John Wallis: writings on music, edited by David Cram and Benjamin Wardhaugh, Farnham & Burlington, VT, Ashgate, 2014, xiii + 239 pp., £65.00 (hardback), ISBN 978-0-7546-68701

Abstract

John Wallis: writings on music, edited by David Cram and Benjamin Wardhaugh, Farnham & Burlington, VT, Ashgate, 2014, xiii + 239 pp., £65.00 (hardback), ISBN 978-0-7546-68701Slowly but surely the important series, Music Theory in Britain, 1500-1700: Critical Editions published by Ashgate, is expanding with new volumes. So far, most of those which have appeared are concerned with the more esoteric and nerdy aspects of music theory. It is indeed thought provoking how much seventeenth century English music theorists and natural philosophers wrote on music and how few of the writers have been the objects of study among musicologists today. The series is seminal for an entirely new interpretation of the position of music theory in early modern English intellectual circles. Looking at the present volumes of the series published so far, it is obvious that there seems to have been a close and influential discussion between professional musicians and natural philosophers; however, also the music connoisseur played a vital role asking inquisitive questions. From a musicological point view, some of the most complex writings, truly demanding a profound knowledge of early modern mathematics, are those concerned with temperament and tuning for instance. The present critical edition comprising the main musical writings of John Wallis (1616-1703) is one of those volumes that the modern reader may find hard to get through.John Wallis, mathematician and for 54 years Savilian Professor of Geometry in Oxford, was ordained in 1640 becoming a doctor in divinity and elected royal chaplain in 1660. He was elected a fellow of the Royal Society in 1661 and published frequently in the Society's journal Philosophical Transactions on a wide range of subjects including hearing, theology, logic, mathematics, grammar and ancient music theory - many of the topics in fact required by the job description as Savilian professor, as the editors of the present volume note. Apparently, it was not until the beginning of the 1660s that Wallis began to show a greater interest in music when the violist, teacher and music theorist John Birchensha presented his musical ideas to the Royal Society. The secretary of the Society, who thought that Birchensha'sideas might be of interest to Wallis, wrote to him about these ideas. Wallis was indeed interested and wrote a treatise on the mathematics of music and musical tuning. The treatise, here edited as Chapter 1, sets the basis for Wallis's later writings on music, in particular the coincidence theory of consonance. Wallis was also fascinated by the syntonic diatonic scale (Ptolemaic scale) which, contrary to the medieval Pythagorean scale which was most often mentioned and explained in contemporary music theoretical treatises, included not only pure octaves, fifths and fourths but also thirds and hence sixths. Though the tuning was nearly impossible to use in practice since it advocated two distinct sizes of the whole tone, it nevertheless drew some attention, especially from natural philosophers and musical connoisseurs. Musicians still argued in favour of the Pythagorean tuning though it certainly was not used in practice. There was, as Wallis mentions, a discrepancy between music theory and music practice and he was simply trying to describe in theory what musicians did in practice. As the editors argue (6-7),Walliswasmostlikelyinspiredbyothercontemporary natural philosophers such as Johannes Kepler, Marin Mersenne and Rene Descartes who all seem to have based their ideas regarding the Ptolemaic scale on Gioseffo Zarlino's famous Le Istitutioni harmoniche first printed in 1558.In 1677, Wallis became aware of the discussions concerning the sympathetic vibrations of strings and nodes of vibration. He wrote a letter on the matter to the Royal Society which was subsequently published in the Philosophical Transactions as a New Musical Discovery (Chapter 2 in the present edition). The article was, with a few revisions, later published in a Latin version in 1693. …