The role of acoustics and music theory in the scientific work of Robert Hooke

References

• AN copies and the original of the essay are in the Royal Society Library: ‘Classified papers’, vol. 2 no. 31 (original), no. 32 (copy, incomplete, beginning from ‘Since, therefore the effects of music …’). Royal Society Register Book 13 3 10 complete copy. Also ‘Register book’ copy, vol. 13, 3–10, complete copy.
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• Royal Society . Journal book , 14 153 – 154 .
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• Birch , T. 1756–57 . History of the Royal Society of London Vol. 4 , 75 – 75 . London vol. 1 76, 80, 81, 87, 125, 416, 418 are the references to music and musical committees in the years 1662–64.
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• British Library, Sloane Ms, 1039. ff. 118–119, ‘Notice by Dr. Robert Hooke of Prof. John Wallis' edition of Ptolemy's Harmonica, 1682’; Trinity College Library, Cambridge, Ms. 0 11a 11–12. These include ‘A new synopsis of music’ and notes on composition. A discussion of these musical writings by Hooke will appear in my forthcoming Ph.D. thesis: Music in the natural philosophy of the early Royal Society
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• Such is the implication in the following works: Hollander J. The untuning of the sky: ideas of music in English poetry 1500–1700 Princeton 1961 381 381 and G. L. Finney, Musical backgrounds to English literature 1580–1650 (1961, New Brunswick), 75, 155. Both adopt the thesis that once a mechanical explanation for the cause of music was accepted, the Neoplatonic ideas of the ‘world Sprit’, the ‘harmony of the spheres’, and the macrocosmic-microcosmic relationship between the universe and man, became meaningless. For example, Finney writes: ‘Studies in physiology and acoustics explained away both the law of sympathy and the divine origin of harmonic proportions’ (p. 75). I believe that there is no inherently simple cause-and-effect relationship between a scientific understanding of the physical nature of sound and the breakdown of a Neoplatonic approach towards music.
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• Boyle , R. 1744 . Works Edited by: Birch , T. Vol. 5 , 41 – 41 . London
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• See The diary of Robert Hooke 1672–80 Robinson H.W. Adams W. London 1935 October 11 11 (28
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• Boyle . 1744 . Works Edited by: Birch , T. Vol. 5 , 42 – 42 . London vol. 1 As well as this projected experiment with compressed air, two other experiments using strings and pipes in the receiver were suggested, but these never took place either.
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• Royal Society ‘Classified papers’, vol. 2, no. 35; ‘Register book’, vol. 1, 197–205, Walter Charleton's ‘Apparatus phonocampticus’. This essay on echoes is discussing the following works: Mersenne M. Harmonie universelle Paris 1636 ‘Traité de l'echo’, 48–67; and A. Kircher, Musurgia universalis (1650, Rome), Lib. 9 pt. 4, ‘Magia phonocamptica’, 247–308.
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• Birch . 1756–57 . History of the Royal Society of London Vol. 1 , 446 – 447 . London 4 vols. 449, 451, 455, 456, 458, 460. There were weekly experiments from 6 July to 4 August 1664.
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• 1888–1950 . Oeuvres complètes de Christiaan Huygens Vol. 22 , 307 – 308 . La Haye (publiée par la Societé Hollandaise des Sciences vol. 3 311–313 (letters of Huygens to Moray, 1 and 19 August 1661 [N.S.]). In dating I have adopted the following conventions. Dates from 1 January to 25 March conform to the modern calendar year, hence 1 Feb. 167 1/2 is shown as 1 Feb. 1672. [O.S.] and [N.S.] mean ‘old style’ and ‘new style’; the former, used in England, is 10 days behind the latter, which was used on the Continent. (Hence 1 Feb. 1672 [O.S.] = 11 Feb. 1672 [N.S.]) I have kept the dating of letters in their original form. Any date without an indication as to its style is to be taken as English O.S. Huygens's writing on logarithms is in Oeuvres, vol. 20, 49–58. For a discussion on the 31-division of the octave see J. Murray Barbour, Tuning and temperament (1953, East Lancing); and for a more detailed study of Huygens's ideas see H. F. Cohen, ‘Christiaan Huygens' musical theories’, Proceedings of the Christiaan Huygens Symposium (held in Amsterdam, August 1979).
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• Brouncker , W. 1653 . Renatus Des-Cartes excellent compendium of musick and animaversions of the author London In this work Brouncker attempts to divide an interval of an octave and a 4th into 17 equal parts using logarithms (see D. P. Walker, ‘Some 17th century scientists’ views on intonation and the nature of consonance’, Archives internationales d'histoire des sciences, 27 (1977), 263–273 (pp. 268–269)).
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• Birch . 1756–1757 . History of the Royal Society of London Vol. 1 , 416 – 416 . London 4 vols. 418; Royal Society ‘Letter book’, vol. 1, 143–148, ‘An extract of a letter to the Royal Society by Mr. Birchenshaw concerning musick’, read 26 April 1664. The letters of Wallis (ibid., 149–164, 173–174) are printed in A. R. Hall and M. B. Hall (eds.), The correspondence of Henry Oldenburg (11 vols., 1965–77, Madison and London), vol. 2, 179–181, 190–201, 202–203 (7, 14, 25 May 1664).
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• See Birch History of the Royal Society of London London 1756–1757 1 446 447 4 vols.
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• Birch . 1756–1757 . History of the Royal Society of London Vol. 1 , 446 – 447 . London 4 vols.
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• At present day pitch, on a piano the G above middle C has a frequency of 392cps. The note closest to 272 cps is C# (C sharp), of 277·5 cps. Even allowing for a dramatic change in pitch, their approximation is wildly inaccurate. On this topic, see Mendel A. Pitch in the 16th and early 17th centuries Music quarterly 1948 34 28 45 199–221, 336–357, 575–593.
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• Huygens . Oeuvres , 5 100 – 100 . (see footnote 21). Mersenne (footnote 15) discusses this in ‘Traitez des sons’, Liv. 3, prop. 1, 157–160, prop. 9, 174–175, prop. 12, 180–182
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• Birch . 1756–1757 . History of the Royal Society of London Vol. 2 , 471 – 471 . London 4 vols. The Florentines were the Marquis Bartholomei and Count Bardi, who were with an unnamed ‘resident of Venice’. According to the editors of Oldenburg (footnote 19) these two men have not been identified (see vol. 7, 518). In the Dizionario biografico degli Italiani (1950-, Rome) vol. 6, 313–315 there is an entry for a certain Bardo Bardi Magalotti (1629–1705), who might have been the one mentioned. I have not been able to find a likely entry for Bartholomei, an extremely prolific family going by this name.
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• This is in the same letter as Huygens Oeuvres 5 99 99 Accounts of the defective experiments are in Birch (footnote 3), vol. 1, 460, 474, 475.
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• Bacon . 1627 . Sylva Sylvarum London Century 1, 3, ‘Of the motion of bodies upon pressure’. The copy presented to the Society by Williamson was the 10th edition (1676, London).
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• Birch . 1756–1757 . History of the Royal Society of London Vol. 4 , 46 – 46 . London 4 vols. The experiment of 14 March 1683 seems merely a repetition: ‘for proving an attraction from the surface of a glass of water to the place struck with a fiddlestick on the side’ (p. 194).
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• ‘Dr. Wallis' letter to the publisher, concerning a new musical discovery’ Philosophical transactions of the Royal Society 1677–78 12 839 842 This discovery was that of the existence of nodes in a vibrating string, found almost simultaneously and independently around 1673 by two Oxford musicians, William Noble and Thomas Pigot.
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• 1671–72 . Philosophical transactions of the Royal Society , 6 : 3056 – 3058 .
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• Kircher's claim: Oldenburg The correspondence of Henry Oldenbury Madison and London 1965–77 9 155 157 11 vols. (Dodington to Oldenburg, 22 July 1672 [N.S.]). This is an extract of a letter by Kircher claiming to have invented such a trumpet 24 years before. For accounts of the Paris experiments see ibid., vol. 8, 567–568; vol. 9, 14, 55. Also J. de Hautefeuille (1647–1724) wrote Explication de l'effet des trompettes parlantes (1674, Paris).
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• Robinson , H.W. and Adams , W. , eds. October 1935 . The diary of Robert Hooke 1672–80 October , 11 – 11 . London (28
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• Robinson , H.W. and Adams , W. , eds. January 1935 . The diary of Robert Hooke 1672–80 January , 206 – 207 . London (1 209–210 (8 January).
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• Robinson , H.W. and Adams , W. , eds. 1935 . The diary of Robert Hooke 1672–80 223 – 223 . London (28 March 1676), ‘Directed Tompion about sound wheels. The number of teeth’. (T. Tompion (1639–1713) was a clockmaker who collaborated with Hooke.) The quotation of 1681 is from Birch (footnote 3), vol. 4, 96.
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• Gillispie , C.C. , ed. 1970–78 . Dictionary of scientific biography Vol. 12 , 129 – 130 . New York 15 vols. For a similar device invented by Huygens dated around 1682 see Huygens (footnote 17), vol. 19, 375–376. See also S. Dostrovsky, ‘Early vibration theory: physics and music in the 17th century’, Archive for history of exact sciences, 14 (1975), 169–218 (pp. 199–200).
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• Robinson , H.W. and Adams , W. , eds. 1935 . The diary of Robert Hooke 1672–80 351 – 351 . London 361 (4 April, 1 June 1678).
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• Waller , R. , ed. 1705 . The posthumous works of Robert Hooke xxiv – xxiv . London
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• Hooke , R. 1665 . Micrographia London preface, sigs. b4–c1.
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• Centore , F. 1970 . Robert Hooke's contribution to mechanics 67 – 67 . La Haye See also M. Hesse, ‘Hooke's philosophical algebra’, Isis, 57 (1966), 67–83; and ‘Hooke's vibration theory and the isochrony of springs’, ibid., 433–441.
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• Centore . 1970 . Robert Hooke's contribution to mechanics 63 – 91 . La Haye cap. 4 ‘The mechanics of terrestial local motions’, discusses Hooke's debt to Descartes.
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• Hooke , R. 1678 . Lectures de potentia restitutiva 7 – 7 . London
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• Waller , R. , ed. 1705 . “ ‘Discourse on the nature of comets’ (1682) ” . In The posthumous works of Robert Hooke 184 – 184 . London in
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• See Bacon F. Sylva Sylvarum London 1627 and 38.
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• Galilei , G. 1638 . Two new sciences , trans. S. Drake (1974, Madison), 94–108; M. Mersenne (footnote 15), ‘Traitez des sons’, Liv. 3, prop. 21, 209–213. On the background to the work of the Royal Society on pendulums, see C. Truesdell, ‘The rational mechanics of flexible or elastic bodies, 1638–1788’, introduction to L. Euleri opera omnia, ser. 2, vol. 11, pt. 2 (1960, Zurich), 15–141 (pp. 15–58). On the work of Hooke and Wren, see L. D. Patterson, ‘The pendulums of Wren and Hooke’, Osiris, 10 (1952), 277–321.
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• Dr. Wilkins was familiar with Galileo's work and no doubt shared his interests with other members. Hooke read Riccioli's G. Almagestum novum Bologna 1651, 1653 which suggested using the pendulum as a measuring device. (see Patterson ibid., 279).
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• Sprat , T. 1667 . History of the Royal Society 313 – 313 . London
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• Sprat , T. 1667 . History of the Royal Society 226 – 226 . London Birch (footnote 3), vol. 2, 90–92, 97, 99, 105–106; Post. works (footnote 54), xii.
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• Huygens could determine the centre of oscillation of a compound pendulum by 1664 (see Huygens Oeuvres 5 147 150 (Huygens to Moray, 21 November 1664 [N.S.])). Hooke notes the limitations of using a pendulum for a universal measure in his ‘Lectures concerning navigation and astronomy’ (1683), in Post. works (footnote 54), 547–548; also in Birch (footnote 3) vol. 1, 505–507.
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• Waller , R. , ed. 1705 . The postumous works of Robert Hooke 135 – 135 . London
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• Latham , R.S. and Matthews , W. , eds. 1970- . The diary of Samuel Pepys Vol. 9 , 239 – 239 . London vol. 7 In fact Hooke had written on this subject a year earlier in his Micrographia (footnote 55), 172–174. See also O. Sotavalta, ‘Flight-tone and wing-stroke frequency of insects and the dynamics of insect flight’, Nature, 170 (1952), 1057–1058.
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• For example, Bacon makes a comparison between the properties of sound and light in his Bacon F. Sylva Sylvarum London 1627 Century 2, 68–69 ‘A consent of visibles and audibles’.
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• Robinson , H.W. and Adams , W. , eds. 1935 . The diary of Robert Hooke 1672–80 238 – 238 . London
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• See The diary of Robert Hooke 1672–80 Robinson H.W. Adams W. London 1935 January 206 207 (1 and 50.
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• This synopsis Music in the natural philosophy of the early Royal Society attempts to replace musical notes with syllables, using vowels for pitch and consonants for length. This could be the ‘orthography of music’ he refers to on 1 January (see Diary (footnote 49), 207).
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• Kircher . 1627 . Sylva Sylvarum London One example, out of many possible extracts, is Lib. 2, cap. 6, 67–71, ‘De musica, ac instrumentis Veterum Graecorum’.
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• Kircher . 1627 . Sylva Sylvarum London Lib. 9 pt. 2, cap. 1, 213–214, ‘De causis, et modo, quo morbi per musicam curantur’; cap. 2, 214–216, ‘Quomodo David cytharae sono Saul a spiritu maligno curavit’; cap. 3, 216–218, ‘De mirabili historia Regis cuiusdam Daniae vi musicae ad insaniam redacti’; cap. 4, 218–220, ‘De Tarantulae morsu intoxicatorum cura prodigiosa per musicam’.
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• 1704 . The practise of physic London originally appeared as De praxi medica (1696, Rome). Baglivi (1668–1707) became a Fellow of the Royal Society in 1697 (see DSB (footnote 6), vol. 1, 391–392). For G. Borelli (1608–1679) see DSB, vol. 2, 306–314.
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• Shadwell , T. 1676 . The virtuoso 47 – 49 . London is an entire scene on the subject of the Tarantula (p. 49). It is a matter of debate whether Gimcrack is a parody of Hooke alone. Shadwell himself said that the character was fictional and he had drawn from many examples. However, it seems that Hooke himself took it as a personal insult (see his Diary (footnote 48), 234–235). On this issue see E. L. Jones, ‘Robert Hooke and “The Virtuoso”’, Modern language notes, 66 (1951), 180–181.
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• Royal Society . Journal book , 8 118 – 118 . (Birch's account of Royal Society meetings (footnote 3) ends in 1687.) The section on Ovid is in Hooke's ‘Discourse on earthquakes’, Post. works (footnote 54), 322–325, 371–384.
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• Bacon , F. 1609 . De sapienta veterum liber … trans. Sir Arthur Gorges, The wisdom of the ancients (1619, London). See also on this subject B. Carman, ‘Study of Natalis Comes’ theory of mythology and its influence in England’ (Ph.D. thesis, 1966, London); and her ‘Francis Bacon, Natalis Comes, and the mythological tradition’, Journal of the Warburg and Courtauld Institutes, 33 (1970), 264–291.
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• Aristotle . De anima , 2 ( 8 ) 419b – 420a .
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• 1673 . Phil. trans. Roy. Soc. London , 8 : 7000 – 7000 .
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• The best account of the sources of the ‘praise of music’ tradition is in Hutton Some English poems in praise of music English miscellany, no. 2 Praz M. Rome 1951 1 63 The earliest sources are Plato, Republic, 3, 398–399; 10, 617; Timaeus, 36, 47; Laws, 1 and 7; and Aristotle, Politics, 8, ch. 5, 7. These were added to and elaborated. Boethius, De musica, 1, ch. 1 includes the account of the sleeping infant, and the effects of music on all ages and all classes. This opening of Hooke's essay could be drawn from many sources, but it seems that he was at least strongly influenced by Butler's account (footnote 97) in his Principles of music. Hooke is known to have had a copy of this work (see H. Feisenberger, Sale catalogues of libraries of eminent persons, vol. 11 (1975, London), 104).
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• The story of Saul is in I Samuel 16, v. 2, 3. This is cited by Butler The principles of music London 1636 5 5 ‘Of the Aeolic mood was that enchanting music of the harp, provided for King Saul, when the evil spirit troubled him’.
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• Butler . 1636 . The principles of music London cites the sources of the King of Denmark story as Saxo Grammaticus, Historia Danae Lib. 1, cap. 12, and also Krantzius, Daniae, Lib. 5, cap. 3, Krantzius is the source that Kircher (footnote 95) gives: Lib. 9, pt. 2, cap. 3, 216.
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• Butler . 1636 . The principles of music 6 – 6 . London gives a strikingly similar quotation from Aristotle, citing Politics, 8, ch. 5: ‘Thus does the Philosopher describe this mood: Phrygia distrahit ac rapit-animum, et quasi extra se ponit’. Butler says of the Phrygian mode, ibid., 2: ‘The Phrygian mood is a manly and courageous kind of musick, which with its stately, or loud and violent tones, rouseth the spirit, and inciteth to arms and activity’. On theories of the modes and their effects in the 16th and 17th centuries see Walker (footnote 92).
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• The musician probably changed to the Ionic mode, of which Butler says: ‘The Ionic mood is contrary to the Phrygian: an effeminate and delicate kind of music, set unto pleasant songs and sonnets of love and suchlike fancies’ Butler C. The principles of music London 1636 2 2
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• On the question of the Tarantula see sub-section 4.3 above and footnotes 100–102. The story of the Tarantula as given by Kircher Sylva Sylvarum London 1627 is mentioned in a popular music manual; J. Playford, Introduction to the Skill of musick (revised 4th ed. 1666, London), ‘Of musick in general and its divine and civil uses’, A3. It appears for the first time in this edition.
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• On the connection of this with the Baconian tradition, see sub-section 4.3 above, and Bacon F. De sapienta veterum liber … 1609
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• Kircher . 1627 . Sylva Sylvarum London Lib. 9, pt. 1, cap. 5, ‘Experimentum’, 212.
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• Aristotle . De anima Vol. 11 , 8 – 8 . (footnote 103). Kircher (footnote 15), following on from this, says in Lib. 1, cap. 1, 2–3: ‘sonum definit esse motionem eius, quad eo motu moveri potest, quo ca quae a corporibus invicem percussis resiliunt, moventur’. In cap. 2, 3: ‘sonus nihil alius sit, quam qualitas passibilis successiva’.
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• On the possible influence of Mengoli's book, see sub-section 4.3 above, and Phil. trans. Roy. Soc. London 1673 8 6194 7000 Kircher (footnote 15). Lib. 1, caps. 7–9, 13–19 deal with the ear's structure. This physiological question of the ear's role in interpreting music has yet to be fully examined in its historical context.
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• This definition of the ear's comfortable limits of hearing parallels the traditional limits of the human voice; according to Butler The principles of music London 1636 9 9 these are ‘from the lowest note of a man's bass unto the highest of a boy's treble’, and according to T. Morley, Introduction to musick (1597, London), 7, when these limits are exceeded ‘under Gam-ut the voice seem'd as a kind of humming, and above E la a kind of constrain'd skriccing’.
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• The importance of variety in music was well established in music books. Morley Introduction to musick London 1597 150 150 quotes a translation of a passage from G. Zarlino's Istitutioni harmoniche (1558, Venice), pt. 3, cap. 29: ‘for even as a picture painted with divers colours doth more delight the eye to behold it than if it were done with one colour alone, so the ear is more delighted and taketh more pleasure of the consonances by the diligent musician placed in his composition with variety, than of the concords put together without any varietie at all’. The need for variety in composition is also emphasised by Descartes in his Compendium musicae (footnote 18), 3. ‘ad cramben’: crambe,-es, fem. (literally a kind of cabbage) means ‘warmed over, an old story’ (A latin dictionary (eds. C. Lewis and C. Short, 1975 imp., Oxford), 477).
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• On x! see sub-section 4.3 and Mersenne Harmonie universelle Paris 1636 113. According to the chart that Kircher gives ((footnote 111), 5), the number that Hooke applies to 17 notes rather than 16. In Mersenne (footnote 111), 108, the number is for 17 also. The correct number for 16 notes is 20,922,789,888,000; even this is wrong for two octaves, for example C-c″. since there are only 15 notes in this range. The number of combinations from 15 notes is 1,307,674,368,800.
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• According to Butler The principles of music London 1636 24 24 the eight notes were the following: a larg, a long, a brief, a semibreve, a minim, a crotchet, a quaver, a semiquaver. As successively shorter notes were added to the original larg and long, these two notes became obsolete by the 17th century.
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• According to Butler The principles of music London 1636 25 25 duple time is when ‘to a stroke or semibreve, is sung 2 minims (and consequently 4 crotchets 8 quavers and 16 semiquavers)’. Triple time is when ‘three minims (and consequently 6 crotchets and 12 semiquavers) go to the semibreve stroke’. Concerning the statement about the notes in triple time being relatively faster, C. Simpson says in his Principles of music (2nd ed., 1667, London), 30, that in triple time ‘each minim is about the length of a crotchet in common time’, which means the notes were relatively faster.
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• The idea of consonance being explained in terms of the relative coincidence of vibrations was accepted by the mid 17th century as an alternative for the explanation based upon the perfection of the numbers 1–6 by which all perfect consonances could be expressed as ratios of their string lengths. Huygens accepted the new explanation (see his Oeuvres 20 32 32 esp. Another author who states this is Francis North in A philosophical essay directed to a friend (1677, London), 9. On views of consonance, see Walker (footnote 18).
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