without the actual monochord to which such a device notionally referred; or it might have been a mathematical description of the musical scale in textual form. Equally, ‘rectified’ could refer to an experimental or a purely computational (or geometrical) process. 2 Key: i.e. keynote. 3 ‘Reasons’ might mean ‘ratiocinations’, but the meaning ‘ratios’ was not unknown, and seems more likely here. The ‘eminent Musicians’ referred to here cannot be identified with certainty, but it seems fair to imagine that they included James Paisible, mentioned in this letter, and perhaps Frederick William Steffkin. See pp. 25–6 on Paisible, and pp. 23–4 on Frederick Steffkin. 4 Wee: i.e. Salmon and the ‘eminent musicians’. 5 This observation would become a different and more precise precept about the tuning of and placement of the frets for the note D in the Proposal (at p. 22), where the practical observation was linked to ‘Old Mr. Theodore Stefkins (though he knew not the Mathematical reason)’. Steffkin had been dead since 1673. The more general issue of the exact size of the fourth between adjacent strings recurred in ‘The Use of the Musical Canon’, fol. 36r–36v. 6 Salmon was thinking of a white-note syntonic diatonic scale; he would propose two slightly different forms of this scale in his later writings (see the Introduction, pp. 12– 13). Salmon’s statement that the interval A–D is larger than a pure perfect fourth implies that he was thinking of the form of the scale (the ‘C’ form) in which C–D is a major, not a minor tone. 7 In the ‘C’ form of the white-note syntonic diatonic scale, D–F is smaller than a true minor third because it contains not a major but a minor tone in addition to a diatonic semitone. For a more precise discussion of the position of the third fret on the sixth string see ‘The Use of the Musical Canon’, fol. 36r. 8 I have not traced the source of the phrase ‘adapted scale’, which does not occur in Wallis’s published or manuscript musical writings but was apparently supposed to be understood by him. The context here and in its next use suggests that it referred to a general class of practical approximations which could replace both diatonic (as here) and chromatic scales: thus, perhaps, equal divisions of the octave, here into 12. 9 See the Introduction, pp. 25–6, on James Paisible. 10 Nowhere did Salmon return explicitly to this alleged observation (which would constitute relatively rare evidence for the use of the syntonic diatonic scale in early modern musical practice) or elaborate on how it was made: by measuring the positions of Paisible’s fingers on his instrument? By matching the pitches he produced with those on an experimental instrument? Its echo may perhaps be discerned in Salmon’s later assertion about the potential of unfretted instruments for producing mathematically excellent harmony: see ‘The Division of a Monochord’, fol. 8r. See also the Introduction, pp. 12–14. 11 The notch: i.e. the proper position. It seems very doubtful that word was intended to have its literal sense of a groove or indentation, which surely would have caused problems for stopping the string properly. 12 See note 8 above; here an ‘adapted scale’ might mean an equal division of the octave into 24 parts.

50

Thomas Salmon: Writings on Music

13 Salmon would later refer to ‘Guido restoring Musick’ (‘The Practicall Theory’, fol. 4v); he quite probably, therefore, meant to allude to the invention of staff notation in the early eleventh century. 14 This is a garbled description of the chromatic genus of ancient Greek harmonic practice, in which the intervals forming the tetrachord were, in modern terms, roughly a minor third (Salmon’s ‘semiditonus’) and two semitones. 15 Salmon’s acknowledgement of Wallis’s contribution in his published works prior to this date amounted to no more than the remark in Vindication (p. 10) that it was he who had introduced him to the rudiments of musical mathematics. 16 Salmon would give the same reference more fully in ‘The theory of musick reduced’, p. 2076: Pierre Gassendi, Manuductio ad theoriam seu partem speculativam musicae, in his Opera omnia (6 vols, Lyon, 1658, facs. edn Stuttgart, 1964), vol. 5, pp. 633–58, at p. 635. 17 See pp. 2–3 on the implications of this passage for Salmon’s mathematical competence. 18 Salmon referred to the unattributed Greek epigram at the end of Marcus Meibom’s brief preface to Bacchius in his Antiquæ musicæ auctores septem (Amsterdam, 1652), fol. *2v, of which lines 3–5 read: Τούτῳ συνῳδὰ διονύσιος γράφων / Τὸν παμμέγιστον δεσπότὐν κωνσταντίνον / Σοφὸν ἐραστὴν δείκνυσι τεχνημάτων. Edmund Chilmead discussed the identity of Dionysius in Αρατου Σολεως Φαινόμηνα καὶ Διοσημεῖα. Θεωνος Σχόλια. … Accesserunt annotationes in Eratosthenem et Hymnos Dionysii (Oxford, 1672), pp. 52–3, and it seems to be implied that Salmon and Wallis had previously been discussing the identities and dates of the individuals mentioned there. 19 If ‘so frequently’ seems to imply a large volume of correspondence, it must be read in conjunction with the earlier statement that Salmon had been slow to reply to Wallis’s previous letter. 20 See p. 43 above. 21 This description of ‘lines drawn with ink’ should be compared with the elaborate system of lines showing fret positions described in ‘The Use of the Musical Canon’: see Figure 2.2 on p. 73. 22 An Eighth: i.e. producing a pitch an octave below. 23 The ‘denominator’ of a ratio is, here, its fractional or numerical equivalent: thus the denominator of the ratio 2 : 1 is 2/1 or 2; that of 1 : 2 would be 1/2. 24 In modern notation (4/3 × 3/2) ÷ 4/3 = 3/2 and (4/3 × 3/2) ÷ 3/2 = 4/3. 25 Here ‘denominator’ has its modern meaning: the first or upper element of a fraction. 26 In modern notation: 2/1 ÷ 4/3 = (3 × 2) ÷ (4 × 1) = 6/4 = 3/2, and 2/1 ÷ 3/2 = (2 × 2) ÷ (3 × 1) = 4/3.

Chapter 2

‘The Use of the Musical Canon’ (?1686–8) Editorial Note Bound with the Bodleian Library’s copy of the pamphlet ‘The Musicall Compass’ (see p. 12), in MS Mus. Sch. d375*, appears a manuscript text with the title ‘The Use of the Musical Canon’. This is an elusive text, but it bears an unmistakable relationship with Thomas Salmon’s musical ideas, and seems to me best understood as a product of the period of work which also resulted in the Proposal of 1688. The text falls into three parts: the first discusses the construction and properties of the scale and the second the detailed placement of frets on a viol with a separate set of frets for each string, while the third provides, in detail, compromise sets of frets for various keynotes, in each of which a single set of frets governs all six strings. The chromatic scale under discussion throughout is the one Salmon would describe in his writings of 1702–5: distinct from Wallis’s form of the scale, and espoused by no other writer, as far as I know (see pp. 12–14). The two-sided discussion of the placement of frets on a viol under, first, the assumption that a separate set of frets can be provided for each string, and, second, under the different assumption that a single set of frets must govern all six strings, strongly recalls the Proposal, although this text goes into very much more detail. In particular, it gives much more detailed justifications for the choices of fret positions, displaying much more explicit manipulation of mathematical ratios than we see elsewhere in Salmon’s writings. Three features point to the possibility that John Wallis played a part in the genesis of the text. The style in which musical fractions are written (‘4/3’ rather than ‘3/4’, ‘4 to 3’ or ‘three quarters’), hardly ever seen in Salmon’s other work, is that of Wallis’s letter to him in 1686.1 An initial description of experimental work with a monochord, verifying the correspondence of intervals with ratios, adopts a sequence of operations broadly similar to what was carried out by the Royal Society in 1664. And the text relies heavily on a diagram, missing from our manuscript but described in detail, involving lines of various different types – ‘pricked’, solid, or formed of crosses – to indicate the different possible positions for each fret. This could well reflect Wallis’s suggestion in his both letter of 1686 and his ‘Remarks’ on Salmon’s Proposal of the use of a system of lines to show the possible positions for a set of individually moveable frets. This text, then, embodies ideas which seem substantially to be Salmon’s, but contains what may well be specific contributions from Wallis. The evidence seems consistent with the possibility that this was the text on which Salmon was working, with Wallis’s advice and possibly his collaboration, at the time of their correspondence

52

Thomas Salmon: Writings on Music

in the winter of 1685–6. It also seems consistent with the idea that this text or something very like it was the subject of Salmon’s allusion to ‘demonstrations I rely upon’ which he had deliberately omitted from the Proposal; perhaps this was the ‘arithmetical’ or the ‘geometrical’ ‘part of music’ which he claimed at the end of that book to have ready to communicate. I believe, therefore, that it makes sense to consider this text a predecessor or to some extent a companion to the Proposal, a work dating from 1686–8 and containing the mathematical details and complexities which underlay the relatively simplified proposal Salmon made in print. The single manuscript copy of the text which we have is in a hand (see Figure 2.1) which Margaret Crum identified as that of James Sherard (1666– 1738).2 Sherard worked for most of his life as an apothecary, retiring, apparently a wealthy man, in about 1720 to take up botany. He became a Fellow of the Royal Society in December 1706.3 He took an active interest in music until roughly 1711, as an amateur violinist and composer, a ‘collector of prints and manuscripts acquired in Italy and Germany as well as the copyist of music by Corelli, Bassani, Finger, Grecke and others’.4 He published two collections of trio sonatas in 1701 and 1711. Items from his music library, and some in his hand, are now to be found in the Bodleian Library, having passed – according to Crum – through the hands of Richard Rawlinson after the death of Sherard’s widow in 1741; the present manuscript volume is apparently an example.5 We know that at least from 1702 Salmon took his ideas about tuning in a somewhat different direction from that represented in this text (see Chapters 4–7), making it less likely he would have allowed it to be copied. Sherard probably therefore made his copy of ‘The Use of the Musical Canon’ either before about 1702, or after Salmon’s death. In the first case it would be evidence for contact between Salmon and Sherard, and evidence that Salmon was prepared to countenance the circulation of this text despite its unfinished state (see p. 3). In the second case it would be evidence for the posthumous circulation of some portion of Salmon’s manuscripts to at least one Fellow of the Royal Society. I do not think that either possibility can be ruled out using the evidence we have. ‘The Use of the Musical Canon’ occupies fols 32r–40r of the volume in which it appears, and ‘The Musicall Compass’ fols 28r–31r. Fols 27 and 40 comprise a single sheet and were apparently at one stage the wrapper for both of the two items: fol. 40r contains the final portion of text for ‘The Use of the Musical Canon’, while a rough manuscript copy of one of the diagrams from the ‘Compass’ is drawn on fol. 27r. All of these leaves measure approximately 185mm × 245 mm; they form gatherings of two leaves each, apart from the first four leaves of ‘The Use of the Musical Canon’ (fols 32–5), which form one gathering. The whole has been bound together with a quantity of blank paper of a slightly larger size – 28 sheets at the front of the volume and 28 at the back,6 presumably with the intention of later copying further material onto it; Crum dates the binding to the period of Rawlinson’s ownership of the volume, that is the 1740s or 1750s.7 Parts of the manuscript text are all but concealed by the binding. Incorporated as the volume’s outer wrapper, attached to the outside of

‘The Use of the Musical Canon’ (?1686–8)

53

the endboards, is a copy of the will of one Thomas Rivolin or Ravolyn (the name appears twice with different spellings), whom I cannot identify.8 The manuscript text is quite neat, and contains very few deletions or alterations. The text on the first 12 sides (to fol. 37v) is divided into four numbered sections (the fourth is wrongly labelled ‘III’), with numerous marginal headings, some catchwords (on fols 33r, 35r, 35v, 36r and 36v), and page numeration in ink. It ends at the bottom of a page, with the word ‘Finis’. Fols 38r–39v (a complete gathering) look like a second, more condensed, version of the fourth section of the text, with a different style of headings, and no numeration or catchwords. The material on fol. 40r (the rear part of the wrapper) has no earlier parallel, and seems like a continuation of the text, an unnumbered section V. The implication seems to be that Salmon had made more than one draft of this text, and that his original intention to end it where the present fol. 37v ends was later superseded. (The sections of material on fols 38r–39v and on fol. 40r could possibly be Sherard’s own prècis of the preceding section and his further deductions about the scale under discussion, but this would require of him a high, perhaps an improbably high, level of confidence in dealing with this mathematical material.) Perhaps Sherard had access to a somewhat complex, if not necessarily a particularly large, set of Salmon’s manuscripts, and perhaps he was copying without Salmon’s guidance. This may lend weight to the possibility that this text was copied after Salmon’s death, but I am not sure that we can make any more positive deduction from these features of this manuscript. It will be evident that this is not an easy text to interpret, and that the remarks made here are somewhat tentative in character. Sherard’s activities as a music collector and copyist have not yet been exhaustively studied, and it is quite possible that further study will shed rather more light on ‘The Use of the Musical Canon’ and its importance for Salmon’s work and reputation. Notes 1 ‘The Division of a Monochord’ and ‘The theory of musick reduced’ both style musical fractions ‘3/4’, while the Proposal and ‘The Practicall Theory’ very largely avoid fraction notation, the former speaking of, for example, ‘9ths’ of a string, and the latter using the ratio terminology ‘4 to 3’. 2 See Jessie Ann Owens, ‘“el foglio rigato” Revisited: prepared paper in musical composition’, in M. Jennifer Bloxam, Gioia Filocamo, and Leofranc HolfordStrevens (eds), Uno gentile et subtile ingenio: studies in Renaissance music in honour of Bonnie J. Blackburn (Brepols, 2009), pp. 53–61, at p. 58 with note 27, citing an unpublished typescript of Margaret Crum, ‘James Sherard and the Oxford Music School Collection’ (1982), in the Bodleian’s music collection. Owens (personal communcation) has confirmed Crum’s identification by comparing it with letters from Sherard to Richardson of 1716–18 in MS Radcliffe Trust c. 3. 3 See W.W. Webb, rev. Scott Mandelbrote, ‘Sherard, James (1666–1738), apothecary and botanist’, in ODNB; Michael Tilmouth and Robert Thompson, ‘Sherard, James’,

54

4 5 6

7 8

Thomas Salmon: Writings on Music in Grove Music Online; and ‘List of Fellows of the Royal Society 1660–2007’: http:// royalsociety.org/WorkArea/DownloadAsset.aspx?id=429497281. ‘Some of Crum’s discoveries about Sherard are summarized’ in the Grove entry, according to Owens: ‘“el foglio rigato” Revisited’, p. 57, n. 25. Owens, ‘“el foglio rigato” Revisited’, p. 58, n. 28. Owens, ‘“el foglio rigato” Revisited’, n. 27. Two of these are pasted to the front endboard and one to the rear, and are therefore not numbered in the foliation used here; some of those at the front and all of those at the back, folded in quarto fashion, are uncut; each set of 28 leaves forms a single gathering. Owens, ‘“el foglio rigato” Revisited’, p. 58, n. 27. One of the will’s witnesses seems to have been a ‘Will Brereton’: possibly William, third Baron Brereton of Leighlin (1631–80), one of the original Fellows of the Royal Society and a member of the music committee the Society set up in April 1662 to examine work by John Birchensha (Salmon’s composition teacher). See Volume I, pp. 8–9 above and Christopher D.S. Field and Benjamin Wardhaugh (eds), John Birchensha: writings on music (Farnham, 2009), p. 12, n. 37. The other witnesses are Tho[mas] Wood, [?Alice] Wood, and Fran[…] W[…]; the last could be William Brereton’s wife Frances Willoughby (see Anita McConnell, ‘Brereton, William, third Baron Brereton of Leighlin’, in ODNB).

‘The Use of the Musical Canon’ (?1686–8)

Figure 2.1

The first page of ‘The Use of the Musical Canon’. Bodleian Library, MS Mus. Sch. d375*, fol. 32r. Reproduced by permission of the Bodleian Library, University of Oxford.

55

Thomas Salmon: Writings on Music

56

Text [fol. 32r]

The use of the Musical Canon. 1 By dividing & setting forth the proportion of every interval upon the Monochord. The Octave.a The Monochord being divided into two equal parts, so that the whole open is compared to half of it stopt, gives the Sound of an Octave, which is always the proportion of 2 to 1.1 The Fifth. The Monochord being divided into three equal parts, so that the whole open (supposed to consist of the said three parts) is compared to two parts, from the Stop to the bridge, gives a Fifth, which (if true)2 is always the proportion of 3 to 2. The Fourth. The Monochord being divided into four equal parts, so that the whole open (supposed to consist of the said four parts) is compared to three parts, from the Stop to the bridge, gives a Fourth, which (if true) is always the proportion of 4 to 3. All the rest of the Intervalls used in Diatonick Musick. The Monochord likewise being divided into five equal parts, does, compared with four of them, give a greater third, which is as 5 to 4. So a lesser Third is as 6 to 5. A Major Tone as 9 to 8. A Minor Tone as 10 to 9. A Hemitone as 16 to 15. The generation of Intervals now used. These Intervals are all generated by dividing the Octave sound, or duple proportion, & it’s progeny into those two parts, which their doubled numbers give, & the figure that comes between them in Arithmetical order, setts forth. a

  Heading appears in the margin; so do similar headings until fol. 37r.

‘The Use of the Musical Canon’ (?1686–8)

57

An Octave divided into a Fifth & a Fourth. So 2 compared to 1, in double numbers are 4 to 2, the figure between them is 3; So the duple proportion is divided into 3 compared to 2, and 4 compared to 3: that is in practise, an Octave is divided into a Fifth and a Fourth. A Fifth divided into a Greater & a Lesser Third. So 3 compared to 2, the proportion of a Fifth, in doubled numbers are 6 to 4, the Figure between them is 5; so this proportion [fol. 32v] is divided into 5 compared to 4, & 6 compared to 5: That is in practise, a Fifth is divided into a Greater & Lesser Third. A Greater Third into a Major Tone & Minor Tone. So 5 compared to 4, the proportion of a Greater Third, in doubld numbers are 10 to 8, the figure between them is 9; So this proportion is divided into 9 compared to 8, and 10 compared to 9: that is in Practise a Greater Third is divided into a Major Tone & Minor Tone. The Hemitone is most easily found by Geometrical Addition. The Hemitone is that proportion, which makes a Major Tone become a Lesser Third, & a Major Third become a Fourth, most easily found by measuring, what proportion upon the Monochord remains for compleating either of those two proportions; & this always is 16 compared to 15.3 So that these Major Tones, Minor Tones, & Hemitones are the Lowest constitutive parts4 of an Octave.

II. By orderly placing the Tones & Hemitones upon the Monochord, so as they may best constitute the Intervals of Musick, does the use of this Canon appear. The particulars just contained in an Octave. It is proved by experience & must be granted, that three Major Tones, two Minor Tones, & two Hemitones added together reach just to the middle of the Monochord; & consequently make up an exact Octave or duple proportion.5 The proper train of particular Notes in an Octave. Which being true in General, there must be a particular order or train of them, so as may best serve for the uses of Practical Musick, that we may most

58

Thomas Salmon: Writings on Music

conveniently come at every chord, in that place especially, where the Composer principally designs it. The two different dispositions of the Octave. The Composer first designes his Key; which may be considered, as the disposition of his Octave, or as the Pitch of his Musick, from the Key note. We will now insist upon the Disposition of the Octave, & afterwards upon the several Keys as they are only alterations of the Pitch. [fol. 33r] There are but two different dispositions of the Octave now in use. 1 The movable intervals when greater. 1 A Greater Third, Sixth, & Seventh; then the order of the intervals must be as if all stood Natural in C Fa ut. viz C Tone Major D, D Tone Minor E, E Hemitone F, F Tone Major G, G Tone Minor A, A Tone Major B, B Hemitone C. 2 The movable intervals when Lesser. 2 A Lesser Third, Sixth, & Seventh, then the order of the intervals must be, as if all stood Natural in A re: viz, A Tone Major B, B Hemitone C, C Tone Minor D, D Tone Major E, E Hemitone F, F Tone Major G, G Tone Minor A. One variation in assigning the proportions to the Letters. Where the only difference in assigning the Proportions of the intervals to the Letters in these two differently disposed Octaves, is, between C & D, D & E; when there is a greater Third, then from C Tone Major D, D Tone Minor E; when there is a Lesser Third, then from C Tone Minor D, D Tone Major E.6 And the Reason is, because the Division of a Monochord will not allow that two Major Tones should be in the interval of a Fourth, as would fall out; if in A Tone Major B, B Hemitone C, C Tone Major D, which reaches below the fifth Fret. Each interval falls conveniently by the way, & the Octave is consummated in the exact middle of the String. But orderly placing the Tones & Hemitones upon the Monochord according to these two dispositions of the Octave, you will not only arrive at an exact duple proportion in the middle of the String; but by the way fall exactly upon every interval the Key requires. This demonstration upon a Monochord most easily discovers the Nature of Musick; but the practice of it upon several strings & frets, requires that we should proceed to shew how each of them may obtain a just assignation.

‘The Use of the Musical Canon’ (?1686–8)

59

III. By orderly placing the Tones & Hemitones according to the two different dispositions of the Octave from the Pitch of any Key, upon what String or fret soever it be placed. The two Monochords set forth the two dispositions of a Octave in C fa ut & A re. Were we to play only upon a Monochord, & the String open to be always the Key, ’twere already sufficiently delineated upon the Canon; the C fa ut string determines all the intervals when there is a Greater Third, Sixth, & Seaventh: The A re [fol. 33v] string determines these intervals when they are Lesser; The Second, Fourth, Fifth, & Eighth, standing the same in both.7 How the proportions are placed upon instruments of many Strings. But since we use many Strings, & tune them unisons to the third, fourth, or fifth fret of the foregoing,8 we run not up to the middle of the String to make eight notes, as the Monochord does, but pass on to the next string so soon as we find it unison to some stop of its predecessor: & therefore tis requisite to know how to place each Fret, when the String open begins upon any interval in the two differently disposed Octaves. An account what the frets may at any time serve for. This shall be set forth, 1 By giving an account of the Frets in general; 2, With respect to each particular key. The use of the first fret. The first fret consist[s] in general of three strokes,9 the uppermost stroke of points drawn three quarters through is the Minor Hemitone; the second of Points drawn quite through is the Major Hemitone (for if we have Major Tones & Minor Tones, we must have Major Hemitones & Minor Hemitones, it being impossible that half a greater thing, & half a lesser thing should be of the same size)10 the 3rd stroke is black, and but half way over, denoting the a Hemitone, eminently so called, because ’tis self subsistent, & makes a compleat step in an Octave; Not as being half a Tone but much less then a Tone, & vulgarly denominated a Hemitone, yet Diatonick. The use of this first fret then is thus; When you have computed from your key, what place in the Octave your string open is, you must consider what interval you are next to rise to from the string open; if to a Minor Tone, then take the first stroke as the Minor Hemitone, & best mediation to it; if to a Major Tone, then take the second stroke as the Major Hemitone, & best mediation to it;11 if you are to rise   Deleted: Diatonick.

a

60

Thomas Salmon: Writings on Music

the Diatonick Hemitone, that is the black line. One of these it must be, & thus may you know which is required. [fol. 34r] The use of the 2nd fret. The 2nd fret consists also of three strokes; the first black & three quarters through, determines the Minor Tone; which if the Octave requires there to be from the string open, the fret must be placed upon it: but if the Octave requires a Major Tone; you must take the second stroke, black & quite through: if you went before but to the Diatonick Hemitone upon the first fret, now you must go to the stroke of points drawn half way; which is a Major Hemitone from the foresaid Hemitone, & the best mediation from thence as you are rising to the following Major Tone.12 This is all that can fall out upon the second fret. The use of the 3rd fret. The 3rd fret consists also of three strokes, the two uppermost of points, being the two differing Hemitones rising from those two different Tones, which were compleated upon the foregoing 2nd fret. The first stroke of Points quite through is the Major Hemitone, being the best mediation from the compleated Minor Tone to the next Major Tone to which the Octave proceeds; the 2nd stroke of Points three quarters through is the Minor Hemitone, being the best Mediation from the compleat Major Tone to the next Minor Tone, to which the Octave proceeds: for if from the string open, the Octave proceeds to a greater Third, it must be one of these two ways.13 But if the Octave does require that you make a lesser third upon this fret, then the Hemitone above the Minor Tone falls upon the black in the Stroke of Points;14 but the Hemitone above the Major Tone (which is the true Lesser third) falls upon the whole black stroke. This is all the Variety that can fall upon the 3rd fret. The use of the 4th Fret. The 4th Fret consists but of two strokes, the uppermost all black, & compleats the two Tones, (whether the Major or Minor come first or last) that they become a greater Third: And here the Fret must always stand, if the disposition of the Octave requir’d a greater Third, or two [fol. 34v] Tones from the string open. The under stroke of Points is in case you were to compleat a Lesser Third upon the foregoing Fret, which will in course by a Minor Tone proceed to a Fourth; this therefore is the Minor Hemitone (set forth by a stroke of points three quarters through) the best Mediation to the Minor Tone where the Fourth is compleated.15 Which is all the usefull variety that can fall out upon this 4th Fret.

‘The Use of the Musical Canon’ (?1686–8)

61

The use of the 5th Fret. The 5th Fret consists of one black stroke quite through; because the Fourth is there compleated by what way soever you came to it: and there is but one occasion for any other position of the Fret; which is, when from a Le[ss]a third upon the 3rd Fret you would rise a Major Tone; & for this you have the place marked with a black quarter stroke.16 The use of the 6th Fret. The 6th fret consists of two strokes, the uppermost of little Crosses, which is a Tritonus to the string open: the under stroke of Points is the Major Hemitone, the best mediation from a Fourth to a Fifth. Nor can there be any other use for this Fret between the 5th & 7th frets, but one of these two assigned.17 The use of the 7th Fret. The 7th Fret consists chiefly of one black stroke quite through, because we usually expect it should be a true Fifth to the string open, which is there determined. Though a Minor tone from the Fourth would make it fall short; And the NoteTuning is in danger of such an accident: so that it is accordingly marked with another black stroke a quarter through.18 Direction for beyond the 7th Fret. These Seven Frets are all that are used upon the Viol; but when we have occasion to go beyond them, or to play upon the Lute & Gittar, which have more, these following directions will prove a Sufficient guidance. If above the Fifth our Octave is disposed for a greate[r]b Sixth & Seaventh, We have them marked upon the Monochord C; if a Lesser Sixth & Seaventh, they a[re]c set out upon the Monochord A: and their Major and Minor Hemitones, are the exact middle of the Major & Minor Tones.19 [fol. 35r] All concludes with one black stroke ‹just› in the middle of the two Monochords, where the perfect Octave ever falls; as being the ‹duple› d proportion to the String open.

a

    c   d   b

Binding is tight. Binding is tight. Binding is tight. Deleted: ?double.

Thomas Salmon: Writings on Music

62

III. By accommodating the Frets measured from the Canon, to each disposition of the Octave in every Pitch. The Note-tuning upon the Viol chosen for describing the proportions. For demonstrating this, we will take the common Note-tuning20 upon the Viol & see how the intervals must be disposed from the C fa ut key; where all the Notes are assigned to their Letters in the Natural position: That this may be the first instance of an Octave with a greater Third, Sixth, & Seaventh; & then see what Alteration will happen, when we remove this Octave into another Pitch. C fa ut key, where the g[rea]ter intervals are in their Natural position. The Fourth string is C fa ut open, then a Major Tone to D sol re, requires the second fret upon the black stroke which goes quite through: Then a Minor Tone to E la mi falls true upon the through black stroke of the 4th Fret, which is a true greater Third, & unison to the Third string open; we therefore now remove to that String open, & from thence to F fa ut is the Diatonick Hemitone, which requires the first fret to be upon the black stroke that goes half way: Then a Major Tone to G Sol re ut requires the 3rd Fret upon the black line which goes quite through, becausea that must be a true lesser third to the String open: Then to A la mi re a Minor Tone, which places the fifth fret upon the Through black line, being a true Fourth to the String open, & unison to the second String; we therefore now remove to that, & from thence to B fa b mi is a Major Tone, requiring the second fret upon the black stroke – quite through, as D Sol re before did; Then to C sol fa ut is the Diatonick Hemitone which requires the third fret upon the through black stroke, being a true Lesser Third to the string A la mi re open; as G sol re ut required it in the same place being a true Lesser third, to the String E la mi open.21 [fol. 35v] An Harmonicon22 for the Voice. And thus this Octave has all it’s Notes disposed in the most absolute perfection; for nothing can be more exact then the determinations of Arithmetick & Geometry: here then is a most certain Guide for framing the Voice, which by the help of a good eare is capable of expressing the purest proportions. The accommodation to all the rest of the Notes. But the Viol must not be confined to single notes & the Compass of one Octave; we must therefore proceed to consider how the notes both above & below it are to   Source has beause.

a

‘The Use of the Musical Canon’ (?1686–8)

63

be placed; that so if their demands fall cross, we may accommodate the difference, as well as the Instrum[en]t & tuning will bear. The notes above the Principal Octave From C sol fa ut to D La sol re must be a Major Tone (as there was from C fa ut to D Sol re, the Octaves in the same Key being always alike disposed) which will not fall upon the through-black stroke of the 5th Fret, that being a Minor Tone from C Sol fa ut; but upon the quarter-black stroke beyond it; & to this must the Treble String be tuned unison, that D La Sol re may be a Major Tone from C sol fa ut: Then for E la mi a Minor Tone, the second fret is required to fall upon the uppermost black stroke three quarters through: Then to F fa ut a Diatonick Hemitone; which falls upon the quarter-black stroke of the third fret; because this is not a true Lesser Third to the string open, but the Diatonick Hemitone above a Minor Tone, instead of a Major Tone: Then to G sol re ut a Major Tone is a true fourth to the String open, & will be compleated upon the through-black stroke of the 5th fret: A la mi re being but a Minor Tone further, falls short upon the black Stroke a quarter-through; before it arrives at the through-black stroke, which would make the 7th fret a true fifth to the string open. Notes below the Principal Octave. On the other Side we are to take an account of the Notes below C fa ut, which we find ina unison to the Throughblack Stroke of the 5th fret upon the fifth String; from thence we [fol. 36r] pass backwards a Diatonick Hemitone to B mi, which falls right upon the through-black stroke of the 4th Fret, being a true greater Third to the string open: Then to A re a Major Tone; tis required the second fret should stand upon the uppermost black stroke three quarters-through: And so to Gamut the 5th string open, the Minor Tone will happen right.23 Gamut being tuned unison to the through-black stroke of the 5th Fret, we must go back a Major Tone to double F fa ut, which is to the quarter black stroke upon the 3rd Fret: Then to double E la mi a Diatonick Hemitone, which falls upon the three-quarter-black stroke of the 2nd fret, as A re did; from whence to double D sol re is the Minor Tone, which happens right from the foresaid stop to the String open.24 The difference upon the 2nd fret determined b a Minor Tone; the first fret being a Diatonick Hemitone The different demands we have among these Notes are chiefly upon the 2nd Fret, where D sol re & B fa b mi in the principal Octave require a Major Tone from the String open; but E la mi above it, & A re, & double E la mi below it a Minor   Source has finding.   Deleted: ?to.

a

b

Thomas Salmon: Writings on Music

64

Tone from the string open: Here we consider of what importance these Chords are to the C fa ut Key; Those of the Major Tone partya are but two a Second & a Seventh; Those of the Minor Tone partyb are three, two in the State of Thirds, & one in the State of a Sixth; which last ought certainly to preponderate that we place the second fret but a Minor Tone to the String open: And hereby also we shall have further convenience, we may tune the Treble string unison to the second string where the 5th fret makes a true Fourth; for as the D sol re stop upon the fourth string draws nerer the Nut, by the difference between the Major Tone & Minor Tone; So does the D la sol re stop upon the second string draw nerer the Nut by the difference between the three quarter-black stroke & the through black Stroke upon the 5th Fret: A true Octave ever observing the same due distance between its two extremes.25 The difference upon the 3rd fret determined a Lesser Third. Another different demand we have, is upon the Third fret, where G sol re ut upon the third string being a Fifth to the key C fa ut, & C sol fa ut upon the second string being the Octave, require a true lesser third to the string open, & therefore will have the fret placed upon the through-black stroke; but F fa ut upon the Treble string & double F fa ut upon the Sixth, wanting of a true Lesser Third (as being a Diatonick Hemitone above the Minor Tone) fall upon the quarter-black stroke of the 3rd fret; but here we cannot [fol. 36v] allow that so considerable Chords as the 5th & Octave from the Key should abate any thing of their perfection, especially since F fa ut is only in the state of a Fourth, & double F fa ut may be accommodated by shoving that part of the Fret, which is under the Bass a little nerer the Nut.26 An imperfection to be made up. One other little disagreement there is, that as we ascend by single Notes, the A La mi re upon the Treble String falls short of a true Fifth upon the 7th Fret: which will be required in Consort, to be a true Octave to the second string open; therefore in this & the like Circumstances, the Player is to consult what is most his Interest.27 The Key Gamut with F fa ut Sharp. Having thus given a Large & particular instance of disposing all the proportions in C fa ut natural,28 we will remove this Octave into another Pitch, & consider how the Notes may best be ordered when they fall in other places: The first transposition shall be into Gam ut with F fa ut sharp, as requiring a greater Seventh; but we will not trace it from the Key (the manner whereof has been sufficiently demonstrated   Source has partly.   Source has partly.

a

b

‘The Use of the Musical Canon’ (?1686–8)

65

already) only consider under what Circumstances each fret lies, with respect to those demands which are made upon it. 1st Fret Chromatick. The first fret has none of the eight Notes situated upon it (F fa ut sharp falling upon the 2nd fret of the 3rd String) we have therefore liberty to express the Chromatick Musick in this place; which is by disposing this first fret upon the stroke of points quite through, the best mediation to the Major Tone upon the 2nd fret; but all the Notes of the Diatonick Octave are of such Consequence, that the Frets must be always at their Service, only here it happens that they are all absent. So that the Composer may be assured that if he make an occasional sharp out of the Key, it will be very well performed. The 2nd fret a Major Tone. The 2nd fret is required to be a Major Tone for the Sixth, Fifth, Fourth, & Third Strings; but the second & Treble Strings require a Minor Tone, wherefore the former must prevail, not only as being the greater number; but because D sol re which is a Fifth to the Gamut Key, & of the g[rea]test consequence requires the principal regard. 3rd fret a lesser Third. The 3rd fret must unquestionably stand upon the through-black stroke, because there G sol re ut, which is Octave to the Key, requires a true lesser Third open, & therefore must be in perfection, whatever other occasion there be: though therea is none very considerable. 4th Fret a greater Third. The 4th fret is unanimously required (by all the Strings that have occasion to make use of it) to be a true greater Third, So that it may be here determined without any further dispute. 5th Fret a true Fourth. The 5th fret is very much importuned by the Third, Second & Treble Strings to remove from the through-black stroke (which makes a true [fol. 37r] Fourth to the string open) to the quarter-black stroke beyond it; not only that A la mi re stopt there upon the 3rd string may be a Major Tone from G sol re ut, but that D la sol re stopt there upon the second String, & G sol re ut upon the Treble, may be in the   Source has here.

a

Thomas Salmon: Writings on Music

66

state of a true Fifth & a true Eighth to the Key: But then this may be accommodated by tuning the 2nd & Treble sharper then the unison stopt upon that fret will allow29 (the not-observing whereof usually causes the Viol to be ill tuned upon this Key) & then the 5th & Octave will be compleat by such an allowance; which is the best way, because from a Skip from that fret to the String open will be a true Fourth, as is always designed by the Composer, & expected by the Ear: So that this & the 7th Fret, had best always keep a constant situation upon the through-black strokes; The 6th fret also being designed for the best mediation between them, need never move from the through stroke of Points, except upon the design of a Tritonus in the Harmonicon for Singing; which being not to the present purpose, we will not any more examin these three frets, but leave them determined to the aforesaid, as their proper, places.30 The Key D sol re with F fa ut, & C fa ut sharp The next Key we enquire into shall be D sol re with two sharps, & there the notes of this Octave will be best accommodated in the following manner. 1st fret Chromatick. The first fret has but one note to obey, which is C fa ut sharp upon the 4th string, next before we come at the Key; which being the full distance of a Diatonick Hemitone requires this fret to withdraw towards the Nut, at least as far as the 3-quarter stroke of points;31 which falls out very well, because tis the best mediation to 2nd Fret a minor Tone. The 2nd fret, a minor tone from the string open: because D sol re the Key must have a Major Tone to E la mi, F fa ut sharp must be also a Minor Tone from thence, & B fa b mi a minor Tone to the string open, & A re a Minor Tone to the String open; all which fall upon this second fret, & so much preponderate that we must suffer E la mi upon the Treble to be imperfect, accommodating double E la mi upon the 6th Bass by inclining the fret as far as we can towards the Major Tone. 3rd Fret a false Lesser Third. The 3rd fret has but one peice of Service to perform, which is not in the usual place, but upon the greater black stroke,32 & ‹that› for the sake of G sol re ut upon the 3rd string; & there it must be a Diatonick Hemitone from F fa ut sharp, as also a Major Tone from A la mi re stopt upon the 5th Fret of the said String; or (which is all one) a Major Tone from A la mi re the second String open, for that is tuned Unison there: both which demands are satisfyed in the most perfect manner[.]

‘The Use of the Musical Canon’ (?1686–8)

67

4[th] Fret a greater Third. The 4th Fret is everywhere required to make a true third to the string open, & therefore has one undisputed determination upon the stroke quite through black. And thus are all things so well agreed, that this Key requires no further Consideration.33 [fol. 37v] F fa ut with B mi flat.a 1st Fret must be a Diaton[ic] Hemit[one] from the String open, for the situation of F fa ut, & B fa b mi flat. 2nd Fret a Min[or] Ton[e] for A re, D sol re; with a little declination towards the Major Ton[e]; for the Service of E la [mi.]b 3rd Fret a Lesser Third for F fa ut upon the Treble, C sol fa ut upon the Second, G sol re ut upon the Third: but under the Fifth Bass for B mi flat, & the Sixth Bass for F fa ut, it must incline to the quarter-black stroke. ‹All the rest must stand in the throug[h]c black strokes, to express the perfect Concords.› B mi flat with E la mi flat. 1st Fret a Diatonick Hemitone for B fa b mi, & E la mi flat. 2nd Fret a Minor Tone for D sol re; if the Practiser does not finde a Major Tone more Convenient for A re, which are all the notes that fall upon this fret & the later most desirable, because 3rd Fret is a true Lesser Third for the sake of B mi flat (which must be a true Octa[ve]d to B fa b mi) E la mi flat (therefore the foregoing fret must be a Major Tone) C sol fa ut & E la mi flat again upon the Treble. The rest perfect. Next we proceed to an Octave with the lesser 3rd, 6th, & 7th; & begin the first Example in A re Natural. 1st Fret a Diatonick Hemitone for F fa ut. 2nd Fret should be for E la mi & A re a Minor Tone, for D sol re & B mi a Major Tone; but the two former as most considerable, must prevail. 3rd Fret a Lesser Third for G sol re ut, & C sol fa ut, but F fa ut has an inclination to the black quarter-stroke. a

    c   d   b

From here onwards the headings appear centred on the line. Binding is tight. Binding is tight. Binding is tight.

Thomas Salmon: Writings on Music

68

D sol re with one flat in B mi. 1st Fret a Diatonick hemitone for F fa ut, & B fa b mi flat. 2nd Fret a Minor Tone for the Key; & A re the 4th below; though two E la mi’s are for the Major Tone, but they must be overruled. 3rd Fret a lesser Third for G sol re ut, & C sol fa ut, but F fa ut retains his former Inclinatio[n.]a,34 Gamut with two flats in B & E. 1st Fret a Diatonick Hemitone, for F fa ut, B fa b mi, & E la mi flat. 2nd Fret a Major Tone, for A re the second, & D sol re the Fifth from the Key; for in this Octave from sol to la in this place is a Major Tone. 3rd Fret a true Lesser Third.35 E la mi with one sharp in F fa ut. 1st Fret a Minor Chromatick Hemitone. 2nd Fret a Minor Tone for the Key double E la mi, for A re, & D sol re (which in this Octave a[re]b Minor Tones) for B mi & E la mi upon the Treble; none falling amiss but F fa ut sharp[.] 3rd Fret must be brought to the black quarter-stroke, because neither G sol re ut nor C sol fa ut are true Lesser Thirds to the String open.36 B mi with two sharps F, & C. 1st Fret a Minor Chrom[atic] Hemit[one] for C fa ut sharp upon the 4th String, that there may be a full Diatonick Hemitone to D sol re. 2nd Fret a Major Tone to D Sol re, that there may be but a Minor Tone to E la mi; which F fa ut sharp also requires upon the same fret, & B mi; But A re & E la mi have an inclination to the Minor Tone. 3rd Fret, G sol re ut, & C sol fa ut require to be a true Lesser Third. Finis.37 [fol. 38r]

a

  Binding is tight.   Binding is tight.

b

‘The Use of the Musical Canon’ (?1686–8)

69

Directions how to set the Frets in every different Key.38 There are ‹two› several dispositions of Octaves, with a greater Third, Sixth, & Seventh;a as in C fa ut Natural: & with a lesser Third, Sixth, & Seventh; as in A re Natural. All other Variety is only difference of Pitch. Proposing therefore Each of these as the head of his Octave, you have a Transposition of them, into one or two sharps, & into one or two Flats. The three uppermost frets need only be movable, which are here calculated39 for the Hemitones, Minor Tones, Major Tones, true or imperfect Lesser thirds as each key shall require. The four Lowermost frets had best all stand upon the through-black stroaks (except the sixth fret which is placed upon the through-stroak of Points) for these are the best & most usefull divisions of the Monochord; and have so necessary a relation to the string open that they cannot well be alterèd. C Fa ut Natural. 1st Fret, the half-black stroke, a Diatonick Hemitone for F fa ut. 2nd Fret, the three-quarter black stroak, b a Minor tone, for the two E la mi s, & A re: Though D Sol re & B fa b mi require a major tone, but the former preponderate, because they are more in number, better Chords, & then the Treble may be tuned ‹both› a true Octave to D Sol re, & a true unison to thec 5th fret of the second string: but perhaps Consort to make a good 5th upon the 2nd fret with a String open may prevail on the other side, or to make a bearing.40 [fol. 38v] 3rd Fret, the through-black stroke, a lesser Third to the string open, for G sol re ut & C sol fa ut; but double F fa u[t]d wanting the proportion of a true lesser third, from dou[ble]e D sol re, should be inclined to the quarter-black strok[e.]f, 41 Gam ut with f fa ut sharp. 1st Fret, the through stroke of points, a Major C[h]romatick Hemitone; because none of the Diatonick notes fall upon it (F fa ut sharp being upon the second fret) that here is an excellent place for a sharp note out of theg key. 2nd Fret, the through-black stroke, a Major Tone, especially to make D sol re a perfect 5th from the Key, to which we must ever have the principal regard. a

    c   d   e   f   g   b

Source has Se?e??th, with three illegible letters, perhaps altered from seaventh. Deleted: for. Illegible deletion. Binding is tight. Binding is tight. Binding is tight. Source has they.

Thomas Salmon: Writings on Music

70

3rd Fret, the through-black stroke, a lesser third for G sol re ut, an Octave to the Key; This being of such importance, that nothing can deservea an abatement of its perfection. The Second & Treble must be tuned to the quarter-black stroke of the 5th fret, that they may be a true Fifth, & Octave to D Sol re.42 D Sol re with F & C sharp. 1st Fret, the three-quarter stroke of points, for C fa ut sharp, a Major Tone from B mi, a Diatonick Hemitone to D sol re. 2nd Fret, the three-quarter black stroke, a minor tone, for all but E la mi, which must be accommodated by inclining the Fret. 3rd Fret, the quarter-black stroke, for G sol re ut, a Diatonick Hemitone from F fa ut sharp, & a Major tone to A la mi re.43 [fol. 39r] F fa ut with B mi flat. 1st Fret, half black stroke, a Diatonick Hemitone for F fa ut & B fa b mi flat. 2nd Fret, three quarter-black stroke a Minor Tone, for A re & D sol re, with a little declination towards the Major Tone for the Service of E la mi. 3rd Fret, through-black stroke, a lesser Third, for F fa ut upon the Treble, C sol fa ut upon the second, & G sol re ut upon the Third: But under the fifth Bass for B mi, & the Sixth Bass for double F fa ut it must incline to the quarter black stroke.44 B mi flat with E la mi flat. 1st Fret, the half black stroke, a Diatonick Hemitone for B fa b mi, & E la mi flat. 2nd Fret, the through-black stroke, a Major Tone for A re; except D sol re be found to prevail for a Minor Tone, then it must be the three quarter black stroke.45 The rest perfect. A re Natural. 1st Fret, the half-black stroke, a Diatonick Hemitone for F fa ut. 2nd Fret, should be a three quarter black stroke, a Minor Tone for E la mi & A re: except D sol re & B mi prevail for the Major Tone, & that the second fret may be a true Fifth to the String open that went before it.46 3rd Fret, a Lesser Third, the through-black stroke for G sol re ut & C sol fa ut; but F fa ut has an inclination to the black-quarter stroke. [fol. 39v] a

  Deleted: ?ab.

‘The Use of the Musical Canon’ (?1686–8)

71

D sol re with one flat in B mi. 1st Fret, a Diatonick Hemitone, the half-black stroke for F fa ut, & B fa b mi flat. 2nd Fret, the three-quarter black stroke, a Minor Tone, for the key and A re: though the two E la mi’s are for a Major Tone, but they must be overruled. 3rd Fret, the through-black stroke, a Lesser Third, for G sol re ut, & C sol fa ut; but F fa ut retains his former inclination. Gam ut with two flats, in B, & E. 1[st] Fret, a Diatonick Hemitone, for F fa ut, B fa b mi, & two E la mi’s flat. 2[nd] Fret, the through-black stroke, a Major Tone, for A re the second, & also D sol re the Fifth from the Key: which in this disposition of the Octave, from Sol to La requires a Major Tone. 3rd Fret, the through black stroke, being a Lesser Third. E la mi with one Sharp in F fa ut. 1st Fret, a minor Chromatick Hemitone, being the a three-quarter stroke ‹(of Points[)].› 2nd Fret, the three-quarter black stroke, a minor Tone, for the Key double E la mi, A re, D sol re, B mi, & E la mi, none falling amiss but F fa ut Sharp. 3rd Fret, must be brought to the black-quarter stroke; because neither G sol re ut, nor C sol fa ut are true lesser thirds to the string open. B mi with two sharps F, & C. 1st Fret, the three-quarter stroke of Points, a minor Hemitone47 for C fa ut sharp upon the fourth string; that there may be a full Diatonick Hemitone to D sol re. 2nd Fret a major Tone, being the through-black stroke; that D sol re being there, there may be but a Minor Tone to E la mi; so also would F fa ut sharp have it, & B mi upon the same Fret: but A re & E la mi have an inclination to the Minor Tone. 3rd Fret, the through-black stroke, G sol re ut and C sol fa ut requiring a true lesser Third to the string open. [fol. 40r]

Harmonical Coincidence.48 1 From the String open to the Minor Hemitone 20/19, to the minor Tone 20/18 = 10/9, to the minor Tone & major Hemitone 20/17, to the Major Third 20/16 = 5/4, to the Major 6th 20/12 = 5/3, to the Octave 20/10 = 2/1. a

  Illegible deletion.

Thomas Salmon: Writings on Music

72

2 From the string open to the Major Hemitone 18/17, to the Major Tone 18/16 = 9/8, to the Minor Third 18/15 = 6/5, to the Fifth 18/12 = 3/2 to the lesser Seventh 18/10 = 9/5, To the Octave 18/9 = 2/1. 3 From the String open to the Hemitone 16/15, to the Fourth 16/12 = 4/3, to the Lesser Sixth 16/10 = 8/5, to the Octave 16/8 = 2/1. 4 From the Hemitone Stopt, to the Major Hemitone 18/17, to the Major tone 18/16 = 9 /8, To the Fifth (which is the lesser a Sixth open) 18/12 = 3/2. 5 From the Major Tone stopt to the Minor Hemitone, 20/19, to the Minor Tone 20/18 = 10/9, to the greater Third (which is a Tritonus open 64/45) 20/16 = 5/4, to the Fourth (being Fifth open) 20/15 = 4/3, to the greater Sixth (being a greater Seventh open) 20 /12 = 5/3. 6 From the Lesser Third stopt to the Minor Hemitone 20/19, to the minor Tone 20/18 = 10 /9, to the Third Major Hemitone above the minor Tone 20/17, to the Greater Third (being a Fifth open) 20/16 = 5/4, to the fourth (being a lesser Sixth open) 20/15 = 4/3. Notes 1 The experiment described here had been performed several times during the seventeenth century and described in manuscript and – at least three times – in print, so we need not assume Salmon had carried it out for himself; see pp. 18–20. By ‘Sound’ Salmon meant ‘interval’. 2 If true: i.e. ‘if the interval is tuned correctly’ (not ‘if this observation is correct’). 3 The mathematical derivation of the diatonic semitone would remain something of an embarrassment to Salmon; compare ‘The Practicall Theory’, fol. 3r: ‘We are forced to go a great way to fetch in this last note 16 to 15’. There he would derive it from repeated division of the fourth; in the Proposal he avoided addressing the matter. 4 Compare ‘The Division of a Monochord’, fols 3v–4r, where these intervals are called the ‘common measures’ of other intervals. 5 Salmon presented this point – that this collection of intervals adds up to an octave – as an observation, but he had in fact already described the mathematical relationships which make it inevitable: the octave can be divided into a fifth and a fourth, the fifth into a major and a minor third, the fourth into a major third and a hemitone, the major third into a major and a minor tone, and the minor third into a major tone and a hemitone. 6 In all of Salmon’s later discussions of tuning this nuance was absent, allowing each fret layout to be used twice, for instance both for C major and for A minor; see p. 4. The change may have been prompted by a concern to reduce the number of different fingerboards needed. 7 The ‘canon’ referred to here may have been a chart like those shown in Proposal, a

  Deleted: ?6th.

‘The Use of the Musical Canon’ (?1686–8)

Figure 2.2

A possible reconstruction of the diagram accompanying ‘The Use of the Musical Canon’.

73

Thomas Salmon: Writings on Music

74

pp. 9, 12. It is hard to see that it can have been (part of) the same diagram as that described later in this text. 8 Later in this text Salmon would imply that he was thinking of the traditional ‘viol way’ tuning, d'–a–e–c–G–D (not the ‘lyra’ tuning he had proposed in his Essay, p. 50). 9 Here Salmon moved abruptly from a discussion of principles and (allegedly) existing practice to a description of a specific diagram, presumably intended to be provided with this text, which would facilitate the fretting of instruments somewhat as the diagrams in the Proposal did, though apparently this one was more complex. Salmon evidently had the diagram before him as he wrote, but if it was ever copied as part of the present manuscript, it has been lost. From what Salmon wrote, we can recover most of the diagram’s characteristics. It showed various ‘strokes’ indicating the possible positions of different frets and distinguished by the use of dots, dashes or solid lines. The fact that some of the strokes reached only a quarter, half or three-quarters of the way across the diagram seems to have been, similarly, a visual device to distinguish one stroke from another rather than a practical proposal to make frets of those lengths. The characteristics of the different strokes were as follows.

Table 2.1 Fret 1

2

3

4 5 6 7 8 9

Stroke 1 2 3 1 2 3 1 2 Extra 3 1 2 1 2 1 2 1 2 1 2 1 2

Description Points, 3/4 through Points quite through Black 1/2 way over Black, 3/4 through Black, quite through Points, half way Points, quite through Points, 3/4 through Quarter-black Black, through Black Points, 3/4 through Black, quite through Black, quarter stroke Little crosses Points Black, a quarter through Black, quite through C string only A string only C string only A string only

Position 19/20 17/18 15/16 9/10 8/9 85/96 17/20 38/45 27/32 5/6 4/5 19/24 3/4 20/27 32/45 17/24 27/40 2/3 19/30 5/8 3/5 85/144

Interval (from open string) Minor hemitone Major hemitone Diatonic hemitone Minor tone Major tone Diatonic + major hemitone Minor tone + major hemitone Major tone + minor hemitone Minor tone + [diatonic] hemitone Minor third Major third Minor third + minor hemitone Fourth Minor third + major tone Tritonus Fourth + major hemitone Fourth + minor tone Fifth Fifth + minor semitone Lesser sixth Greater sixth Lesser sixth + major semitone

‘The Use of the Musical Canon’ (?1686–8) 10 11 12

1 2 1 2

C string only A string only C string only A only Black

17/30 5/9 8/15 19/36 1/2

75

Greater sixth + major semitone Lesser seventh Greater seventh Lesser seventh + minor semitone Octave

The diagram may have shown all six strings, but only two, for A and C, are specifically mentioned in the text (fol 34v). With two strings, and with the addition of ratios indicating the position of each stroke, the diagram would have looked something like Figure 2.2. 10 Compare the spurious sixth ‘common notion’ in Euclid, Elements 1: ‘Things which are halves of the same thing are equal to one another’ (Thomas L. Heath, The Thirteen Books of Euclid’s Elements, 2nd edn (3 vols, Cambridge, 1926), vol. 1, p. 223). Since he was presumably thinking, as usual, of an arithmetical division of intervals carried out geometrically, Salmon’s use of the word ‘half’ was meant literally here. 11 The minor tone was subdivided into 20/19 and 19/18; it was not clear at this stage to which of these intervals Salmon intended to apply the name ‘minor hemitone’, but it would later emerge that he intended the smaller – and in his division the lower – of the two, 20/19. Similarly ‘major hemitone’ would turn out to mean 18/17 rather than 17/16. 12 The third stroke for the second fret thus fell at 17/18 of 15/16 of the length of the string, or 85/96. 13 The first stroke of the third fret thus fell at 17/18 of 9/10, or 17/20, of the string; the second stroke at 19/20 of 8/9, or 38/45. 14 This passage is ambiguous, but it is clear from later references to it that a ‘quarterblack’ stroke fell between the second and third strokes of the third fret, positioned so as to make a diatonic semitone plus a minor tone with the open string, thus at 15/16 of 9/10, or 27/32, of the string’s length. 15 The second stroke of the fourth fret stood at a minor third plus a minor hemitone, 19/20 of 5/6, or 19/24, of the string. 16 The first stroke of the fifth fret stood at 3/4 of the string; the second stroke at 8/9 of 5/6, or 20/27, of the string. 17 In Salmon’s tuning the ‘tritonus’ consisted of the two major tones and one minor tone which made up the interval F–B, with a ratio of 45/32. The second stroke for this sixth fret fell at 17/18 of 3/4, or 17/24, of the string. 18 The strokes for the seventh fret stood at 2/3 and 27/40 of the string. 19 Two possibilities are sketched here, giving the positions of marks to guide the placement of the fingers rather than, it would seem, actual frets. The first, for C strings, would place the greater sixth (fifth plus minor tone) on ‘fret’ 9 and the greater seventh (octave minus diatonic hemitone) on ‘fret’ 11, with ‘frets’ 8 and 10 dividing arithmetically the minor tone between fifth and greater sixth and the major tone between greater sixth and greater seventh. The second, for A strings, would place the lesser sixth (fifth plus diatonic hemitone) on ‘fret’ 8 and the lesser seventh (octave minus minor tone) on ‘fret’ 10, with ‘frets’ 9 and 11 arithmetically dividing the minor tone between lesser sixth and lesser seventh, and the major tone between lesser seventh and octave. See Note 9 for the resulting positions.

Thomas Salmon: Writings on Music

76

20 The common Note-tuning: i.e., d'–a–e–c–G–D (see Volume I of this edition, Chapter 1, note 61). 21 The first octave of the major scale on C was thus produced using only five frets, making intervals of a diatonic semitone, major tone, minor third, major third and perfect fourth with the open strings. 22 Harmonicon: Salmon evidently meant ‘a guide for tuning’, but the OED records no such meaning for the word. 23 Text seems to be missing here, introducing the sixth string. 24 C major thus required frets as follows (fret 6 was never used):

Table 2.2

Fret

1 2 3 4 5 7

6

5

9/10 27/32

9/10 5/6

3/4

3/4

String 4

3 15/16

2

1

5/6

8/9 5/6

9/10 27/32

3/4

20/27

3/4 27/40

8/9 4/5

This was not identical to the set of frets presented in scheme 1 of Proposal, because a slightly different form of diatonic scale would be envisaged there. 25 This passage seems somewhat opaque, and Salmon was perhaps still wrestling with the problem of how to realise a satisfactory scale using a single set of frets for all strings. He had earlier specified that the first string (D) should be unison to a second-string fret placed at 20/27 of the string’s length, reflecting the fact that in ‘C fa ut key’ the interval A–D consisted of a minor third A–C plus a major tone C–D. In the present compromise fretting, however, he had suggested that the second fret should be placed so as to make a minor tone with the open string, which, for ‘C fa ut key’, would be satisfactory for the D and G strings but unsatisfactory for the A and C strings, producing a B and a D which were not really where the mathematics required them. Naturally the open D of the first string needed to be in tune with this new D (an octave lower, on the second fret of the fourth string), and this could be achieved by tuning that open string a pure fourth (not a minor third plus a major tone) above the second string, as Salmon suggested here. Similarly, the fifth fret would also need to move so as to form a pure fourth with the open string, moving from its previously-described position by the same amount – 81/80, the difference between a major and a minor tone – as the second fret had. 26 The point here was that while E–G and A–C were supposed to be true minor thirds (5/6), D–F was supposed to incorporate the diatonic semitone E–F as well as the minor tone D–E, placing the fret ideally at 27/32 of the string. The suggestion of ‘shoving’ part of a fret presumably originated with an experienced violist. 27 This was a consequence of the re-tuning of the first string (see note 25). 28 The compromise fretting which Salmon described places frets at 15/16, 9/10, 5/6, 4/5 and 3/4 of the string. It was thus less complex (by the omission of the major tone fret) than the compromise fretting which would appear as plate VIII in the Proposal (see Figure 3.4).

‘The Use of the Musical Canon’ (?1686–8)

77

29 This sentence is obscure as much for syntactical as for technical reasons, and Salmon’s meaning is best elucidated by a comparison with the terse second version of this passage on fol. 38v. He meant that: (1) the fifth fret should be placed at the throughblack stroke, forming a perfect fourth with the open string; (2) the second string should not, however, be tuned unison to the third string stopped at this fret, but somewhat higher (in unison, in fact, with the third string stopped at the quarter-black stroke of the fifth fret); (3) the first string should also be tuned higher than its relationship with the third string would suggest, and by a similar amount (in other words it should be tuned a pure fourth above the second string, ignoring the third string). This placed the open A and D at the correct pitches for this key. 30 The fretting for G major had frets at 17/18, 8/9, 5/6, 4/5, 3/4, 17/24 and 2/3 of the string. 31 Salmon was in principle free at this stage in setting up a two-sharp scale to make any assumption he wished about where the chromatic note C$/B# should fall. Since B–C# was a major tone, we would expect C–C# to be 17/16 and therefore for C# to fall at 16/17 of the C string. This would coincide with none of the strokes of the first fret. In fact Salmon took a different approach: he considered that the interval between first and second frets was supposed to be a diatonic semitone (C#–D), and therefore insisted that the first fret must fall as low in pitch as possible. With the strokes previously described, that meant it must be at 19/20, the position of the ‘3-quarter stroke of points’ he mentioned. He gave no indication that he had thought through the (complex) implications of this for the position of frets on this or other strings. 32 This stroke, standing at a minor tone plus a diatonic semitone, 27/32 of the string, was elsewhere described as ‘black in the stroke of points’ or a ‘quarter-black stroke’. 33 Salmon’s discussions became more and more sketchy from here on. The two-sharps scale had frets at 19/20, 9/10, 27/32 and 4/5 (and presumably also 3/4 and 2/3). 34 F and B@ major and A and D minor all had the following series of frets: 15/16, 9/10, 5/6, (4/5, 3/4, 2/3), save that for B@ Salmon, having vacillated about the second fret, settled on 8/9 as its position. His repeated notices to ‘incline’ certain frets for certain strings were rather at odds with what seems to have been the initial intention of this section to give compromise frettings in which a single set of positions would work for all six strings. 35 G minor had frets at 15/16, 8/9 and 5/6. 36 E minor had frets at 19/20, 9/10 and 27/32. 37 B minor had frets at 19/20, 8/9 and 5/6. 38 These ‘directions’ amount to a second, generally briefer, version of section III (recte IV: fols 35r–37v), taking into account in particular the fact that ‘the three uppermost frets need only be movable’. 39 The phrase ‘here calculated’ may have alluded to a (lost) table intended to be read with the text at this point. But it could equally, and perhaps more likely, have been another reference to the main chart as reconstructed in figure 2.2 above. 40 In this presentation of his suggestion of tuning the first string lower than true, Salmon gave so few details as to make the point practically incomprehensible. Compare fol. 36r and note 25 above. ‘Bearing’, here and elsewhere (Proposal, pp. 16, 25–7; ‘The Practicall Theory’, fols 5v, 7r) seems to mean a detuning away from mathematical perfection. 41 The discussion of the seventh fret, found in the earlier draft of this passage, was omitted here.

78

Thomas Salmon: Writings on Music

42 Discussion of the position of the fourth and fifth frets, present in the first draft, was omitted, and the intended position of the fifth fret is not clear. In the previous draft it was placed at 3/4 of the string, and the first and second strings tuned independently of it, and that was probably what was intended here. See note 29 above. 43 Once again, the discussion of the fourth fret, which was brief in the first draft, was here omitted altogether. 44 In this and the following paragraphs this second version generally expands slightly upon the first, by specifying explicitly which stroke was to be used for each fret, as well as what interval was to be formed. The wording is otherwise very similar to the first version. 45 Compare the vacillation in the first draft, which eventually reached the same conclusion: the second fret should be at 8/9 of the string. 46 In the first draft the minor tone option was strongly preferred (‘must prevail’). 47 A minor chromatic hemitone was clearly intended, and was specified in the first draft. 48 This rather telegraphic final section enumerates the different intervals, with their ratios, which could be produced by the frets at their various different positions, and was possibly based on a table of such intervals. Its purpose seems to have been less to provide a list of intervals for its own sake than to reduce various sets of interval ratios to a common denominator, perhaps to facilitate the production of fretting diagrams like those in the Proposal or of a diagram like that in Figure 2.2. The first paragraph, for instance, shows that if the whole string is divided into 20 parts, strokes at positions corresponding to 19, 18, 17, 16, 12 and 10 of those parts will be required. Subsequent paragraphs describe divisions of the whole string into 18 or 16 parts, of 15/16 of the string into 18 parts, of 8/9 of the string into 20 parts, and of 5/6 of the string into 20 parts.

Chapter 3

A Proposal to Perform Musick (1688) Editorial Note As with Salmon’s Essay to the advancement of musick, it seems that the appearance of his 1688 Proposal was preceded by a fairly lengthy period of work on the material which it contains. Salmon corresponded with John Wallis from 1685 – perhaps earlier – and by late 1685 had ‘rectifed’ his ‘Harmonicall Canon the third time’. Another two years would pass before his ideas about musical tuning were printed. The Introduction to Chapter 2 discusses the possibility that ‘The Use of the Musical Canon’ is evidence for Salmon’s work during that period. Based on the dates and assertions contained in the book, it seems that the main text of the Proposal was set up in type during November 1687 and copies sent to John Wallis and Edward Bernard on 5 December.1 These could have been, in effect, proof sheets, but we have no evidence that the printing of the full set of copies was delayed to wait for the responses. Bernard’s very brief note of approbation was dated 15 December; Wallis replied with his ‘large remarks’ two days later.2 There presumably followed some correspondence, now lost, in which Salmon sought and received Wallis’s permission to print the ‘remarks’ with the book; it seems that, at nearly 5,000 words (to the 7,000-plus of the Proposal proper), they were substantially more extensive than anything Salmon had anticipated or could have been expected to anticipate. The responses of the two Savilian professors were printed on a separate set of sheets from the main text, forming two gatherings of their own at the end of the book. Salmon also at this stage added a note after the dedicatory epistle, drawing attention to Wallis’s remarks and their character as a supplement to the book.3 That epistle bore the date 1 November 1687, but its mention of Wallis’s remarks means that it cannot have been printed until after the middle of December. It, too, occupied its own gatherings. The book’s title page, finally, drew further attention to the ‘approbation’ of Wallis and Bernard, and bore the date 1688. What happened next to the Proposal is not clear. On the one hand, it was advertised in the London Gazette for 23 January 1687/8, suggesting rather strongly that by that date all the parts of the book had been printed and the whole was ready for sale. (Some printed copies of the main text of the Proposal in apparently its final form certainly existed in December 1687 – Wallis provided references to page and line in his ‘Remarks’.) A Proposal to perform Music, in Perfect and Mathematical Proportions. By Thomas Salmon, Rector of Mep[sal] in the County of Bedford. Approved by

80

Thomas Salmon: Writings on Music both the Mathematic[k] Professors of the University of Oxford. With large Remarks upo[n] this whole Treatise, by the Reverend and Learned John Wallis D. [D.] Sold by John Lawrence at the Angel in the Poultrey.4

Rather more than a year later another advertisement appeared, in the London Gazette for 18–21 March 1688/9: All sorts of fretted Instruments, especially Lutes and Viols, are fitted with exact and perfect Stops (According to Mr. Salmon’s Calculation, approved by the Mathematical Professors of both Universities) by R. Meers Instrument-maker, against the Catherine-wheel in Bishopsgate-street. The Book is sold by J. Lawrence at the Angel in the Poultry.5

‘R. Meers’ was Richard Meares (d. ?1722), ‘possibly the leading maker of viols of his time’. Few (if any) viol-makers were more distinguished than Meares, and Salmon could hardly have hoped for more weighty support for his proposals to modify musical instruments.6 The reference to the mathematical professors of ‘both universities’ may seem to suggest that Salmon had already made contact with Newton, the Lucasian Professor at Cambridge, but it is probably more likely that whoever provided the text for the advertisement simply made a mistake. Only several months later still, however, was the Proposal listed in a ‘term catalogue’ of books for sale in London: it appeared in the catalogue for Trinity term 1689, dated in June.7 This is curious. It may be an error by the compiler of the catalogue, but it is supported by Meares’s advertisement, which would otherwise have appeared when the Proposal was year-old news, and indirectly by the fact that Lawrence, the publisher, seems to have sharply reduced his activities during the troubled period 1688–9. As against an average of about five books per year over his whole career, the Proposal was his only book to bear 1688 as its imprint date. Possibly he ceased to sell books during that period, delaying the release of the Proposal until the capital was in a calmer state in the spring of 1689. Mere error in the term catalogue, however, cannot be ruled out. John Lawrence, the publisher of the Proposal, was, starting in 1681, quite a prolific publisher (ESTC lists more than 300 items, although many of these are second and subsequent editions), specialising for the most part in sermons and other religious materials of a fairly obviously nonconformist character (authors who described themselves as ‘minister of the Gospel’, tracts on occasional conformity, and so forth).8 He also published works on shorthand and on language, he handled some more exotic books including material in Hebrew, and he was one of the several booksellers for Boyer’s English–French dictionary in 1700. It seems reasonable to suppose that it was through the nonconformist world that Salmon made contact with Lawrence, who published no other works about music, and only two on mathematics or natural philosophy: Sir Jonas Moore’s Mathematical compendium in 1695 and Sir Samuel Morland’s

A Proposal to Perform Musick (1688)

81

Hydrostaticks in 1697. More than this about their relationship it is difficult to say, but it is noteworthy that Salmon did not publish any of his four subsequent books with Lawrence. Of John Cutts (1660/1–1707), the dedicatee of the Proposal, we know more, but his connection with Salmon is if anything less explicable. He had studied at Cambridge and the Middle Temple, and at the time when Salmon composed the Proposal and dedicated it to him he was near the beginning of what would be a fairly prominent career as an army officer and a politician (in 1690 he would be created Baron Cutts of Gowran). Between 1686 and 1688 he served in the army of the imperial general Duke Charles of Lorraine, fighting the Turks and distinguishing himself apparently at Buda and at Mohacs; in 1688 he would join the army of William of Orange (it is just possible that his absence from the country delayed the appearance of the Proposal by delaying his acceptance of the dedication and therefore the printing of the dedicatory epistle). He had published, anonymously, a letter in verse in 1685 and would publish Poetical Exercises in 1688.9 The dedication of Salmon’s Proposal to a man primarily known as a professional soldier is rendered somewhat less strange by Cutts’s literary activities, but it is not at all obvious that he would have been interested in Salmon’s musical and mathematical work. A self-conscious attempt made in the dedicatory epistle to link the profession of the soldier with the contents of the book seems almost embarrassingly contrived.10 It probably follows that Cutts was an acquaintance or a friend of the Salmon family to whom the dedication was intended as a selfserving compliment. But, beyond the rather generic references in this dedication (‘my Excellent Friend’, and so on), I have not discovered any evidence for such a connection, or for the possibility that Cutts was in fact a relative of Salmon. Cutts’s letters and papers are fairly voluminous, and I have not attempted to locate correspondence between him and Salmon (perhaps through his mother in law) in which the dedication was offered and accepted.11 Despite the contributions of Wallis and Bernard, and the letter of dedication, the Proposal is slimmer than either of Salmon’s previous books. It is a quarto of about 175mm × 230 mm. The collation is A2[a]4B–D4E2F–G4, with the main text occupying gatherings B–E and Wallis’s response F–G. It therefore looks somewhat as though the dedicatory letter in gathering A and [a] was printed later than the main text, which may indicate that Salmon had experienced some difficulty or delay in finding a dedicatee, very possibly connected with John Cutts’s absences from England. I have seen no copy of the Proposal which lacks any of the parts of the text. There are eight diagrams on four additional leaves, which Salmon referred to as appearing at ‘the end of this Treatise’ and which are bound after gathering E in many copies (see Figures 3.1–3.4).12 These are often folded, in order to fit inside trimmed copies of the book, but in untrimmed copies (such as Savile G.2 in the Bodleian Library, and that in Cambridge University Library) they fit within the volume without folding. All of the printed errata occur in the main text, that is

82

Thomas Salmon: Writings on Music

gatherings B–E, but in what seems to have been John Wallis’s copy the list of errata has been extended in manuscript to include seven more items, all of which refer to his ‘Remarks’, that is gatherings F and G. It therefore looks as though Wallis, not surprisingly, was not given the opportunity to correct proofs of his ‘Remarks’. The final leaf of gathering G is filled on both sides with a brief catalogue of John Lawrence’s books, listing four works of piety and four of history. This catalogue is the same in all the copies I have seen; it is not included in this edition. One copy of the Proposal, now in the Bodleian Library, appears to have belonged to John Wallis, but his annotations, which are reported in the present edition, do not go much beyond the correction of errors in the printed text, including but not limited to those recorded in the printed Errata. (This copy includes the printed ‘remarks’, and is therefore evidently not the copy on the basis of which Wallis wrote those ‘remarks’).13 Another copy, now held in the Senate House Library in London, is bound with a copy of Richard Sault’s New Treatise of Algebra (1694) and bears the inscription of Thomas Eliot, a former owner who is otherwise unknown.14 A copy in the British Library has some marginal pencil marks which suggest that an individual began to note passages for comment, but it bears no owner’s name and the marks – which may in any case be of a later date – go no further than the first few pages.15 Various copies of the book were offered for sale during the eighteenth century, but none, unfortunately, can be unambiguously associated with the library of a specific individual.16 Samuel Pepys owned a copy of the Proposal, but on the evidence of the sale catalogues of their libraries neither Elias Ashmole, Robert Hooke, Edmund Halley, Anthony à Wood, nor John Locke did, though Ashmole and Wood seem to have had Salmon’s Essay in their collections.17 Copies, of which 14 are known, are held by the following libraries:18 Germany: Münster, Musikwissenschaftliches Seminar der Westfälischen WilhelmsUniversität. Great Britain: Cambridge, Magdalene College, Pepys Library; Cambridge, Trinity College Library; Cambridge, University Library; Durham, Cathedral Library;19 London, British Library; London, University of London, Senate House Library; Oxford, Bodleian Library (two copies); Oxford, Christ Church Library; Windsor, Eton College Library.20 United States: Boston, MA, Boston Public Library, Music Department; Berkeley, CA, University of California, Music Library; Washington, DC, Library of Congress. Salmon’s Proposal appears in the Early English Books microfilm series and Early English Books Online.21 The EEBO version, a digital facsimile of the Library of Congress copy, served as the basis for this edition, which has been checked against the two Bodleian copies, with shelfmarks 4o P 37 Art: and Savile G.2. I have detected no variations in the text among these three copies. The copies in the British Library, Cambridge University Library and the Wren library were also inspected.

A Proposal to Perform Musick (1688)

83

Notes 1 See Proposal, p. 29. 2 The original of Wallis’s letter does not survive; nor does Salmon’s of 5 December to which Wallis referred. 3 Proposal, sig. a4r. 4 I am very grateful to Christopher D.S. Field for drawing this piece of evidence to my attention. 5 London Gazette, 18–21 March 1688 (no. 2439), verso. 6 Peter Ward Jones and David Hunter, ‘Meares [Mears, Meers]’, in Grove Music Online. The address given in the advertisement closely matches that on the label of a viol in the Victoria and Albert Museum: ‘Richard Meares, without / Bishopsgate, near Sir / Paul Pinders. London / Fecit 16{77}’ (Christopher D.S. Field, personal communication). See also John Milnes (ed.), The British Violin (Oxford, 2000), pp. 7, 14–18, 254–5. 7 Edward Arber (ed.), The Term Catalogues, 1668–1709 A.D. […] (3 vols, London, 1903–6), vol. 3, p. 274: catalogue no. 34, for Trinity Term, June 1689. Anthony à Wood (or rather the editor of the second edition of his Athenae) gave the date of the Proposal as 1689 (Athenae Oxonienses (2nd edn, 2 vols: London, 1721), vol. 2, col. 1075); possibly he was following the term catalogue. 8 See Henry R. Plomer, A Dictionary of the Booksellers and Printers who were at Work in England, Scotland and Ireland from 1668 to 1725 (Oxford, 1922), p. 184; and D.F. McKenzie, Stationers’ Company Apprentices 1641–1700 (Oxford, 1974), p. 127, item 3423. John Lawrence was bound apprentice to Thomas Parkhurst in the same year, 1674, as John Dunton. 9 H.M. Chichester, rev. John B. Hattendorf, ‘Cutts, John, Baron Cutts of Gowran (1660/61–1707), army officer and politician’, in ODNB. 10 Proposal, sig. A2r–[a2]r. 11 Chichester and Hattendorf in ODNB list 17 volumes of manuscript materials in the British Library, plus more in Ireland. 12 See Proposal, p. 22. The diagrams appear at the very end of the book in the British Library’s copy and in both of the Bodleian’s copies; they appear after gathering E (the main text) in copies in: Cambridge, Cambridge University Library; Cambridge, Trinity College, Wren Library; Oxford, Bodleian Library (both copies); and Washington, DC, Library of Congress. 13 Shelfmark Savile G.2. In this copy the printed list of errata is, as mentioned above, extended to record seven corrections to Wallis’s ‘remarks’ (these are noted in Salmon’s Chapter 3 below); all of these corrections have been carried out in manuscript upon the printed text. The hand is certainly similar to Wallis’s, although there is not enough material here to be absolutely certain it is his. The correction of detailed errors in the ‘remarks’, including a mistake in the mathematical notation, points very strongly to Wallis as the author of these annotations; the Savile shelfmark (implying that the book was given to the library by a Savilian professor, though providing no certain information about which professor, or about the date of accession) is consistent with this. See C.J. Scriba, Studien zur Mathematik des John Wallis (1616–1703): Winkelteilungen, Kombinationslehre und Zahlentheoretische Probleme im Anhang die Bücher und Handschriften von Wallis in der Bodleian Library zu Oxford (Wiesbaden, 1966), pp. 112–42: ‘Anhang: die Bücher und

84

14 15 16

17

18

19 20 21

Thomas Salmon: Writings on Music Handschriften von John Wallis mit einem Überblick über die Geschichte der Savile Collection (jetzt Teil der Bodleian Library in Oxford)’. Shelfmark * L2 [Sault]. Shelfmark 557*.e.25.(4.). The pencil marks, which consist of vertical lines and zigzags, with no words or even letters, end on p. 4 of the main text. Thomas Payne, A catalogue of twenty thousand volumes, including the library of the late eminent Mr. Ralph Thoresby, gent. F.R.S. late of Leeds, and of several other libraries, lately purchased […] [London, 1764], p. 136 (pamphlets, quarto, item 5052); Thomas Payne, A catalogue of the libraries of the late Sir John Barnard, Knt, late vicar of St. George’s in the East, Dr. Middleton of Bristol, and Dr. Ross, deceased […] [London, 1765], p. 145 (quarto pamphlets, item 5919); Benjamin White, A catalogue of a valuable collection of books; consisting of several libraries, and particularly those of the Rev. Thomas Negus, D. D. rector of St. Mary’s Rotherhithe, and Mr. William Price, a very ingenious painter of glass, both lately deceased [London, 1766], p. 50 (item 1466); James Fletcher, A small catalogue of useful and valuable books, in most branches of literature: containing two collections, recently purchased [Oxford, 1793], p. 12. Robert Latham (ed.), Catalogue of the Pepys Library at Magdalene College, Cambridge (Woodbridge, 1978–), vol. 4, item 1730.1; H. Feisenberger, Sale Catalogues of Libraries of Eminent Persons, vol. 11: Scientists (London, 1975); Nicolas K. Kiessling, The Library of Anthony Wood (Oxford, 2002), p. 531, item 5719 (copy of Salmon’s Essay described as ‘Missing in 1837’); J. Harrison and P. Laslett, The Library of John Locke (Oxford, 1965, 1971). The ESTC reports copies in the University of Iowa and the University of Texas at Austin, and a second copy at the University of California, Berkeley, none of which in fact exists. I am grateful to David E. Schoonover, David Hunter and Manuel Erviti for information about these alleged copies. I am grateful to Alastair Fraser for information about this copy. I am grateful to Katie Flanagan for information about this copy. Early English Books, 1641–1700 (Ann Arbor, University Microfilms, 1966), reel 226, no. 3 (no. S418 in Wing’s Catalogue).

A Proposal to Perform Musick (1688)

85

Text [sig. [A1r]]

A PROPOSAL TO Perform Musick, IN Perfect and Mathematical Proportions. CONTAINING, I. The State of MUSICK in General. II. The Principles of PRESENT PRACTICE; according to which are, III. The Tables of PROPORTIONS, calculated for the Viol, and capable of being Accommodated to all sorts of Musick. By Thomas Salmon, Rector of Mepsal in the County of BEDFORD. ——— Exemplaria Græca Nocturnâ versate manu, versate diurnâ.1

Hor. de art. Poet.

Approved by both the Mathematick Professors of the University of Oxford.2 With Large REMARKS upon this whole Treatise, By the Reverend and Learned John Wallis D. D. IMPRIMATUR. Gilb. Ironside, Vicecancel. Acad. Oxon.

[sig. A2r]

LONDON: Printed for John Lawrence,3 at the Angel in the Poultrey. 1688. TO The Valiant and Learned John Cutts Esq; Adjutant General in the Service of His Imperial Majesty.4

THIS, Sir, is so far from the common road of Dedications, that at first sight it will appear neither fit for me to give, nor you to receive. Shall a Person so publickly employed in the greatest Attempts, and most victorious Successes, which the World has seen for these many Ages, have leisure for Philosophical Speculations, or divert to a Science proper for ease and pleasure?

Thomas Salmon: Writings on Music

86

Or should one consecrated to the Divine Service, so laboriously search into the Intrigues of Nature, and assist in the advancement of an [sig. A2v]a Art, which with its Airy Pleasures often captivates the Soul to sensual things, and makes it more devoted to the World, that is to be conquered with another sort of Victory than your Arms can obtain? All this I have thought on, yet still find so much in this affair, as not only to excuse me, but to make it acceptable to you. This Mathematical Discourse is indeed the Anatomy of Musick, wherein the infinite Wisdom of the great Creator appears: How delightfully and wonderfully is it made! Marvellous are thy works, O Lord, and that my Soul knows right well.5 All the best Proportions, are the best Chords of Musick, and strike the Ear with a pleasure agreeable to the dignity of their Numbers. The effects of this the Sensualist is satisfied with, and desires to seek no further. But is it not grateful to every Gentleman, who is ennobled with such a [sig. [a]1r]b Soul as yours, to know the divine Harmony of the pleasure he enjoys? Is it not the duty and Felicity of a Rational Being, to consider how the whole System of the World is framed in Consort? How Musical Instruments observe their Arithmetical Laws, all the little Meanders of the Ear6 faithfully conveying the organiz’d sounds, and the Soul of man made to receive the delight, before he himself knows from whence it comes?7 How great is this! How mean am I, to set forth such a Divine Subject! However charming this still voice may be, yet no body will believe it can be heard amongst Drums and Trumpets: Why should these Papers hope for acceptance in the Camp? I must confess I should think them unseasonable, had not you, my Excellent Friend, told me that your [sig. [a]1v] most Renowned General Lorain8 does in all the intervals of Action govern his Army like a Colledge, and allow time for the repose of the Mind, as well as for the over-running subdued Countries. You may then reflect upon the great Creator and Governour of the World, who gave you being, and now preserves you in the most eminent Hazards; these shall help you to contemplate the infinite Wisdom, and shall be of the greatest advantage to you, since Piety is the best support of Courage, and gives a refreshing Ease amidst the Rage of War. But the design of War is Peace, and your Friends here long for the return of those cool hours, wherein you may not only have leisure for these Theoretical Studies, but advance true Practical Wisdom; which you have already represented to us in the most advantageous dress, and enflamed our desires to have her in[sig. [a2]r]cterest promoted to greater heights.   Running head (sigs Α2v–[a]3v): The Epistle Dedicatory.   The siglum includes the square brackets: [a]. c   The siglum includes the square brackets: [a 2]. a

b

A Proposal to Perform Musick (1688)

87

I know the glory of the Field is very tempting, but still you retain as great a passion for Learning; this hath ever found a place in the noblest Breasts: The first great Conqueror of this Island9 is as glorious for his Pen as his Sword, and by his Commentaries perpetuated his Victories. We have incomparably more of Athens here in England, than your Confederates the Venetians this year got possession of:10 That ancient Treasury was long ago rifled, and its Jewels brought into the Western part of Europe: this the learned Proprietors were very sensible of. When Cicero return’d home from Greece by Rhodes, the famous Orator there Apollonius begg’d the favour of a Declamation: All the Company were amazed, and strove with the highest Expressions to acknowledge the Obligation; but Apollonius sate sad and silent: which when he perceived [sig. [a2]v] Cicero took amiss, he said, Σὲ μὲν, ὦ Κικέρων, ἐπαινῶ καὶ θαυμάζω, τῆς δὲ Ἑλλάδος οἰκτείρω τὴν τύχην, ὁρῶν, ἃ μόνα τῶν καλῶν ἡμῖν ὑπελείπετο, καὶ ταῦτα Ῥωμαίοις διὰ σοῦ προσγινόμενα, παιδείαν τε καὶ λόγον. ‘I value and admire you, O Cicero; but in the mean time I must pity the fortune of Greece, since those excellent Goods, Learning and Eloquence, (which were all that was left) are now by you brought over to the Romans.’a Plutarch, in the Life of Cicero.11 The Offers made in these Papers, are the Musical Spoils and Relicks of Athens, a long time buried in obscurity; and though some years ago published to the World in their own Language,12 yet never known to those whose greatest concern it was to be acquainted with them. And indeed Musick now very much wants such Patrons as you are, whose Reverence to Antiquity and Learning, may give Preheminence to the Nobler part; which would at once both advance and regulate the Practick Pleasures. [sig. [a]3r] It must be acknowledged that this Divine Science has a great while sunk with the Devotion of Churches, it has been little learned and little regarded by the Religious; so that the Angelical Praises, which we have the honour to communicate in upon Earth, are faintly and unfrequently celebrated: This celestial accomplishment, which God ordained to enliven our dull Affections, is everywhere wanting; that the pleasure is as low as the skill of performing this most grateful part of Worship.13 Hence has Musick of late sought its principal Glory in Theatres,14 and sensual Entertainments, too mean a Service to be reckoned the designe of such an excellent Art: The infinite Wisdom created it for better purposes. And when God shall please to bless the World with greater degrees of Love, and a better Adoration of himself, He will raise up Men [sig. [a]3v] and Means thus to promote his Glory. Which directs me now to seek your Patronage to the Endeavours of,

a

  Original lacks ’.

Thomas Salmon: Writings on Music

88



SIR, Your most Humble and most Affectionate Servant,  Mepsal, Nov. 1. 1687.

Thomas Salmon.

[sig. a4r] Advertisement To the READER. I Would not suffer this Proposal to be published, till I had first communicated it to the most eminent Professors15 of this Science, because having omitted the demonstrations I rely upon,16 the Reader might be satisfied in their Testimonies. I know it is not fair to offer any thing in Mathematicks, without giving the Demonstration with it as we go along; but I considered that the Principles of this Science are very little known, and would not have been much regarded by Gentlemen, till they first had seen the use and necessity of them. As I thought this the best course, so it has proved much better than I expected: for the most experienced Professor in this part of Learning,17 hath sent me not only his Approbation, but his Demonstration of my Principles; from whence the more inquisitive Reader may receive a compleat satisfaction. [sig. a4v] Page

ERRATA. 6.———Line 16. for intension read intention. 7.————–– Penult. for Six read Sixth. 10.————– 24. for there read these. 13.————– Antepenult. insert the word add. 23.————– 7. for Numb. III. read Numb. IIII. 27.————– 18. insert the word cross. Ult.————– ult. two Iota’s subscripts are wanting.

[sig. B1r = p. 1]

A Proposal to Perform Musick (1688)

89

A PROPOSAL To perform Musick, IN Perfect and Mathematical Proportions. Chapter I. Of the State of Musick in General. WHEN the great Empires of the World, were in the height of their Glory, especially the Grecian and Roman, (whose Authors have left us lasting Monuments of their Excellency) Then did all sorts of Learning flourish in the greatest Perfection: The Arms of the Conquerors ever carrying along with them Arts and Civility. But to bring about a fatal Period, did the North swarm with barbarous Multitudes, who came down like a mighty Torrent, and subdued the best Nations of the World; which were forc’d to become Rude and Illiterate, because their New Masters and Inhabitants were such. [p. 2]a Amidst these Calamities, no wonder that Musick perished: All Learning lay in the Dust, especially that which was proper to the Times of Peace. But this Darkness was not perpetual; The Ages at last clear’d up; and from the Ruines of Antiquity, brought forth some broken Pieces, which were by degrees set together; and by this time of day are Arriv’d near their ancient Glory. Guido18 has been Refining above Six Hundred Years. Two things are chiefly conducing to this Restoration: The great Genius of the Age we live in, and the great Diligence in searching after Antiquity: The excellent Editions of the best Authors, and the most laborious Comments upon them, abundantly testifie the Truth of this. In both these Felicities, Musick has had as great a share as any; Aristoxenus, Euclide, Nichomachus, Alypius, Bacchius, Gaudentius, Aristides, Martian, have been with a great deal of Diligence, set forth by Marcus Meibomius, at Amsterdam, in the Year 1652. And above all, is, Claudius Ptolomæus, who Corrected and Reconciled the Pythagoreans, and Aristoxeneans, the speculative and practical Parties: This Author was Published by Dr. Wallis, at Oxford, in the Year 1682, who added an Appendix, comparing the Ancient and Modern Harmony;19 which is as the Key to all our Speculations, and without which the former Authors were hardly Intelligible. Nor are we less beholding to the Excellent Genius of our Modern Musicians: There are, indeed, only two Fragments (as I know of) remaining of the ancient Grecian Compositions; One of Pindar’s, found [p. 3] by Kircher, at Messana in a   Running head (pp. 2/3–26/27): A Proposal to perform Musick / in Perfect and Mathematical Proportions.

90

Thomas Salmon: Writings on Music

Sicily; the other of Dionysius’s, rescued by Dr. Bernard, from lying hid amongst some Papers of Arch-Bishop Usher’s; both Published with Chilmeads Notes in the end of Aratus, at the Oxford Theatre:20 These are very short, and very imperfect, and therefore we cannot make any Judgment of their Songs or Lessons. But by all that we can discern from their Harmonical Treatises, There never was such regularity in the designing of Keys, such a pleasing sweetness of Air, such a various contexture of Chords, as the Practical Musicians are at this day Masters of.21 It may seem now, that there remains nothing to be added, or to be learn’d out of those Eminent Authors I have here Recited; And the mighty Power of Musick, Recorded by the most Grave and Authentick Historians, may be lookt upon as Romance, since all the Excellencies now perform’d, cannot conquer the Soul, and subdue the Passions as has been done of Old. But before we quit the Testimonies of what Musick has done, and despair of any further Advancement; Let us enquire whether there be not something very Considerable still wanting, something Fundamental very much amiss, even that which the forementioned Philosophers were likely to be most Excellent at, when the Learned and Practical Part were met in the same Persons: Whether this be not the Accurate Observation of Proportions, which the Soul is from Heaven inform’d to Judge of,22 and the Body in Union with it, must Submit to. Surely, I need not prove, that all Musick consists in Proportion; that the more exact the Proportions, [p. 4] the more Excellent the Musick:23 This is that, all the World is agreed in. For this, I have every Man of my side, that except the Voice, the Instrument be well in Tune, the best Composition that was ever made, will never please; And what is it to be in Tune, but for every Note to bear a due Proportion to one another? Indeed, the Proportions of Musick are twofold; First, In respect of Tune, and Second, In respect of Time: The latter of these, which Dr. Vossius24 contends so much about, is certainly very considerable; that the Musick should agree with the Poetical Prosodia; that all the Variety of Rythmical Feet should have their proper Movements. Then would the Sense be favoured by such Measures, as were most fit to Excite or Allay the Passions aim’d at; and the Words of a Song would be capable of a more easie and intelligible Pronunciation. Since Musicians have not undertaken to be Poets, and Poets have left off being Musicians; this now disjoynted Work, of making Words, and setting Tunes to them, has not been so exactly done as formerly, when the same Authour perform’d both. But were it never so well done for Time, and the Proportions of Tune neglected; it could signifie nothing: None will pretend to make Musick by playing good Time, except the Instrument and Voice be in Tune. However, till both these Fundamental Points be observed with such Exactness and Excellency, as the Ancients took care of; we must not say we do all they did, or that they could not prevail more than we can; all the Modern Excellencies may

A Proposal to Perform Musick (1688)

91

be rendred Ineffectual, [p. 5] by tolerating so many unproportionate imperfections, as are every where found amongst us. I shall not here give an account of all those accurate Proportions, which the Ancients contended for, nor their little enharmonical Distances,25 whereof their more curious Musick did consist; but only of what is now practised amongst us, that the certain Knowledge of our Fundamental Principles may produce Performances, much more exact and powerful. CHAP. II. The present Practice of Musick THE Hours of Study are tedious to some and precious to others: I cannot therefore suppose any man will search into the demonstrative Reasons, or acquaint himself with the Mathematical Operations belonging to this Proposal, till he be first assured of the truth and usefulness of it. So that what is purely Speculative shall be reserv’d at present: This offers nothing but the Principles of continual Practice, whereby the Reader may be lead into the knowledge of what he is always to design; and taking the String of any Instrument, may give his Eye, and his Ear, and his Reason, an immediate satisfaction, in all that is here dictated to him. Before we compose or perform any Musick, two things must be provided for. I. That we have some little gradual Notes,26 which [p. 6] may (whilst the Voice rises or falls) succeed one another in the best Proportions possible; whereof (as of so many Alphabetical Elements) the whole Musick must consist. II. These gradual Notes must be placed in such order, that the greater Intervals (compounded of them) may in the best Proportions possible arise out of them, and be come at with the greatest conveniency: That in all the Points, where the single Notes determine, there the larger Chords may be exactly coincident; if it was not for this, there could be no Consort-Musick. To set forth this, we may as well use the first seven Letters of the Alphabet, as all the hard Names27 of Guido’s Gamut; because they were framed long before Musick was brought into that good order wherein it now stands, and the first intentiona of them is not agreeable to the present practise. Only this will be worth our Observation, that whereas in the Scale of Musick, there are three Octaves, (besides the double Notes and Notes in Alt) viz. the Base, Mean, and Treble, we may use Three Sizes of Letters in a greater, middle and lesser Character: as will be found in the Tables of Proportions.28 For understanding the two things pre-required, we suppose the proportion of one gradual Note to be contained between A and B, then between B and C the proportion of another gradual Note, though much lesser; these two single proportions, viz. that of A B, and that of B C being added together, must exactly   Source has intension: see the Errata on sig. a4v.

a

Thomas Salmon: Writings on Music

92

constitute a lesser Third; the proportions of the two gradual Notes must determine in that point, where the compounded interval may be coincident with them. [p. 7] To proceed, if we add another gradual Proportion from C to D, then must arise the exact proportion of a Fourth, from the first given A to the Note D: if one more be added from D to E, there must be found the exact proportion of a Fifth, from A to E, and of a greater Third from C to E. Thus must the Gradual Notes be contrived to be exactly subservient to the greater intervals thorough all the Octaves: and if at any time this cannot be (as may happen in two or three instances) such particular Chords must be esteem’d inconcinnous29 and inconvenient, but they are very few, and lye much out of the way. If we settle one Octave, the whole work is as good as done; all the rest is only repetition of the same Notes in a larger or more minute figure: for the eight Notes which are used in constant practise, proceeding gradually, take up just half the string, from the sound open to the middle of it: And if we have occasion to go further, ’tis but just the same over again. The great concern is in what order our gradual Notes (which are of different sizes) must stand, from the Key or Sound given, till we arrive at the Octave; for there will be a great variety, according as the lesser gradual Notes are placed sooner or later: This must be lookt upon as the internal constitution of an Octave, which practical Musicians commonly understand by their Flat or Sharp, that is, their greater or lesser Third. But as much as I can observe from the Compositions of the most Eminent Masters for these last Twenty years, this internal constitution of an Octave is but twofold: either with a greater Third, Sixth and Seventh; or a Lesser Third, Sixtha and Seventh: In the same composition all are lesser, or all greater. [p. 8] There needs then only this twofold constitution of the Octave to be considered by us, the two Keys A and C: all the rest serve only to render the same series of Notes in different pitches; which is demonstrable by transposing Tunes from one Key to another: The Tune remains the same, only the compass of the Voice or Instrument is better accommodated. These two Keys A and C are called Natural, because the Proportions, originally assigned to each Letter, keep those proper places, which either Guido the first restorer or immemorial Custom hath allotted to them; Whereas by taking other Keys, as suppose G for A, the proportions or different sizes of the gradual Notes are forced to shift their quarters, and by flats or sharps to straiten or widen their usual distances. ’Tis sufficient demonstration for all this, that when any Tune is transposed into A or C, it wants no flats nor sharps, whatever it did before.   Source has Six: see the Errata on sig. a4v.

a

A Proposal to Perform Musick (1688)

93

I shall in the first place give you the natural order of the gradual Notes as they stand in the Key A, where we have a lesser Third Sixth and Seventh, exactly coincident with the Third Sixth and Seventh gradual Note. You have between every Letter, that part or proportion of the string assigned which each gradual Note requires: underneath you have the proportion of each compounded interval, what part of the string it’s stop must be when compared with the whole string open from the Nut to the Bridge.30 [p. 9] The Constitution of the Key A. A. 9. B. 16. C. 10. D. 9. E. 16. F. 9. G. 10. a. A Lesser Third A Fourth A Fifth A Lesser Sixth A Lesser Seventh An Eighth

6 4 3 3

/8 4

/9 2

The Experiment must be thus: You are to take any one String, and suppose it to be the Key A, when it is open: then measure the 9th part of it, you will have B or one gradual Note. Not that the first Fret must stand there, but the second; for we are not reckning according to Tableture, but Notes specified by the first Letters of their hard names:31 the half Notes shall be considered afterwards. From the place of B measure the 16th part of the remaining String, there will be C, the least gradual Note: And there you will arrive at the 6th part of the whole String,32 which is the proportion of the Lesser Third; and the Ear will acknowledge it to be so.33 From the place of C take the 10th part of the remaining String, there will be D, another gradual Note, much wider than the last, between B and C, but something less than the first between A and B. At the place of D, you will arrive at the 4th part of the whole String, which is the proportion of a practical Fourth. [p. 10] Here, to prevent all perplexity and mis-understanding, the Reader must carefully distinguish in the Terms of Art: The Practical Musician reckons how many gradual Notes he has gone over from his Key or Sound given, and accordingly calls his Intervals a Third, Fourth, and Fifth, as having so many gradual Notes contained in them; but the Mathematician regards only the parts of the String, what proportion the part stopped bears to the String open.

Thomas Salmon: Writings on Music

94

Here indeed the Practical and Mathematical Terms are the same, a fourth part of the String mathematically measured, is a practical fourth; but in all other Chords they differ, as we have seen a Lesser Third to be the sixth part of a String. From the place of D take the 9th part of the remaining String, (which is a gradual Note of the same proportion with the first, between A and B;) here will be E: and here you will find you are arrived at the third part of a String, which is the grateful proportion of a Practical Fifth. The proportions of the Lesser Sixth and Seventh, viz. 3/8 and 4/9, are of a different sort from the rest; the former Chords arise from the natural division of an Octave or Duple proportion, thesea are formed by an artificial addition of a second or a third to the Fifth: The former proportions are called by Arithmeticians Superparticular, these are super-partient.34 I believe the Reader will not desire to be troubled with the nature of them here, but only to be informed how to measure them for his present satisfaction: He is to know then, that he must not take the upper number 3 of 3/8 for the third part of the whole String, for then a [p. 11] Lesser Sixth would be the same as a Fifth; but he is to devide the whole String into eight parts, as the lower number specifies, and then where three of those parts determine from the Nut, there will be a Lesser Sixth. This is the addition of the 16th part of the remaining String from E to F: for A open to E was the third part of the String, that is a Practical Fifth; from A open to F will be three parts of the whole String divided into eight parts, which is a practical Lesser Sixth. A Lesser Seventh is produced by taking a 9th part of the remaining String from F to G, which is a Lesser Third above E, this will be found to determine at 4 when the whole String is divided into 9 parts, and therefore is the proportion 4/9. From G take a 10th part of the remaining String, you will arrive at a, the precise middle of the whole String, so that an Octave is a duple proportion; the fullest and most perfect satisfaction that can be given to the Ear. And by this is the whole proceeding demonstrated to be right, because not only by the way, every interval was exactly found in its proper place, but at last this Chord, the sum total of all Musick, does just contain all its Particulars. After the same manner may the internal-constitution of an Octave in the Key C be demonstrated: I shall set it down without any explication, because the Experiment and Reason of both are alike. [p. 12]

  Source has there: see the Errata on sig. a4v.

a

A Proposal to Perform Musick (1688)

95

The Constitution of the Key C. C. 10.D. 9. E. 16. F. A Greater Third

A Fourth A Fifth A Greater Sixth A Greater Seventh An Eighth

9. g. 10. a. 9. b. 16. c.

5

4 3 2

/5 7

/15 2

Though we have all along supposed a Monochord or single String, to make this demonstration more evident, and to shew that all the gradual Notes of an Octave put together, arrive just at the middle of the String; yet the progress of the Proportions is the same, when we take some of them upon one String, some upon another. For each String is tuned Unison to some part of that which went before; so that ’tis all one whither the Proportions go along upon the same String, or go on to the next, when we come at the place of tuning Unisons. As suppose upon the Viol the Fourth String be C open, when you come to E, or the Fourth Fret, you have a greater Third; then ’tis all one whether you take the 16th part of the same String to make F at the fifth Fret, or the 16th part of the next whole String to make F upon the first Fret: ’Tis all one, because the [p. 13] third String open is tuned Unison to E, or the fourth Fret upon the fourth String. As I would avoid troubling my Reader with needless difficulties, so I would not omit any thing of necessary information; this last consideration makes me here add a discourse of Seconds, which is the name whereby the gradual Notes are commonly called: for reckning inclusively in Musick, one Interval, which must needs be contain’d between two Sounds, is term’d a Second. It is best to treat of them in that method, which our Authors used in the Classical times, because ’tis their Perfection we are now aiming at: They divided their Musick into three sorts, Diatonick, Chromatick, Enharmonick, which was so diversified by those several sorts of Seconds or gradual Proportions they used therein. 1. In Diatonick Musick, the foregoing constitution of an Octave discovers three several sizes of Seconds, viz. the 9th part of a String, the 10th part, and the 16th part.35 I would satisfie the Reader in this variety, because he will think much to enter upon an Observation, not yet received, except he knows some necessity for it. We must have the Proportion of the 16th part of the String between B and C, as also between E and F, or we cannot bring our gradual Notes into the form of an Octave, into the compass of a duple proportion; this is already acknowledged both by speculation and practice: No one ever yet pretended to rise or fall eight Notes one after another, all of the same size.

Thomas Salmon: Writings on Music

96

To this 16th part we must adda a 9th part, or we can never have an exact Lesser Third, which is the 6th part of the whole String;36 but if we add another Note of the [p. 14] same size, viz. a 9th part to make up that Lesser Third a Fourth, we shall find that we have a great way over-shot the fourth part of the String, and without taking the 10th part, we can never hit it; as will appear by the former demonstrations upon the Monochord, in many instances. I must confess, this is so contrary to the common Opinion of Practical Musicians, that I would not insist upon it, did not necessity compel me, did not the greatest Reason and Authority assure me, that it will not be hereafter denied: Of these three sizes of Seconds does the whole progress, from the Key to the Octave, consist in the forementioned order, being all along exactly coincident with the larger Intervals. My Authorities are Cartes’s Musick, Gassendus’s Introduction, Wallis’s Appendix,37 and all other Learned men, who have in this last Age reviewed the Harmonical concerns. ’Tis time certainly to receive into practice those Improvements, which the greatest Modern Philosophers in the World have afforded Musick. And indeed ’tis in vain to stand out, Nature always acknowledged and received them; a good Voice performing by it self, a faithful Hand guided by a good Ear upon an unfretted unconfined Instrument, exactly observes them:38 All that I contend for is, that the Practiser may know what he does, and may always make that his design, which is his excellency. When we have thus much granted, then may the last Chapter of this Proposal be very acceptable; which puts into his hands the Tables of Proportions calculated for every Key, that he may perform them upon those Instruments, which have not hitherto been capable thereof. But to pursue our present subject. [p. 15] 2. Chromatick Musick is that which ascends and descends gradually by half Notes. I don’t mean such as is commonly call’d the half Note in Diatonick Musick, the 16th part of the String, the proportion assigned between B and C, between E and F: These are self-subsistent, and reckned as two compleat Steps, as well as any of the rest. And if we consider the value of their proportions, deserve rather to be reputed three-quarter than half-Notes.39 Chromatick half Notes arise by the division of Diatonick whole Notes into the two best proportions, so that they will follow one another, and be all along coincident with the greater Intervals.40 But those two vulgar half Notes in the Diatonick Scale will not do so; ’twould make mad work, to place two or three of these (viz. 16th parts) one after another, you would neither have true Thirds, Fourths, nor Fifths, in your whole Octave; you could not maintain any coincidence with other Intervals. A Chromatick half Note is truly made by placing the Fret exactly in the middle between the two Frets of the Diatonick whole Note:41 This I first learn’d by the   Source omits add: see the Errata on sig. a4v.

a

A Proposal to Perform Musick (1688)

97

mathematical division of an Octave or duple Proportion into its natural parts; then I was confirmed in it by Aristides, lib. 3. pag. 115.42 who requires such a Fund for the Enharmonical Dieses, and since upon tryal I find Practical Musicians very much satisfied in the Experiment of such a Division as fully answering their expectations.43 I think only this last Age, ever since Musick has began to revive, has aspired after these Chromatick Hemitones, and now they are used three, four, or five of them, in immediate sequence one after another; if their [p. 16] proportions be truly given them, they are certainly the most charming Musick we have: but whereas a natural Genius easily runs into the Diatonick Intervals, these are not perform’d without a great deal of Art and Practice.44 3. Enharmonick Musick is that which ascends and descends gradually by quarter Notes, which the Ancients called Dieses: I don’t mean that the whole Octave, either in this or the Chromatick Musick, did consist only of these; but after having used some of them, they took wider Steps and larger Intervals afterwards to compleat the Fourth and Fifth. I could here add an account of the true Enharmonical quarter-Notes; the same Mathematical Operations produce their Proportions: The Grecian Authors (particularly Aristides in the fore-cited place) determine and record them, and they may become practical again; but I resolve to propose nothing here, but what is of present practice. This I must say, that those invented for the Harpsichord,45 are nothing to the ancient purpose: The Harpsichord quarter-Notes are designed only for playing more perfectly in several Keys, with lesser Bearings, which are never used in sequence, so as to hit four or five of them one after another; but the true Enharmonick Scale offer’d its Dieses, as gradual Notes, whereby Musick stole into the Affections, and with little insinuating Attempts got access, when the bold Diatonick would not be admitted. [p. 17] Chap. III. An Account of the Tables of Proportions. IT is very possible, that those, who are devoted only to the Pleasures of Musick, may not care to trouble themselves with the foregoing Considerations: ’Tis not every mans delight to be diving into the Principles of a Science, and to be enquiring after those Causes which produce an Entertainment for his Senses; ’tis satisfaction enough to the greatest part of the World, that they find them gratified. And indeed the delights of Practical Musick enter the Ear, without acquainting the Understanding, from what Proportions they arise, or even so much, as that Proportion is the cause of them: this the Philosopher observes from Reason and Experience, and the Mechanick must be taught, for the framing Instruments; but the Practiser has no necessity to study, except he desires the Learning as well as the Pleasure of his Art.

98

Thomas Salmon: Writings on Music

I have therefore so Calculated my Tables,46 that a man may without thinking perform his Musick in perfect Proportions; the Mechanical Workman shall make them ready to his hand, so that he need only shift the upper part of his Finger-board as the Key requires. This I have tried, and found very convenient;47 I shall therefore give a Table of Proportions in every Key, that the Mechanick may accordingly make a sett of Finger-boards for each Instrument, according to its particular [p. 18] length; the Proportions ever remaining the same, though the size be various. It is evident that one Fret quite cross the neck of the Instrument, cannot render the Proportions perfect upon every String; because sometimes a greater Note48 is required from the Nut or String open, sometimes a lesser: if then the Fret stands true for one, ’twill be false for the other; if it stands between both, it will be perfect in neither. As for example: Take the Viol tuned Note-ways,49 (which is ever the same) if you look back to the natural Constitution in the former Chapter, you will find that from the String D open, you must take the 9th part of the String; from the String G open, you must take the 10th part of the String: accordingly the first Fret from D (which is the Chromatick or just half the space of the whole Note) must be a great deal sharper, than the first Fret of the String G.50 And the first Fret of the String E being the least Diatonick Note to F, must be a great deal sharper than that which belonged to the String D, or G. So that every String must have its particular Fret, whose Proportions are here given to the Mechanick, and he is to make use of them to the best advantage: Not that I would confine him to the way of shifting Finger-boards; ’tis possible the Makers of Instruments may find out some other way much more convenient:51 Their great excellency and industry in making Organs and Harpsichords, proves them sufficient to accommodate the designs of Musick: I only proposed what I had made use of, to shew that the Experiment is practicable, which is enough for a Scholar to do, whose Province lies only in the Rational part. [p. 19] As I here inform the Mechanick, what Proportions he is to set upon every String, so I must inform the Practiser what Keys he may play in, which is absolutely necessary; for no man can set about performing any thing in Musick, without knowing his Key. This deserves to be consider’d, that the Writers of Musick may more certainly know where to fix their Flats and Sharps at the beginning of a Lesson or Song, and the number of them that is requisite: for as in Vocal Musick ’tis a vast trouble in Sol-fa-ing to put Mi in a wrong place, so it is in Instrumental Musick, to have an Information renewed in several places thorough the whole Lesson by a Flat or a Sharp, which might have been known at first, once for all. As for instance, C Key is now often chosen for a Lesser Third; there is no doubt but the Composer would have a Lesser Sixth as well as a Lesser Third, (as appears by the interspersed Flats); if so, there ought to have been three Flats prefixed, that A might be flat as well as E.

A Proposal to Perform Musick (1688)

99

I shall in this Catalogue of Keys offer you the variety of fourteen; seven with a Greater Third, Sixth, and Seventh, the other seven with all these Intervals Lesser. But for these fourteen Keys, you need to have only seven Finger-boards; for when the Proportions are lodged between the same Letters, then there will need no shifting: so that though the Key be different, yet the Instrument must be disposed in the same manner. As for instance, in the two Natural Keys A and C, the same Finger-board will serve; you begin indeed in two different places, the Key A is a Lesser Third before C, but the series of Proportions required, will be found [p. 20] exactly the same for both, according to the forementioned Internal Constitution. You may take this following Catalogue of Keys, with the due Proportions assigned between each Letter.

I. A. 9. B. 16. C. 10. D. 9. E. 16. F. 9. G. 10. a. 9. b. 16. c.



II. One Flat. D. 9. E. 16. F. 10. G. 9. A. 16. B@ 9. C. 10. d. 9. e. 16. f.



III. One Sharp. E. 9. F# 16. G. 10. A. 9. B. 16. C. 9. D. 10. e. 9. f.# 16. g.



IV. Two Flats. G. 9. A. 16.
 B@ 10. C. 9. D. 16. E@ 9. F. 10. g. 9. a. 16. b@.



V. Two Sharps. B. 9. C# 16. D. 10. E. 9. F#. 16. G. 9. A. 10. b. 9. c#. 16. d.



VI. Three Flats. C. 9. D. 16. 
 E@ 10. F. 9. G. 16. A@ 9. B@ 10. c. 9. d. 16. e@.

VII. Three Sharps. F# 9. G# 16. A. 10. B. 9. C# 16. D. 9. E. 10. f.# 9. g# 16. a. [p. 21] By this may we understand what a Key is, and observe a series of Notes in their just Proportions passing on from the sound first given to the Octave: The

100

Thomas Salmon: Writings on Music

Keys with Lesser Thirds have always in the first place a 9th part of the String, then a 16th part, and so on till you come to the same Letter again in a lesser Character: The Keys with Greater Thirds have always in the first place a 10th part, then a 9th and so on till you come to the same Letter again; but the three last Letters are in a lesser Character, to shew, that as you began a Lesser Third short of the other, so you go a Lesser Third beyond it. Thus you have as many Keys provided for you, as need be used; some things indeed have been set with four Flats, but they are very difficult to the Practiser, and I never saw any of them published; but if it were requisite, other Finger-boards might also be made for them, by the same Rule as these are calculated. I know the Keys B and F# with Lesser Thirds are seldom used, but D and A with Greater Thirds are:52 Now because the same Finger-boards that serve for the two later, serve also for the two former, and the Practiser may have them into the bargain, I thought it better to give these also, than to omit any thing that might easily be useful. When the Composer finds that the Instrument goes well in tune upon these Keys, he will not hereafter be so much afraid of them. This Calculation in the Tables is but for one length, viz. of 28 Inches from the Nut to the Bridge,53 and but for one Tuning upon the Viol; but the Workman may be directed from these Proportions given to fit them to the length of any Instrument: and from the Key given [p. 22] in any Lyra tuning, for any sort of fretted Instruments, he may find out what Proportions fall upon every String. Indeed Harpsichords and Organs, and such Instruments, where Frets are not used, cannot be accommodated the same way; but the Proportions and order of the Notes, are the same in them: They have something that makes the different gravity and acuteness of their Sounds, which may be so rectified, as also to render their Musick in a Mathematical perfection; but this is left to the ingenuity of the Artificer. I shall now observe something particularly of the Tables of Proportions, according to the numbers of the forementioned Keys, which you will find prefixed at the head of each of them, as they are annexed to the end of this Treatise. You will find, Number I. That A and C will not allow the sixth Base and Treblestring to have their fifth Frets upon the fourth part of the String,54 which makes a true Practical Fourth to the String open: For besides the least Diatonick Note, there falling two greater Notes upon the Strings D open, the stop G at the fifth Fret falls a pretty deal sharper; and accordingly the Fifth and Sixth Bases will not be a good Fourth to one another, but the Fifth Base must be tuned Unison at that place where the Table is marked.55 I have upon every Plate marked where the exact 4th and 5th and 6th part of the String falls, that you may see when the gradual Notes are not coincident with those larger Intervals, as in the forementioned case. Old Mr. Theodore Stefkins,56 (though he knew not the Mathematical reason) yet to make some allowance for this, was wont to direct the tuning of those Strings sharper than [p. 23] ordinary; by this Table you will find exactly how much sharper the tuning and the stops must be.

A Proposal to Perform Musick (1688)

101

Numb. II. In D and F with one Flat, you will find the same accident upon the fifth Base, where the same care must be taken, and all the Proportions will fall perfect. Numb. IIII.a, 57 In G and B@ with two Flats, you have another affair to be consider’d; which is the tuning the third String to the Chromatick Note at the fourth Fret of the fourth String, which causes those two Strings not to be a true greater Third to one another. The reason is, because E, to which the third String is commonly tuned, does not in these Keys (G and B@ with two Flats) fall upon the fourth, but the third Fret of the fourth String, which is E flat; so that the fourth Fret is now the Chromatick division between E flat and F: hence it follows also, that the first Fret upon the third String, which is F, is not the 16th part of the String, but the 17th, viz. the later part of that divided Note. These two Accidents are all that I think need be taken notice of in all seven of them, because though they do occur in the rest, yet being of the same nature, the Reader will know how to understand them. This may seem a difficulty and inconveniency; that after all, the Intervals of Musick could not every-where be given in perfect Proportions: And I will confess that there are a few instances wherein they cannot, as the lesser Note being the 10th part of a String, and the least Note which is the 16th part, will not make a true Lesser Third, that is the 6th part of the whole String.58 But this does not proceed from the defect of this Proposal, Nature it self will have it so; Scholars are not [p. 24] to alter Nature, but to discover her Constitutions, and to give opportunity for the best management of all her Intrigues: I still perform my design, because I maintain those perfect and Mathematical Proportions in every place, where demonstration either requires or permits them. That the Reader may know how few, and how easie to be avoided, these inconcinnous Intervals are, I will give him an account of all and every one of them: There are three in each Constitution of an Octave, which are exact and necessary to carry on the progress of single gradual Notes, but they must not be allowed in the Composition of Parts. Inconcinnous Intervals from the Key C. 1. A Lesser Third, from the Seventh to the Ninth above the Key. 2. A Fourth, from the Second to the Fifth above the Key. 3. A Fifth, from the Fifth to the Ninth above the Key. Inconcinnous Intervals from the Key A. 1. A Lesser Third, from the Second to the Fourth above the Key. 2. A Fourth, from the Fourth to the Seventh above the Key. 3. A Fifth, from the Seventh to the Eleventh above the Key. This is the exactness, which Reason, guided by Mathematical Demonstration, requires of us; and this ex-[p. 25]actness is rewarded by a proportionable pleasure,   Source has III: see the Errata on sig. a4v.

a

102

Thomas Salmon: Writings on Music

that arises from it. Indeed since Musical Ears, (especially where Sence has no great acuteness) are commonly debaucht with bearings and imperfections, they may not perhaps at first observe the advantage offer’d; but I am sure Nature desires it, and will rejoyce in those Proportions, which by the Laws of Creation she is to be delighted with. Yet there may be many an one, who will not care either for the trouble or charge of changing Finger-boards; if some little thing would mend their Musick, it might be acceptable: I shall therefore add one more Table, Number VIII. which any person that uses a fretted Instrument, either Lute, Viol, or Gittar, may easily make use of, and find the benefit of it.59 I call it the Lyrick Harmony, because our Lyra-tunings require all the Proportions to be most conveniently accommodated to the Strings open: Now if the Frets be placed at the distance assigned in this Table, they will be generally perfect. This Table is calculated like the rest for a String 28 inches long from the Nut to the Bridge; but whatever length your instrument be, keep the same Proportions, and you will be right: a fourth part of a String is a fourth part, and the same Proportion, whether the String be longer or shorter. For the first Fret then, take the 16th part of the whole String from the Nut, which is the least Diatonick Second that lies between B and C, between E and F; so that this will be always right, except in the Chromatick half Notes, not much used in Lyra Musick; but if the excellency of the Chroma be desired, then must the Pra-[p. 26]ctiser put himself to the expences of what has been formerly proposed: Jewels can never be had cheap. For the second Fret you have two Lines, the uppermost is the 10th part, the lowermost is the 9th part of the whole String from the Nut; we use no Proportion in Musick between the 16th and the 10th, as will appear by speculative Demonstration, and practical Experiment. If the tuning be with a greater Third, then the second Fret had best stand upon the 10th part; if the tuning be with a lesser Third, this second Fret had best stand upon the 9th part; for in Lyra-tunings the Key is generally some String open, and you will find by the twofold constitution of an Octave in the former Chapter, that the lesser Third requires the greatest Second from the Key, which is the 9th part, as from A to B; but the greater Third requires the lesser Second from the Key, which is the 10th part from C to D. This may not be always convenient, in respect of Composition, and therefore the Practiser may set his Fret where he pleases between these two strokes, according as he desires his bearings: however it can’t but be a very advantageous satisfaction, to know his Latitude within which he may be right, and above or below which he must be wrong: These are the bounds, Quos ultra citraque nequit consistere rectum.60 The third Fret must be the 6th part of the String from the Nut, which is the Proportion of a lesser Third to the String open; for ’tis demonstrable, that in

A Proposal to Perform Musick (1688)

103

Musick we use no Proportion between the 9th and the 6th part: but if you are not to have a true lesser Third to [p. 27] the String open, as may sometimes happen, when the tuning does not well favour your design, you may then use what bearing you please. The fourth Fret must be a 5th part of the whole String, as being the Proportion of a greater Third to the String open. The fifth Fret must be a 4th part of the whole String, as the just Proportion of a Practical Fourth. The length of the Plate would not suffer me to give the sixth and seventh Frets, which are upon Viols; but the direction is easie. The seventh Fret must be just the third part of the whole String from the Nut, as being the grateful Proportion of a Practical Fifth. The sixth Fret standing between the 4th and third parts of the String, may be usually placed in the precise middle,61 where you may make a stroke crossa the Finger-board of your Viol: but if the tuning requires any important Note to fall upon it, then may you tune your Fret by moving it higher or lower, as its Octave upon some of the higher Frets requires. Thus you may keep your former Gut-frets, which are movable and tyed quite cross the Viol; the strokes made upon the Finger-board,62 being as so many Landmarks, either to keep you just in the right, or else to give you aim in the Variation. I acknowledge that this will not come near perfection in the Note-way,63 nor always do in the other; but ’tis an advantage to make a good guess, and not always to do things at random: If I travel without a certain Track, an Information that I must leave a Town a quarter of a mile on the right hand, is a satisfactory direction, though I am not to go thorough it. [p. 28]b For a Conclusion of this Proposal, I need only add, that the truth of it is evident, both from Rational and Sensible Demonstrations; for the usefulness and necessity of it, every Man that wears a Musical Ear shall be Judge; the difference of Seconds, the greater and lesser Note, (which have hitherto been used without any regard) is so very considerable, that whoever takes but a transient view of them, will confess his Frets must be rectified, he cannot bear so great a deviation from what is truly in Tune; and accordingly the Practical Master does rectifie them, when he passes from one suit of Lessons to another. For assigning these particular Proportions, and denying that others are now to be used (as was asserted in the Lyrick Harmony) the Author desires no longer to be trusted, than there shall appear an inclination in any to study the Arithmetical and Geometrical parts of Musick, which are ready to be published.64 Μουσηγέτῃ Θεῷ Δόξα.c, 65   Source omits cross: see the Errata on sig. a4v.   Running head: A Proposal to perform Musick, &c. c   Source omits the two iota subscripts: see the Errata on sig. a4v. a

b

104

Figure 3.1

Thomas Salmon: Writings on Music

The first plate for A Proposal. British Library, shelfmark 557*.e.25.(4.). Reproduced by permission of the British Library.

A Proposal to Perform Musick (1688)

Figure 3.2

105

The second plate for A Proposal. British Library, shelfmark 557*.e.25.(4.). Reproduced by permission of the British Library.

106

Figure 3.3

Thomas Salmon: Writings on Music

The third plate for A Proposal. British Library, shelfmark 557*.e.25.(4.). Reproduced by permission of the British Library.

A Proposal to Perform Musick (1688)

Figure 3.4

107

The fourth plate for A Proposal. British Library, shelfmark 557*.e.25.(4.). Reproduced by permission of the British Library.

Thomas Salmon: Writings on Music

108

[p. 29]

TO Mr. THOMAS SALMON, M. A. RECTOR of Mepsal in Hartfordshire.a, 66 Decemb. 17. 1687.

SIR, YOurs of Decem. 5. I received this week, with the printed Sheets,67 of which you desire my Judgment: which I did the next day consider of, and made some Remarks on them. Not by way of contradiction to your Design, (which I approve of) but for explaining some particulars, which seem either not so clearly, or not so cautiously expressed. An account of which I send you with this, from, Sir, Your Friend to serve you, John Wallis. Remarks on the Proposal to perform Musick, IN Perfect and Mathematical Proportions. DIvers things you suppose therein, or take for granted, as agreed by those who have Philosophically discoursed of Musick; and thence proceed to what you direct, as to the Instrumental Practice thereof. [p. 30]b You first suppose, as agreed by all, (pag. 3. line penult.) that Musick consists in Proportion; and this Proportion (p. 4. l. 7.)68 twofold, in Tune, and in Time; meaning by that of Time, the different proportion of length and shortness of the intermixed Sounds; and by that of Tune or Tone, their different greatnessc and acuteness. There are some other things considerable, for the improvement of Musick: As, the different loudness and softness of the Sound or Voice, wherein a pleasing variety addeth much to the embellishment of the Musick, and may much conduce to that Pathos (or moving the Affections) which the Ancients seem much more to have affected than we do: And many other Appurtenances to Musick, more remote from your present business. You tell us then, (p. 4. l. 26.) That none will pretend to Musick by playing good Time onely, without that of Tune. You might here have excepted the Drum, the Tabor, and the Huntsmans Horn; which make a kind of Musick (though not that which you are here treating of) by a due mixture of long and short sounds of the   Corrected to Bedfordshire in Wallis’s manuscript errata.   Running head (pp. 30/31–40/41): Dr. Wallis’s Remarks on the / Proposal to perform Musick, &c. c   Corrected to Graveness in Wallis’s manuscript errata. a

b

A Proposal to Perform Musick (1688)

109

same Tone. And (as you there intimate, l. 10.) Dr. Isaac Vossius (in his Book De Viribus Rythmi) contends this to have been the Charming Musick of the Ancients, without taking notice of any difference of Tone therein. But this is not the part of Musick that you are treating of; but that other part which lieth in the proportion of Sounds, as to their Graveness and Acuteness, which by the Ancients was called Harmonica. You next take for granted, (p. 5. l. ult.) that in order to this, we are to have a Series or Sequence of certain Gradual Notes or Sounds succeeding one another, by which the Voice riseth and falleth;69 and this in the best proportion70 possible; that by a due mixture of these in several orders (as by a mixture of Letters to make words) the whole Musick may be best composed: And such are those Notes which we now call by the names of la mi fa sol la fa sol la, (and so forth in the same Sequence) which make up what we call an Octave, and the Ancients a Dia-pason, (the last of one Octave beginning another, in the same order, and so onward as far as there is occasion); to which the Ancients gave the names of Proslambanomenos, Hypate hypaton, Parypate hypaton, and so onward to a double Octave, or Dis-diapason; and which, in Guido’s Gammut, are called A re, B mi, C fa ut, &c. His A re answering to the Greeks Proslambanomenos, and the rest to [p. 31] the rest in order. (The original and reason of which names, I have given you elsewhere, and shall not here trouble you with them;)71 but are now wont (by Writers of Musick) to be expressed by the initial Letters of these names, A, B, C, D, E, F, G; and then (for another Octave) by small Letters, a, b, c, d, e, f, g; and (for a third Octave) by small Letters of another shape, or by small Letters doubled, aa, bb, cc, &c. And, if there be occasion to go backward from Γ or GG, by double great Letters, FF, EE, DD, CC, &c. And between every two of these Notes are certain Intervals, (as they are wont to be called) different according to their different proportions of the Graveness or Acuteness of those Notes each to other. ’Tis next presumed (p. 4.72 l. 27. p. 7. l. 21.) as agreed on all hands, that the little Intervals (between Note and Note next following) are not all equal. In the Diatonick Musick of the Greeks, and in Guido’s Gammut, they are accounted to be Tones and Hemitones intermixed; or, as we now call them, Notes and Half-notes, in this order. A. la.

B. C. D. E. F. G. a. b. c. d. e. f. g. aa. mi. fa. sol. la. fa. sol. la. mi. fa. sol. la. fa. sol. la. t. h. t. t. h. t. t. t. h. t. t. h. t. t.

&c. &c.

Not that they are exactly such, but near the matter. And what is the exact proportion of each, we are after to consider. What it is in the Chromatick or Enarmonick of the Greeks, comes not into our present Enquiry. And here we are to take notice of the ambiguous or double sence of the word Note. Before, it signified one particular Sound or Note, as la, mi, fa, &c. but here, when we speak of Notes and Half-notes, it signifies an Interval between Note and

110

Thomas Salmon: Writings on Music

Note. The Greeks had two words for it, Phthongus, and Tonus; but we use Note promiscuously for both. In an Octave thus constituted, from mi to mi (or from B to b, which is the natural place of mi) there are five Tones, and two Hemitones; (fa rising every-where half a Note, and the rest a [p. 32] whole Note:)73 and, therein two Tetrachords or Diatessaron’s, or (as we call them) Fourths; where, from mi or la, we rise by fa sol la, (that is, mi fa sol la, or la fa sol la, according as mi or la come next before fa;) and moreover, one Tone, or whole Note, la mi: which added to the Tetrachord, either next before it, or next after it, makes a Pentachord or Dia-pente, which we call a Fifth; whereby the Octave is near equally divided into a Fourth and a Fifth, as BE and Eb.74 And the same we have, for quantity, in any other Octave; as from A to a, from C to c, &c. though not in the same order: for the same Notes still return after one Octave, in the same sequence as before, the last Note of one Octave being the first of the next; so that what is cut off at the one end, is supplied at the other, at what place soever we begin: but the order is different. If we begin at A, then is la mi (the odd Note) in the first place, (before the two Tetrachords:) If at B, ’tis in the last place (after both:) If at E, ’tis just in the middle between both, (and will make a Pentachord with either.) If at any other place, one of the Tetrachords will be divided; and what of it is wanting at the one end, will be supplied at the other end of the Octave. Sutably hereunto, the Greeks observed seven Species or sorts of Octaves, (all equal in quantity, but different in order) according to their different beginnings. The first Aa, and second Bb, the third Cc, &c. of which each had its peculiar name. The first of them begins at A, which was their Proslambanomenos, (a sound given, or assumed,) answering to what our Musicians now call the Key: A Note at which (in the Base-part) the Song begins, and to which great respect is had through the whole. The other Species had their several beginnings, or respective Keys. Which, and how many of these, they did make use of in their Musick, is hard to say. Our Ancestors, about Guido’s time, seem chiefly to have affected that of G; as appears by their Scale beginning at Gamm-ut; and their Series of Notes, Ut re mi fa sol la: where we have two Notes lower than mi. And our MusickMasters, to this day, when they teach to sing, begin commonly with sol la mi fa, &c. as if ut, or the nearest sol below mi, were the Key or Note most regarded. Beside which, they seem (by the Gamm-ut) to have had two more75 (upon a remove) but of the [p. 33] same constitution, at C, and F, where (in the Gamm-ut) the Note ut returns again. For twenty years last past, you tell us (p. 7. l. 29. p. 8. l. 2.) in the compositions of the most eminent Masters, they scarce make use of any other Key (as to the internal constitution of the Octave) than A and C.76 That is, their Key or leading Note, at which their Base-part begins, is either la next before mi, or fa next above mi. And, because you are much better acquainted with the eminent Masters of Musick, and their Compositions, than I am, I take it, as to matter of fact, so to be.

A Proposal to Perform Musick (1688)

111

But at whatever Note they please to begin, and make it their Key, it is, as to this point, much one. If these Keys be transferred to any other place (to accommodate the Voice or Instrument) mi is transferred also, (by help of Flats and Sharps) and the other Sequence of Notes with it; which alters the Pitch but not the Tune (p. 8. l. 3, 12.) that is, the same Tune is sung by a higher or lower Voice. As for instance: If I would remove these Keys from A and C, to B and D, (that is, if I would set the whole Tune a Note higher) then must la (which is now at A) remove to B, and mi (from B) to C, and fa to D, and so forth. But then I find, that BC (an Half-note) is not wide enough to receive la mi, (a whole Note:) and therefore C (by a Sharp) must be raised half a Note higher, that B C# may be fit to receive la mi; and thence to D, will remain half a Note for mi fa; thence to E, an whole Note for fa sol; but thence to F, is but half a Note, not capable of sol la, an whole Note: and therefore F (by another Sharp) must be advanced half a Note higher, that E F# may receive sol la; and F# G receive la fa, (an Half-note;) and G a receive fa sol; a b receive sol la; and then b c# receive la mi, and so forth. So that C and F must everywhere have a Sharp, but the other Notes remain as before, in this form. B. la.

t.

C#. mi.

h.

D. fa.

t.

E. sol.

t.

F#. la.

h.

G. fa.

t.

a. sol.

t.

b. la.

t.

c#. mi.

h.

d. fa.

&c. &c.

[p. 34] In like manner, if I would bring back A and C, to Γ and B, that is, if I would set the Tune a Note lower; then must la come back to Γ, and mi to A, and fa to B, and so forth. But because A B (an whole Note) is too wide for mi fa (an Half-note) there B (by a Flat) must be taken down half a Note; that so A B@ may just receive mi fa, and (instead of B C an Half-note) B@ C (an whole Note) receive fa sol; and (for a like reason) another Flat at E. And so every-where at B and E. The rest remaining as before, in this form. Γ. la.

t.

A. mi.

h.

B@. fa.

t.

C. sol.

t.

D. la.

h.

E@. fa.

t.

F. sol.

t.

G. la.

t.

a. mi.

h.

b@. fa.

&c. &c.

And the like in other cases; of which you give us the particulars, at pag. 20. And it is, in effect, no other than the common Rules by which Learners are taught to find mi: Only there, by the Flats and Sharps we find the place of mi; and here, by the assigned place of mi, you find the Flats and Sharps, if any be. Of those two Keys, at A and C, in their natural position, you observe aright (p. 7. l. 31. p. 8. l. 21. p. 21. l. 3.) that if you begin at A, then are C, F, G, the lesser Third, Sixth, and Seventh, from the Key: If at C, then are E, a, b, the greater third, Sixth, and Seventh, from the Key. And therefore the Composer, if he design those, should chuse the Key A; if these, the Key C: or the equivalents of these transferred (as is shewed) to other places.

Thomas Salmon: Writings on Music

112

And thus far we have pursued the Language of Aristoxenes77 and his Followers the Aristoxeneans, and the Practical Musicians, who content themselves with the names of Notes and Half-notes, without enquiring into the Proportions of each Interval. But Pythagoras and his Followers, whom you call the Speculative Musicians, enquired further into the Proportions (of Graveness and Acuteness) at several Intervals. [p. 35] And here it was first discovered by Pythagoras, and since admitted by all, (which therefore you suppose as granted) that the Proportion for an Octave (as A a, or B b,) is Double, or as 2 to 1: That for a Fifth, (as A E, or E b,) Sesquialter, or as 3 to 2: That for a Fourth, (B E, or E a,) Sesquitertian, or as 4 to 3: And consequently, that for the Tone (A B, or a b,) Sesquioctave, or as 9 to 8. Hence Euclide (in his Musical Introduction, and Section of the Canon)78 taking all Tones to be equal, computes, that for the Ditone, fa sol la, to be as 81 to 64, (which is the duplicate of 9 to 8;) and therefore the Hemitone mi fa, or la fa, to be so much as that wants of a Fourth; that is, 256 to 243: which is somewhat less than half a Tone, or the sub-duplicate of 9 to 8.79 And so Boethius (after him) and others downward, till that (about an hundred years ago) Zarline revived the Doctrine of Ptolomy in this point.80 That of Ptolomy (in his Harmonicks) is this:81 The Proportions for the Octave, the Fifth, and Fourth, he retains as before; and that of the Dia-zeuctick82 Tone la mi; which, together with the two Fourths, compleats the Octave; and doth, with either of them, compleat the Fifth (And so far Pythagoras proceeded, and no further.) But the Ditone fa sol la, (which is the greatesta Third) he reckons to consist of two Tones, but unequal. The one as 9 to 8, (which is called the major Tone, and is equal to that of la mi;) the other as 10 to 9, (called the minor Tone:) and therefore the Compound of both, as 5 to 4; (which is a much more Musical Interval, than 81 to 64:) And consequently the Hemitone or Half-note mi fa, or la fa, (so much as 5/4 wants of 4/3) as 16 to 15, (which is somewhat more than half a Note:) and this together with a major Tone, (which make the lesser Third) as 6 to 5; as la mi fa (from A to C,) or la fa sol (from E to G,) or mi fa sol (from B to D) taking fa sol for a major Tone, and therefore sol la for a minor Tone. These Proportions setled by Ptolomy, (for the Diatonick kind) were afterward disused, till revived by Zarline about a hundred years since; who is followed by Kepler, Mersennus, Cartes, Gassendus, and others, (p. 14. l. 15.)83 and generally admitted by Speculative Musicians since Zarline’s time. And these you presuppose (upon their Authorities) referring to their Reasons for it. [p. 36] You pre-suppose further, (which Ptolomy had shewed at large, and is since admitted) that (in the same or like String) the degree of Acuteness is in counterproportion to the length: That is, if the Acuteness of the sound be as 2 to 1, (as in   Corrected to greater in Wallis’s manuscript errata.

a

A Proposal to Perform Musick (1688)

113

the upper Note of an Octave) the length of the String is as 1 to 2, (the Sound twice as sharp, the String half so long.)84 And where the Acuteness of the Sound is as 3 to 2, (as in the upper Note of a Fifth) the length is as 2 to 3. Where that is as 4 to 3, (as in a Fourth) this is as 3 to 4. Where that is as 5 to 4, (as in the greater Third) this is as 4 to 5. Where that, as 6 to 5, (as in the lesser Third) this, as 5 to 6. Where that, as 9 to 8, (as in the greater Tone) this, as 8 to 9. Where that, as 10 to 9, (as in the lesser Tone) this, as 9 to 10. And thus every-where, the length of the String is in the counter-proportion to the height or sharpness of the Sound. These things being premised, or pre-supposed, you proceed to the Constitution of the Keys A and C, (p. 9. and p. 12.) where, by 9, 16, 10, you mean 1/9, 1/16, 1/10, (which, I suppose, you so expressed, lest the small Fraction-figures should not be so easily seen and read.) And so, by 6, 4, 3, 2, (the portion of the String from the Nut to the Fret, for the Key A) you mean 1/6, 1/4, 1/3, 1/2, (sutable to85 3/8 and 4/9:) And (for the Key C) by 5, 4, 3, 2, you mean 1/5, 1/4, 1/3, 1/2, (in the same sence with 2/5 and 7/15;) according the Exposition your self gives, pag. 9, 10, 11. I should rather have chosen to express the place of the Fret, by the length of the other part of the String, from the Bridge to the Fret, than from the Nut to the Fret: (For it is that, not this, that gives the Sound.) In this manner. /9

8 B 9

15

/10

9 D 10

8

A

8

C

9

5 /16 C 6

/9

4 E 5

3 D 4

8

3 /16 F 4

8

/10

9

15

/9

2 E 3

15

/9

2 G 3

9

5 /16 F 8

8

3 a 5

8

/10

/9

5 G 9

9

/9

8 b 15

15

/10

1 a. 2

1 /16 c. 2

[p. 37] That is, from the Bridge to B, is 8/9 of what it is to A; and from the Bridge to C, is 15/16 of what it is to B: and so elsewhere. Again, from the Bridge to B, is 8/9 of that whole String; from the Bridge to C, is 5/6 of the whole. And so of the rest. But the sense is the same with that of yours. But herein I dissent from you; namely, whereas you say, C 10 D 9 E; I would rather say, C 9 D 10 E. That is, of fa sol la, I would make fa sol the bigger Tone, and sol la the lesser; at C D E, as well as at F G a.86 And then my Proportions would stand thus: /9

8 B 9

15

/9

8 D 9

9

A

8

C

8

5 /16 C 6

/10

4 E 5

/9

8

20 D 27

3 /16 F 4

15

/10

2 E 3

15

/9

2 G 3

9

9

8

5 /16 F 8

8

3 a 5

8

/10

/9

5 G 9

9

/9

8 b 15

15

/10

1 a. 2

1 /16 c. 2

Thomas Salmon: Writings on Music

114

The reason why you did otherwise at C D E, than at F G a, is (I presume) that A D might be a true Fourth to the Key A. Whereas otherwise 20/27 is a false Fourth. Though very near a true one: for 21/28 would be a true Fourth, being the same with 3/4. My Reasons to the contrary, are these. First, a Fourth (now a days) is scarce allowed as a good Concord;87 and therefore the less to be regarded: especially at this place. For, I suppose, it is not usual, from A the Key, to rise a Fourth at one step; but rather a Fifth, or a Third. And when from the Key you rise an Octave at two steps, the Fifth always begins, and the Fourth follows, (not first a Fourth, and then a Fifth:) For a Fifth being much the sweeter, this is first chosen; and the Fourth, which follows, (though not of it self so sweet) is helped by being an Octave to the Key; which is in fresh memory, as being the Sound last heard but one. (And of an Interval never used, we need have the less regard.) And if from any other place we [p. 38] move to D, the Note from whence we move (which was last heard) is more to be regarded, than the Key, which had not been heard for some while. And then, by preserving this Fourth at A D, you spoil a good Third (which is more considerable) at D F, and againa at B D, and a fourth at D G, and a Fifth at D a,b and again at Γ D; and so leave no place from whence to move to this D. And if perhaps you will say from d; at that it is as hard to come as at this D. So that your D will be of no use at all. And for such reasons, it was a Rule with the Greeks, that the two conjoyned Tetrachords, mi fa sol la, at B C D E; and la fa sol la, at E F G a; should ever be divided in the same manner. For though they had their μεταβολὴ κατὰ γένος,88 (a Transite from one kind of dividing the Tetrachord to another;) yet they would have this Transite to be always at the Disjunctive Tone la mi. Allowing to the Tetrachord above it, a different division from that below it; but not a different division to the two conjunct Tetrachords above it. Again, if you make your Key at C, and thence sing fa sol la; it is most natural for the greater Tone to begin, and the lesser to follow. (Upon the same account as when we rise an Octave at twice, the Fifth leads, and the Fourth follows; and when at two steps we would rise a Fifth, it is most proper for the greater Third to begin, and the lesser to follow.) And therefore here, not to make fa sol the lesser Tone, and sol la the greater; but, that the greater, and this the lesser; as your self do at F G a. And if, for these reasons, you give the same division to C D E, that you do to F G a; it will relieve all those inconcinnous Intervals mentioned pag. 24. I have now done with the Constitution of your two Keys at A and C, (and indeed of any other Key) in the natural Constitution. And consequently, with all the Essential Flats and Sharps, which serve onely to remove it to a higher or lower pitch, without changing the sequence of the Notes: And which are wont to be   at D F, and again noted for deletion in Wallis’s manuscript errata.   Corrected to G d in Wallis’s manuscript errata.

a

b

A Proposal to Perform Musick (1688)

115

noted at the beginning of the Tune, so as to influence the whole, without repeating them at the several Notes. [p. 39] But, besides these, there are some Accidental Flats and Sharps, which occur in the middle of the Musick, affecting some one Note. These you call Chromatick Half-notes, (p. 15. l. 10, 20. p. 18. l. 16.) which, you say, are truly made by placing the Fret exactly in the middle between the two Frets of the Diatonick whole Note wherein it falls. Which is not so cautiously expressed as not to be liable to a mistake.89 The Reader, by exactly in the middle, will be apt to understand an Arithmetical middle: as for instance, if F G be an Inch, F F# and F# G should be each of them half an Inch. Or, a Geometrical middle, (which we call a mean Proportional;) as, if the proportion for F G be as 8 to 9, that for F F# and F# G should be as 28 to 29a (the square Root of 8 to the square Root of 9.) Neither of which are your meaning. But you mean (I presume) a kind of Musical middle, which is thus to be taken: Supposing the Proportion for F G to be as 8 to 9, that is, (doubling both numbers) as 16 to 18; this is to be divided by help of the middle number 17. So that the Proportion for F F# shall be 16 to 17; and for F# G, 17 to 18. Which, together, make F G as 16 to 18, or 8 to 9. In like manner, if G a be as 9 to 10, that is as 18 to 20; then is G G# as 18 to 19, and G# a as 19 to 20: which, together, make 18 to 20, or 9 to 10. And this, I presume, (though the Book be not at hand) is the meaning of Aristides at the place cited;90 and your meaning here. And this, I suppose, may do pretty well in most places. But if we would be exact, we must, in each place, consider, what is the particular design we aim at in such a Flat or Sharp; and make the division accordingly. As for instance, if to the Key A, instead of a lesser Sixth at F, I would have a greater Sixth at F#; I must not so much aim at such equal division (or near-equal) of F G; as, to take out of it so much as will make E F# a minor Tone, (whatever chance to be the remaining part to G.) Which will make for F F#, (not 16 to 17, but) 24 to 25. (For this, with 15 to 16, for E F, will make that for E F# as 9 to 10; and for A F# as 3 to 5, a greater Sixth; instead of A F as 5 to 8, a lesser [p. 40] Sixth.) In like manner, if I would, from C, rise a Fourth to F, at two near-equal steps, (as when we rise an Eighth by a Fifth and Fourth; or a Fifth, by greater and lesser Third;) that is, if I would divide the Proportion of 3 to 4, or 6 to 8, into two near-equals; those are to be 6 to 7, and 7 to 8: And therefore C D# as 6 to 7, and D# F as 7 to 8, (whatever chance thereby to be the division of D E.)91 And the like for other cases. So that for instance, the same D# or F#, as to different purposes, shall signifie differently. And such Arts we must make use of, if we would revive the Greeks Chromatick and Enarmonick Musick. But the Speculation is too nice for most of our present Practisers. To return therefore to our Diatonick Notes, in their Natural or Primitive Constitution, together with their Essential Sharps and Flats incident upon removing   Corrected to √8 to √9 in Wallis’s manuscript errata.

a

Thomas Salmon: Writings on Music

116

the Key to an higher or lower pitch: having once fixed their Proportions as to the Monochord, (as supposing them all set off upon one String;) it is easie to transfer them to as many Strings as you please, (by the substitution of a smaller String, instead of a shorter distance) as you direct, p. 12. l. 9. And from thence to the Finger-board, p. 17. l. 23. p. 19. l. 25. p. 21. l. 17. Nor do I take exception to any of your Numbers herein; save that I think D with its Octaves (or the Equivalent upon removing the Key to an higher or lower pitch) should be tuned somewhat sharper than you direct.92 And therefore you may, if you please, cause a Mark to be made for it, in each of your Finger-boards, (as is already done in that at Numb. VIII.) a little below yours, in such proportion as I have before directed: That so the Practiser may, at his discretion, make use of yours or mine, as his Ear shall direct him. Your Reader also may be advertised, That though your Measures be fitted, on the Plates, (p. 21. l. 29.) to a String of 28 Inches; yet, on the Paper, they may chance to be somewhat less than so: For (being printed upon wet Paper) the Measures will shrink, as the Paper dries. [p. 41] And, because (p. 18. l. 29.)93 you do not confine your Artificer to this Method (of distinct Finger-board)a onely; you will give me leave to propose another. Which is (without changing the Finger-board) to have the Frets, for each String, to slide up and down in a Groove, (whereby they may be removed from place to place as you please) with Lines or Marks on the Finger-board (of several Colours, as Black, White, Red, &c.) at the place where every Fret is to stand for each Tuning.94 By help of which, the Practiser may at pleasure set his Frets to any of these Tunings, (or to any other upon emergent occasion) with what exactness he please; as well as in any unfretted Instrument. Nor do we herein depart from the Ancients: For there are manifest places in Ptolomy, that their Frets (μαγάδια) were movable, not in Tuning onely, but even in Playing.95 FINIS. [p. 42]

  Corrected to Finger-boards in Wallis’s manuscript errata.

a

A Proposal to Perform Musick (1688)

117

To the Reverend Mr. SALMON.

Reverend, I Thank you for the great kindness of your Letter,96 of which I am altogether undeserving: And as for your good contrivance in the Art of Musick, I wish that the use of the Masters of that Art may not hinder the best Method to obtain it.a However, you have left a Specimen to Posterity, of what might have been done; and also by this Present, much obliged, Oxon. Dec. 15. 1687.b

Reverend, Your Humble and Affectionate Servant, E. Bernard.

Notes 1 Horace, De arte poetica, 268–9; the lines are normally quoted in the form ‘vos exemplaria Græca …’: ‘Turn over, night and day, your Greek exemplars.’ See Q. Horatius Flaccus Opera edidit D.R. Shackleton Bailey (4th edn, Munich and Leipzig, 2001), p. 321. 2 Namely John Wallis and Edward Bernard, respectively the Savilian Professors of Geometry and of Astronomy. On Bernard see pp. 4–5 above. 3 On John Lawrence see p. 5 above. 4 On John Cutts see p. 81 above. 5 Psalm 139:14: ‘marvellous are thy works; and that my soul knoweth right well’ (AV). 6 Compare Essay, p. 3: ‘the little intrigues of the ear’. 7 Compare Essay, p. 79: ‘A brisk and lively Air will penetrate the thickest skull’, and J. Bruce Brackenridge and Mary Ann Rossi, ‘Johannes Kepler’s On the More Certain Fundamentals of Astrology. Prague 1601’, Proceedings of the American Philosophical Society, 123 (1979): 85–116, at p. 139: ‘a peasant does not reason what geometric ratio one voice bears to another voice. And yet that external harmony of chords flows through the ears of the rustic into his mind and cheers the man.’ 8 Lorain: Charles V, Duke of Lorraine (1643–90), the imperial general to whom Cutts was appointed adjutant-general in 1686. 9 The first great Conqueror: Julius Caesar. 10 After the siege of Vienna in 1683 a ‘Holy League’ of Austria, Poland and Venice was formed and, under Francesco Morosini (1619–94), began to conquer the European parts of the Ottoman Empire. The Athenian campaign took place in September 1687. 11 Plutarch, Life of Cicero, 4.7.6. The Teubner text has: σὲ μὲν ὦ Κικέρων ἐπαινῶ   Source omits it.   The volume is completed by sig. G4r–G4v, comprising ‘A / Catalogue of Books, / Printed for, and Sold by John Lawrence, / at the Angel in the Poultrey, Bookseller’. a

b

118

Thomas Salmon: Writings on Music

καὶ θαυμάζω, τῆς δ’ Ἑλλάδος οἰκτίρω τὴν τύχην, ὁρῶν, ἃ μόνα τῶν καλῶν ἡμῖν ὑπελείπετο, καὶ ταῦτα Ῥωμαίοις διὰ σοῦ προσγινόμενα, παιδείαν καὶ λόγον. See Plutarchi Vitae parallelae Recognoverunt Cl. Lindskog et K. Ziegler, vol. 1, fasc. 2 (Leipzig, 1964), p. 316. 12 Various ancient Greek musical texts had been printed in Greek and/or Latin from the very late fifteenth century, but Salmon probably alluded specifically to Marcus Meibom, Antiquæ musicæ auctores septem (Amsterdam, 1652). 13 This passage provides a rare piece of evidence about Salmon’s own religious leanings at this time, and indicates clearly that he was no fanatical puritan. 14 Salmon may have been thinking in particular of his former opponent Matthew Locke, much of whose music was for the London stage. 15 The ‘eminent Professors of this Science’ were presumably Wallis and Bernard, whose ‘testimonies’ appeared later in the book; each had written or published on ancient musical theory and could in that sense be said to ‘profess’ the subject. 16 The possibly disingenuous ‘omission’ of these demonstrations makes it unclear how far Salmon was at this (or any) stage dependent on Wallis for the mathematics behind his proposals, although his manuscripts show him capable at least of setting out that mathematics in what seem his own words. More unfortunately, this passage leaves obscure the question of whether Salmon considered the mathematical or the experimental ‘demonstration’ of his ideas to be the more conclusive. 17 Wallis was described thus on – presumably – the basis of his Claudii Ptolemaei harmonicorum libri tres (Oxford, 1682), a labour which according to a notice in the Philosophical Transactions he considered was ‘a Task well agreeing with his Province’ (Philosophical Transactions, 13 (1683): 20–21, at p. 20). 18 Guido: Guido of Arezzo (c. 991/2 – after 1033), the theorist who developed the system of staff notation for pitch and the system of solmisation for sight-singing. 19 John Wallis, ‘Appendix de veterum harmonica ad hodiernam comparata’ in Claudii Ptolemaei harmonicorum libri tres, pp. 281–328. 20 Athanasius Kircher, Musurgia universalis, sive ars magna consoni et dissone (Rome, 1650), vol. 1 p. 541. Αρατου Σολεως Φαινόμηνα καὶ Διοσημεῖα. Θεωνος Σχόλια. …Accesserunt annotationes in Eratosthenem et Hymnos Dionysii (Oxford, 1672), pp. 47–69; Kircher’s specimen of Greek musical notation was reprinted on p. 69. 21 Salmon would repeat broadly similar remarks about the excellence of modern music in his later writings (see for example ‘The Practicall Theory’, fols 5r–5v); usually he seemed to allude in particular to the absence of harmony, as opposed to melody, from ancient Greek music. 22 This was an elaboration, but not necessarily a development, of the idea expressed in the Essay that ‘God hath created a peculiar faculty of hearing’ (p. 2). 23 Salmon’s principle that ‘music consists in proportions’ had appeared in the Essay (p. 22) and would reappear in some form in nearly all of his later musical writings. On the remarkable claim that its excellence varied with the exactness of those proportions, see the Essay pp. 2–3 with notes 8 and 11 in Volume I of this edition, and compare ‘The Division of a Monochord’, fol. 6v. 24 Isaac Vossius, De poematum cantio et viribus rythmi (Oxford, 1673). 25 Later Salmon would describe the Greek enharmonic genus, not particularly accurately, as involving a division of semitones into quarter-tones; see p. 16. 26 Salmon’s ‘gradual Notes’ were not the various degrees of the scale, but the intervals or scale steps between them, as becomes clear in the following paragraphs: tones and

A Proposal to Perform Musick (1688)

27 28

29

30

31 32 33 34 35 36

37

38

39

119

semitones, in other words. See Wallis’s remarks on the ambiguity of the word ‘note’ on p. 31 below. Compare Essay, p. 11: ‘a Fardle of hard names’. As Rebecca Herissone points out (Music Theory in Seventeenth-century England (Oxford, 2000), p. 108), this passage may be Salmon’s belated response to one of Locke’s criticisms: see Observations, p. 28, where Locke had censured Salmon for failing to appreciate the use of capital, lower case and double letters to distinguish one octave from another. Inconcinnous: intervals which may be used harmonically but not melodically: see p. 24 (‘exact and necessary to carry on the progress of single gradual Notes, but they must not be allowed in the Composition of Parts’) and compare Wallis, ‘Appendix’, p. 154. Salmon did not describe the contents of his table very accurately; he would seem more secure when he came to discuss the ‘experiment’ which put it into practice. Between each pair of letters there appears a number, indicating the proportion by which a string must be shortened in order to move from the lower to the higher of the two pitches: to rise from A to B, for instance, we must shorten the string by 1/9 of its length. Those pitches which form harmonious intervals with the keynote A are labelled with the names of those intervals (C forms ‘A Lesser Third’, for instance) and with either a number or a fraction denoting the proportion by which the A string must be shortened to produce them (to produce C we shorten the A string by 1/6, for example). The ‘hard names’ were the gamut names (see note 27), such as ‘A la mi re’, in which the ‘first letter’ was the note’s letter-name. See Wallis, ‘Remarks’, p. 31. This passage may suggest that Salmon had now attained a greater degree of confidence with ratio operations than he possessed in 1685; see the Introduction, pp. 2–3. Here we see mathematical and aural ‘demonstration’ working together. On the role of the ear in musical experiments see pp. 18–19 above. A ratio is superparticular if the remainder after dividing the larger term by the smaller is 1 (3 : 2 is an example); it is superpartient if the remainder is more than 1. This particular set of intervals occurred in what Ptolemy called the diatonic of Didymus, a special case of the diatonic genus. See Ptolemy, Harmonics 2.13 (GMW, p. 349). This account of the motivation of the syntonic diatonic scale seems to have been Salmon’s own: the scale might more naturally be introduced by noting that the coexistence of major tones and pure major thirds in the same scale requires the use of some minor tones as the difference between the two. René Descartes, Renatus Des-Cartes excellent Compendium of musick, ed. and trans. anon. [trans. Walter Charleton, ed. William Brouncker] (London, 1653); Pierre Gassendi, Manuductio ad theoriam seu partem speculativam musicae, in his Opera omnia (6 vols, Lyon, 1658, facs. edn Stuttgart, 1964); Wallis, ‘Appendix’. Salmon had claimed in 1685 to have observational evidence of this from the practice of James Paisible, and the fact that he did not here mention that evidence or name the performer may be significant: possibly Paisible had declined to be named in print in this connection. Salmon’s diatonic semitone was about 112 cents, roughly 55 per cent of his major tone of 204 cents. Salmon’s description of them as ‘three-quarter’ notes here may have been little more than a vague guess; he would probably not have had the mathematical knowledge to work out their sizes in cents or any equivalent thereof, although Wallis could in principle have done so for him.

120

Thomas Salmon: Writings on Music

40 This description of the role of chromatic notes seems more concerned with the seventeenth-century diatonic context than with the Greek chromatic genus, although any interest in the chromatic notes being ‘coincident with the greater Intervals’ would be belied by Salmon’s actual procedure for placing them. 41 This was the same placement of the chromatic notes which Salmon specified in more mathematical detail in his other writings, dividing the major tone into semitones of 16/17 and 17/18, and the minor tone into semitones of 18/19 and 19/20. 42 Salmon referred to Meibom’s edition, in his Auctores septem; Aristides described a process of arithmetical division, generating intervals down to the ‘dieses’ with ratios such as 36 : 35. See GMW, pp. 495–6, and compare Salmon’s own expositions of such a procedure in ‘The Practicall Theory’, fols 2r–2v and ‘The Division of a Monochord’, fols 2r–3v. 43 Since this division placed the chromatic notes so that they could never form pure consonances with any diatonic note, the claim that practical musicians found it satisfactory seems very doubtful. 44 As was often the case in his Essay, it seems Salmon was talking about his own experiences as a performer. He had slipped from a discussion of the viol – where playing a series of semitones was easy – to a context in which it was difficult, most probably that of vocal music. 45 Various proposals had been made for modified keyboard layouts incorporating larger numbers of keys per octave than the usual 12, including the complex designs illustrated by Marin Mersenne in Harmonie universelle (Paris, 1636) and Harmonicorum libri (Paris, 1635/6); it seems more likely that Salmon was referring to the much less exotic ‘split keys’ which provide, for instance, E@ and D# as two separate pitches. See for example Christopher Simpson, A compendium of practical musick in five parts (London, 1667), p. 100: ‘the slitting of the Keyes’. 46 See Figures 3.1–3.4. 47 ‘I have tried’ could mean that Salmon had organised a trial of the scheme by professional or amateur performers, or that he had tried his proposal as a performer himself. The absence of specific references to the opinions of others in the Proposal may point to the latter interpretation. 48 Note: i.e. interval. 49 Tuned Note-ways: i.e. ‘the common Note-tuning’ (see ‘The Use of the Musical Canon’, fol. 35r), d'–a–e–c–G–D. 50 This slightly confusing sentence points out that since the major tone D–E was larger than the minor tone G–A, so must D–D# be larger in Salmon’s chromatic scale than G–G#, and thus the position of the first fret for the G string must differ from that for the D string. 51 This uncharacteristically defensive paragraph may have been a concession to Wallis’s insistence in his letter of 1686, to be repeated in his ‘Remarks’, that moveable frets were a better solution than interchangeable fingerboards. 52 Compare Christopher Simpson, Chelys / The division-viol, p. 16, where sixteen keys are illustrated (eight major, eight minor) with the key-notes G, A, B@, C, D, E@, E and F. Bearing out Salmon’s remark about ‘things … with four Flats’, even Simpson’s E@ minor has only four flats. 53 In ‘The Practicall Theory’, fol. 7r, Salmon would assert that 28 inches was ‘the most common Measure of a Viol-string’, although in ‘The theory of musick reduced’ he would use a slightly longer string of 30 inches.

A Proposal to Perform Musick (1688)

121

54 In Salmon’s major scale the interval from the second to the fifth degree was larger than a pure fourth, requiring, in this case, the fourth fret to be placed closer to the bridge on the D strings than on the other strings. 55 The G string must be tuned not a pure fourth from the D string below it, but in unison with the displaced fret just mentioned. Compare Salmon’s remark on, in effect, the same subject to Wallis in 1685, where the suggestion was, equivalently, to tune the D string a little sharp, and see note 5 in Chapter 1. 56 Theodore Steffkin (early seventeenth century–?1673) was named as an authority in the Essay (p. 82), and his two sons would take part in Salmon’s experimental performance in 1705; the family as a whole therefore appear as his most visible supporters and informants in the musical world. See the Introduction to Volume I, pp. 14 and 110, and the Introduction to this volume, pp. 23–4. 57 Here Salmon’s placement of the chromatic notes got somewhat in his way: in B@ major or G minor, E is a chromatic note, and both its appearance at the fourth fret of the C string and as the open E string must be governed by Salmon’s practice of arithmetically dividing the diatonic interval E@–F which contains it. Frets must be placed on the C string for E@ and F, a fret for E placed between them by arithmetical division, and the E string tuned in unison to the resulting pitch. As Salmon noted, this meant that the interval C–E was not a pure major third (but rather the arithmetical average of a minor tone and a perfect fourth). It also meant that all of the frets on the E string must fall at slightly different places from their cousins on any other string; Salmon remarked only on the position of the F fret. 58 A minor tone plus a diatonic semitone does not make a pure minor third. This affects, for instance, the interval E–G in the white-note scale. 59 Table VIII is a compromise of a similar kind to those found towards the end of ‘The Use of the Musical Canon’, showing how a single set of frets might govern all strings. Here frets for both minor tone and major tone were included, and frets were placed at 15/16, 9/10, 8/9, 5/6, 4/5 and 3/4 of the total length of the string, representing respectively a diatonic semitone, minor tone or major tone, minor third, major third and perfect fourth above the open string. 60 Horace, Satires I.1.107: ‘on either side of which right cannot be found’. See Horace: Satires, Epistles and Ars Poetica, trans. H. Rushton Fairclough (London and Cambridge, MA, 1929), p. 12. 61 A fret ‘in the precise middle’ between 3/4 and 2/3 of the string would divide the major tone separating the fourth and fifth above the open string into Salmon’s characteristic semitones of 17/18 (below) and 16/17 (above). 62 This reference to ‘strokes … upon the Finger-board’ recalls the language of ‘The Use of the Musical Canon’, although in the present context it need be read as no more than a description of Salmon’s Plate VIII. 63 See note 49 above. 64 The ‘Arithmetical and Geometrical parts of Musick’ were never published by Salmon. Those terms were used by John Birchensha, and it is possible that Salmon had acquired some of Birchensha’s material (he died probably in 1681). The type of material which may have been envisaged is indicated by the manuscript writings edited in this volume, and by Wallis’s ‘Remarks’ which filled in some of the technical groundwork which Salmon omitted. See Christopher D.S. Field and Benjamin Wardhaugh (eds), John Birchensha: writings on music (Farnham, 2009), chapter 3. 65 ‘Leader of the Muses, praise God.’ I cannot identify a source for this line.

122

Thomas Salmon: Writings on Music

66 Mepsal is in Bedfordshire, although the parish did extend into Hertfordshire, and on the title page of his Discourse concerning … baptism (London, 1701) Salmon would mention both counties (see the Introduction, note 31, and the Introduction to Volume I, p. 4). The plain contradiction of the title page of the Proposal seems odd, though, and would surely not have gone uncorrected by Salmon if it had been clear in Wallis’s manuscript; perhaps the most likely explanation is a printer’s guessing at Wallis’s unruly handwriting. 67 From what follows it seems clear that ‘the printed Sheets’ amounted to the whole of the Proposal’s main text; Wallis’s comments are consistent with that text as printed; the few discrepancies are explicable as his errors in counting lines, or slips of the pen. 68 Wallis ignored one very short line when counting the lines on this page. 69 Salmon’s text as printed has ‘rises or falls’. 70 Salmon had ‘proportions’. 71 Wallis quite possibly referred to his ‘Appendix’ to Ptolemy rather than to a letter to Salmon. 72 Properly p. 6. 73 That is to say, fa is always a semitone higher than its neighbour below. Other pitches are a tone higher than their lower neighbours. 74 Wallis constructed the octave from a fourth plus a tone plus a fourth, which could also be considered a fourth plus a fifth. The procedure recalls the ancient Greek construction of scales from tetrachords with or without intermediate tones. 75 Two more: i.e. two more scales. 76 The italicised passage is mostly made up of quotations from Salmon, but Salmon’s printed text has ‘for these last Twenty years’, and lacks the phrase ‘they scarce make use of any other Key’. 77 On the two approaches to music theory described here see Wallis, ‘Appendix’ (passim) and GMW, pp. 4–6. 78 The Isagoge harmonice formerly attributed to Euclid is in fact by Cleonides (and the attribution of the Sectio canonis is disputed: see Andrew Barker, The Science of Harmonics in Classical Greece (Cambridge, 2007), pp. 366–70); both texts were edited by Meibom in his Auctores. 79 If all tones have the ratio 9 : 8, it follows that the major third, the ditone, containing two tones, must have the ratio 81 : 64, and the diatonic semitone, equal to a fourth minus a ditone, 256 : 243. In ‘the sub-duplicate of 9 to 8’ Wallis employed a precise terminology meaning that this ratio was to be divided in two to produce 3 : √8, which is indeed greater than 256 : 243. 80 Gioseffo Zarlino promoted the syntonic diatonic scale in his Istitutioni harmoniche (Venice, 1558). 81 The division of the tetrachord described here does appear in Ptolemy’s Harmonics, at 2.13 (GMW, p. 349), but it is not given the special prominence which Wallis’s description might suggest. 82 Dia-zeuctick: i.e. with a ratio of 9 : 8. 83 Salmon cited only Descartes and Gassendi at the place noted. 84 Absent any indication of how the ‘acuteness’ of a pitch could be quantified – other than by the length of the string which produced it – this and the following assertions seem somewhat empty. Wallis had elsewhere considered seriously the possibility that the pitch of a sound was determined by the frequency of the vibrations which caused or constituted it, and was almost certainly aware of the experimental evidence for this,

A Proposal to Perform Musick (1688)

123

including work with long strings reported by Mersenne, by Charleton, and the Royal Society, but he adopted an agnostic stance about the matter. See The Correspondence of Henry Oldenburg, ed. A. Rupert Hall and Marie Boas Hall (13 vols, Madison, Milwaukee and London, 1965–86), vol. 1, pp. 192–3; David Cram and Benjamin Wardhaugh (eds), John Wallis: writings on music (Aldershot, forthcoming), chapter 1. 85 Sutable to: i.e. ‘in the same sence with’. 86 On the different versions of the syntonic diatonic scale, see pp. 12–14 and Chapter 5, notes 15 and 26. 87 This passage is the most extensive discussion we have from Wallis on the status of the fourth. Mathematical theory, and various Greek texts, ranked it as the next most consonant interval after the fifth, but seventeenth-century practice viewed it as an interval which, at least, required resolution. See Wallis, ‘Appendix’, p. 182, and H. Floris Cohen, Quantifying Music: the science of music at the first stage of the scientific revolution, 1580–1650 (Dordrecht, 1984), pp. 63–5, 95. 88 Literally, a shift from genus to genus: the phrase appears in ‘Euclid’ (i.e. Cleonides), Isagoge, at p. 20 in Meibom’s edition in his Auctores, and was quoted by Wallis in his ‘Appendix’, p. 166. 89 Rather obviously, Wallis did not think this incautiously expressed; he thought it false. Salmon’s words clearly indicated an arithmetical division of the intervals in question, and he would continue to set out such a division more clearly in his later writings until ‘The theory of musick reduced’. Wallis’s proposal of a ‘musical’ division (at the ‘harmonic mean’ of the two lengths concerned: see Introduction, p. 17) was consistent with his suggestion of always placing the major tone below the minor tone when dividing a major third. Simply stated, his proposal was this: a pair of frets producing a ratio of string lengths of 9 : 8 should be divided by a fret which is 9 units from one and 8 units from the other, placing the larger interval at the bottom. Where Salmon’s procedure of arithmetical division would turn 9 : 8 into its equivalent ratio 18 : 16 and place a fret at the midpoint, 17, Wallis would turn it into 153 : 136 (multiplying both terms by 17, that is 9 + 8), and place the new fret at the point 144. In both cases the ratios produced by the new fret are 18 : 17 and 17 : 16, but the two strategies put them opposite ways around. Wallis obscured all of this by describing his proposal in terms not of string lengths or fret placements but in terms of what amount to frequencies. This is indicated by the phrase ‘Supposing the Proportion for F G to be as 8 to 9’, where the assignment of a lower number to a lower pitch shows that he was not thinking of string lengths. 90 Wallis was wrong: Aristides, like Salmon, was concerned with the arithmetical division of string lengths (see GMW, pp. 495–6). 91 This division of the fourth into ratios of 6 : 7 and 7 : 8 Wallis had discussed in letters to Henry Oldenburg in 1664 and in his ‘Appendix’ to Ptolemy (see The Correspondence of Henry Oldenburg, vol. 1, p. 198–9; Wallis, ‘Appendix’, pp. 178, 180; and John Wallis: writings on music, chapters 1 and 3), and Salmon would return to it in ‘The Division of a Monochord’, fols 3v, 4v, arguing against the feasibility of including the resulting intervals in the scale. Wallis again envisaged a harmonic division of intervals, with the larger interval falling below the smaller. The modified D# he described would nevertheless fall only about 63 cents above D. 92 This referred not to the de-tuning of G relative to D discussed in the 1685 letter and the Proposal, p. 22, but to Wallis’s suggestion of reversing the order of major and

124

93 94

95

96

Thomas Salmon: Writings on Music minor tones between C and E, slightly raising the pitch of D. Compare Descartes’s provision of two versions of the notes G and D: Compendium, pp. 32, 35. Line 25 was intended. This refined Wallis’s similar suggestion in his letter of 1686; explicit mention of a ‘groove’ was new for him (but compare Salmon’s ‘notch’ in his letter), as was the idea of using different colours to distinguish the different possible positions for each fret. Compare the use of lines of points and crosses in ‘The Use of the Musical Canon’. If this assertion can be defended it is probably on the basis of Harmonics 3.1, where the word in question occurs in the discussion of a multi-stringed, though not obviously a practical, instrument. Barker translates it as ‘bridges’ (GMW, pp. 362–5), and the context seems to be an experimental/theoretical one rather a description of a practical instrument. Compare Harmonics 1.8, where the context is plainly experimental. I have not attempted to locate the letter among Bernard’s voluminous papers.

Chapter 4

‘The Practicall Theory of Musick’ (1702) Editorial Note A manuscript of 11 folios held in the British Library (MS Add. 4919, fols 1–11) is the first evidence we have for Salmon’s musical activities after the publication of his Proposal in 1688. The text bears the date 1702, and the following title: The Practicall Theory / of Musick / To perform Musick in perfect proportions / and / To set out the proportions upon the Viol / so that they may fall right / upon the frets.

The manuscript consists of individual leaves, each measuring approximately 150mm × 195mm, mounted in a guard book which contains no other material. The text is in two short sections with separate headings, namely ‘To Perform Musick in perfect proportions’ (fols 1–5) and ‘To set out the proportions upon the viol so that they may fall right upon the frets’ (fols 7r–9r); each consists of continuous text, with catchwords throughout. Fols 6, 10 and 11 contain only diagrams (two on fol. 6, while fols 10 and 11 in fact contain a single diagram, probably originally drawn on a single large leaf and subsequently cut in half, with some loss of text, though it is difficult to be certain: see Figure 4.4 on p. 136). There is a pagination which could be contemporary with the text, obscured in several places by damage to the edges of the paper; it appears originally to have run from 1 to 13 on fols 1r–5v and 7r–9r, omitting to number either side of fol. 3. The diagrams at this stage were apparently inserted so as to face page 3 and page 9 (they are labelled, in Salmon’s hand, ‘Page 3’ (fol. 6r) and ‘Page 9’ (fol 10r)). There is also a cancelled foliation running from 44 to 54, which similarly places the first page of diagrams between fols 3–4 and the second (seemingly now divided into two leaves) between fols 8–9. The present edition places the three diagrams approximately where they seem to have been intended to appear in the text. There are two endorsements; the first appears on fol. 12r and reads: ‘11 folios, may 1903 b.g.b. / Examined by […]’, ending with three indecipherable initials. (The present binding appears to be consistent with this date.) The second appears on the recto of the leaf preceding fol. 1; its substance is as follows: ff. 1(part), 6, 10v–11 appear to be same hand as letters of Thomas Salmon in Sloane MS. 4040, ff. 103, 108. [Lady Jeans]

126

Thomas Salmon: Writings on Music

This is likely to date from after about 1950, when Susanne, Lady Jeans (1911–93) began to publish on musicological subjects. The Sloane manuscripts she referred to are those edited in Chapter 7 of the present volume. It seems to me that her judgement is correct, and that (part of) the title page, and the diagrams, are in Salmon’s own hand. Several fairly substantial insertions on fols 4v and 7v–9r (see Figure 4.1) also appear to be in Salmon’s hand, as do many smaller emendations elsewhere (it is not always possible to be certain, where brief, sometimes cramped interlineations are concerned; places where I am confident which hand is involved are noted in the footnotes to the text). This was thus a scribal copy which was later worked on by Salmon; it may perhaps have been made by a member of his household – one of his children? – in Mepsal. The hand is not the same as that of ‘The Use of the Musical Canon’. Having apparently begun as a fair copy, complete with catchwords, of an earlier text, now lost, this manuscript thus became the basis for Salmon’s revisions and second thoughts, none exceeding about half a sentence. It was not revised thoroughly, however, since some rather obvious numerical errors (5 repeatedly appears for 3) went uncorrected. Salmon himself was never mentioned by name, even when his Proposal was cited on fol. 9r, but the close relationship of this text to his ideas, together with the presence of his hand, puts it beyond reasonable doubt that he was its author, not just its reviser. Concerning the audience for which this copy was made, and its history before 1778, we can do no more than guess; in that year it was given to the British Museum by Sir John Hawkins, who possibly had collected it in connection with work on his History.1 Turning to the content of this text, the title and one or two phrases (notably the assertion that ‘All harmony consists in proportions’) clearly recall Salmon’s Proposal, as does the final diagram, which takes the form of a chart for placing the frets on a viol. The text describes and recommends the same chromatic scale, with five different sizes of semitone, which Salmon discussed in his Proposal. It is distinguished, though, by certain innovations; one of the most prominent is a more systematic account of the derivation of musical intervals from one another, in which larger intervals are successively broken down by doubling their terms and ‘clapping in’ the intermediate number: 2 : 1 becomes 4 : 2, which is split into 4 : 3 and 3 : 2, for example. Four stages of such division, illustrated by a sort of ‘family tree’ of intervals, sufficed to produce all the intervals in which Salmon was interested, plus many more, whose rejection he spent some time trying – unconvincingly – to justify; it is rather obvious that his commitment to his scale, and therefore to a specific set of intervals, preceded the systematic account of their derivation. This mathematical derivation of the musical intervals was also set out more briefly in ‘The Use of the Musical Canon’ (Salmon may ultimately have taken it from an ancient source such as Aristides,2 though by the time of this text he could also have seen the related material in William Holder’s 1694 Treatise of the Natural Grounds, and Principles of Harmony). Together with the failure of the present text to adopt or even mention the harmonic as opposed to arithmetical

‘The Practicall Theory of Musick’ (1702)

127

procedure for dividing intervals which Wallis had suggested in his ‘Remarks’ on the Proposal,3 this gives the impression that Salmon was now self-consciously re-working his own ideas and perhaps revisiting material from the period when he was writing the Proposal, not following the line of development which had been indicated by Wallis. Similarly idiosyncratic is a second innovation compared with the Proposal: the proposal to alter the tuning of the viol’s strings from the ordinary d'–a–e–c–G–D to the rather exotic c'–a–f–c–F–C (the ‘harp-way sharp’ used in Salmon’s Essay, transposed down a tone).4 This change enabled a single set of frets, each crossing the whole fingerboard perpendicularly, to do the whole work of tuning a certain set of pitches, namely the white notes plus c#, d#, f#, g# and b@, together with a stray a# on the a string.5 If these were not sufficient, the more complex solution of separate frets for each string would still be needed, and it is far from clear to whom this retuning would have been attractive. (If Salmon was thinking of the lyra viol, the tuning of whose strings was very much less standardised, he did not say so.) These changes compared with the Proposal suggest that Salmon had perhaps not altogether ceased to ponder over musical theory during the intervening 14 years. Unfortunately we can only guess what might have prompted him to set his thoughts down in this particular form in 1702, laying the foundations for his final and most public musical work a few years later, in 1705. Notes 1 The British Library Catalogue of Additions to the Manuscripts 1756–1782 (London, 1977), pp. 283–4; see the Introduction, p. 28 for Hawkins’s opinion of Salmon. I am indebted to Christopher D.S. Field for this reference. 2 See Aristides in GMW, pp. 495–6, for instance, and note Salmon’s citation of this passage at Proposal, p. 15. 3 John Wallis, ‘A question in musick lately proposed to Dr. Wallis, concerning the division of the monochord, or section of the musical canon: with his answer to it’, Philosophical Transactions, 20 (1698): 80–84. 4 Essay, p. 50. It is possible that Salmon was once again thinking of the ‘unstop’d freedom’ with which the tonic triad may sound in such a tuning; the downward transposition would fit it for F rather than G major (Christopher D.S. Field, personal communication). 5 See Figure 4.4. I am indebted to Christopher D.S. Field for his remarks on this point.

128

Figure 4.1

Thomas Salmon: Writings on Music

A page of ‘The Practicall Theory’, showing Salmon’s hand in a marginal addition to the text. British Library, Add. MS 4919, fol. 4v. Reproduced by permission of the British Library.

‘The Practicall Theory of Musick’ (1702)

129

Text [fol. 1r]

The Practicall Theory of Musick

To perform Musick in perfect proportions and To set out the proportions upon the Viol so that they may fall right upon the frets. 1702. [fol. 2r]

To Perform Musick in perfect proportions. The power of Musick lies in moving the affections, which are entertained with a delight that arises from harmoniou[s]a sounds: All harmony consists in proportions, so that the more exact the proportions are, the more powerfull will the harmony be[.]1 Nature hath both prepared man to receive the delights of harmony by his ear, & sounds in proportionate Numbers to cause such delights: Wee will therfore first consider what Harmony is found in Naturall Musick, what are the proportions of its Numbers, how these may be set forth upon a string & made use of by us; then we will consider what proportions art has made choice of, in what order they lye, & how our practical musick is composed of them. It must be laid down, that every Musicall Note is made by a comparison of two sounds which bear a proportion to one another: & the greater2 the Proportion is, the more satisfactory it will be to the ear. There is no greater or better proportion, than that of 2 to 1, the whole string divided into two parts, & compared to one of them; then follows the proportion of 3 to 2; then 4 to 3, & so on as long as the ear is able to distinguish & judge of them. It has been a great prejudice to the speculations of Musick, that authors have represented musicall proportions in such vast Numbers, that no eye is able to judge of them by the view, no hand can divide a string into so many parts as are requisite to set them forth.3 You shall therefore have here that plain & easy Division which Nature makes; that you [fol. 2v] may presently see what the proportion is & set ‹it› forth with your Compasses upon the finger board of your Instrument. We can’t divide the proportion of 2 to 1 the two smallest numbers, except we run into fractions or double these two original Numbers. All fractions make proportions seem intricate, we will therefore ‹separately›b double 2 & 1, which so doubled will make 4 & 2: between these you will find the intermediate number three; so that placing them thus 4, 3, 2, you have a

  Edge of paper is damaged.   Insertion in Salmon’s hand.

b

Thomas Salmon: Writings on Music

130

the first proportion 2 to 1 divided into two subordinate proportions, viz, 3 to 2, & 4 to 3. This is the first Descent from the Duple. To proceed in the same Method, we double the proportion of 3 to 2, & clap in the intermediate number thus 6, 5, 4, so that we have two more proportions in the ‹second.›a, b Descent viz, 5 compared to 4, & 6 to 5. Again we double the proportion of 5 to 4, & clap in the intermediate number thus, 10, 9, 8, so that we have two more proportions, 9 compared to 8, & 10 to 9, which is the ‹third›c, d Descent. We make use of but one Descent more, dividing these two last proportions after the same manner; which will make four. viz, the proportion of 9 to 8, will make 18 to 17, & 17 to 16. The proportion of 10 to 9, will make 20 to 19, & 19 to 18. Thus far we are gone on in the right line of the elder house, which was the proportion of 3 to 2 made out of the first proportion 2 to 1. But Nature also regards the younger house, the proportions of 4 to 3, & 6 to 5, out of which arises a vast variety of proportions. These nature hath taught the birds to form with their melodious voices, & are commonly called their wild notes;4 But Man whose voice was given more for the Sake of speaking than singing, is not by nature endowed with the utterances of all this variety of proportions; his Ear is delighted with it [fol. 3r] when he hears it, but the difficulty of practice, (which must come by the custom of imitations)5 makes him choose out some only, which are the plainest & fullest of them; & then take two or three of the lesser Proportions whereby he may pass on, & arrive at the greater. [fol. 6r]e The Naturall Division of a Duple Proportion: All the Proportions used in Diatonick Musick are enclosed in black circles; the other are prick’d about. [fol. 3r] Here you must look upon the Scheme6 which sets forth the Natural Progeny of a duple proportion, where you have all the subordinate proportions which arise from it; Those which humane art makes use of are mark’d with black circles, those that would not fall in with our artificiall composures are only prickt round. In the lower part of the Scheme, you have the practical Division of an Octave: The duple proportion is call’d an Octave, because you have eight notes or sounds inclusively as you pass on from the terminus à quo to the terminus ad quem. This is the reason of a practical fourth & fifth, with all the like Denominations, till you come to the a

    c   d   e   b

Insertion probably in Salmon’s hand. Deleted: ?third. Insertion probably in Salmon’s hand. Deleted: ?fourth. Labelled Page. 3. in Salmon’s hand.

‘The Practicall Theory of Musick’ (1702)

Figure 4.2

131

The first ‘scheme’ for ‘The Practical Theory’. British Library, Add. MS 4919, fol. 6r. Reproduced by permission of the British Library.

gradual notes, which are of three sorts, a greater note the proportion of 9 to 8, the lesser note 10 to 9, & the least note, 16 to 15. We are forced to go a great way to fetch in this last note 16 to 15 ’tis the least proportion of the fourth Descent from the Duple,7 but without this we could not make a true practical fourth nor a lesser third, nor pass on thro’ harmonious intervals to the octave. The not understanding of these things, has brought intolerable imperfections into the practice of Musick; ‹so as› to make no distinction between a greater & a lesser Note, between the half Notes of these, & that least Note, which makes a distinct step in the Octave. But every [fol. 3v] learned man sees the difference of the proportions, & how great it is when he comes to set it forth upon his string: Nor is the practical Musician able to bear it, but will be removing his frets as he changes his Key. Indeed those Instruments which have no frets, are not capable of being so helped; upon which account some kind of sound is taken between both, as is commonly call’d the best bearing; which is true to neither proportion but as little offensive as possible; & by custom the ear accep[ts]a of it, tho’ the a

  Paper is damaged.

Thomas Salmon: Writings on Music

132

Musick cannot be powerful since the Harmony which consists in proportions is so much diluted.8 The Progress from the Key given to its Octave is thro’ the foregoing gradual Notes placed in a certain order: They are by the learned call’d Tones, from whence this sort of Musick has the name of Diatonick; & if you place them one after another, as they stand in the Scheme,9 you will find that they exactly constitute those principall Concords which we stand most in need of. [fol. 6r]a The Diatonick Division of an Octave All the Naturall Notes are in black circles; those which are Artificially brought in, are prick’d about.

Figure 4.3

The second ‘scheme’ for ‘The Practical Theory’. British Library, Add. MS 4919, fol. 6r. Reproduced by permission of the British Library.

[fol. 3v] To be assured of this, we may proceed by those Arithmetical operations which Gassendus has laid down in his Theory of Musick;10 by adding & subtracting, by multiplying & dividing, you have undeniable Demonstrations of all the proportions here assign’d. Those of them which are produced by our natural way of Division,   Labelled Page. 3. in Salmon’s hand.

a

‘The Practicall Theory of Musick’ (1702)

133

you have, set out by black lines but such as art has brought together for composing the Intervals we now make use of, you will find distinguished by prickt Lines.11 The first Artifice of this sort, is the composure of a lesser Third, which has not its own Progeny 11 to 10, and 12 to 11, but 16 to 15, and 9. to 8. however if you add the two former proportions together, & the two latter proportions together, they w[ill]a both make that same proportion of 6 to 5: & take up the same length of a string. [fol. 4r] The reason why we do not take the Natural Progeny of a lesser Third is evident, for those two gradual Notes of 11 to 10, & 12 to 11, would encrease our difficulties in learning to sing such new proportions which are not useful in composing other Intervalls. All this holds in a practical fourth, the proportion of 4 to 3: if we took all its natural Progeny, we should have two more proportions of the second Descent, & three more of the third Descent to learn; which yet would not contribute any thing more to the common Interest of a Diatonick Octave, than those three 9 to 8, 10 to 9, 16 to 15 which we had learn’t before. But when we come beyond a practical fifth, which is the greatest Interval we have out of the natural Division of the duple proportion we add one Note & make a sixth; in like manner by adding one Note more we make a seventh: both which having the gradual Notes whereof they are constituted, added together, do not make superparticular but superpartient proportions; & therefore taken by themselves are not good Concords;12 yet have ‹they›b a very good Relation to all the rest of the Chords & being skillfully mixt with them are of very great use in Musick. Here it must be considerd that the placing the greater third 5 to 4 next the Key, or the lesser Third 6 to 5 makes a very great Difference in Musical Compositions: tho’ the common Musick Masters can’t distinguish a Tone major from a Tone minor,13 yet he is to be look’t upon as no Master at all, that can’t distinguish between a greater Third & a lesser Third. According to the positions of these two thirds from the Key, there arises the twofold Constitution of the Octave: and correspondent to the Thirds are the Sixths & Sevenths: If you have a greater Third, you must have a greater sixth & seventh; if a lesser Third, a lesser sixth & seventh. All the Intervals of Musick c are managed either by the letters of the Alphabet A. B. C. &c or four Monosyllables, fa, sol, la, mi; in Vocal Musick we chiefly make use of the Monosyllables, in instrumental Musick of the Alphabetical letters. [fol. 4v] For the natural Constitution of the two sorts of Octaves, we begin with the letters A, & C, because in those two Keys we have no Essential Flats or Sharps. The Key A having a lesser Third next to it, is more feminine & languishing; the letter a

  Paper is damaged.   Insertion probably in Salmon’s hand. c   Illegible deletion (of two words). b

Thomas Salmon: Writings on Music

134

C having a greater Third is more heroick and Masculine. But Guido restoring Musick, after the barbarous Nations had ‹destroyed›a, b the learned practise of it, & not having a full Understanding of its true Nature, was pleased to begin with the letter of his own Name; which is still the common way of teaching. ‹which in the Naturall course makes a lesser Seventh with a greater Third. & therefore now in Gamut Key F fa ut is always sharp.›c The Monosyllables contain the Mathematical proportions of the gradual Notes, & do something help in the pronouncing of them: from fa to Sol is always a major Tone 9 to 8, from Sol to La always a minor Tone 10 to 9;d & from the preceeding Tone to fa is always the Tone Minim14 or 16 to 15. These always come twice over in their order in every Octave & besides these there is the odd note mi, which from the preceeding note ‹La› is always the proportion of a major tone 9 to 8. You shall see all these in their order at the bottom of the Scheme, every Interval mark’d both with the Monosyllables & Letters: but these are not sufficient for the uses of Musick except we descend one degree Lower, the major & minor Tones must be again divided, which being done exactly in the middle15 make the Chromatick half Notes which are described by accidental flats & sharps; if these be skillfully brought in, & their due proportions given to the Ear, by the Instrument, they are a most charming sort of Musick, & therefore must be provided for. They were so considerable among the ancients that they constituted a particular Species of Musick call’d the Chromatick; & besides these, learned antiquity descended [fol. 5r] to a further Division of these into quarter Notes which were produced out of the Chromatick half Notes, after the same manner as these were derived from the whole Notes. Which least divisions of all, were called Dieses & constituted the Species of Enharmonick Musick.16 It is not now possible that we should be entertained with the power of Chromatick Musick, whilst our Instruments are framed with such Imperfections, as to make no Distinction between the major & minor tones, so that the subdivision of their half Notes cannot be much affecting; & for the quarter Notes, as things now stand, there cannot be any account at all made of them; though it is very possible this learned age may first set forth their proportions upon some Instruments, and then find the use of them.17 It is certain that the Romans received their Musick from the Grecians, & the Grecians from the more Eastern part of the world; among which we may reckon the Hebrews e, and if God took as much care of the Musick of the Temple, as he did of the building of it at Jerusalem,18 without doubt it was in the greatest Excellency there. Thus much we find that Aristoxenus & the most ancient Greek Musicians a

    c   d   e   b

Insertion in the scribe’s hand. Deleted: ?restored. Marginal insertion in Salmon’s hand, cued with X. Altered from: 9 to 8. Deleted: ?Musick.

‘The Practicall Theory of Musick’ (1702)

135

complain, that even in their time there was a great decay of Musick, and that the Enharmonick was almost lost.19 I know there is an opinion that Musick was never more excellent than in this present age, and it may be partly true.20 If we distinguish of the two parts whereof it doth consist, Time and Tune: The Time of Notes with the ancients, perhaps was nothing more than the different quantity of pronouncing syllables in their verses,21 whereas we subdivide from Sem[i]briefs to Demisemiquavers; & hereby arises that pleasantness of air, which captivates the phancy and hurries on the Notes so fast, that the imperfection of their Proportions cannot be consider’d by the Judgment. [fol. 5v] But after all ’tis very suspicious, that we have lost much more by the neglect of the proportions to be observed in Tune, than we have gained by the variety of Time. The skillfull Organist dare not have any Chord tuned perfect but his Octave, & accordingly reckons his Instrument best in Tune when there is the least observable Discord by the best contriv’d bearing, though there be nothing of exact Concord in the bowels of an Octave. Add to this failure of the Diatonick, the Corruption of the Chromatick, and the utter loss of the Enharmonick, and we have reason to believe, that we do not now find the ancient power of Musick, because we do not observe the ancient proportions.22 The pleasantness of air in the Multiplicity of Time is that which indeed gratifies Sense, but is very prejudicial to the Understanding: not only because the phanciful Composer takes a liberty to make long syllables short and short ones long, but he will repeat some impertinent words so many times over as to tire the thoughts, & breaks ‹the›a words into such a multitude of syllables that no auditor can tell what they mean.23 Now certainly a wise man is cheifly moved by his Understanding, and if excellent sense be conveyed to him by harmonious Sounds, this is that which captivates the soul with power. Whereas our present hurry of Musick is only agreeable to a giddy mind, and is more proper to ruin than advance the Interest of Morality. There was as great a difference with respect to vertue and vice between the times of K. Charles the first, & K Charles the second, as there was with respect to the movements of their Musick.24 [fol. 7r]

To set out the proportions upon the viol so that they may fall right upon the frets.

[fol. 11r] The New Tuning of the Viol according to the Perfection of the Proportions, both for Vocall & Instrumentall Musick.25 r [fol. 7 ] a

  Insertion in Salmon’s hand.

Thomas Salmon: Writings on Music

136

Figure 4.4

The ‘Scheme of proportions’ for ‘The Practical Theory’. British Library, Add. MS 4919, fols 10v, 11r. Reproduced by permission of the British Library.

It will appear ‹at the bottom of the first›a, b Scheme of proportions,26 that ‹whereas›c the two lowest strings in the common tuning of the viol,27 double D sol re & Gamut ‹being open require next›d, e the Nut of the Viol f a Minor Tone, g the fourth string which is C fa ut, & the second string which is A la mi re will have a major ‹Tone›; the third string E la mi has next to it F fa ut which is a Tone minim;28 and accordingly the proportions which follow from the open strings fall so differently upon the frets, that those which stand true to some, will stand false to others, or else must have such bearings, as are true to none at all. a

    c   d   e   f   g   b

Insertion in Salmon’s hand. Deleted: by ?the. Insertion in Salmon’s hand. Insertion in Salmon’s hand. Illegible deletion. Deleted: ?require. Deleted: but.

‘The Practicall Theory of Musick’ (1702)

137

To prevent this we must find out a ‹new› tuning, where the Major Minor & Minim Tone may fall upon the same frets,29 & the Chromatick Semitones be placed in the exact middle of each Note, which gives their true proportions. The Tone Minim requires no Semitones,30 so we must find a proper place for that by it self. To this purpose it is very convenient for every person that desires to be Master of his own Speculation and Practice, to have a board, upon which he may draw six lines to the length of 28 inches,31 which is the most common Measure of a Violstring from the Nut to the Bridge, because this is the only sounding part of the String. Let him begin with the lowest string, which we must call double C fa ut, it will ‹be›a but one Note lower than the common tuning, to which purpose his String may be a little bigger than usual: let him here mark out all his proportions as upon a Monochord, and then he will be able to set them out upon his other Strings. You have here a Scheme supposing the string to be divided into 28 Inches: but whatever ‹length›b your String be, your distances must be of the same proportions, which are here set down. It will be very convenient for this purpose to have a foot Rule divided into Inches, & each Inch into twenty parts. [fol. 7v] You may in the first place take the fourth part of the String, which (if your length be 28) will be 7 Inches, this at the second turn of your Compasses will bring you to 14 Inches the exact middle or Octave to the String open. That fourth part fixes the fifth fret upon the Viol, which is a practicall fourth to the string open, or the proportion of [4 to 3].c After this you must take the ninth part of your string, which will be about 3 inches, & 3 twentieth parts: This at the first setting down gives you a Tone major, 9 to 8; & at the third turn of your Compasses, you will come just to the third part of your string. So that as you had your second fret fix’t for a Major Tone you have the seventh fret fixed for a practicall fifth to the string open which is the proportion of 3 to 2. In the next place we must provide for our greater third, which is the proportion of 5 to 4: This consists of 5 Inches & 12 twentieth parts; whereby you have the fourth fret of your viol fixed; being a greater third to the string open. The intermediate frets, which make the Chromatick Hemitones are the just middle between the Notes; so that your ‹first› fret is the 18th part of the string being the half of the Tone major 9 to 8: And thus the third fret must be fixed in the exact middle between the Tone major 9 to 8, & the greater third 5 to 4, which whole distance from the major Tone to the greater third is an exact Minor Tone 10 to 9 from the second to the fourth fret, for with the foregoing major tone 9 to 8, it constitutes

a

  Insertion in the scribe’s hand.   Insertion in Salmon’s hand. c   Source has 5 to 4. b

Thomas Salmon: Writings on Music

138

a greater third 5 to 4. ‹And the third fret must be the exact middle between the second & fourth frets being the Chromatick half Note of the Minor Tone.›a, 32 Above the 7 frets, (that is, a practical fifth,) the proceeding is artificiall there is no natural Progeny of an Octave greater than 3 to 2. So that you must finish your duple proportion [fol. 8r] upon this Monochord, by adding a minor Tone 10, 9, to your seventh fret, which will be a greater sixth; & then a Tone major 9, 8, to that, which will be a greater seventh, & last of all a Tone minim 16 to 15, which will bring you to the exact middle.33 ‹As is mark’d out upon the sixth string or double C fa ut Base.›b, 34 But we cannot perform all our Musick upon a Monochord, for one string cannot make such Harmony as we desire: Upon one string you can only hear the proportions in Sequence, one Note after another, but if there be two or more strings, you may hear the proportions sounding together. If you tune your fifth string Unison to the fifth fret of your sixth string, which was double C fa ut, this will be double F fa ut; & by Consequence these two strings will bear the proportion of 4 to 3, because the fifth string open gives the same Sound as the sixth string did, being stopt c at the fifth fret, or fourth part of it. Tho this be not apparent to the eye; because the encrease of the proportion does not arise from the different longitude of the strings; but the difference arises partly from the size of the string, & partly from the stiffness of the Tensure, which is not taken Notice of in the winding of the peg. Yet these causes of proportion are visible when they are represented in another manner: Take two strings of equal size & length, hang a weight of 4 pound upon one, & a weight of 3 pound upon another, & they will produce the same harmonicall Sound, as there is between your double C fa ut, & double F fa ut strings.35 According to the old story of the Greek Philosopher, who passing by a Smith’s forge, & hearing the repeated sound of a Diatessaron, call’d for the scales, weighed the hammers, & found that they were exactly in the proportion of 4 to 3; Tis said further that he got another hammer made of half the ‹weight›d, e of the first viz: 2 to 4; He set another man to work & heard the Musick of an Octave divided practically into a fifth & fourth. [fol. 8v] As to the size of the string, its proportion is visible by the size of pipes in wind Musick; for where the length is the same, but the breadth as big again, you will have the octave sound in the duple proportion.36 We had tuned off the fifth string, & made it unison to the fifth fret of the sixth string, so that you are now advanced a practicall fourth in your Octave; for from a

    c   d   e   b

Insertion in Salmon’s hand. Insertion in Salmon’s hand. Deleted: ?being. Insertion in Salmon’s hand. Illegible deletion.

‘The Practicall Theory of Musick’ (1702)

139

the fourth fret to the fifth fret are just 16 parts of the string compared to 15, which added to the greater third 5 to 4, make a fourth, which is 4 to 3. This fifth string is double F fa ut, & the major Tone & minor Tone proceed upon it, just as they did upon the former double C fa ut, but instead of coming by a Tone minim to another practical fourth, at the [fourth]a fret you must have a major Tone 9 to 8 for the odd Note Mi, which you will find upon the sixth fret, & then adding one Tone minim 16 to 15 more, you complete your Octave upon These two strings.37 Here you tune your fourth string to the seventh fret which makes it C fa ut, as it is in the old tuning; & the third string is tuned F fa ut from the fifth fret of the fourth string, so that these two strings C fa ut & F fa ut being Octaves to the two former strings double C fa ut & F fa ut, all the Notes fall upon the same frets as they did in the former Octave. But we dare not tune the 2 first strings Octaves to these, because we must strain up the second string to C sol fa ut which would be a lesser third higher than it was in the old tuning; & we must strain the Treble to G sol re ut which is a fourth higher. So that the strings would not only be continually breaking, but the most usefull Notes, which are often struck in Chords, would lye inconveniently for the hand, ‹a great way down upon the frets.›b We therefore tune the 2nd string A la mi re as it was before, & expect from it only the odd note mi to be stopt upon the 2nd, which falls out to be a Major tone as the other strings requir’d: ‹the rest of the string will only serv for a contrivance in singing.›c, 38 Then we Tune the Treble a lesser third higher which will be C sol fa ut, Octave to the 4th & 6th strings, so that all the Notes will fall upon it just as they did upon those other 2. This string being 1 Note lower than the old Tuning, may be of something larger size than the usual Treble, which will make the Musick stronger. [fol. 9r] Having thus gotten the Notes in their perfection, it will be a g[reat advant]aged to form the voice by them, according to the twofold constitution of an Octave, Masculine or Feminine, with a greater or lesser third: The singing up & down the eight Notes in their proper order will put the voice in tune to sing any thing that falls in the same Key. ‹either fa sol la, fa sol la, mi fa: or La mi, fa sol la, fa sol la.›e You must choose out your 8 Notes as may be most agreeable to the voice of the learner: if it be a Base voice you may begin your feminine Octave upon A re, the fourth fret of the fifth string; & the Masculine will begin upon ‹C fa ut› the 4th string open. By these you may also teach a Treble voice the true formation of the Notes, for it will naturally raise it self 8 Notes higher. a

    c   d   e   b

Source has fifth. Insertion in Salmon’s hand. Insertion in Salmon’s hand. Text obscured by pagination and foliation. Insertion in Salmon’s hand.

Thomas Salmon: Writings on Music

140

But if you would come nearer the Unison of a Treble voice, we will make the 2 uppermost strings serve the purpose: In the Feminine Octave begin upon the 2nd string A la mi re you will find Mi the 2nd fret, & the Treble39 a lesser 3rd from the Key; upon which Treble string you are to proceed as upon a Monochord by 2 greater thirds, which will complete your Octave at a Mark above the 7th fret, being one superadded Minor Tone.40 For the Masculine Octave you m[ay]a begin upon the same 2nd string, but you must call it fa & proceed a greater 3rd upon it,41 that is to the fourth fret, then ‹skipping the Second›b proceed another greater 3rd upon the Treble, & a lesser 3rd, more from the 4th to the 7th fret will complete your Octave: ‹The treble string being tuned one note higher to D la sol re, as in the old tuning.›c Thus you have all your Notes demonstrated & fixt upon their frets; but if you will by essential flats & sharps remove the proportions fro[m]d their Natural Situation in the Keys A & C ‹to any other Keys,›e you will not find them in a state of f perfection.g ‹Therefore›h to wit the present practice which is to begin the Masculine or Feminine Octave upon every Key, you must have a particular fingerboard for every Key, & a particular fret for every string, according to a proposal printed by Mr Lawrence bookseller in the Poultry, London 1688. Yet all this contrivance to shift the proportions from their natural Keys is only to favour the pitch of the Musick, that a masculine or Feminine Octave may begin upon any Key; for all songs or lessons whatsoever may be reduced to the 2 Natural Keys A & C. But whether the lovers of Musick will confine themselves to these Keys, or put themselves to the trouble of changeable fingerboards, is left to their choice: certainly they will no longer bear these Imperfections which destroy the power of Harmony. Notes 1 Compare Proposal, pp. 3–4, where it was music rather than harmony which consisted in proportions, and became ‘more Excellent’ with more exact proportions rather than ‘more powerfull’. 2 There is no evident mathematical sense in which 2 : 1 is ‘greater’ than all other proportions, save that it involves smaller numbers; presumably this was what Salmon meant here. a

    c   d   e   f   g   h   b

Paper is damaged. Insertion in Salmon’s hand. Insertion in Salmon’s hand. Paper is damaged. Insertion in Salmon’s hand. Deleted insertion: im-. Illegible deletion. Insertion probably in Salmon’s hand.

‘The Practicall Theory of Musick’ (1702)

141

3 It is not clear whether Salmon meant proportions which involved vast numbers or proportions which were vastly numerous; the closely similar passage in ‘The Division of a Monochord’, fol. 7v is equally ambiguous, although there the blame was laid upon ‘contriving a representation of the Notes & Half-Notes in a state of equality’, which may indicate that vast numbers – the decimals involved in describing equal temperament mathematically – were meant. Brouncker’s logarithmic calculations for equal temperament, to ten or 11 decimal places (René Descartes, Renatus Des-Cartes excellent Compendium of musick, ed. and trans. anon. [trans. Walter Charleton, ed. William Brouncker] (London, 1653), pp. 85–94), might then be the most likely object of Salmon’s complaint. 4 Salmon elaborated slightly on the nature of birdsong at ‘The Division of a Monochord’, fol. 5r; he may have been inspired by Kircher’s discussion of the subject: Musurgia universalis (2 vols, Rome, 1650), vol. 1, pp. 27–32 and plate facing p. 30. 5 The parallel passage in ‘The Division of a Monochord’, fol. 5r, makes a slightly different point – that the diatonic scale itself cannot be learned except by imitation – but allows us to surmise that here Salmon intended to refer to the imitation of a master by a student. 6 See Figure 4.2. 7 In other words, the lineage of this ratio is thus: 2 : 1 begets 4 : 3, which begets 8 : 7, which begets 16 : 15. Salmon was evidently embarrassed by the fact that the ‘impractical’ interval 8 : 7 appeared here, but did not dwell on the fact. Compare Wallis, ‘Remarks’, p. 40, and ‘The Division of a Monochord’, fol. 3v. 8 This paragraph seems to overturn Salmon’s (alleged) 1685 observation of major and minor tones in Paisible’s musical practice; but compare fol. 4r, where it was specifically ‘the common Musick Masters’ who could not distinguish between major and minor tone. See ‘The Division of a Monochord’, fol. 6v for a similar acknowledgement that use might result in the ear tolerating impurities. 9 See Figure 4.3. 10 Pierre Gassendi, Manuductio ad theoriam seu partem speculativam musicae, in his Opera omnia (6 vols, Lyon, 1658, facs. edn Stuttgart, 1964), vol. 5, pp. 633–58 (the same text to which Salmon had referred in his letter to Wallis of 1684). 11 Salmon referred to the ‘genealogy’ of intervals shown in Figure 4.2. 12 Salmon implied a criterion that good musical intervals must have superparticular ratios (where the two terms differ by 1), which he nowhere stated explicitly. A related principle, permitting also ‘multiple’ ratios, where one term of the ratio is a multiple of the other, a case which Salmon nowhere mentioned, is found in ancient sources including the Euclidean Sectio canonis; see GMW, p. 193. 13 We should probably take Salmon’s meaning to be that common musical practice did not distinguish between major and minor tones, rather than imagine that he had submitted ‘common Musick Masters’ to aural tests. The major and minor tones differ by 22 cents: 204 compared with 182. 14 The curious use of the word ‘tone’ for the diatonic semitone seems to be unique to this text; it occurs in none of Salmon’s other writings. 15 As in the Proposal, Salmon described an arithmetical division of intervals; he ignored Wallis’s suggestion (‘Remarks’, p. 39) of substituting a harmonic division. See the Introduction, p. 17. 16 This paragraph suggests only the very sketchiest acquaintance with the Greek chromatic and enharmonic genera, and may indicate that at this stage Salmon believed

142

Thomas Salmon: Writings on Music

them to consist merely of a 12-note, one-octave scale of semitones and a 24-note scale of quarter-tones, perhaps following Christopher Simpson’s description of ‘chromatic’ and ‘enharmonic’ scales in A compendium of practical musick in five parts (London, 1667), pp. 98–9. Compare ‘The Division of a Monochord’, fols 6v–7r, where Salmon described the construction of Greek pitches in a rather different way, one which owed something more to the Greek theoretical texts. 17 Compare Salmon’s 1685 letter (‘I would fain proceed to a tuning & fingerboard for the genuine Chromatick Musick’) and ‘The Division of a Monochord’, fol. 7r (‘any learned man […] may form the Grecian Musick after the same manner as it was of old’); both passages seem more optimistic about a restoration of the Greek genera than the present one. 18 Salmon probably alluded to the elaborate descriptions of Solomon’s temple in 1 Kings 6–7, 2 Chronicles 3–5, and elsewhere in the Old Testament. 19 See Aristoxenus, Elementa harmonica 1.23 (GMW, pp. 141–2 with note 91). 20 Compare John Wallis, ‘A letter of Dr. John Wallis, to Mr. Andrew Fletcher; concerning the strange effects reported of musick in former times, beyond what is to be found in later ages’, Philosophical Transactions, 20 (1698): 297–303, where Wallis had argued that (p. 302) ‘If we aim only at pleasing the Ear, by a sweet Consort, I doubt not but our modern Compositions may equal, if not exceed those of the Ancients’. 21 Compare Chilmead’s assertion in Αρατου Σολεως Φαινόμηνα καὶ Διοσημεῖα. Θεωνος Σχόλια. … Accesserunt annotationes in Eratosthenem et Hymnos Dionysii (Oxford, 1672), p. 65: ‘Probabilior itaque eorum est opinio, qui dicunt, toni seu vocis prolationem, syllabæ quantitates semper sequi.’ 22 Wallis’s answer to the same question (see note 20 above) had been different; he argued that the key to musical power was simplicity of means ‘if we would have our Musick so adjusted as to excite particular Passion, Affections, or Temper of Mind (as that of the Ancients is supposed to have done) we must […] apply more simple Ingredients, fitted to the Temper we would produce’ (‘A letter of Dr. John Wallis’, pp. 302–3). 23 Compare Roger North’s description of the modern ‘cackling’ style of singing: Roger North’s The Musicall Grammarian 1728, ed. Mary Chan and Jamie C. Kassler (Cambridge, 1990), section 119. 24 For Salmon, born in 1647, this was a historical remark rather than a reminiscence as far as the reign of Charles I was concerned. 25 The figure which follows covers both fol. 11r and fol. 10v; it has probably been cut in half in order to bring it down to the same size as the rest of the manuscript. Fol. 10 is labelled ‘page 9’ on its otherwise blank recto. This diagram shows frets intended to produce the C form (see p. 13) of syntonic diatonic scale in white notes with a viol tuned c'–a–f–c–F–C. Frets fell at 17/18, 9/8, 38/45, 5/4, 4/3, 17/12 and 3/2 of the string, with the first, third and sixth frets placed by arithmetically dividing the gap between adjacent frets. Pitches available were the white notes plus c#, d#, f#, g# and b@, together with a# on the a string. 26 See Figure 4.4. 27 The common tuning of the viol: i.e., d'–a–e–c–G–D. 28 Tone minim: i.e. a diatonic semitone of 16 : 15; see note 14 above. 29 This was the main innovation in this text, and represents a drastically different approach from anything seen elsewhere in Salmon’s writings on pitch; his idea here was that a carefully chosen tuning of the strings could reduce the complexity of the system of frets which would be needed.

‘The Practicall Theory of Musick’ (1702)

143

30 That is to say, the diatonic semitone requires no subdivision. 31 Compare Proposal, p. 21, where strings of this length were mentioned, but no justification was given. 32 The third fret was therefore at the midpoint of 8/9 and 4/5, or 38/45 of the whole string. 33 The eighth fret was placed at 9/10 of 2/3, or 3/5, of the whole string, the ninth fret at 8/9 of this, that is 8/15, and the tenth fret at 15/16 of this, that is 1/2 of the whole string. 34 Salmon did not say explicitly where his sixth fret fell, but the principle that it should come at the exact middle of the major tone between fifth and seventh frets implies that it was at 17/24 of the whole string. 35 As Salmon implied in the next paragraph, he had taken this ‘experiment’ from the tradition of Pythagoras and the harmonious blacksmith, and he had not checked it for himself; as Galilei had pointed out in 1589, it does not work. Because frequency is proportional to the square root of tension, weights in the ratio of 16 to 9 would be required to produce a frequency ratio of 4 : 3, a perfect fourth. See H. Floris Cohen, Quantifying Music: the science of music at the first stage of the scientific revolution, 1580–1650 (Dordrecht, 1984), p. 82. Gassendi, whom Salmon cited more frequently than any other modern musical author (and Salmon’s ‘winding of the peg’ here sounds like an echo of his ‘contorsione claviculi’), stated the correct relationship: Manuductio, p. 644. 36 The fault this time seems to be an error or at least an ambiguity on Gassendi’s part: he stated that a 2 : 1 ratio of frequency was produced in pipes by a doubling of breadth or length or an octupling of ‘crassitude’ (thickness, or perhaps density): ‘in vocati organi tubo duplæ latitudinis, altitudinísque, crassitudinisque octuplæ’ (Manuductio, p. 644). 37 The frets for the F string were thus at 8/9 (second fret), 4/5 (fourth fret), 32/45 (sixth fret) and 2/3 (seventh fret). 38 The A string was useable either open or stopped at the second fret, which would produce a correctly tuned B. Salmon stated that no higher fret was useable, but in fact the fifth, seventh and tenth frets would produce, respectively, correctly-tuned D, E and a, and the first fret would produce what for Salmon was a correct chromatic A#. Frets 3, 4, 6, 8, and 9 would indeed be unusable. 39 The Treble: i.e. the top (C) string. 40 This ‘Mark above the 7th fret’ would have been at 9/10 of 2/3, or 9/15 of the whole string, and would indeed produce A on the first (C) string. The complete set of frets that Salmon described was as follows: Fret

Position

1 2 3 4 5 6 ‘mark’ on F string 7 8 9 10

17

/18 /9 38 /45 4 /5 3 /4 17 /24 32 /45 2 /3 3 /5 8 /15 1 /2 8

144

Thomas Salmon: Writings on Music

41 Rather than give a ‘masculine’ scale of C as he did for the bass voice, Salmon constructed such a (major) scale on A, for which he could use the complete set of frets he had described. The price was that the first string must be re-tuned to D in order to be useable.

Chapter 5

‘The Division of a Monochord’ (?1702–6) Editorial Note Our final manuscript treatise by Thomas Salmon is bound in a volume of manuscript writings and notes by Isaac Newton, some on music but most on optics. It bears the title ‘The Division of a Monochord’, and is in Salmon’s hand (see Figure 5.1). It does not seem possible to be absolutely certain that the manuscript was owned by Newton rather than inserted among his papers after his death; our other evidence for an interest on Newton’s part in Salmon’s work is very slender indeed (see Introduction, p. 10). Nonetheless, the most natural hypothesis is surely that this copy was at least seen by Newton, if not requested or read closely by him. The manuscript is held in Cambridge University Library in Add. MS 3970; the text occupies fols 2–11. The pages have been numbered starting at p. 1 = fol. 2r prior to the modern foliation. The manuscript has catchwords throughout; the text is divided into three numbered chapters, and it has only occasional corrections. It is therefore very much a fair copy, and it is also the only one of Salmon’s surviving manuscript treatises which we have in his own hand. The remainder of the volume includes an extract from Simpson’s Division Violist, notes on the speed of sound, and over 600 folios of material connected with Newton’s optical work and 1704 Opticks. The text refers to three ‘schemes’, which are missing. Their contents can be reconstructed almost entirely from what Salmon says, and I have provided discussions and some reconstructions as part of the endnotes to this edition. The text bears no date, and its interpretation must depend to some extent on where it is placed in the sequence of Salmon’s musical writings. It seems natural to connect it with the period of Salmon’s appearance at the Royal Society in 1705, when Newton was the Society’s president, and it seems to me that a date fairly close to, but later than, that of the 1702 ‘Practicall Theory’ is borne out by internal evidence. Specifically, the present text shares several distinctive phrases with ‘The Practicall Theory’ (‘clap in’, ‘essential’ flats and sharps, ‘vast numbers’ of proportions’) and in a number of places parallels its line of thought closely. It bears no such close relationship with any other text we have from Salmon, and it therefore seems reasonable to suppose that the two treatises originated during a single – if perhaps a protracted – period of work. Reappearing from ‘The Practicall Theory’ are the systematic principle of interval division as well as Salmon’s idiosyncratic form of the syntonic diatonic scale. Once again the division is arithmetical, not harmonic as Wallis had suggested in 1688. The tuning of the viol to which ‘The Division of a Monochord’ refers inexplicitly can be reconstructed with virtual certainty as c'–a–f–c–F–C: that set out in ‘The Practicall Theory’.

146

Figure 5.1

Thomas Salmon: Writings on Music

The first page of ‘The Division of a Monochord’. Cambridge University Library, Add. MS 3970, fol. 2r. Reproduced by kind permission of the Syndics of Cambridge University Library.

Where the two texts differ in their content, moreover, ‘The Division of a Monochord’ almost invariably says more, and its handling of the material seems more assured. The most obvious such difference concerns the description of the Greek chromatic and enharmonic genera. Salmon had been interested as early as 1685 in the practical realisation of the ancient Greek genera, but in ‘The

‘The Division of a Monochord’ (?1702–6)

147

Practicall Theory’ had given no details and sounded a note of pessimism about its achievement. In ‘The Division of a Monochord’, by contrast, he gave detailed descriptions of the genera in the form of fretting instructions, subsuming them into the same general scheme of repeated division of intervals as the diatonic and modern chromatic scales, but distinguishing the Greek chromatic genus clearly from the modern chromatic scale. If his understanding of Greek musical practice was still very incomplete – he made no mention of a two-octave system and presented his single-octave scales as unproblematic realisations of the genera – it had nonetheless reached a higher level than was represented in any of his other musical writings. Similarly, Salmon’s mathematical discussion here focussed on the length of the sounding rather than the non-sounding part of the string, a change which seems like an improvement upon ‘The Practicall Theory’ (and which had been hinted at in Wallis’s ‘Remarks’). On the other hand, this text does not refer to Salmon’s experimental performance of 1705 or, like his discussion of that performance in ‘The theory of musick reduced’, adopt John Wallis’s form of the chromatic scale, features which seem to place it earlier than the summer of 1705. In view of all these features of the text, I am inclined to place it between ‘The Practicall Theory’ and Salmon’s appearance at the Royal Society, that is between 1702 and June 1705. Estimates of the date of ‘The Division of a Monochord’ have varied; the online catalogue of the Newton manuscripts at Cambridge University Library places this text ‘c.1670–c.1680’, while Penelope Gouk has suggested that Newton acquired it ‘some time from the late 1680s’.1 An earlier date cannot be ruled out, and my argument about the relationship of this text to ‘The Practicall Theory’ is admittedly in large part a subjective one. Equally, Salmon had asserted in his Proposal that he had the ‘arithmetical and geometrical parts of music’ ready to print, and there is room to suppose that some of the ideas expressed in the present text represented the culmination of a long period of development and refinement, whatever the exact date at which they were written down. Note 1 Penelope Gouk, ‘Newton, Sir Isaac’, in Grove Music Online.

Thomas Salmon: Writings on Music

148

Text [fol. 2r] a, 1

The Division of a Monochord Chapt[er] 1.

Musicall Proportions are best demonstrated upon a Monochord, because therein is no difference of cise or tension, b but the different longitude alone is the cause of the variety of the Notes. Every Musicall intervall consists of two sounds, which may be compared to one another: One intervall harmonically divided generates two more: c By dividing the Duple proportion, and the best proportions, which descend from it, wee shall arrive at all the little intervalls, that are usefull in Musick. Harmonicall Division is perform’d in one constant Method, by always taking the exact middle of the intervall to be divided.2 The Practice of Musick d proceeds to six divisions; beyond which, the Ancients were of opinion, that the voice could not form a Note, nor the Ear distinguish of it.3 To perform this first in numbers, & then to set them out upon the Monochord, this course must be taken. Double the two Numbers of the intervall given, then clap in the intermediate Number,4 & you will have two intervalls arise which are the naturall offspring of the intervall to be divided; as you will find in the following particulars, a Duple Proportion being given, as the Originall of all the rest. [fol. 2v] I. The Division of a Duple proportion 1/2 or the whole string compared to half of it, is thus perform’d: Double each Number & they will be 2 & 4, clap in the intermediate 3, & you will have these two intervalls arise 2/3 & 3/4. When you come to set them upon the Monochord, if you place the least proportion 3 /4 first, you will find that it stands upon the quarter of the string, which is the exact middle of the half, that was to be divided: But then you must consider, that when you go to the second quarter of the string, the first quarter is cut off by the stop, from whence you begin to compute a new intervall, of the 3 remaining parts compared to 2 parts or half of the string. So that though the division in respect of the Longitude was into equall parts, yet the two arising intervalls being struck successively; & the first being cut off, when the second begins; there are two different proportions 3/4 & 2/3, which ought accordingly to be set out distinctly upon the Monochord, taking allways the string open, for the Terminus à quo. As is set forth ‹with the other divisions› upon the first line in the first s[c]heme. So that you have here found, the two proportions which ‹are› best next to a Duple: 2 /3 which was the Ancient Diapente our Modern Fifth, & 3/4 the Diatessaron our a

    c   d   b

Marginal note: Scheme. 1.st. Altered from: tention. Deleted: So that. Deleted: has.

‘The Division of a Monochord’ (?1702–6)

149

Practicall Fourth. ’Tis always to be observ’d, that the better5 the proportion of Numbers is, the more satisfactory is the [fol. 3r] Musicall a intervall; these are next to the Duple, & therefore most to be valued. II. Wee proceed in the same Method to the division of the intervall 2/3; which numbers doubled make 4 & 6; by putting 5 between them, you have 4/5 & 5/6. These are the Ditonus & Semiditonus of the Ancients; our greater & Lesser Third. III. Wee proceed upon 4/5, the better of these two Proportions; whose doubled Numbers make 8 & 10, then 9 put between them gives us 8/9 & 9/10; two graduall Tones, which give the denomination to our present Diatonick Musick. IIII. Wee proceed upon these, as ‹wee› did upon the foregoing intervalls. so that between 16 & 18, wee put 17: between 18 & 20 wee put 19. Which are the true half Notes, & were by the ancients call’d Chromatick, as distinguishing a particular kind of Musick. The same is to be done in the Minor Tone 9/10. b V. The last Division ‹is› of these into Quarter Notes, that arise by the same Method, in which wee have hitherto proceeded: as when 16 & ‹17› c are doubled, & the intermediate Number plac’d between them, you will have 32/33 & 33/34. The like division must be made of all Chromatick Notes, whose progeny is call’d Enharmonick; which was accounted by the Ancients, the most difficult but most excellent part of Harmony. But it may be objected, that wee have not here divided the intervall of 3/4 the Practicall Fourth, the so much celebrated Diatessaron of the Ancients, & one of the constituent parts of [fol. 3v] the Duple. Why should not 3 & 4 be doubled into 6 & d 8, which with the intermediate 7 give us the intervals of 6/7 & 7/8? e these are better proportions, & must needs give us better Musicall chords, than the progeny of the Ditonus 4/5 which are 8/9 & 9/10.6 This very well deservs consideration, & the clearing of this objection will give us a great deall of light to the affairs of Musick. ’Tis of the greatest importance in Musick to pass in perfect proportions from one intervall to another, or else the Air cannot be harmonious: And there must be a liberty to pass from any one intervall to any other or else the Phansy of the Composer would be confin’d. It is therefore requisite that there should be some common Measures,7 whereof the Chords consist; that by means of them, wee may hit exactly upon the intervall requir’d. These were first found out by subtracting a lesser intervall from a greater, & so the difference made a common measure: for a

    c   d   e   b

Deleted: inf. Deleted: and in the Hemitone. Deleted: 18. Deleted: ?This. Deleted: whi.

Thomas Salmon: Writings on Music

150

the Chord might be taken, either with or without that difference. As for example, subtracta 3/4 a Diatessaron out of 2/3 a Diapente, there remains a Major Tone 8/9 which is the [fol. 4r] common Measure that gives denomination to our Diatonick Musick. In like manner wee subtract a Ditonus 4/5 from a Diatessaron 3/4 and there remains 15 /16 the Diatonick Half Note; which is also taken for a common Measure. But the Ancients did not proceed to subtract a Tone Major 8/9 from a Ditonus 4/5 from whence remains 9/10. So the Practicall men reckon’d upon an equality of Tones, but the learned always b demonstrated the falsness of that Notion: as Euclid in his Sectio Canonis.8 The Minor ‹Tone› being now received, there are three common measures, which constitute all the Musicall intervalls; and universall Practise agrees, that they are most conveniently placed in the following order. 8/9. 9/10. 15/16. 8/9. 9/10. 8/9. 15/16. ‹These seven intervalls make a duple proportion, & with the two inclosing Notes an Octave.› So that you may proceed from any one intervall to any other intervall by perfect proportions, except in these 3 instances. viz: when the Minor Tone 9/10 added to the Hemitone 15/16 should make a Semiditonus ‹5/6›: when two Major ‹8/9› tones added to an Hemitone ‹15/16› should make a Diatessaron 3/4: And when two Minor tones fall within the compass of a Diapente. Which the Composer ought to understand, & to avoid the passing ‹to› such an intervall, as He usually [fol. 4v] avoids a Tritonus or Semidiapente. Thus wee may understand, how it comes to pass that wee cannot make use of the proportions 6/7 & 7/8, though they be the naturall progeny of 3/4 a Diatessaron, & better proportions than 8/9 & 9/10 the progeny of 4/5 a Ditonus; because these will ‹not be› common measures to constitute the proportion of 2/3 a Diapente, which is of the cheifest importance next to 1/2 a Diapason. But the three common measures already taken viz: 8/9. 9/10. 15/16 exactly constitute both a Diatessaron and a Diapente, & consequently a Diapason; with such graduall Notes as may ‹be› fixed stages to pass to & from any intervall.9 This may give us an account of Naturall & Artificiall Musick: that which is naturall observs the naturall constitution, by dividing it self into the exact middle of the intervall. As a Diapason naturally breaks into a Diapente & a Diatessaron: a Diapente again naturally breaks into a Ditonus & Semiditonus. But when the Diatessaron is divided into three parts, a Major Tone, a Minor Tone, & Diatonick Hemitone; this is entirely artificiall. If a Diatessaron ‹3/4› was divided into it’s two naturall intervals 6/7 & 7/8, this division with respect to it self, would undoubtedly be very harmonious: but then they would spoil all the common measures of an Octave, & could not conveniently be placed upon any instrument. so that it is necessary to lay them aside, as being not practicable in any sort of Musick, which has as yet been used.   Deleted: the.   Deleted: ?the.

a

b

‘The Division of a Monochord’ (?1702–6)

151

[fol. 5r] But what is not practicable in Artificiall Musick, may be found in the naturall performancies of singing birds.10 Their wild Notes are in just proportions or they could not be Harmonious, & yet they are vastly different from our Artificiall Musick; as is very easy to be observ’d, when they have been taught a Diatonick Tune, which is quite of another sort from that they were by Nature enabled to perform. Naturall singing is the property of Birds: Man is only born with a capacity of receiving Musick, and performing that, which ‹He› Artificially makes for himself. He finds out the most consonous sounds, & contrives those graduall steps, whereby He a may most conveniently pass from one to another: But no man ever did sing eight Notes, as they stand in our Scale, by Nature;11 or was able to perform a Diatonick Tune, before He was taught the manner & method of it. b The Composer himself must use a great deal of contrivance to frame it, & He cannot communicate it to another but by the rules of Art, nor ‹any receiv it but by the› imitation of a Master.

The Proportions set out according to a Scheme of the Grecian Musick. Chapter. II.12 c

As in dividingd a Monochord wee proceed downwards, from the string open at it’s full sounding length to the severall Notes set forth upon it in shorter lengths; so in the performance of Musick wee always proceed upwards from the lowest & most grave sound to the highest [fol. 5v] or most acute. Thus wee sing the eight Notes; & thus wee write them in our Musicall Diagramms. The reason of this, being observed by all Nations & Ages, may be from the formation of the Voice in the Larinx or wind pipe: wee go as low or deep as wee can for the Base, & come to the top of it for sounding the Treble. The Grecians did not use lines & spaces for writing their Musick as wee do; but set forth their Notes by the letters of their Alphabet: and accomodated all the severall kinds of it by breaking or inverting their letters into severall forms. These are not now understood,13 or at least not at all practised among us, & therefore ’tis necessary for us to use the seven first letters of our Alphabet according to the modern practise: that so when wee set forth the proportions, wee may have an idea where they were in their account. Wee make use only of seven letters, be[c]ause at the return of the first again, we have completed our Octave or Duple Proportion. And an Octave is a complete a

    c   d   b

Deleted: ?mos. Deleted: If. Marginal note: Scheme. 2nd. Altered from: ?diving.

Thomas Salmon: Writings on Music

152

Model of Musick; all more than an Octave is only the same over again in the same order.14 The first Column of the second Scheme15 contains our Letters, which set forth the order of the Notes. The second column contains [fol. 6r] the proportions according to the order wherein they stand in the Diatonick Musick. The third has the Chromatick. And the fourth the Enharmonick. The ‹last› contains the Names which the Grecians used. Their Proslambanomenos was our Key ‹A›: Their Hypate Hypaton our Second B: Their Parhypate Hypaton our Third C. Their Lichanos ‹Hypaton› a our Fourth D. Their Hypate Meson our Fifth E. Their Parhypate Meson our Sixth F. Their Lichanos b Meson our Seventh G. Their Mese our Eighth a. Their Diatonick Musick was the same that ours is now, & the proportions fell in the same places; only that wee take the liberty to begin upon any Letter or Key: Which makes a great alteration. For if wee begin upon A, wee have a Semiditonus c 5/6 from the Key; if wee begin d upon C wee have a Ditonus 4/5. Yet this makes no confusion in the constant perfect proportions, as they Lye in the Octave; but then a greater liberty which is taken to begin upon any other ‹Key,› does require that e the Notes & half Notes should be all of an equall cize, or else the proportions will not answer the expectations of the Practicall Composer.16 The Modern practise is to make all the Notes & half Notes of equall cize; but it spoils the exactness of the proportions, & [fol. 6v] the power of the Harmony, and are as ungratefull to the ear, as soil’d & faint colours are to the Eye. But what the senses have been long accustom’d to they patiently bear; and so this practise will continue, till learning prevails to offer the naturall faculties of Man, that exactness & excellency of proportion, which the God of Nature has fitted him for.17 The two other Kinds of Musick, the Chromatick and Enharmonick are very different from the Diatonick;18 their Parhypate, that is their third & fourth, & consequently their Sixth & Seventh are of different proportions; The Diatessaron or Fourth of the Chromatick is a Ditonus 4/5,f and the Diatessaron or Fourth of the Enharmonick is but a Semiditonus 5/6: as you will see by the sinking of their Lichanos so much below the Lichanos of the Diatonick. The Parhypate of each of them is the exact middle proportion betweeng the Hypate & the Lichanos;19 which was the best graduall passage, & did most opportunely concur to complete the next following chord. The Lesser they were, the more of discord they had in them; but then they struck the ear with anh attention to a

    c   d   e   f   g   h   b

Deleted: Meson. Altered from: Lechanos. Illegible deletion. Illegible deletion. Deleted: either. Source has a caret but no corresponding interlineation. Source repeats between. Source repeats an (across line break).

‘The Division of a Monochord’ (?1702–6)

153

what was to follow, & made it receiv a greater satis-[fol. 7r]a satisfaction by the perfected proportion which did ensue. Thus may wee see all the Kinds of Musick in their perfect proportions; and though the Chromatick & Enharmonick have not been restor’d, since the ruine of arts & sciences by the deluge of the barbarous Nations, yet now they lye plainly before us: That if any learned man has a Genius for practicall composition, & shall get an idea of such distances in his head, He may form the Grecian Musick after the same manner as it was of old: But because our present Air & Art of performing (especially Consort-Musick) vastly exceeds any thing they give an account of, it must be incomparably more excellent. One thing may be taken notice of in the Grecian Enharmonick Musick; that their quarter notes, which naturally fell only between the Hypate & Lichanos, were the division of the Diatonick Hemitone 15/16, the distance between B & C, and E F; so that they were the best proportions, in the forementioned 5th & last Division, where 15 & 16 being doubled, & the middle number taken, wee have 30/31 & 31/32. Though occasionally, the whole Notes might be so divided; and if the proportions 32 /33 & 33/34 for the Major Tone, & so on for the [fol. 7v] Minor Tone were not so good in themselvs, yet they were b in their places better, because ‹they› c perfectly completed that Chord to which they were to pass. And thus Musick might have the greatest variety, & yet be performed always in perfect Proportions.

Chapter. III. Of placing the Notes upon Musicall instruments in their perfect Proportions. It has been a very great prejudice to the speculations of Musick that proportions of Notes have been ‹set› forth in such vast numbers,20 as the difference of them was not perceivable by the Eye, nor were they practicably applicable to the division of a string upon an instrument. This ‹has› been cheifly occasion’d by contriving a representation of the Notes & Half-Notes in a state of equality; which (when all is done) only assists towards continuing the imperfections of Musick: And ’tis unworthy of Philosophers to contriv the corrupting of the true proportions. But if they be taken in their radicall numbers, wee may both discern their value, & by the help of a pair of compasses determine their situation upon an instrument with greater exactnessd than the nicest ear is able to do. [fol. 8r] Instruments are tuned either by notes gradually ascending, or by some consonous intervalls between the strings. Upon the Harp, Organ, Harpsichord, & ’Spinet, a

    c   d   b

Catchword: satisfaction. Deleted: at. Illegible deletion. Original has exactsness.

Thomas Salmon: Writings on Music

154

every Key is a Note or half Note distant from the next before & after it, and for the accomodation of half a Note between every intervall of a whole note, there ‹are› Keys inserted, which are commonly called Sharps. Upon the Lute, Viol, & Gittar, the strings are tuned at greater distances; either three, four, or five notes asunder; and there a are frets tied cross the neck of the instruments, by which the intermediate Notes & Half Notes are made. The strings of the violin are tuned by the intervall of five Notes ‹between each other string;› but then the Notes & half Notes are formed by the person that plays, without being confined to any frets; wherein the power of a good ear & well practis’d hand is very much to be admir’d: That when there is no direction to the Eye, no sound given to the ear before the finger is actually placed upon the string, yet the Notes shall be more perfect, than can be expres’d upon our common fretted instruments.21 It follows that the Violin, well plaid upon makes better Musick, than any of them can; but if the Ear & Hand be not good ’tis the worst of all. This perfection of the Treble & Base Violin is therefore at present most highly esteem’d, but were the frets of other instruments placed in true Mathematicall Proportions, they must needs excell: Not only because the division ‹of the Notes› would be more exact, than ’tis possible [fol. 8v] for the unguided hand & ear to make them: but because even those, who were but indifferently befreinded by the faculties of Nature, would not be capable of playing out of Tune. Some instruments, as the Lute & Harpsichord, contain so many Notes that one person may alone make a Consort; but then ’tis the more difficult to perform such lessons, & the frequent repetitions in the long practice of them, takes away much of the pleasure wee should enjoy when wee come to the performance of them. But a Consort of Viols, where one person takes care but for one part is easily perform’d by sight, and the bow gives such a particular advantage in drawing out the melody of the instrument, favouring the air upon every suddain occasion with a proper loudness & softness, that where a society of Musicall people meet together, this Consort, which was formerly much esteem’d in England, is to be preferr’d.22 Musicall Proportions may be best set forth upon the Viol, because it has the fewest & the longest strings; though there is a great difficulty both in this, & all other fretted instruments, upon the account that no tuning has been framed with regard to the Mathematicall proportions, but upon a supposition that all the Notes & consequently all the half Notes are of an equall cize.23 So that when one ‹string› is tuned at a distance from another, the graduall Notes which fall upon the same fret [fol. 9r] b ‹are› mismatch’d: The same fret which was a Major Tone upon one string must be a Minor Tone upon another, and where wee want a Diatonick Hemitone, wee shall find a Chromatick. To avoid this wee must cheifly consider the constitution of an Octave according to it’s common Measures, in it’s three graduall proportions 8/9, 9/10, 15/16. and to take care that they all fall upon the same frets or have particular frets reserv’d for them. a

  Altered from: ?their.   Catchword: are.

b

‘The Division of a Monochord’ (?1702–6)

155

For this purpose the Ancients made the greatest account of their Diatessarons, which consisted in the orderly proceedure of these three proportions in their Diatonick Musick; and they had the same advantage by thus managing those Proportions, which they made use of in the Chromatick & Enharmonick.24 Would two Diatessarons 3/4 make an Octave 1/2, the work would be easy; there needed nothing more than to tune all the strings four Notes asunder, & all the stops would fall right in Mathematicall proportions: but a Diapente 2/3 & a Diatessaron 3/4 are necessary to make a Diapason 1/2. So that a Major Tone 8/9 must be inserted either at the beginning or end of the Octave, which was ‹either› their Proslambanomenos or Paramese according to their Key; and is our odd ‹Note› Mi. Which if placed for the first a intervall ‹before the two Diatessarons› makes our movable intervals, the Third, Sixth & Seventh all flat or lesser; if it be placed at the later end, it makes them all Sharp or greater.25 [fol. 9v] This has driven all our tunings out of Order: The common Tuning of the Viol goes all by Diatessarons, except one string; The Common tuning of the Violin all by Diapenties, but neither of them accomodate the Octave, one going as far beyond as the other falls short of it. It is necessary therefore that another tuning should be proposed, b for regulating the Notes, so that the same Proportions may fall upon the same frets: c this will be found in the 3rd Scheme,26 which is indeed particularly calculated for the six strings of the Viol, but will serv for direction in tuning all fretted instruments. The Diapenties & Diatessarons are so laid, that three of the strings open are Octaves: two others also make an Octave; & the second string which stands by it self, accomodates the tuning with a good Chord; easiethd the hand, & saves the lesser strings from being too much upon the stretch. If this Tuning be used only upon the two Naturall Keys ‹A & C› (called Naturall because there are no flats or sharps essentially necessary to them) you have all the Diatonick & Chromatick Notes in Mathematicall perfection. But then the first & third frets must stand upon the prickt lines, that they may be the true Chromatick half Notes to the Major & Minor Tones. [fol. 10r] This will not serv all the present purposes of Musick, which demands the Systeme of an Octave from every ‹one› of the Keys in both it’s constitutions. As for example, the Key or fundamentall Note is G, from thence wee must have a Lesser Third, Sixth, & Seventh; from thence wee must also have a greater Third, Sixth, & Seventh: and the demand must not be denied.

a

    c   d   b

Deleted: Note. Illegible deletion. Marginal note: 3rd Scheme. Altered from: ?easies.

Thomas Salmon: Writings on Music

156

It is necessary therefore, that as by prefixing flats & sharps at the beginning of the Lesson, the Composer designs to remove the Notes & half Notes to other places, so our Scheme should be ready to comply with him. This must be done by taking care to have a semiditonus or lesser Third 5/6 from the Key, as well as a Ditonus or greater Third 4/5; and by taking care that the Diatonick half Note 15/16 does in the alteration fall in it’s a ‹true proportion›. This is done by placing the first & third frets upon the black lines assigned for them, & the Practicall Musician will find He has satisfaction. Indeed the Major Tones & Minor Tones will not have the same order, as if wee were confined to the two Naturall Keys; [fol. 10v] as for example in G, a Minor Tone falls next the Key; if the same lesson be transposed to A, a Major Tone upon this tuning will fall next the Key. But the Composer has no consideration of the preceedency of Major Tones & Minor Tones in framing his Tune; so that as long as they exactly answer one another in the constitution of the Octave, the Harmony will be the same. b  If the Key requires essentiall Sharps, which brings the odd Note Mi upon one of them, there will not be indeed a Mathematicall exactness, because that Major Tone 8 /9 must be made up of the Diatonick Hemitone 15/16 & a Chromatick half note as it shall happen: but the difference is so small, that ’tis hardly discernable.27 And such a small allowance may well be granted for accomodating the whole affair of Musick according to the present practise. Tis no great matter, when there are essentiall Sharps in a Lesson, to remove the first & third frets to the distances set forth by the prickt lines:28 But to play upon a new tuning, when a man has been all his life time accustom’d to another that is different from it, is a difficulty that will sacrifice all the rationall interests of Musick to a practicall resentment. [fol. 11r] Yet upon triall, it will not be found so great a difficulty as may justify the refusall. It is much the same thing, whether wee learn the Notes in new places upon the instrument or upon the book; now every new cliff wee learn, wee find all the Notes upon different lines & spaces, and this task Masters impose upon their Scholars in a great variety, without any emprovement to the Musick; when the Notes may ‹be› adjusted by one position; Why then should ‹it› be esteem’d so intolerable to learn the different position of notes upon two tunings, or to take a new one & layc aside the old one, when it is done to perform the Harmony in reall & more powerfull proportions? There are three Cliffs, F fa ut for the Base, C sol fa ut for the Mean, & G sol re ut for the Treble: A mark determining where each of these Notes stand, all the other Notes in the severall lines & spaces must be calculated from them. The Harps[i]chord is indeed an instrument of so vast a compass, that two of them F fa ut & G sol re ut must be used upon two staves of six lines in different places: but all other instruments   Deleted: proper place.   Deleted: Then. c   Altered from: laid. a

b

‘The Division of a Monochord’ (?1702–6)

157

need but one invariable position of the Notes upon the book. The F fa ut Cliff which determines G to the lowest line may very well be observ’d in all the parts of Musick, only with a Character specifying which Octave is design’d.29 Though these things are not acceptable to Practicall Men, who will not put themselvs to the least trouble of changing that to which they have been accustom’d; yet when the learned shall [fol. 11v] be pleased to acquaint themselvs with this noble branch of the Mathematicks, there is no doubt but they will prevail to the establishment of those Methods, which conduce to the ease & perfection of Musick.

Figure 5.2

A possible reconstruction of the first ‘scheme’ for ‘The Division of a Monochord’.

Notes 1 Later references indicate that this missing ‘scheme’ displayed the various different divisions of the string. There seems nothing to say whether it was a diagram of the ‘genealogy’ of intervals like that shown in Figure 4.2, or a depiction of the divided string itself. If it was the latter, it is difficult to see how Salmon’s words ‘set out distinctly upon the Monochord, taking allways the string open, for the Terminus à

158

2 3 4 5 6 7

8

9

10 11

12 13

Thomas Salmon: Writings on Music quo’ could be reconciled with the pattern of division he described, in which it was always the upper interval produced by one division which was divided in the next. Nor is there anything to say exactly what verbal or numerical information such a diagram might have given. Figure 5.2 shows one possible reconstruction, a diagram similar in form to that in Christopher Simpson, A compendium of practical musick in five parts (London, 1667), p. 106. Salmon had made it clear he was talking about the ‘longitude’ of strings; as in the Proposal, ‘taking the exact middle’ indicated an arithmetical mean, not a harmonic mean, of string lengths, despite Salmon’s use of the phrase ‘Harmonicall Division’. Six divisions of the kind Salmon envisaged were carried out by Aristides (see GMW, pp. 495–6); the latter part of this sentence seems to echo Aristoxenus, Elementa harmonica 14.20 (see GMW, p. 135). Compare ‘The Practicall Theory’, fol. 2v. Salmon’s unexplained assumption was that ratios involving smaller numbers were ‘better’; compare ‘The Practicall Theory’, fol. 2r, with note 2 there. See Wallis, ‘Remarks’, p. 40. The term ‘common measure’ occurs in Euclidean geometry and number theory, although it is not actually defined in the Elements (see book 7, definitions 12 and 14 and book 1, definition 1): a is a common measure of b and c if b and c are both exact multiples of a. In the context of (pure) musical ratios, exact multiples are rare, and Salmon used the term in the looser sense that x, y, z – as a set – function as ‘common measures’ of intervals a and b if a and b can be constructed as the sums of multiples of x, y and z. If he had a source for this use of the term I have not discovered what it was. It is not clear to exactly which part of the Sectio Salmon intended to refer; the construction of a diatonic system in Proposition 20 in fact uses two equal tones within the tetrachord (see GMW, pp. 206–8). It is possible that he was thinking of Propositions 14 and 15, which challenge the Aristoxenian idea of equal tones, or that he was applying Proposition 18 (which concerns the enharmonic genus) improperly to the diatonic genus. See GMW, pp. 201–2, 204. Salmon’s argument was essentially that the intervals 6/7 and 7/8, though desirable in themselves, could not be accommodated within the system of major and minor tones and diatonic semitones to which he – with other theorists – was already committed. Compare Wallis, ‘Remarks’, p. 40, where these intervals were described not as theoretically problematic but as ‘too nice for most of our present Practisers’. Compare ‘The Practicall Theory’, fol. 2v, and see note 4 there. Compare Salmon’s assertion in 1685 that Paisible ‘observs the Major & Minor Tones by the direction of ‹an› excellent ear’ (and later in the present text (fol. 8r) that notes on the violin are ‘more perfect’ than those on a conventionally-fretted instrument). Salmon seems to have been distinctly pessimistic about the capabilities of the voice compared with the hand. See note 15 below. The interpretation of the surviving Greek musical notations was disputed; Chilmead’s discussion (in the printed form in which Salmon would have seen it) referred to opinions or interpretations by Galilei, Bottrigarius, Kircher and Meibom: Αρατου Σολεως Φαινόμηνα καὶ Διοσημεῖα. Θεωνος Σχόλια. … Accesserunt annotationes in Eratosthenem et Hymnos Dionysii (Oxford, 1672), pp. 47–69; Benjamin Wardhaugh, ‘Edmund Chilmead Revisited: musical scholarship in early seventeenth-century

‘The Division of a Monochord’ (?1702–6)

159

Oxford’. in Scott Mandelbrote (ed.), The Peterhouse Partbooks: music and culture in Cambridge in the 1630s (forthcoming). 14 Compare Essay, p. 12 (‘I make my Scale or Musical Ladder but seven rounds high’) and passim. 15 This missing ‘Scheme’ may be reconstructed as follows. Letter name A G F E D C B A

16 17 18

19 20 21 22

23

Diatonic 1/2 9/16 5/8 2/3 3/4 5/6 8/9 1

Chromatic 1/2 3/5 19/30 2/3 4/5 38/45 8/9 1

Enharmonic 1/2 5/8 31/48 2/3 5/6 31/36 8/9 1

Greek name Mese Lichanos Meson Parhypate Meson Hypate Meson Lichanos Hypaton Parhypate Hypaton Hypate Hypaton Proslambanomenos

It is not absolutely clear what form of diatonic scale Salmon had in mind here. It seems most likely that it was to consist, like his chromatic and enharmonic scales, of a major tone plus two identically-divided conjunct tetrachords, which would lead to the ratios given above. (His remark that ‘The Parhypate of each of them is the exact middle proportion between the Hypate & the Lichanos’ was presumably not supposed to apply to the diatonic scale, for which it would produce strange results.) This was different from the diatonic scales he discussed elsewhere, however; it placed two major tones consecutively between G–A and A–B and would therefore have had rather more impure intervals than either of the two forms of ‘just intonation’ he usually espoused. This remark on equal temperament, and the one which follows, are a noteworthy testimony to (Salmon’s impressions of) existing fretting practice. Compare Proposal, pp. 3–4 and ‘The Practicall Theory’, fol. 3v. See the table in note 15 above, which is reconstructed largely from the information in this passage: Salmon constructed one-octave chromatic and enharmonic ‘scales’ consisting in each case of a tone (9/8) plus two tetrachords divided identically. His ‘absolute middle’ was apparently once again the arithmetical midpoint of the relevant section of the string. This cannot be true of the diatonic genus, where it would lead to the intervals B–C and C–D being roughly equal. A–B was probably supposed to be 9/8 in every genus. See ‘The Practicall Theory’, fol. 2r and note 3 there. Compare fol. 5r, and note 11. We have no evidence that Salmon ever heard more than two viols fitted with his fingerboards playing together, but there is a good deal of seventeenth-century repertoire for which their effect would probably have been acceptable. On the other hand, Salmon’s scheme would have been quite inappropriate for the enharmonic modulations contained in the works of Ferrabosco, Tomkins or Jenkins, or the widelymodulating fantasias and In Nomines of Purcell. See the Introduction, note 80. I am grateful to Christopher D.S. Field for the substance of this note. Since Salmon had elsewhere cited, for instance, Descartes, this sentence can only have been a conscious exaggeration: Salmon certainly knew that some tunings had been described mathematically in which tones took different sizes, and they had been

160

24 25

26

27

28

29

Thomas Salmon: Writings on Music set out specifically for stringed instruments, as in Descartes, Excellent Compendium, pp. 66–7. Salmon perhaps referred to the ‘immutable’ pitches of Greek tuning, which provided a framework within which ‘movable’ pitches could be placed according to the genus in use. This seems like a moment of confusion on Salmon’s part, or perhaps a slip of the pen. The diatonic scale he supposed to be made up of two tetrachords and a major tone; each of the tetrachords was to comprise, from the bottom, a hemitone, a minor tone and a major tone. Placing the additional major tone ‘for the first intervall’ would indeed make a minor scale. It is hard, though, to see how placing it ‘at the Later end’ would produce a major scale, as Salmon claimed here. Salmon’s description indicates a diagram very similar to that shown in Figure 4.4, showing all of the strings of a viol with a single set of frets to serve for all strings. What he wrote here is consistent with the c'–a–f–c–F–C tuning of ‘The Practicall Theory’, and he was describing the same (C) form of syntonic diatonic scale; the frets would thus fall as they did there: at 9/8 (second fret), 5/4 (fourth), 4/3 (fifth) and 3/2 (seventh) of the string, the first, third and sixth filling in the gaps by arithmetic division (namely at 17/18, 38/45 and 17/12 of the string). The only new feature was the use of ‘pricked’ lines here for the chromatic frets. Salmon envisaged playing an instrument in a key (A) other than the one for which its frets were set up (G). His first observation was that since the difference between major and minor tone was commonly neglected, the resulting substitution of one for another would not be perceived to matter (‘the Harmony will be the same’). He went on to mention that, for example, the mi of the new scale had a tone upon it which was in fact made up of a diatonic and a chromatic semitone (its ratio would be 64 : 95), and to claim that such a difference might ‘well be granted’. This is the only time that Salmon considered the problems raised by modulation without retuning, and his discussion is disappointing; see the Introduction, p. 14. This paragraph reads like an unlabelled putative ‘objection’ in the style of the Essay, to which Salmon’s response follows. The fact that this sentence seems to envisage individually moveable frets (Wallis’s proposal), not Salmon’s interchangeable keyboards, therefore raises the intriguing possibility that it was actually written by Wallis. This was, of course, the system of clefs that Salmon had proposed in his Essay.

Chapter 6

‘The Theory of Musick Reduced’ (1705) Editorial Note In 1705, Salmon was permitted to attend two meetings of the Royal Society. The first took place on 27 June: June 27th, 1705 The President In the Chair Mr. Salmon and Mr. Maul were permitted to be Present. […] Mr. Salmon Shewed a Finger board of a viol which is freeted or Divided after a New Manner Vizt. so as to give the Sound in Exact or Mathematicall proportions which he Conceives will much add to the Melody of Our Music. The President Mr. Roberts, and Mr. Tollett were Desired to Consider of this Matter.1

(‘The President’ was Sir Isaac Newton.) This is hard to interpret. We know nothing of what contact between Salmon and the Society had preceded this; no letters from him to the Society are noted in the Journal Books, nor any submission of papers. Salmon’s paper in the Transactions contains a passage which could reflect his impression of what took place on this occasion (pp. 2072–69, with note 3); if this is correct, Salmon gave some sort of presentation about musical proportions and ‘exhibited […] finger-boards calculated in Mathematical proportion’. ‘This was demonstrated upon a Viol’; Salmon presumably at least showed how his special fingerboards fitted to a viol, even if he did not play the instrument. In any case, it is not clear that the ad hoc committee was provided with much information about the content of Salmon’s ideas, and it may have been intended to consider the practicalities of the demonstration performance Salmon was proposing rather than the musical or intellectual merits of his work.2 It is possible that the treatise ‘The Division of a Monochord’ was connected with this occasion, but its presence among Newton’s papers rather than those of the Society, the absence of any mention of such a document from the Society’s records, and most particularly its use of a different chromatic scale from Salmon’s ‘The theory of musick reduced’, written a few weeks later, make this seem unlikely.

Thomas Salmon: Writings on Music

162

‘Mr. Roberts’ was Francis Robartes (1650–1718), a Fellow of the Royal Society since 1673, and known to Roger North as an amateur musician and composer, as well as a natural philosopher and politician; North compared his compositions to those of Lully: ‘all the compositions of the towne were strained to imitate [Lully’s] vein; and none came so neer it as the honourable and worthy vertuoso, Mr. Francis Roberts’. He was also the author of an important treatise on the trumpet marine.3 ‘Mr. Tollett’, the third member of the ad hoc committee, was very probably George Tollett (d. 1719), a commissioner of the Navy, a founding member of the Dublin Philosophical Society and a correspondent of William Holder; he was friendly with Newton, Pepys, Evelyn and Edmund Halley. He was also a musician: one of his compositions appeared in Playford’s The Division-Violin (1684); he owned a violin by Nicolò Amati; and he had been a city musician in Dublin prior to his 1688 move to England. His brother Thomas (d. 1696) had been a member of William III’s private music.4 He was not elected a Fellow of the Royal Society until 1713, but in view of these connections it does seem comprehensible that his involvement on this occasion received no special note in the Society’s minutes (it is not absolutely clear from the minute that he was present at the meeting on 27 June). Finally the ‘Mr. Maul’ who was ‘permitted to be Present’ alongside Salmon could well have been Harie Maule (1659–1734; the name is not a common one), whose activities as musical patron and collector have attracted a good deal of scholarly interest in recent years.5 He was a younger brother of George and James, 3rd and 4th Earls of Panmure (the family was later deprived of its title); his music collection, much of it acquired in France during the 1670s and 1680s and now in the National Library of Scotland, includes the autographs of otherwise unknown pieces by Marin Marais and music by Marais’s teacher Jean de SainteColombe, by Lully, and by English composers such as Jenkins, Charles Coleman and Christopher Simpson. Patrick Cadell has suggested that Harie was a pupil of Sainte-Colombe, and has remarked that ‘The Maules must have been very competent musicians, Harie especially so. They must have been able to perform at least acceptably in the very highest musical circles in Paris’.6 It is certainly plausible that Harie Maule might have been interested in Salmon’s presentation about viols. The committee looked kindly upon Salmon; he was permitted to be present again at the Society’s meeting the following week. July 3d. 1705 The President In the Chair […] Mr. Salmon Caused an Experiment To be made before the Society of what he had Discoursed with Them before: Two Bass Viols haveing his new finger boards

‘The Theory of Musick Reduced’ (1705)

163

Playing Together One of them A Lesson the other the Bass; and afterwards both of Them Joyning Together as A Bass to a Sonata of Corelli performed by Two Violins ’twas Observed that the Viols kept very well in Tune, both to One Another and Likewise to the Violins.7

Salmon’s experiment followed reports from Halley on the variation of the compass, from the microscopist Leeuwenhoek, and from a Mr Thoersby at Leeds on Norman coins. This report is quite bald, and the observation that ‘the Viols kept very well in Tune’ suggests that the secretary, and perhaps the Fellows in general, did not understand the point of Salmon’s demonstration in any detail. Even with Salmon’s rather fuller account of the performance in his paper in the Transactions, it is not at all clear what music was played, or even how many performers were involved. (For a discussion of the performers – the Steffkin brothers and Gasparo Visconti – see the Introduction, p. 23–5.) Each account mentions two pieces, but it is quite possible that each was describing only a selection from a programme of three, four, or even more items.8 Thus the Journal Book’s ‘Two Bass Viols […] Playing Together One of them A Lesson the other the Bass’ may refer to the same piece as Salmon’s ‘Sonata […] perform’d by those two most eminent Violists, Mr Frederick and Mr Christian Stefkins’, but even if it does we can hardly narrow down quite what was played beyond that a sonata for bass viol and thoroughbass seems to match the accounts best.9 Next, according to the Journal Book, the two viols ‘Joyn[ed] Together as A Bass to a Sonata of Corelli performed by Two Violins’; while according to Salmon ‘the famous Italian, Signior Gasperini, plaid another Sonata upon the Violin in Consort with them’. These sound very much like two different pieces, a mistake or omission concerning the number of violins involved seeming scarcely plausible for either Salmon or the Royal Society’s secretary. The Corelli piece could have been any of the sonatas ‘a tre’ in his opus 1, 2, 3, or 4.10 As to the second ‘Sonata’ mentioned by Salmon, Corelli’s Sonate a violino e violone o cimbalo, Op. 5 (1700) or perhaps Visconti’s Op. 1 sonatas (1703) seem the most probable candidates. It is perhaps worth remarking that no mention was made of an accompanying harpichord – or even archlute – and, since it would have enormously complicated the tuning experiment, it seems unlikely that one was present. More likely, perhaps, is that one of the Steffkin brothers played the bass itself while the other ‘divided’ and filled out the harmony: ‘Joyning Together’ in this sense rather than providing the relentless unison which the text might seem to suggest.11 On 31 October, with the president again in the chair, ‘Some Letters and papers from Mr. Salmon Concerning Musick were Read’.12 This is tantalising, particularly since this was after the Society’s summer break, so that we cannot know exactly when this material was written or received. These ‘Letters and papers’ presumably included the text which appeared in the Transactions, the text edited in this chapter: ‘The theory of musick reduced to arithmetical and geometrical proportions, by the Reverend Mr Tho. Salmon’, Philosophical Transactions 24/302 (August 1705): 2072ff. [the pages are misnumbered]. (It seems that the Transactions’ cover date

164

Thomas Salmon: Writings on Music

should not be taken at face value: Salmon’s letter to Sloane thanking the Society ‘for ordering my papers to be printed’ was dated 4 December, and he apparently did not did not receive a copy of the issue in question until the very end of the year.) The phrase seems to imply that more material was involved than this single essay,13 but if that was the case, the remainder is lost. There is once again the temptation to think of the manuscript text ‘The Division of a Monochord’, but the objections mentioned above – its association with Newton, not with the Royal Society, and particularly its use of a different chromatic scale from ‘The theory of musick reduced’ – as well as the fact that it does not mention the July experimental performance, seem to me to rule this out.14 The text, which describes the experiment as having taken place ‘last week’, takes the form of a letter to the First Secretary of the Society and editor of the Transactions, Hans Sloane; it is conceivable that Salmon produced this account entirely on his own initiative, but it seems very much more likely that he had received some encouragement either from Sloane or from Newton. It contains Salmon’s briefest and arguably most lucid account of a system of frets at different positions for each string, with the details of his chromatic scale set out more clearly than in his Proposal and with an extensive diagram illustrating the fret positions described. A highlight is of course Salmon’s description of the performance at the Royal Society, and he took the opportunity to report in rather ambitious terms what had supposedly been demonstrated on that occasion to both performers and audience. Another is the remarkable fact that in this text alone Salmon adopted John Wallis’s suggested form of the chromatic scale, placing the larger semitone below the smaller every time a tone was subdivided. Peripheral material, meanwhile, on such matters as the derivation of the intervals and the possible reconstruction of the Greek genera, was kept to a minimum compared with Salmon’s manuscript writings. The pages in this issue of the Transactions were wrongly numbered; they seem typically to be bound in the order in which they are printed below (and which sense requires), namely 2072, 2069, 2041 (containing the first figure), 2080, 2076, 2073, 2077. An unnumbered foldout containing the second figure was perhaps intended to appear after p. 2076, and is placed at that position in this edition.15 There are no running heads. This text has recently been edited by Stewart Pollens in his Stradivari.16 Notes 1 London, Royal Society, Journal Book Original, vol. 10, pp. 109–10. 2 I am grateful to Christopher D.S. Field for this suggestion. 3 Michael Hunter, The Royal Society and its Fellows 1660–1700: the morphology of an early scientific institution (Oxford, 1982, 1994), fellow no. 306; Roger North’s The Musicall Grammarian 1728, ed. Mary Chan and Jamie C. Kassler (Cambridge, 1990), pp. 261–2 (quote); Francis Robartes, ‘A discourse concerning the musical notes of

‘The Theory of Musick Reduced’ (1705)

4

5 6 7 8 9 10 11

12 13 14 15 16

165

the trumpet, and trumpet-marine, and of the defects of the same, by the Honourable Francis Roberts, Esq; R. S. S.’, Philosophical Transactions, 17 (1692): 559–63; Cecil Adkins and Alis Dickinson, A Trumpet by any other Name: a history of the trumpet marine (2 vols: Burn, 1991), vol. 1, pp. 74–6; Jamie Kassler, The Beginnings of the Modern Philosophy of Music in England (Aldershot, 2004), pp. 101–2. I am indebted to Christopher D.S. Field for information about Robartes. I am indebted to Christopher D.S Field for this identification of Tollett, and for the information about him. See Barra R. Boydell, ‘Tollet, Thomas (d. 1696?), musician and composer’, in ODNB; London, British Library, Sloane MS 1388, f. 136; ‘Mr George Tollitts division upon a ground’ in John Playford, The division-violin (London, 1684). I am indebted to Christopher D.S Field for this identification of ‘Mr Maul’, and for the information about him. Patrick Cadell, ‘French Music in the Collection of the Earls of Panmure’, in James Porter (ed.), Defining Strains: the musical life of Scots in the seventeenth century (Bern, 2007), pp. 127–37 at p. 137. London, Royal Society, Journal Book Original, vol. 10, pp. 110–11. I am indebted to Christopher D.S. Field for the remarks which follow. Possible composers of such a sonata include August Kühnel or Gottfried Finger, both of whom had been in England during the previous two decades (Christopher D.S. Field, personal communication). See Peter Allsop, Arcangelo Corelli (Oxford, 1999), pp. 190–191 on the availability of opus 1. See David Watkin, ‘Corelli’s Op. 5 Sonatas: “Violino e violone o cimbalo”?’, Early Music, 24 (1996): 645–63; his remarks about cellists having been accustomed to provide figured bass realisations may also have been true of (some) viol players (Christopher D.S. Field, personal communication). London, Royal Society, Journal Book Original, vol. 10, p. 113. See Chapter 7 (text), note 1. I am grateful to Christopher D.S. Field for his thoughts on this point. My thanks to Christopher D.S. Field for advice about this point. Stewart Pollens, Stradivari (Cambridge University Press, 2010), pp. 293–6.

Thomas Salmon: Writings on Music

166

Text [p. 2072] IV. The Theory of Musick reduced to Arithmetical and Geometrical Proportions, by the Reverend Mr Tho. Salmon. SIR, HAving had the honour last week1 of making the trial of a Musical experiment before the Society at Gresham College, it may be necessary to give a farther account of it; that the Theory of Musick, which is but little known in this Age, and the practice of it, which is arriv’d at a very great excellency, may be fixed upon the sure foundations of Mathematical certainty. The Propositions, upon which the Experiment was admitted, were: That Musick consist-[p. 2069]ed in Proportions, and the more exact the Proportions, the better the Musick:2 That the Proportions offer’d were the same that the ancient Grecians us’d: That the Series of Notes and Half Notes was the same our Modern Musick aim’d at: which was there exhibited upon finger-boards calculated in Mathematical proportion. This was demonstrated upon a Viol, because the Strings were of the greatest length, and the proportions more easily discern’d; but may be accommodated to any Instrument, by such mechanical contrivances as shall render those sounds, which the Musick requires.3 To prove the foregoing Propositions, two Viols were Mathematically set out, with a particular Fret for each String, that every Stop might be in a perfect exactness:4 Upon these, a Sonata5 was perform’d by those two most eminent Violists, Mr Frederick and Mr Christian Stefkins, Servants to her Majesty;6 whereby it appear’d, that the Theory was certain, since all the Stops were owned by them, to be perfect. And that they might be prov’d agreeable to what the best Ear and the best Hand performs in Modern practice, the famous Italian, Signior Gasperini, plaid another Sonata upon the Violin in Consort with them, wherein the most compleat Harmony was heard. The full knowledge and proof of this Experient may be found in the two following Schemes, wherein Musick is set forth, first Arithmetically and then Geometrically: The Mathematician may, by casting up the proportions, be satisfied, that the five sorts of Half-Notes here set down, do exactly constitute all those intervals, of which our Musick does consist. And afterwards he may see them set forth upon a Monochord, where the measure of all the Notes and HalfNotes comes exactly to the middle of the String. The Learned will find that these are the very proportions which the old Greek Authors have left us in their Writings, and the Practical Musician will testifie, that these are the best Notes he ever heard. [p. 2041]a

  Catchword: An.

a

‘The Theory of Musick Reduced’ (1705)

Figure 6.1

167

The first diagram for ‘The Theory of Musick Reduced’; p. 2041. Reproduced by kind permission of the Royal Society of London.

[p. 2080]

The Explication of the first Figure. Between the two lowest Lines, you have the Series of all the 12 half Notes in an Octave, from A re to A la mi re, which added together make an Octave or exact Duple Proportion: The several parts also added together make all those intervals of which it is constituted. As for example, the two half Notes from A to A# 17/18, and from A# to B 16/17a make a Major Tone 8/9; to which if an Hemitone from B to C 15/16 be added, you have a lesser Third 5/6. In like manner between the two next lines, you have the series of all the 12 half Notes, in an Octave from C fa ut to C sol fa ut: the two first Tones added together make a greater Third: and so you may add a Tone or Hemitone till you arrive at every interval in the Octave, which so call’d because eight sounds are required for expressing those seven gradual steps whereby we comonly ascend to it. It may be also observ’d, that the proportions falling upon the same Notes in two Keys, one finger-board will be sufficient for both. ’TIs acknowledg’d by all that are acquainted either with Speculative or Practical Musick, that every interval is divided into two parts, whereof one is greater than the other: An Eighth 1/2 into a Fifth 2/3 and a Fourth 3/4. Again, a Fifth 2/3 into a greater Third 4/5 and a lesser Third 5/6. Thus also a greater Third 4/5 must be divided into a Tone Major 8/9 and a Tone Minor 9/10. The Lesser Third (to comply with the practice of Musick) is rather compounded of, than divided into a Tone Major 8/9 and an Hemitone, which is its complement, 15/16.7   Source has 6/17.

a

168

Thomas Salmon: Writings on Music

Three Tones Major, two Tones Minor, and two of the foresaid Hemitones, placed in the order found in the Scheme, exactly constitute the practical Octave; which is so call’d because it consists of eight sounds, that contain the seven gradual intervals. But it is also necessary [p. 2076] to set down the Divisions of the whole Tones, which are the true Chromatick half Notes, because there is great use of them in Practical Musick. To make all our whole Notes, and all our half Notes of an equal size, by falsifying the proportions, and bearing with their imperfections, as the common practice is, may be allow’d by such Ears as are vitiated by long custome:8 But it certainly deprives us of that satisfactory pleasure which arises from the exactness of sonorous numbers; which we should enjoy, if all the Notes were truly given according to the Proportions here assign’d. It is very easie to satisfie our selves in the Arithmetical Scheme, by those operations which Gassendus has set down in his Manuduction to the Theory of Musick, Tom. V. pag. 635.9 As for example, his rule for Addition is, That two Proportions being given, if the Greater number of one be multiplied by the Greater number of the other, and the Lesser by the Lesser, the two numbers produc’d exhibit the compounded Proportions. Thus take a Practical Fifth 2/3 and a Practical Fourth 3/4 for the two Proportions given, multiply 3 by 4 and you have 12, then multiply 2 by 3 and you have 6: which compounded proportion of 12 to 6 makes the Practical Octave 1/2. Thus, according to his Arithmetical operations of Addition, Substraction, Multiplication or Continuation, and Division, is our whole System proved, which for the more easie application to Practical Musick, shall be also set forth Geometrically upon the 6 strings of a Viol. See Figure the 2[n]d. [foldout] The 2[n]d Figure, wherein the Proportions of Musick are described Geometrically.

‘The Theory of Musick Reduced’ (1705)

Figure 6.2

169

The second diagram for ‘The Theory of Musick Reduced’; foldout. Reproduced by kind permission of the Royal Society of London.

170

Thomas Salmon: Writings on Music

The Explication. THese six lines represent the six Strings of the Viol in the common Tuning.10 The sounding part of each String from the Nut to the Bridge is suppos’d to be 30 inches long;11 the two middle Strings C and E are drawn out to 15 inches, the half of the whole. ’Tis easie to measure every interval with a pair of Compasses. Suppose you are to take the 20th part of the String G; ’tis an inch and a half for the first half Note: If you take the whole Note from G to A, ’tis the tenth part, and must be 3 inches. After these are taken away, your String will be but 27 inches long, so that if you advance one Note, or a Major Tone further, you must take a 9th part of it, which will be 3 inches more, whereby you arrive at a greater Third, being the fifth part of the whole String. Thus the series of all the Notes may be demonstrated. All the Strings are Unison at the stops where the tuning requires:12 So that though the Proportions be carried on as far as the frets allow, yet the string is open the same with the stop of that string to which it is tuned; and accordingly the series of the Notes proceeds as if they were all upon a Monochord. This Calculation serves but for two Keys A and C, which are called Natural, because they have no essential flats or sharps. But because the Composer begins upon any Key, and the series of Notes must take its terminus à quo from thence; the Instrument-maker can provide such movable Finger-boards as will serve exactly for every Key. They are taken out and put in upon the Neck of the Viol, with as much ease, as you pull out and thrust in the Drawer of a Table.13 Three, or at most five of them will be sufficient to accommodate all the Keys that are made use of.14 [p. 2073] This Mathematical fixing of the Frets enables every Practitioner, who stops close to them,15 to give the Proportions of the Notes in a greater exactness, than can be done upon the Bass-Violin or Violin itself: since they may be set forth more perfectly by a pair of Compasses dividing a line, than the nicest Ear can direct.16 Though the Frets for the several Strings do not stand in a strait line, and the places are also shifted in different Keys, yet the Ear naturally directs the Fingers to them: insomuch that those persons, who have all their lives time been accustom’d to stop upon Frets that go quite cross the Finger-boards of their Instruments, do with very little practice fall right upon these.17 Such is the power of a Musical Genius, as may be undeniably proved by those that play upon the Violin; who, when they change the Key, fall upon the right Stops, tho’ they have no visible direction where to stop, nor time to alter, by the Ear, the Note they first pitched upon.18 By this Standard of Regular Proportions may the Voice be formed to sing the purest Notes; they are all the same in Vocal and Instrumental Musick; if then the Instrument which governs the Voice be perfect, the Ear will of necessity bring it to perfection. It is a great pity that a good natural Voice should be taught to sing out of Tune, as it must do, if it be guided by an imperfect Instrument; and this may be

‘The Theory of Musick Reduced’ (1705)

171

the reason why so few attain to that melody, which is so much valued; but since we now know wherein perfection lies, a constant practice will come to the attainment of it. The dividing Wholes into Chromatick Hemitones is very necessary, but very difficult for the Voice to be broken to: If it learns from an Instrument whose whole Notes and whose half Notes are supposed to be equal, the sound must needs be very uncertain and unharmonical; whereas the proportions truly fixed, would bring it to a perfection in the nicest and most charming part of Musick.19 [p. 2077] The Chromatick Hemitones are the smallest Intervals our Modern Musick aims at, tho’ the Ancients had their Enharmonick quarter Notes, which they esteem’d their greatest excellency: These may also in time be recover’d, since we know their proportions; for as the Diatonick Tone is divided into Chromatick Hemitones, so after the same manner may the Chromatick Hemitones be divided into those least Enharmonick Intervals, which were ever made use of. But if we go no further, yet this Experiment demonstrates the true Theory of Musick, and brings the practice of it to the greatest perfection. Notes 1 This seems to indicate that the composition of this text was begun in the second week of July 1705; the Society received a copy by the end of October (see pp. 163–4). 2 Compare Proposal, pp. 3–4, where an almost identical statement was made, and ‘The Practicall Theory’, fol. 2r (with note 1), where ‘harmony’ replaced ‘music’ and ‘more powerful’ replaced ‘better’. 3 This passage may be Salmon’s description of his first appearance at the Royal Society, in which case it indicates that a brief presentation on the theory of mathematical proportions in music was followed by the display of some fingerboards for a viol. On the basis of these ‘propositions’, Salmon was then permitted to attend another meeting at which a performance would ‘prove’ (demonstrate, illustrate) them. 4 It is not clear from this or from the report in the Royal Society’s Journal Book (above, pp. 162–3) whether the ‘two Viols’ belonged to the Steffkin brothers or were loaned to them for the occasion. In either case they would surely have needed a period of time (despite Salmon’s assertion about ‘very little practice’, p. 2073) to become accustomed to the instruments, and there is therefore at least the possibility that they were used for other performances. Frederick’s offer in 1703 ‘to set the frets of viols […] in perfect proportions’ (see p. 24) suggests that he may have been responsible for their modification on this occasion. My thanks to Christopher D.S. Field for his thoughts on this matter. 5 Concerning precisely what was played, see p. 163 above. 6 See the Introduction, pp. 23–4, on Frederick and Christian Steffkin. 7 Compare the discussion of the minor third in ‘The Practicall Theory’, fol. 3v. 8 Compare ‘The Practicall Theory’, fols 3r–3v and ‘The Division of a Monochord’, fol. 6v; the present passage is slightly stronger in suggesting that the hearing does not just become accustomed to impure harmony but is actually changed (‘vitiated’), in the long run, by hearing it.

172

Thomas Salmon: Writings on Music

9 Compare Salmon’s reference to this text in his letter of 1685; the example he used here was one of those Wallis had sent him in his reply. There was now, of course, no hint that he could not ‘see the reason of it’, yet he still seems to have been a little uncertain about the operation, referring to the ‘greater’ and ‘lesser’ numbers, as he had in 1685, although it might have been more logical to refer to the second and first terms of the ratios. 10 The ‘common tuning’ was, as elsewhere, d'–a–e–c–G–D; Salmon had abandoned the idea, raised in ‘The Practicall Theory’ (fols 8r–8v) and implied in ‘The Division of a Monochord’ (see note 26 to Chapter 5) of tuning the viol to c'–a–f–c–F–C. 11 On the two previous occasions when Salmon had specified the length of the string, it was 28 inches: see Proposal, p. 21, and ‘The Practicall Theory’, fol. 7r. 12 Compare the 1685 letter, ‘The Use of the Musical Canon’, fol. 36r–36v, and Proposal, p. 22, in each of which this simple picture of each string being unison to a certain stop on its neighbour was slightly modified. 13 This description suggests that the specific mechanical arrangement used in the experimental instruments of 1705 (which need not have been worked out in detail by Salmon himself) involved the fingerboards sliding in sideways, perhaps along grooves, to a position where they could be used. Such an arrangement must have involved fairly drastic modification of the instrument, namely removal of part of the original fingerboard: see pp. 26–7. 14 Seven fingerboards were illustrated in the Proposal; possibly Salmon’s impression of which keys were in common use had changed, or possibly he now considered that the infelicities of playing in, say, A major using a G major fingerboard (see ‘The Division of a Monochord’, fol. 10v) were tolerable in practice. Readers might have been taken aback to find that Salmon in fact provided only one fingerboard diagram with this text; the information he had given was adequate to enable the positions of frets for different keys to be deduced (since each fingerboard was to be used for just one scale, no matters of judgement or compromise would arise), but this was asking quite a lot of the reader. 15 The phrase ‘stops close to them’ suggests that Salmon was aware of the possibility of altering, in practice, the exact tuning represented by his frets by a slightly different placement of the fingers. See Penelope M. Gouk, ‘Music in the Natural Philosophy of the Early Royal Society’ (unpublished Ph.D. thesis, London, 1982), pp. 230–231; Alison Crum and Sonia Jackson, Play the Viol: the complete guide to playing the treble, tenor, and bass viol (Oxford, 1989), pp. 163–4. 16 Like the passage in ‘The Division of a Monochord’, fol. 5r, this sentence seems to show much less optimism about the capacity of the ear to produce mathematically pure tuning than some of Salmon’s other remarks on the subject, such as in 1685 and ‘The Division of a Monochord’, fol. 8r. This pessimism might naturally seem to create a problem for Salmon’s appeal to the judgement of the ear concerning the success of his musical experiment earlier in this paper (‘the most compleat Harmony was heard’, p. 2069) – although of course musical execution is not the same thing as musical judgement – but he did not make the connection. 17 We most naturally read this as a remark upon the experience of the Steffkin brothers, and perhaps as an elucidation of their reported comment that ‘all the Stops were … perfect’. If Salmon had received such positive testimony from other experienced performers he would surely have named them. Compare ‘The Division of a Monochord’, fols 10v–11r. 18 Compare Salmon’s remarks about the violin in ‘The Division of a Monochord’, fol. 8r. 19 Compare Salmon’s remark on the modern use of ‘three, four, or five’ chromatic notes together, and their difficulty of execution, at Proposal, p. 15.

Chapter 7

Correspondence with Hans Sloane (1705–6) Editorial Note Two letters from Salmon shed a final light on his relationship with the Royal Society, and on where he believed his musical work might take him after the performance before the Fellows. Both are addressed to Hans Sloane, the First Secretary of the Royal Society since 1695; they appear in the British Library, MS Sloane 4040, fols 103–4 and 108–9, and bear the dates 4 December 1705 and 8 January 1706. We do not have Sloane’s replies. Salmon must presumably have met Sloane when he appeared at the Royal Society earlier in 1705, and his paper in the Transactions was, at least as printed, addressed to Sloane; it would certainly have passed through his hands as editor. These letters, then, are a fragment from at least a slightly larger correspondence, and part of their interest is that they show Salmon asking for help in finding a patron, suggesting that neither Sloane himself nor Newton, nor the Society itself was, in Salmon’s view, likely to provide assistance of the kind and on the scale which was now required. The first letter consists of the usual large single sheet folded once to produce the letter proper (fol. 104) and its cover (fol. 103). The main text fills fol. 104r and continues, written sideways, in the left-hand margin of that page, sprawling across the fold in such a way that the signature falls on the inside of the cover (fol. 103v) (see Figure 7.1). The outside of the cover (fol. 103r) bears the address, while the reverse of the letter proper is blank. The second letter is set out in the same way; fol. 109r contains the text of the letter proper, finishing with a section written sideways in the left-hand margin and continuing onto the reverse of the cover, fol. 108v. Once again the reverse of the letter proper is blank, and the address appears on the outside of the cover.

174

Figure 7.1

Thomas Salmon: Writings on Music

Salmon’s second letter to Hans Sloane, January 1706. British Library, MS Sloane 4040, fol. 109r. Reproduced by permission of the British Library.

Correspondence with Hans Sloane (1705–6)

175

Text Letter 1 [fol. 103r]a To Dr Sloane at his house   in Bloomsbury   in    London [fol. 104r] Sir I am very much oblig’d to the Society for ordering my papers to be printed,1 they will thereby become known to the learned men of the World, that if any thing can be objected against them it may be consider’d, but if all holds good (as I am demonstratively sure) then is the Theory of Musick settled, which being accomodated to the present practise wee may proceed to those emprovments wherein the Grecians excelled us. Now wee are assured of their whole notes & half notes, wee may be also certain what were their Quarter notes, wherein their Enharmonick (which was their best) Musick did consist. When I see the town again I will set the Mechanicks to work, but in this little village, I am not capable of trying any experiment.2 I would be glad to make some acknowledgment of the trouble you take, & have order’d my bookseller to present you with some Historicall Collections of great Britain, which I carried to the press in the summer:3 I hope they will be acceptable to you, as containing the ancient foundations of our goverment both in Church & state, which are better preserv’d in this than in any other Nation of the World: It may beb also usefull at present to consider, that wee are not so much beholding to Rome for the Christian religion as is pretended, & that the generality of the Sects are more akin to us than is commonly known. It will be a greater ‹honour› to mee than a kindness to you, if you please to lett this ‹little› peice have a place in your Library:4 I am sorry it is so false printed, by reason of my absence, but that is of the least trouble to those that are learned, because they presently know what the words should be. I am, [fol. 103v]c Sir   Your Most Obliged Humble Servant T: Salmon. Mepsall.   Decemb: 4.    1705. a

  i.e. the outside of the cover. The address is written sideways.   From this point the text is written sideways in the left-hand margin. c   The text continues on the inside of the cover, still written sideways. b

Thomas Salmon: Writings on Music

176

Letter 2 [fol. 108r]a To Doctor Sloane at his house   in Bloomsbury     in London [fol. 109r] Sir Last week my Bookseller sent mee the Transactions, which gave mee an occasion of reviewing those Musicall affairs, you were pleased to insert in them; they have carried mee further than a Philosophicall contemplation, for the wisdome of God does so evidently appear in the exactness of our Harmony, that I do not think any of the works of Nature can set forth his glory, with greater demonstration & delight. It may therefore be very well worth the while to promote the advancement of this Science, that it may become most usefull to the service of God & Man: but this cannot be done by meer speculation; I must therefore beg of you, to find mee out some Patron, who may espouse this cause: for when a Scholar goes beyond his Theory & endeavours not only to bring it into Practice, but to make the World partake of it, there is a charge & interest requisit[e]b greater than a private person can sustain, at least one in my circumstances.5 There are two things before us; either to give a full consort of the present Musick in the greatest perfection, for what was done at Gresham College, though it was the best I could then compass, was far from coming up to the exactness of the Theory:6 or to make an advancement into the Enharmonick Musick which the world has been utterly unacquainted with ever since the overthrow of Classicall Learning. This will require a new formation c of instruments, & a great interest in Practicall Musicians, who must learn those notes they were never acquainted with, & then contriv the most advantageous use of them in their compositions. I would never ask a Patron to espouse any thing, but I will first give him demonstration, that it ‹wil[l]d› be effectuall; and if upon these terms you can gain mee an interest for the advancement of Musick, I beleiv you will oblige the World: I am sure it will be ever acknowledged as a very great [fol. 108v]e favour by Sir   Your Most Humble & Obedient Servant Thomas Salmon Mepsall a

    c   d   e   b

Jan: 8. 1705/6

i.e. the outside of the cover. The address is written sideways. Edge of paper is damaged. From this point the text is written sideways in the left-hand margin. Word is cut off by the (apparently undamaged) edge of the paper. The text continues on the inside of the cover, still written sideways.

Correspondence with Hans Sloane (1705–6)

177

Notes 1 At this stage Salmon had sent ‘The theory of musick reduced’ to the Royal Society and had been informed – presumably by Sloane – that it was to be printed. The letters in which this was arranged – and any correspondence relating to the details of what would have been a fairly complex item to print – are lost. The use of the plural here may well indicate that Salmon was expecting more items – compare the ‘Letters and papers’ mentioned in the Royal Society’s Journal Book in October 1705 (above, pp. 163–4) – to be printed than just ‘The theory of musick reduced’; but it is not impossible that Salmon meant ‘papers’ in the sense of a single text occupying multiple sheets. I am grateful to Christopher D.S. Field for his thoughts on this point. 2 This sentence sheds some light on Salmon’s attitude to ‘experiment’ as well as to his situation in Mepsal; evidently experiment required practical assistance from ‘the Mechanicks’, and perhaps its purposeful performance required such a learned audience as only London could provide. 3 Salmon referred to his Historical collections (London, 1706); see p. 8–9. 4 There is no copy of Salmon’s Historical collections in the library of the Royal Society; see Alan J. Clark (ed.), Book Catalogue of the Library of the Royal Society (Frederick, 1982). 5 See Volume I of this edition, p. 4: Salmon’s will provides additional, possible, evidence of his circumstances at this time. 6 Salmon’s plan to put on a more ambitious experimental musical performance was pursued in his petition to the London Court of Aldermen a few months later (see p. 11), but it was cut off by his death in August 1706.

Taylor & Francis Taylor & Francis Group http://taylorandfrancis.com

Select Bibliography This bibliography lists the more important sources of information for this edition. Works cited in passing or to illustrate the output of particular authors or printers are not included. Manuscripts Bedford, Bedfordshire and Luton Archives and Records Service P29/25/1: Orders and account book (1698–1705) for the Emery school at Meppershall. Meppershall Parish Register, transcription of 1948/2003. Cambridge, University Library Add. MS 3970, fols 1–11: ‘The Division of a Monochord’. London, British Library MS Add. 4919, fols 1–11: ‘The Practicall Theory / of Musick / To perform Musick in perfect proportions / and / To set out the proportions upon the Viol / so that they may fall right / upon the frets. / 1702’. MS Sloane 4040, fols 103–4, 108–9: Thomas Salmon to Hans Sloane, 4 December 1705 and 8 January 1706. London, Metropolitan Archive COL/CA/01/01/114 (olim REPS/110): Repertories of the Court of Aldermen, 6 November 1705 – 28 October 1706. COL/CA/02/01/004: Fair copy minutes of the Court of Aldermen, 7 February 1706 – 27 March 1716. COL/CA/02/02/008: Original rough minutes of the Court of Aldermen, 1704–6. COL/CA/05/01/007: ‘Papers’ relating to the Court of Aldermen, 1705–6. COL/CA/05/02/003: ‘Miscellaneous petitions’ to the Court of Aldermen, late seventeenth century to 1790s, R–Y.

180

Thomas Salmon: Writings on Music

London, Prerogative Court of Canterbury PROB 11/490: will of Thomas Salmon, proved 13 August 1706. London, Royal Society Journal Book Original, vol. 10. Oxford, Bodleian Library MS. Add. D. 105, fol. 47r: Wallis to Martha Woodcock, 13 February 1674/5 and Wallis to ‘Mrs Salmon at Hackney’, 15 March 1674/5; fols 92–3: Wallis to Salmon, 15 May 1690 and Salmon to Wallis, 16 May 1690. MS Eng. Lett. C 130, fols 27–8: Salmon to Wallis, 31 December 1685; Wallis to Salmon, 7 January 1686. MS Mus. Sch. d375*, fols 32r–40r: ‘The Use of the Musical Canon’. Printed and Online Sources Αρατου Σολεως Φαινόμηνα καὶ Διοσημεῖα. Θεωνος Σχόλια. … Accesserunt annotationes in Eratosthenem et Hymnos Dionysii (Oxford, 1672). Arber, Edward, The Term Catalogues, 1668–1709 A.D. (3 vols, London: privately printed, 1903–6). Ashbee, Andrew and D. Lasocki (eds), A Biographical Dictionary of English Court Musicians, 1485–1714 (Aldershot: Ashgate, 1998). Barbour, J. Murray, Tuning and Temperament: a historical survey (East Lansing: Michigan State College Press, 1951; New York: Dover, 2004). Barker, Andrew, Greek Musical Writings: II. Harmonic and Acoustic Theory (Cambridge, New York and Melbourne: Cambridge University Press, 1989). Barker, Andrew, Scientific Method in Ptolemy’s ‘Harmonics’ (Cambridge: Cambridge University Press, 2000). Birch, Thomas, A history of the Royal Society of London (4 vols, London, 1756–7). Birchensha, John, ed. Christopher D.S. Field and Benjamin Wardhaugh, John Birchensha: writings on music (Farnham: Ashgate, 2010). Blaydes, F.A. (ed.), Bedfordshire Notes and Queries (Bedford: F. Hockliffe, 1882– 93). Brackenridge, J. Bruce and Mary Ann Rossi, ‘Johannes Kepler’s On the More Certain Fundamentals of Astrology. Prague 1601’, Proceedings of the American Philosophical Society, 123 (1979): 85–116. Burney, Charles, A general history of music, from the earliest ages to the present period (4 vols, London, 1776–89). Charleton, Walter, Physiologia Epicuro–Gassendo–Charletoniana: or a fabrick of science natural, upon the hypothesis of atoms (London, 1654).

Select Bibliography

181

Clark, Alan J. (ed.), Book Catalogue of the Library of the Royal Society (Frederick: University Publications of America, 1982). The Clergy of the Church of England Database: www.theclergydatabase.org.uk. Cohen, Albert, Music in the French Royal Academy of Sciences: a study in the evolution of musical thought (Princeton: Princeton University Press, 1981). Cohen, H. Floris, Quantifying Music: the science of music at the first stage of the scientific revolution, 1580–1650 (Dordrecht: D. Reidel, 1984). Crum, Alison and Sonia Jackson, Play the Viol: the complete guide to playing the treble, tenor, and bass viol (Oxford: Oxford University Press, 1989). Descartes, René, Musicæ compendium (Utrecht, 1650); English translation by Walter Charleton, with commentary by William, second Viscount Brouncker, as Renatus Des-Cartes excellent Compendium of musick: with necessary and judicious animadversions thereupon. By a person of honour (London, 1653); ed. Frédéric de Buzon as Abrégé de musique: Compendium musicæ (Paris: Presses Universitaires de France, 1987). Early English Books Online: eebo.chadwyck.com. Eighteenth-Century Collections Online: galenet.galegroup.com/servlet/ECCO. The English Short Title Catalogue: estc.bl.uk. Gassendi, Pierre, Manuductio ad theoriam seu partem speculativam musicae, in Gassendi, Opera omnia, vol. 5, pp. 633–58, trans. as Initiation à la théorie de la musique, texte de la ‘Manuductio’ traduit et annoté par Gaston Guieu (La Calade, Aix-en-Provence: Édisud, 1992). Gassendi, Pierre, Opera omnia (6 vols, Lyon, 1658, facs. edn Stuttgart–Bad Cannstatt: F. Frommann, 1964). Gouk, Penelope M., ‘Music in the Natural Philosophy of the Early Royal Society’ (unpublished Ph.D. thesis, London, 1982). Gouk, Penelope M., Music, Science and Natural Magic in Seventeenth-Century England (New Haven and London: Yale University Press, 1999). Harley, John, Music in Purcell’s London: the social background (London: Dennis Dobson, 1968). Hawkins, John, A general history of the science and practice of music (5 vols, London, 1776). Heath, Thomas L., The Thirteen Books of Euclid’s Elements, 2nd edn (3 vols, Cambridge: Cambridge University Press; New York: Dover Publications, 1926). Herissone, Rebecca, Music Theory in Seventeenth-century England (Oxford: Oxford University Press, 2000). Herzog, Myrna, ‘Stradivari’s Viols’, Galpin Society Journal, 57 (2004): 183–94. Holder, William, A treatise of the natural grounds, and principles of harmony (London, 1694). Hunter, Michael, The Royal Society and its Fellows 1660–1700: the morphology of an early scientific institution (Chalfont St. Giles: British Society for the History of Science, 1982). Hunter, Michael, Editing Early Modern Texts: an introduction to principles and practice (Basingstoke: Palgrave Macmillan, 2007).

182

Thomas Salmon: Writings on Music

The International Genealogical Index: www.familysearch.org. Kircher, Athanasius, Musurgia universalis, sive ars magna consoni et dissone (2 vols, Rome, 1650). Kuhlicke, F.W., ‘The Salmons of Meppershall’, Bedfordshire Magazine, 1/5 (1948): 177–80. Lawrence, R.E., ‘The Music Treatises of Thomas Salmon (1648 [sic]–1706)’ (unpublished M.A. thesis, University of Calgary, 1991). Lindley, Mark, Lutes, Viols and Temperaments (Cambridge: Cambridge University Press, 1984). Locke, Matthew, The present practice of musick vindicated … (London, 1673). Malcolm, Alexander, A treatise of musick; speculative, practical, and historical (Edinburgh, 1721). Matthew, H.C.G. and Brian Harrison (eds), Oxford Dictionary of National Biography: from the earliest times to the year 2000 (60 vols, Oxford: Oxford University Press, 2004; online edition, 2008, at www.oxforddnb.com). McKenzie, D.F., Stationers’ Company Apprentices 1641–1700 (Oxford: Oxford Bibliographical Society Publications, New Series Volume XVII, 1974). Meibom, Marcus, Antiquæ musicæ auctores septem (2 vols, Amsterdam, 1652). Miller, Leta and Albert Cohen, Music in the Royal Society of London (Detroit: Information Coordinators, 1987). North, Francis, A philosophical essay of musick directed to a friend (London, 1677), ed. Jamie C. Kassler as The Beginnings of the Modern Philosophy of Music in England: Francis North’s A philosophical essay of musick (1677) with comments of Isaac Newton, Roger North and in the Philosophical Transactions (Aldershot and Burlington: Ashgate, 2004). North, Roger, ed. Mary Chan and Jamie. C. Kassler, Roger North’s ‘The Musicall Grammarian 1728’ (Cambridge: Cambridge University Press, 1990). Oldenburg, Henry, The Correspondence of Henry Oldenburg, ed. A. Rupert Hall and Marie Boas Hall (13 vols, 1–9, Madison, Milwaukee and London: University of Wisconsin Press, 1965–73; 10–11, London: Mansell, 1975–7; 12–13, London and Philadelphia: Taylor & Francis, 1986). Oxford English Dictionary (Oxford: Oxford University Press, 3rd edition, 2010; online edition, 2010, at www.oed.com). Page, William (ed.), A History of the County of Bedford: Volume 2 (London: Constable and company, 1908), Volume 3 (London: Constable and company, 1912). Pfizenmaier, T.C., ‘Was Isaac Newton an Arian?’, Journal of the History of Ideas, 58 (1997): 57–80. Plomer, Henry R., A Dictionary of the Booksellers and Printers who were at Work in England, Scotland and Ireland from 1668 to 1725 (Oxford: printed for the Bibliographical Society at the Oxford University Press, 1922). Pollens, Stewart, ‘A Viola Da Gamba Temperament Preserved By Antonio Stradivari’, Eighteenth Century Music, 3 (2006): 125–32.

Select Bibliography

183

Royal Society, ‘List of Fellows of the Royal Society 1660–2007’: http:// royalsociety.org/WorkArea/DownloadAsset.aspx?id=429497281. Sadie, Stanley (ed.), The New Grove Dictionary of Music and Musicians (2nd edition, 29 vols, London: Grove, 2001; online edition, 2007–10, at www. oxfordmusiconline.com). Salmon, Thomas, An essay to the advancement of musick … (London, 1672). Salmon, Thomas, A vindication of an essay … (London, 1672). Salmon, Thomas, A proposal to perform musick, in perfect and mathematical proportions … (London, 1688). Salmon, Thomas, The catechism of the Church of England … with a short explication … (London, 1699). Salmon, Thomas, A discourse concerning the baptism and education of children … whereunto are annexed proposals for the settlement of free-schools in all parishes … (London, 1701). Salmon, Thomas, A historical account of St. George for England, and the original of the most noble order of the Garter (London, 1704). Salmon, Thomas, ‘The theory of musick reduced to arithmetical and geometrical proportions, by the Reverend Mr Tho. Salmon’, Philosophical Transactions, 24 (1705): 2072–7, 2069. Salmon, Thomas, Historical collections, relating the originals, conversions, and revolutions of the inhabitants of Great Britain … (London, 1706). Salmon, Thomas, The history of Great Britain and Ireland … with a preface … by Mr. Salmon, author of the modern history (London, 1725). Simpson, Christopher, A compendium of practical musick in five parts (London, 1667). Stephen, Leslie and Sidney Lee (eds), The Dictionary of National Biography (63 vols, London: Smith, Elder & Co., 1885–1900). Wallis, John, ‘Dr. Wallis’s letter to the publisher, concerning a new musical discovery; written from Oxford, March 14. 1676/7’, Philosophical Transactions, 12 (1677): 839–42. Wallis, John, Claudii Ptolemaei harmonicorum libri tres (Oxford, 1682). Wallis, John, ‘A question in musick lately proposed to Dr. Wallis, concerning the division of the monochord, or section of the musical canon: with his answer to it’, Philosophical Transactions, 20 (1698): 80–84. Wallis, John, ‘A letter of Dr. John Wallis to Samuel Pepys Esquire, relating to some supposed imperfections in an organ’, Philosophical Transactions, 20 (1698): 249–56. Wallis, John, ‘A letter of Dr. John Wallis, to Mr. Andrew Fletcher; concerning the strange effects reported of musick in former times, beyond what is to be found in later ages’, Philosophical Transactions, 20 (1698): 297–303. Wallis, John, ‘Dr. Wallis’s account of some passages of his own life’, in Thomas Hearne (ed.), Peter Langtoft’s chronicle (2 vols, Oxford, 1725), pp. cxl–clxx. Wallis, John, ed. David Cram and Benjamin Wardhaugh, John Wallis: writings on music (Farnham: Ashgate, forthcoming).

184

Thomas Salmon: Writings on Music

Wardhaugh, Benjamin, Music, Experiment and Mathematics in England, 1653– 1705 (Farnham: Ashgate, 2008). Wardhaugh, Benjamin, ‘Edmund Chilmead Revisited: musical scholarship in early seventeenth-century Oxford’, in Scott Mandelbrote (ed.), The Peterhouse Partbooks: music and culture in Cambridge in the 1630s (forthcoming). Wood, Anthony à, Athenæ Oxonienses. An exact history of all the writers and bishops who have had their education in the most antient and famous University of Oxford […] The second edition, very much corrected and enlarged; with the addition of above 500 new lives from the author’s original manuscript (2 vols, London, 1721).

Index

affections 97, 108, 129, 142 Aldermen, Court of 11, 35 Aristides 97, 115, 120, 123, 158 Aristoxenus, aristoxeneans 19, 89, 112, 134–5, 158 arithmetical division 15, 17, 56–71, 75, 115, 120–21, 123, 126–7, 129–31, 133, 141–2, 145, 148–9, 153, 158–9, 167 Bernard, Edward 4–5, 38, 79, 90, 117 birdsong 130, 141, 151 Boethius 16, 112 chromatic genus 46, 96–7, 115, 134–5, 142, 146–7, 152–3, 159 Corelli, Arcangelo 24, 163, 165 Cruttenden, Sarah 5 Cutts, John 81 Descartes, René, Compendium musicæ 96, 124, 141, 160 diatonic genus (Greek) 95–6, 109, 112, 135, 152, 155 ear

failures of 133 judgement of 103 tuning by 100, 102, 116, 131, 154, 170 vitiation of 102, 131–2, 152, 168 Emery school 6, 32 enharmonic genus 11, 91, 97, 115, 134–5, 142, 149, 152–3, 159, 171, 175–6 equal temperament 141, 152–4, 159, 168, 171 Euclid Elements of Geometry 75, 158 Sectio canonis 112, 122, 141, 150 fingerboards

diagrams for 4, 103–6, 136, 169 displayed 10, 161, 166 interchangeable 4, 15, 26–7, 43, 45–7, 98–100, 102, 116, 140, 166, 170, 172 marks on 24–5, 103, 121 patterns for 25 frets compromise positions for 51, 102, 107, 127, 136 gut 4, 24, 103 individually movable 27, 47, 51, 116 placement of 59–71, 73–4, 76, 95–6, 98–107, 113, 137–8, 169–70 slanted 26, 40 gamut 91, 109 Gassendi, Pierre 20 Manuductio 20–21, 46–7, 96, 132, 143, 168 Greek music 109, 114, 159–60 effectiveness of 14 genera 142, 146–7 notation 89–90, 118, 151, 158 octave species 110 see also chromatic genus, diatonic genus, enharmonic genus harmonic division 17, 38, 115, 123, 126, 141, 145 harmonious blacksmith 138, 143 Hawkins, John 28, 126 Holder, William 13, 162 Treatise 18, 126 just intonation 12–14 ‘C’ and ‘D’ forms 58, 113–14 chromatic extension of 15–17, 28, 51, 96–8, 115, 126, 130–31, 134, 137–8, 149, 164, 167–8, 171 and key changes 14

Thomas Salmon: Writings on Music

186

mathematical construction of 15, 17, 112, 126 and practitioners 13 produced by instinct 96 unusable intervals in 101, 114, 150 key note, changes of 110–11, 140, 156, 170 keyboard instruments 97–8, 100, 153–4 Kircher, Athanasius 16, 38, 89 Lawrence, John 5, 80–81, 83 Mace, Thomas, Musick’s Monument 1 Maule, Harie 161–2 Meares, Richard 26–7, 80, 83 Mepsal 1, 6, 11, 23, 32, 122, 175, 177 music ancient writers on 89–91 delight of 97 excellence of 86–7 mathematical nature of 90, 108, 129, 132, 166 modern, worth of 90, 135 musical experiments 18–22, 27, 56, 93–4, 138, 175–6 by Mersenne 19, 21 by Ptolemy 19, 21 by Robert Hooke 20–21 at the Royal Society 10, 20, 22, 24, 51, 162–4, 166, 171 Musicall Compass, The 3, 12, 36, 51–2 Newton, Isaac 10–11, 34–5, 80, 145, 147, 161–4 North, Francis 13, 20 North, Roger 142, 162 octave, circulation of 12 Paisible, James 2, 14, 25–6, 46 Proposal advertisements for 79–80 dedication 79, 81, 85–8 printing of 3–4, 79–82, 108 readers of 5, 82 sale of 5, 80 tone of 4 writing of 79

Ptolemy, Harmonics 19, 89, 112, 116, 122 Pythagoras, Pythagoreans 19, 89, 112, 143 ratios calculations with 71–2, 91–2, 132–3, 139, 150, 168 unused 130, 133, 149–50 vast numbers of 129, 153 rhythm 90, 108–9, 135 Robartes, Francis 161–2 Salmon, Thomas Baptism 6–8, 35 Catechism 6, 8, 32, 34–5 death 11 hand 125–6, 128, 145–6, 174 Historical Collections 8–9, 34, 175, 177 legacy 27–9, 52 life 1, 5 mathematical competence of 2–3, 46 and patronage 176 as practical musician 23 and practitioners 3–4, 6, 21, 23, 25–6, 45–6 religion of 7–8, 10, 35 at the Royal Society 10–11, 21–2, 161–3, 166, 173, 176 St George 8–10, 33–4 sources for 16, 18–20 wife and children 2 Salmon, Thomas III 9 scales construction of 57–9, 91–3, 96, 109–10, 132, 150, 155, 167–8 learning 151 on A 67, 70, 93, 99, 101, 104, 107, 113–14, 167, 170 on C 62–4, 69, 94–5, 98–9, 101, 104, 106, 110, 113–14, 132, 167, 170 on other notes 64–71, 99, 104–7, 110 two forms of 58–9, 69, 92, 99–100, 102, 110–11, 133, 139–40, 155

Index

187

with four flats, rarity of 100 semitone, sizes of 15–16, 56–7, 72, 75, 95, 112, 119–21, 130–31, 137, 160 Sherard, James 3, 52–4 Simpson, Christopher 120, 145 Compendium 13, 16, 28, 37–8, 120, 142, 158 Sloane, Hans 11, 34, 164, 173–7 Steffkin, Christian and Frederick 23–4, 49, 163, 166, 171–2 Steffkin, Ebenezer/Cristina 24–5 Steffkin, Theodore 23, 39, 49, 100, 121 Stradivari, Antonio 25 string division of 56–8, 93–5, 137–8, 148, 151, 157, 170 inverse relationship with pitch 112–13

tuning adjustments 62–4, 66–7, 69–70, 100–103, 116, 139 of viol 62, 98, 100, 127, 136–7, 139, 145, 155

Tollett, George 161–2, 165

Zarlino, Gioseffo 112, 122

Visconti, Gasparo 24–5, 163, 166 Vossius, Isaac 11, 90 109 Wallis, John annotations on Proposal 82 correspondence with Salmon 2–6, 10, 12, 43–8, 51, 79, 109 edition of Ptolemy’s Harmonics 89, 96, 123 on the just intonation 16–17 as supporter of Salmon 4–5, 88