John Wallis: Writings on Music

Benjamin Wardhaugh, David Cram

• Publisher: Routledge
• Year: 2017
• ISBN:
  9781351561488
• Edition: 1
• Topic: Media & Performing Arts
• Subtopic: Music

John Wallis (1616-1703), was one of the foremost British mathematicians of the seventeenth century, and is also remembered for his important writings on grammar and logic. An interest in music theory led him to produce translations into Latin of three ancient Greek texts - those of Ptolemy, Porphyry and Bryennius - and involved him in discussions with Henry Oldenburg, the Secretary of the Royal Society, Thomas Salmon and other individuals as his ideas developed. The texts presented in this volume cover the relationship of ancient and modern tuning theory, the building of organs, the phenomena of resonance, and other musical topics.

Chapter 1
Letters to Henry Oldenburg, May 1664

Editorial Note

The three letters presented here were addressed to Henry Oldenburg, the secretary of the Royal Society, during May 1664. They were prompted by a lost letter from Oldenburg of 4 May, reporting on the letter and personal appearance of John Birchensha received by the Royal Society during April, and by a second lost letter from Oldenburg informing Wallis that the first two letters presented here had been read to the society on 18 May.¹ The content of Wallis’s letters, and in particular his evasiveness about his dependence on earlier writings, are discussed in the Introduction (see pp. 2–8 above). The second letter, one of Wallis’s most substantial discussions of the theory of music, should be read in part as his response to the writings of his modern predecessors, acquaintance with which he would acknowledge in a postscript and in the third letter. At the same time, these three letters set out an agenda for the mathematical study of music that was distinctly Wallis’s own. As Wallis’s earliest surviving discussion of music theory and an important source for ‘The Harmonics of the Ancients compared with Today’s’ (Chapter 3 below), they therefore possess considerable interest.

For each letter the version that was sent is now preserved in the archive of the Royal Society: MS Early Letters W1, nos 7–9. Each was copied into the society’s ‘Letter Books’ and subsequently into the ‘Letter Book Copy’; these copies have no independent authority and are disregarded here.²

For the second letter there are two additional copies. We denote the three copies A, B and C.³

A: London, Royal Society, MS Early Letters W1, no. 8. The letter as sent, in Wallis’s hand and dated 14 May 1664.

B: London, Royal Society, Boyle Papers, vol. 41,⁴ fols 23^r–30^r. In Wallis’s hand. This copy is juxtaposed in Robert Boyle’s papers with the unique manuscript of John Birchensha’s ‘Compendious Discourse … of Musick’.⁵ The simplest explanation is that both items were produced for Boyle’s use and at his request, probably shortly after Birchensha’s appearance before the Royal Society on 27 April 1664. Unfortunately there is no evidence, either in Boyle’s own correspondence or published works or elsewhere, to confirm this, and it is possible that one or both of these items became associated with Boyle’s papers in other circumstances or even after his death.

C: Dublin, Marsh’s Library: Z3.4.24. Not in Wallis’s hand.⁶ As with B, it seems most probable that this copy was solicited and produced soon after 27 April 1664. The most natural assumption is that it was made for Narcissus Marsh, who was at this date associated with the same Oxford college as Wallis and was certainly interested in musical topics.

All three versions have the appearance of fair copies. But, setting aside matters of spelling and punctuation (and the placement of paragraph breaks and the choice of parentheses or parenthetical commas), there are about 240 places where the three texts differ. Most of these are very minor matters of re-drafting – the substitution of octave or eight for octave, the choice of 5 to 4 rather than 5/4, the transposition of so do to do so – while a few are accidental omissions of words from one of the copies.

Nearly all of these minor differences show agreement between two of the texts against the third. No pair of texts agrees significantly more frequently than any other. Moreover, we have not located any clearly incorrect reading which occurs in more than one of the texts. These facts are difficult to reconcile with any suggestion that one of the texts is a copy of another; instead they suggest quite strongly that all three are in fact copies of a single lost original.⁷

There are also about 20 places where the three texts show larger differences, with passages of up to a whole paragraph absent or much shorter in one or two of the versions. C – which is not in Wallis’s hand – is nearly always the longest and contains at least nine significant passages which are absent from both A and B, six which are absent from A only (in one case the sense in A is impaired as a result) and one which is absent from B only. While some omissions are thus common to A and B, where t...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Series Editor’s Preface
• List of Figures
• Acknowledgements
• List of Abbreviations
• Introduction
• 1 Letters to Henry Oldenburg, May 1664
• 2 Letters to Henry Oldenburg, March 1677
• 3 ‘The Harmonics of the Ancients compared with Today’s’: Appendix to Ptolemy’s Harmonics, 1682
• 4 Notice of Wallis’s Edition of Ptolemy’s Harmonics in the Philosophical Transactions, January 1683
• 5 ‘A Question in Musick’, Philosophical Transactions, March 1698
• 6 Letter to Samuel Pepys, June 1698
• 7 Letters to Andrew Fletcher, August 1698
• Select Bibliography
• Index