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⁶ For example, the observation that ‘much of the subject matter of music was closely related to that of arithmetic and geometry’ is confined to a footnote on p. 28 of Feingold, M., The Mathematicians' Apprenticeship: Science, Universities and Society in England, 1560–1640, Cambridge, 1984Google Scholar. Likewise little attention is paid to music as a branch of mathematics in Bennett, J. A., The Mathematical Science of Christopher Wren, Cambridge, 1982Google Scholar, even though Wren himself addressed musical topics.

⁷ On Mersenne, Galileo and the laws of vibration, see especially Dostrovsky, S., ‘Early vibration theory: physics and music in the seventeenth century’, Archive for the History of Exact Sciences (1974–1975), 14, 169–218CrossRefGoogle Scholar; Drake, S., ‘Renaissance music and experimental science’, Journal of the History of Ideas (1970), 31, 483–500CrossRefGoogle Scholar; and Cohen, H. F., Quantifying Music: The Science of Music at the First Stage of the Scientific Revolution, 1580–1650, Dordrecht, 1984CrossRefGoogle Scholar. Other studies addressing the relationship between music and science include Cohen, A., Music in the French Royal Academy of Sciences: A Study in the Evolution of Musical Thought, Princeton, 1981Google Scholar; Gouk, P. M., ‘Music in the Natural Philosophy of the Early Royal Society’, Ph.D. thesis, University of London, 1982Google Scholar; eadem, ‘Music in Francis Bacon's natural philosophy’, in Francis Bacon: terminologia e fortuna nel XVII secolo (ed. Fattori, M.), Rome, 1985, 139–54Google Scholar; eadem, ‘The role of acoustics and music theory in the scientific work of Robert Hooke’, Annals of Science (1980), 37, 573–605Google Scholar; eadem, ‘The harmonic roots of Newtonian science’, in Let Newton be! A New Perspective on his Life and Works (ed. Fauvel, John et al. ), Oxford, 1988, 101–25Google Scholar; Gozza, P. (ed.), La musica nella rivoluzione scientifica del seicento, Bologna, 1989Google Scholar; Kassler, J. C., ‘Man – a musical instrument: models of the brain and mental functioning before the computer’, History of Science (1984), 22, 59–92CrossRefGoogle Scholar; Kassler, J. C. and Oldroyd, D., ‘Robert Hooke's Trinity College “Musick Scripts”, his music theory and the role of music in his cosmology’, Annals of Science (1983), 40, 559–95CrossRefGoogle Scholar; Miller, L. and Cohen, A., Music in the Royal Society of London 1660–1806, Detroit, 1987.Google Scholar

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¹¹ Participants at these early meetings included Charles Scarburgh (Merton), Thomas Willis (Christ Church), Walter Charleton (Magdalen Hall), Ralph Bathurst (Trinity) and Nathaniel Highmore (Trinity), all of whom were or became practising physicians, and John Greaves (Merton), who was Savilian Professor of Astronomy.

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¹³ For details, see works cited in note 4 above.

¹⁴ The Diary of John Evelyn (ed. de Beer, E. S.), 6 vols., Oxford, 1955, iii, 110–11.Google Scholar

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¹⁷ Holder not only had a Masters degree from Cambridge and a Doctorate in Divinity from Oxford, but also possessed some skill in composition. See DNB and Stanley, J. M., ‘William Holder: His Position in Seventeenth-Century Music Theory’, Ph.D. thesis, University of Cincinnati, 1983.Google Scholar

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¹⁹ The Harmonics of Claudius Ptolemy of Alexandria (second century AD) not only deals with the quantitative relationships of musical intervals but also shows that these musical structures have their analogues in the soul and the heavens. The work was intimately related to Ptolemy's astronomical and astrological writings Almagest and Tetrabiblos. The other Greek texts edited by Wallis were commentaries on the Harmonics by the Neoplatonist Porpyhry (third century AD) and the Byzantine scholar Manuel Bryennius (fourteenth century AD). For an English translation of Ptolemy and discussion of these and related texts, see Barker, A., Greek Musical Writings Volume II: Harmonic and Acoustical Theory, Cambridge, 1989, especially 270–391.Google Scholar

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²¹ Wallis, J., ‘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. March 5 1697/8’Google Scholar; idem, ‘A letter of Dr Wallis to Samuel Pepys Esquire, relating to some supposed imperfections in an organ. June 27, 1698’; idem, ‘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. Aug. 18 1698’, Philosophical Transactions (1698), 20, 80–8, 249–56, 297–303Google Scholar. See also note 77 below.

²² Charleton, W., Physiologia Epicuro-Gassendo-Charitoniana: Or a Fabrick of Science Natural, Upon the Hypothesis of Atoms, London, 1654, 226Google Scholar. On Charleton and his friendship with Brouncker, see Sharp, L. G., ‘Walter Charleton's early life 1620–1651 and relationship to natural philosophy in mid-seventeenth-century England’, Annals of Science (1973), 50, 311–40, especially 317CrossRefGoogle Scholar. Brouncker's theory was mentioned in the context of Charleton's discussion of ‘the Nature of Sound’; see Gouk, , ‘Music in… the early Royal Society’, op. cit. (7), 39–44Google Scholar. On Brouncker's geometrical division of the scale, see Walker, D. P., ‘Seventeenth-century scientists' views on intonation’, in Studies in Musical Science in the Late Renaissance, London, 1978, 111–22Google Scholar; Lindley, M., Lutes, Viols and Temperaments, Cambridge, 1984, 33–6.Google Scholar

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²⁴ Although they have never been found, ‘Several music lectures’ dating from 1650 are listed in The Petty Papers: Some Unpublished Writings of Sir William Petty edited from the Bowood Papers (ed. Marquis, of Lansdowne, ), 2 vols., London, 1927, ii, 260–1Google Scholar. The dating suggests that Petty may have written these for his Gresham post.

²⁵ On Petty, 's ‘Memoria musicalis’Google Scholar, for example, see Papers, Hartlib, Sheffield University, bundle 71, no. 9, fol. 1, and ‘Ephemerides’, 1648, N 06, 07Google Scholar. This invention is described along with Petty's other musical writings in Gouk, , ‘Music in the… early Royal Society’, op. cit. (7), 126–9Google Scholar. See also Sharp, L. G., ‘Sir William Petty and some Aspects of Seventeenth-Century Natural Philosophy’, Ph.D. thesis, University of Oxford, 1976.Google Scholar

²⁶ In his Advice to W.P. to Mr Samuel Hartlib for the Advancement of some particular Parts of Learning (1648)Google Scholar, Petty suggested that only the most gifted would learn languages and music. Yet in his Ergastula literaria (1649)Google Scholar, a scheme to meet the educational requirements of all children, music was included on the grounds that like drawing it improved manual dexterity: Hartlib, , ‘Ephemerides’, 1649, D-E4Google Scholar; Webster, , op. cit., (4), 214.Google Scholar

²⁷ Hartlib Papers, Sheffield University, bundle 49, no. 9, fol. 12, transcribed in Webster, , op. cit. (4), 550.Google Scholar

²⁸ Charleton, W., op. cit. (22), 208–32Google Scholar, ‘The nature of sound’, 333–7Google Scholar, ‘Flexility, tractility, ductility, etc.’; Hooke, R., Micrographia: Or Some Physiological Descriptions of Minute Bodies made by Magnifying Glasses, with Observations and Enquiries Thereupon, London, 1665, 12, 14–16Google Scholar; idem, ‘An hypothetic explication of memory; how the organs made use of by the mind in its operation may be mechanically understood’, in The Posthumous Works of Robert Hooke (ed. Waller, R.), London, 1705, 138–48Google Scholar; idem, ‘A curious dissertation concerning the causes of the power & effects of music’, Royal Society Library, London, Classified Papers, vol. 2, no. 31Google Scholar; idem, ‘Musick scripts’ and ‘Preaching lecture’, Trinity College, Cambridge, MS O.lla.1 ^11–12 O.lla.14^F–H; Willis, T., De anima brutorum quae hominis vitalis ac sensitiva est, exercitationes duae, Oxford, Oxford 1672Google Scholar; idem, ‘The anatomy of the brain and nerves’ and ‘Two discourses concerning the soul of brutes’, in The Remaining Medical Works (ed. Pordage, S.), London, 1683.Google Scholar

²⁹ Gouk, P. M., ‘Speculative and practical music in seventeenth-century England: Oxford University as a case study’, in Atti del XIV Congresso della Società Internationale di Musicologica: Trasmissione e recezione delle forme di cultura musicale in Bologna, Bologna, 1987, iii, 199–205.Google Scholar

³⁰ Carpenter, N. C., Music in the Medieval and Renaissance Universities, Norman, OK, 1958Google Scholar, provides a valuable European perspective on this whole subject, but for the English universities see pp. 76–92 (up to 1450) and pp. 153–210 (to 1600). For a discussion of Oxford in the sixteenth century, see also Caldwell, J., ‘Music in the faculty of arts’, in The History of the University of Oxford Volume 111: The Collegiate University (ed. McConica, J.), Oxford, 1986, 201–12Google Scholar. On the seventeenth century, see Gouk, P. M., ‘Music’, in History of the University of Oxford Volume IV: Seventeenth-Century Oxford, An Expanding University (ed. Tyacke, N.), Oxford, forthcoming.Google Scholar

³¹ For examples of dispensations to omit the music lecture in the sixteenth century, see Carpenter, , op. cit. (30), 155–6.Google Scholar

³² Wagner, D. L. (ed.), The Seven Liberal Arts in the Middle Ages, Bloomington, 1983.Google Scholar

³³ Barrow, I., The Usefulness of Mathematical Learning, Explained and Demonstrated, London, 1734, 17–18Google Scholar. This was the English translation of his mathematical lectures given in Latin during 1664–66 and first published in 1685.

³⁴ Gouk, , op. cit. (30), 635.Google Scholar

³⁵ Boethius, A. M. S., Fundamentals of Music, translated with introduction and notes by Bower, C. M., New Haven and London, 1989, 50–1Google Scholar (‘What a musician is’).

³⁶ Heather's original gift included a collection of portraits of musicians, stools, a harpsichord, a chest of viols and two sets of part books: Crum, M., ‘Early lists of the Oxford music school collection’, Music & Letters (1967), 48, 23–34CrossRefGoogle Scholar. For developments in the Music School during the seventeenth century, see Gouk, , op. cit. (30), 623–6.Google Scholar

³⁷ For the impact of this struggle on English music, see Le Huray, Peter G., Music and the Reformation in England, 2nd edn, Cambridge, 1978.Google Scholar

³⁸ Temperley, N., The Music of the English Parish Church, Volume 1, Cambridge, 1979, 1.Google Scholar

³⁹ Boyd, M. C., Elizabethan Music and Musical Criticism, 2nd edn, Philadelphia, 1974, 13–36Google Scholar; Simon, , op. cit. (8).Google Scholar

⁴⁰ The best introduction to this subject still remains Woodfill, W. L., Musicians in English Society from Elizabeth to Charles I, Princeton, 1953Google Scholar. Although women played prominent roles as patrons, pupils and daughters of professional musicians (being of course excluded from this sphere themselves), relatively little attention has yet been paid to their role in the English musical market-place.

⁴¹ These included the cathedral schools of music (notably Westminster Abbey, Ely and Gloucester), the choral foundations at Cambridge (King's College, Pembroke College, Peterhouse and Trinity College), and above all the ‘royal peculiars’ of St George's Chapel, Windsor, and the Chapel Royal, Whitehall. For further details and bibliography on the Oxford foundations, see Gouk, , op. cit. (30), 626–9.Google Scholar

⁴² For an impression of a chorister's educational experience, see Brennecke, E., John Milton the Elder and his Music, New York, 1973, 3–24Google Scholar (A day at Christ Church’).

⁴³ At Oxford a bachelor of music was to have spent seven years in the study of music and to be familiar with Boethius's De musica. The degree entitled him to lecture at the university on this work for those taking the arts degree. A D.Mus. ostensibly required a further five years’ study. In fact music degrees were essentially hallmarks of distinction for musicians who had already achieved fame in the field. Williams, C. F. A., A Short Historical Account of the Degrees in Music at Oxford and Cambridge with a Chronological List of Graduates in that Faculty from the year 1463, London and New York, 1893Google Scholar; Bray, R., ‘Music and the quadrivium in early Tudor England’, Music & Letters (1995), 76, 1–18.CrossRefGoogle Scholar

⁴⁴ See Gouk, , op. cit. (30), 622Google Scholar; Williams, , op. cit. (43), 75–83.Google Scholar

⁴⁵ This point is emphasized in Weber, W., The Rise of Musical Classics in Eighteenth-Century England: A Study in Canon, Ritual and Ideology, Oxford, 1992Google Scholar. On the King's Music, see Ashbee, A., Records of English Court Music 1558–1714, 6 vols., i–iv Snodland, 1986–1991, v–vi Aldershot, 1991–1992Google Scholar, and also Holman, P., Four and Twenty Fiddlers: The Violin at the English Court 1540–1690, Oxford, 1993.Google Scholar

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⁴⁷ Crewdson, H. A. F., The Worshipful Company of Musicians, London, 1950Google Scholar; Woodhill, , op. cit. (40), 3–5 on London, 56–132Google Scholar on provincial waits; Harley, J., Music in Purcell's London: The Social Background, London, 1968, 13–22.Google Scholar

⁴⁸ John Baldwin, a city wait in 1603, was licensed for The Bell in 1604; Richard Burren, a city wait in 1628, was a licensed alehouse keeper in 1631. John Gerard, a university musician, was similarly licensed in 1629/30, and also had a music shop (location unknown) where he sold books and instruments. For further details of the city and university musicians see Gouk, , op. cit. (30), 630–2.Google Scholar

⁴⁹ For further details of this genre and its development by Prince Charles's musicians, see Holman, , op. cit. (45), 211–24.Google Scholar

⁵⁰ The classic account of these events and assessment of their impact is Scholes, P. A., The Puritans and Music in England and New England. A Contribution to the Cultural History of Two Nations, Oxford, 1934, repr. 1969.Google Scholar

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⁵³ Chilmead was a noted linguist, composer and an expert on Greek music theory. According to Hartlib, he was a rival candidate for the Gresham Music Professorship that Petty was awarded in 1650. On Chilmead's career and especially his natural philosophical interests, see Feingold, M. and Gouk, P. M., ‘An early critique of Bacon's Sylva sylvarum: Edmund Chilmead's “Treatise on Sound”’, Annals of Science (1983), 40, 139–57.CrossRefGoogle Scholar

⁵⁴ According to Hawkins, J., A General History of the Science and Practice of Music, 3 vols., London, 1875, ii, 71Google Scholar, Chilmead lived in the house once occupied by Thomas East, the Elizabethan printer of music; see Krummel, D. W., English Music Printing, 1553–1700, London, 1975, 19–20Google Scholar and passim.

⁵⁵ Chan, M., ‘A mid-seventeenth-century music meeting and Playford's publishing‘, in The Well Enchanting Skill: Music, Poetry and Drama in the Culture of the Renaissance. Essays in honour of F. W. Sternfeld (ed. Caldwell, J., Olleson, E. and Wollenberg, S.), Oxford, 1990, 231–44.Google Scholar

⁵⁶ Bellingham, B., ‘The musical circle of Anthony à Wood in Oxford during the Commonwealth and Restoration’, Journal of the Viola da Gamba Society of America (1982), 19, 6–70, especially 36–8Google Scholar. Although Wood's account of these meetings dates only from the mid-1650s, it seems probable that Ellis started them several years earlier.

⁵⁷ Price, D. C., Patrons and Musicians of the English Renaissance, Cambridge, 1981.Google Scholar

⁵⁸ For further details, see Bellingham, , op. cit. (56).Google Scholar

⁵⁹ The catch, or round at the unison for three or more male voices (for example ‘London's burning’), was popular in England between the sixteenth and eighteenth centuries. The light-hearted words, generally sportive and often indecent, were appropriate for taverns where they were usually sung. See article in New Grove, op. cit. (51).

⁶⁰ For example, Dean Henry Aldrich wrote several catches that were published in Playford, Henry's The Pleasant Musical Companion (London, 1685)Google Scholar including one intended to be ‘Sung by 4 Men while smoaking their pipes’ (‘Good, good indeed, the herb's good weed’). On Aldrich's musical interests, see below and note 65.

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⁶³ Wood, , op. cit. (52), iv, col. 498Google Scholar. This is confirmed by Marsh's own account given in his Diary; see Archbishop Marsh Library, Dublin, MS Z2. 2. 3. b, fol. 9.

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⁶⁸ These included four MAs from New College, two from All Souls (including Wood himself), and one from Magdalen College (Thomas Janes).

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⁷² Mace, T., 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, 236Google Scholar. A singing man at Trinity College, Mace was known to Newton (who was one of the subscribers to his book) and was a friend of several Cambridge Platonists. See the article in New Grove, op. cit. (51)Google Scholar, and note 83 below.

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⁷⁴ For an explanation of these systems, see Lindley, , op. cit. (22)Google Scholar, and also his article on ‘Temperaments’ in New Grove, op. cit. (51).Google Scholar

⁷⁵ The problems of tuning and temperament were already being addressed by Italian music theorists in the sixteenth cenrury, notably Gioseffo Zarlino and Vincenzo Galilei, Galileo's father. See Palisca, C. V., Humanism in Italian Renaissance Musical Thought, New Haven and London, 1985, 226–79Google Scholar. In the seventeenth century the subject also became of considerable interest to mathematicians and natural philosophers, most notably Marin Mersenne in his Harmonie universelle (Paris, 1636)Google Scholar. See Cohen, , op. cit. (7)Google Scholar, and Walker, , op. cit. (22).Google Scholar

⁷⁶ On Newton's recognition of this relationship, see Gouk, P. M., ‘Newton and music: from the microcosm to the macrocosm’, International Studies in the Philosophy of Science: The Dubrovnik Papers (1986), 1, 36–59CrossRefGoogle Scholar, and ‘Harmonic roots of Newtonian science’, op. cit. (7).

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⁷⁸ According to Wood, , op. cit. (52), ii, col. 366–7Google Scholar, Pigott received his BA in 1675 and MA in 1678 before becoming vicar of Yarnton, Oxfordshire, in 1679; two years later he was admitted to the Royal Society. Apart from his musical interests Pigott was also involved with a group interested in universal language schemes; Salmon, V., The Writings of Francis Lodwick, London, 1972, 8, 19, 92.Google Scholar

⁷⁹ For example in Mersenne, , op. cit. (75), vol. iii, bk 4, prop. ix. 208–11Google Scholar. See Dostrovsky, , op cit. (7).Google Scholar

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⁸³ After the Interregnum it is possible to demonstrate a similar kind of relationship between public music and public science in London. I have explored these parallels further in ‘A Golden Age of English Music? Augustan London as a Site of Musical Production and Consumption’, paper given at a conference on ‘Clusters of Achievement’: ‘Antwerp, Amsterdam and London in their Golden Ages’, Antwerp, 05 1995.Google Scholar

⁸⁴ A celebrated instance is provided by Edward, Lord Herbert of Cherbury, who in his Autobiography claims to have learned music ‘that I might entertain myself at home and together refresh my mynde after my studyes to which I was exceedingly inclined’. For the musical education of the North family, see Wilson, , op. cit. (52)Google Scholar; Jessop, A. (ed.), The Lives of the Norths, 3 vols., London, 1890Google Scholar; and also Chan, M. and Kassler, J. C. (eds.), Roger North's Cursory Notes of Musicke (c. 1698-c. 1703), Kensington, NSW, 1986Google Scholar; and Chan, M. and Kassler, J. C. (eds.), Roger North's The Musical Grammarian 1728, Cambridge, 1990.Google Scholar

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