Writings on Music by John Wallis (review)

For readers of this journal, if he is recognized at all, John Wallis (1616–1703) is perhaps best known as the Oxford Savilian Professor of Geometry and Royal Society member who lent scientific authority to the Reverend Thomas Salmon’s schemes to develop an ‘improved’ tuning system for viols and lutes that would enable them to play in just intonation rather than equal temperament. Certainly it is in this capacity that Wallis makes a very fleeting appearance in Rebecca Herissone’s Music Theory in Seventeenth-Century England (Oxford, 2000), a work that for the most part deliberately concentrates on what can be described as ‘practical’ music theory written by musicians rather than on music theory’s more ‘speculative’ or ‘scientific’ aspects. Although understandable, this entrenched habit among musicologists of sidelining sources that do not seem to fit into the ‘practical’ category has inevitably led to some distortion in our perception of early modern English discourse about music.

It is this distortion that Jessie Ann Owens has sought to correct by creating a welcome series with Ashgate on ‘Music Theory in Britain, 1500–1700: Critical Editions’, which seeks to publish editions of all kinds of writings on music, and it is in this broader context that the full extent of Wallis’s writing about music can now better be appreciated. Indeed, it is only now that readers who understand neither Latin nor Greek will have the opportunity to read Wallis’s most substantial essay on music: the Appendix to his 1699 edition of the Greek mathematician Ptolemy’s Harmonics (2nd century ad) that was originally published in 1682. Although the Harmonics had long been recognized as an invaluable source on ancient music theory, Wallis was the first to provide a critical edition and Latin translation of the most important manuscript versions of Ptolemy’s treatise, the bulk of which were to be found in Oxford libraries. This edition remained unsurpassed until the twentieth century, and still retains some value today. As a long-term resident of Oxford and curator of the university’s archives, Wallis took advantage of his proximity to this material in order to produce an edition of Ptolemy where the Greek and Latin versions are set in columns side by side, with his own notes running beneath them across each page. In the 1682 edition, his ‘Appendix’ on ‘The Harmonics of the Ancients compared with Today’s’ comprises a forty-seven page essay in which he demonstrated his grasp of the relationship between ancient and modern harmonics as well as taking an opportunity to publish his own ideas about modern music theory.

In this edition by David Cram and Benjamin Wardhaugh—who, like Wallis, are both Oxford scholars with historical expertise respectively in linguistics and mathematics—the ‘Appendix’ is chronologically and conceptually at the centre of the volume and is flanked by Wallis’s other reflections on music. These are found in four papers in the Royal Society’s Philosophical Transactions (1677, 1698) and in various items in his correspondence, most notably a couple of letters of 1664 that appear to mark the moment when Wallis first became seriously interested in music theory, in his late forties. In their introduction to the volume the editors do a good job of showing the development of Wallis’s thinking about music over the next thirty years, which typically focused on the nature of consonance, on tuning musical instruments, and on establishing the correct proportions of the musical scale. At all times Wallis seems to have been more interested in the theoretical and historical, rather than practical, implications of his work. For example, a letter of June 1698 ‘is remarkable for the evidence it provides of direct contact between the author and a musical instrumentbuilder [the organ maker Renatus Harris], a representative of a world with which Wallis seems otherwise to have had little contact’ (p. 22). In fact the closest that...