Isaac Newton and the mystery of the major sixth: A transcription of his manuscript 'Of Musick' with commentary

Interdisciplinary Science Reviews

Volumn 31, Issue 4, 2006, Pages 291-306

  Pesic, Peter ^a  

^a ST JOHN S COLLEGE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EXPERIENTIAL QUALITIES; NATURE OF LIGHT; NEWTON'S RINGS; OPTICAL ANALOGUES; OPTICAL WRITING; PLANETARY MOTION; TRANSPARENT BODY; VISIBLE LIGHT;

ASTRONOMY; COLOR;

TRANSCRIPTION;

EID: 33947183495     PISSN: 03080188     EISSN: None     Source Type: Journal    
DOI: 10.1179/030801806X143268     Document Type: Review

References (71)

1. Penelope Gouk began this work in her dissertation, 'Music in the natural philosophy of the early Royal Society' (unpublished doctoral thesis, University of London, 1982), and then presented it more generally in 'The harmonic roots of Newtonian science', in Let Newton Bel, (ed. J. Fauvel et al.), 101-125; 1988, Oxford, Oxford University Press,
2. and more fully in her seminal book Music, Science, and Natural Magic in Seventeenth-Century England, 224-257; 1999, New Haven, CT, Yale University Press.
3. For these notebooks and their contents, see R. S. Westfall: Never at Rest: A Biography of Isaac Newton, 83, n. 52; 1980, Cambridge, Cambridge University Press.
4. I consulted the extremely helpful microfilm collection Sir Isaac Newton: Manuscripts and Papers; 1991, Cambridge,
5. Chadwyck-Healey, and the accompanying volume P. Jones (ed.): Sir Isaac Newton: A Catalogue of Manuscripts and Papers; 1991, Cambridge, ChadwyckHealey. Newton's only other writings on music outside Add. Ms. 4000 known to me (or listed in this catalogue or in any other scholarly references by Gouk) are some very brief notes on semitones in CUL (Cambridge University Library) Add. Ms. 3958, f. 30v, and also brief comments on the octave in his early 1660s 'Questiones qusedam Philosophise', CUL Add. Ms. 3996, f. 33,
6. transcribed in J. E. McGuire and M. Tamny (ed.): Certain Philosophical Questions: Newton's Trinity Notebook, 388-391; 1983, Cambridge, Cambridge University Press.
7. There are also extracts from practical musical writings by Thomas Salmon in CUL Add. Ms. 3970, ff. 1-15, though not in Newton's hand; see P. Gouk: Music, Science, and Natural Magic, pp. 231-233, n. 24 (see Note 1).
8. See Add. Ms. 4000, ff. 104-113, especially the circular diagrams on ff. 109r-109v that strongly resemble those in R. Descartes: Compendium of Music, (trans. W. Robert, with introduction and notes by C. Kent), 34, 36; 1961, American Institute of Musicology. As Westfall notes, during the years Newton was using this notebook he was studying the works of Descartes, including his writings about light;
9. see R. S. Westfall: Never at Rest, pp. 88-105 (see Note 2).
10. See, in particular, P. Gouk: Music, Science, and Natural Magic, pp. 224-257 (see Note 1).
11. Add. Ms, 4000, f. 138; for ease of reading, 1 have regularised the spelling in quotations from Newton's manuscripts given in the body of the paper, while retaining the original orthography in the full transcription presented in the appendix. For the numero senario, see G. Zarlino: The Art of Counterpoint, (trans. G. A. Marco and C. V. Palisca), 8, n. 4; 1968, New York, NY, W. W. Norton. One wonders to what extent Newton might have been aware of Kepler's attempt to found the theory of musical intervals not on arithmetical numerology, but on geometry that (ultimately) refers also to the cosmos;
12. see J. Kepler: The Harmony of the World, (trans. H. J. Aiton, A. M. Duncan and J. V. Field), 129-187; 1997, Philadelphia, PA, American Philosophical Society,
13. also P. Pesic: 'Earthly music and cosmic harmony: Johannes Kepler's interest in practical music, especially Orlando di Lasso', Journal of Seventeenth Century Music, 2005, 11, (1), sscm-jscm.press.uiuc.edu/ jscm/v11/no1/pesic.html,
14. and P. Pesic: 'Kepler and the song of the Earth', in Festschrift for Curtis Wilson, (ed. G. Smith); forthcoming, Cambridge, MA, MIT Press.
15. Hooke's 1672 letter to Oldenburg can be found in H. W. Turnbull (ed.): The Correspondence of Isaac Newton, Vol. 1, 111; 1959, Cambridge, Cambridge University Press; relying on it, Gouk claims that 'it was Hooke, then, who first suggested to Newton the analogy between colour and musical tone' (Music, Science, and Natural Mage, p. 241 (see Note 1)). Note that, in this letter, Hooke does not discuss colour explicitly, saying only that 'the ray is like the string, straind between the luminous object & the eye, & the stop or finger is like the refracting surface, on ye one sight of wch the string has noe motion; on the other, a vibrating one.' To be sure, the extension of the analogy to colour seems implicit in this comparison between string length and ray vibration, but so too would Newton's version of the analogy rather naturally lead him to reflect on this same implication. At the time he wrote in Add. Ms. 4000, though, Newton would only have known Hooke's Micrographia (1665), which does not seem to broach this analogy when Hooke discusses the 'quite differing kinds of vibrations and repercussions' of strings;
16. see R. Hooke: Micrographia, 15; 1961, New York, NY, Dover.
17. Though Robert Boyle does discuss sounds, he does not seem to make any such analogy between sounds and colours in his 1664 Experiments and Considerations Touching Colours, (ed. M. Boas Hall), 76; 1964, New York, NY,
18. Johnson Reprint. Voltaire observed that 'I had often heard it said, that Newton had taken from Kicher this Discovery of the Analogy between Light and Sound', in The Elements of Sir Isaac Newton's Philosophy, (trans. J. Hanna), 149-150; 1738, London, Steven Austen (reprinted 1967, London, Frank Cass), but there is no evidence that Newton was aware of Athanasius Kircher's statements on this (particularly his pungent phrase 'Sound the Ape of Light', quoted by Voltaire), nor that Newton had read much in Kircher at the time he wrote 'Of Musick'.
19. Plato: Republic, 516d: 'If such a man were to come down again and sit in the same seat, on coming suddenly from the sun wouldn't his eyes get infected with darkness?' In De sensu (Sense and Sensibilia), 439b20-440b25, Aristotle compares ratios in music with colours. For a larger perspective on this analogy,
20. see P. F. Ganz: 'Sound and colour: critical remarks of a musician on sound-colour relations', Palette, 1967, 23, 2-10. For alchemical comparisons with the seven musical tones and seven planets,
21. see P. Gouk: Music, Science, and Natural Magic, p. 231 (see Note 1).
22. For Newton's use of square brackets, see A. E. Shapiro: 'Newton's optics and atomism', in The Cambridge Companion to Newton, (ed. I. B. Cohen and G. E. Smith), 227-255, at 253, n. 24; 2002, Cambridge, Cambridge University Press.
23. Unlike the diatonic, the chromatic genus allowed successive semitones, and the enharmonic involved quartcrtones. Regarding the exotic experiments in temperament at the court of Rudolf II, see R. J. Weston Evans: Rudolf II and His World A Study in Intellectual History, 1576-1612, 190-193; 1973, Oxford, Clarendon Press, and P. Pesic: 'Earthly music and cosmic harmony' (see Note 5).
24. For the history of equal temperament before Newton, see J. M. Barbour: Tuning and Temperament; A Historical Survey, 45-64; 1953, East Lansing, MI, Michigan State College Press;
25. also B. Scimemi: 'The use of mechanical devices and numerical algorithms in the 18th century for the equal temperament of the musical scale', in Mathematics and Music, (ed. G. Assayag, H. G. Feichtinger and J. F. Rodrigues), 49-63; 2002, Berlin, Springer-Verlag.
26. Though he does not refer to it here, one wonders whether Newton had read Aristoxenus's Elementa Harmonica, an important ancient source maintaining the opposing view that 'for the student of music accuracy of perception stands just about first in order of importance, since if he perceives badly it is impossible for him to give a good account of the things which he does not perceive at all', as translated in Greek Musical Writings, (ed. A. Barker), Vol. 2, 150-151; 1989, Cambridge, Cambridge University Press. Indeed, in his reading of Kepler's Harmony of the World (p. 197), Newton would have found references to Aristoxenus, whom Kepler cites in connection with his assertion that 'I should also interrogate the ears, yet in such a way that Reason should proclaim what it has agreed are the decisions.'
27. Add. Ms. 3996, ff. 33, 44 in Certain Philosophical Questions, pp. 382-383, 396-397 (see Note 2).
28. For Newton's association of idolatry and corruption with geocentric cosmology, see P. Gouk: Music, Science, and Natural Magic, p. 252 (see Note 1). For Kepler's association of modern polyphonic music with Copernican cosmology,
29. see P. Pesic: 'Earthly music and cosmic harmony' and 'Kepler and the song of the Earth' (see Note 5).
30. This paper is readily available in Isaac Newton's Papers & Letters on Natural Philosophy, (ed. I. B. Cohen), 177-235; 1958, Cambridge, MA, Harvard University Press.
31. Newton also refers to this analogy in a 1685 letter to William Briggs, in Correspondence, Vol. 2, pp. 418-419 (see Note 6).
32. Newton's 1677 letter to John North (Correspondence, Vol. 2, pp. 205-208) does not mention the analogy, though at the end Newton does discuss experiments observing the blue light from prisms;
33. see also J. C. Kassler: The Beginnings of the Modem Philosophy of Music in England; Francis North's A Philosophical Essay of Musick (1677) with comments of Isaac Newton, Roger North, and in the Philosophical Transactions, 175-178; 2004,
34. Aldershot, Ashgate. For other aspects of Newton's application of these arguments to the colour of the sky, see P. Pesic: Sky in a Bottle, 42-52; 2005, Cambridge, MA, MIT Press.
35. Isaac Newton's Papers & Letters, pp. 192-193 (see Note 14); Fig. 1 is taken from p. 193.
36. This phrase also occurs in Newton's 'An Hypothesis explaining the properties of light', sent to the Royal Society in 1675, in Correspondence, Vol. 1, p. 376 (see Note 6).
37. For discussions of Newton's analogy, see H. L. Armstrong: 'Comment on Newton's inclusion of indigo in the spectrum', American Journal of Physics, 1972, 40, 1709;
38. A. E. Shapiro (ed.): The Optical Papers of Isaac Newton, Vol. 1, 537-549, esp. 545 and 550, n. 10; 1984, Cambridge, Cambridge University Press;
39. K. McLaren: 'Newton's indigo', Colour Research and Application, 1985, 10, 225-229;
40. A. R. Hall: All Was Light: An Introduction to Newton's Opticks, 56-57, 112-113; 1993, Oxford, Clarendon Press;
41. D. L. Sepper: Newton's Optical Writings: A Guided Study, 95-99, 205-270; 1994, New Brunswick, NJ, Rutgers University Press;
42. and A. E. Shapiro: 'Experiment and mathematics in Newton's theory of colour', Physics Today, 1994, 37, (9), 34-42.
43. I thank Alan Shapiro for pointing this out to me here and in other places in Newton's Correspondence, in a 1682 letter to Briggs (Vol. 2, pp. 381-385) and a 1690 letter to Harrington (Vol. 4, p. 275): 'I am inclined to believe some general laws of the Creator prevailed with respect to the agreeable or unpleasing affections of all our senses...' (emphasis added), Note also Newton's description in his 1675 'Hypothesis', CUL Add. Ms. 3970, f. 528v, of the way light corpuscles strike the retina and there excite Vibrations' in the aether contained in it, vibrations that then propagate into the brain, where they 'affect the soule with a sensation of various colours according to their various proportions, something after the manner that various sounds are produced by various proportions of the vibrations of the Air'.
44. The Optical Papers of Isaac Newton, Vol. 1, p. 542 (see note 16).
45. In decimal terms, the ratio between these extreme wavelengths, 700:400, is 1.744, compared to the Pythagorean major sixth 27:16 (1.687), the Pythagorean minor seventh 16:9 (1.777), or the major sixth in just intonation 5:3 (1.666). However, the limits of the colours are not sharp, so that the ratio 700:400 reflects a certain arbitrariness in modern definitions of colours; Newton could well have perceived this ratio as smaller and hence closer to the major sixth.
46. Certain insects apparently have a full octave (or more) of colour perception and can find what seems a behaviourally similar identity in two wavelengths of frequency ratio 2:1 as our ear perceives in D and d.
47. For Newton's 'fits' and his concept of 'bigness', see A. E. Shapiro: Fits, Passions, and Paroxysms: Physics, Method, and Chemistry and Newton's Theories of Coloured Bodies and Fits of Easy Reflection; 1993, Cambridge, Cambridge University Press,
48. and his 'Newton's optics and atomism', 'Newton's experiments on diffraction and the delayed publication of the Optick's, in Isaac Newton's Natural Philosophy, (ed. J. Z. Buchwald and I. B. Cohcn), 47-76; 2000, Cambridge, MA, MIT Press,
49. and 'Newton's "achromatic" dispersion law: theoretical backgrounds and experimental evidence', Archive for History of Exact Sciences, 1979/80, 21, 91-128.
50. See also N. R. Hanson: 'Waves, particles, and Newton's 'fits', Journal of the History of Ideas, 1960, 21, 370-391;
51. A. I. Sabra: 'Newton and the 'bigness' of vibrations', Isis, 1963, 54, 267-268;
52. R. S. Westfall: 'Uneasily fitful reflections on fits of easy transmission', Texas Quarterly, 1967, 10, (3), 86-107;
53. A. I. Sabra: Theories of Light from Descartes to Newton, 231-250, 273-342; 1967, New York, NY, American Elsevier;
54. and A. R. Hall: All Was Light: An Introduction to Newton's Opticks, 163-179; 1993, Oxford, Clarendon Press.
55. For Newton's extensive experiments following 'Grimaldo', see the Opticks, Book III, 317-339; 1979, New York, NY, Dover, reprinting the text of the fourth (1730) edition. The experiments end inconclusively with Newton's remark that he was 'interrupted, and cannot now think of taking these things into farther Consideration', and are followed by his long series of 'Queries, in order to a farther search to be made by others'. See also A. E. Shapiro: 'Newton's experiments on diffraction' (sec Note 21).
56. CUL, Add. Ms, 3970, f. 528v.
57. CUL, Add. Ms. 3970, f. 521 v; Shapiro notes the reading '14 to 9' in Optical Papers, Vol. 1, pp. 546-547, n. 28, which contains a very helpful account of the development of Newton's thinking on this issue (see Note 16).
58. CUL, Add. Ms. 3970, f. 336r.
59. I. Newton: Opticks, pp. 211-212 (see Note 22).
60. As Note 19 indicates, such a discrimination between just and Pythagorean sixths would have required accuracy of a few per cent (between quotients of 1.666 and 1.687), in this case corresponding to distance measurements of the order of a few hundredths of an inch, on the edge of distance differences Newton claims to observe (in Opticks, pp. 200-201 (see Note 26), he distinguishes between rings of 55/100 inch and 58/100 inch diameters). Nor does he make an explicit claim to distinguish Pythagorean from just intervals here or elsewhere.
61. J. Kepler: Harmony of the World, p. 138 (see Note 5).
62. The Mixolydian mode has a major third (G A B) where the Dorian has a minor (D E F); placed between the third and fourth degrees of the mode, a 'Mixolydian orange' would have been so indistinguishable from yellow (compared to the 'Dorian orange') that Newton might at that point have preferred the Dorian scheme. However, the indistinguishability of 'indigo' and 'blue' did not move him. Later studies of colour discrimination show that the eye is much more sensitive to colour difference in the yellow than it is in the blue-violet.
63. P. Gouk: Music, Science, and Natural Mage, pp. 232-237 (see Note 1).
64. D. Sepper: Newton's Optical Writings, pp. 123-127, at 123 (see Note 16).
65. For musical analogies in Newton's cosmology, see J. E. McGuire and P. M. Rattansi: 'Newton and the "Pipes of Pan"', Notes and Records of the Royal Society of London, 1966, 21, 108-143;
66. P. Gouk: Music, Science, and Natural Magic, pp. 251-257 (see Note 1);
67. and T. M. Tonietti: 'Does Newton's musical model of gravitation work? A mistake and its meaning', Centaurus, 2000, 42, 135-149.
68. See N. Malebranche: The Search after Truth, (trans. and ed. T. M. Lennon and P. J. Olscamp), 689, 716-717; 2006, Cambridge, Cambridge University Press, which compares the 'determinate number of sounds when an octave is divided harmonically' with the way 'Newton found that the band of simple colours was divided harmonically'.
69. For Voltaire's delightful presentation of the colour/music analogy, including his discussion of the artistic possibilities of colour organs, see Newton's Elements, pp. 149-158 (see Note 6).
70. For general background, see A. R. Hall: All was Light, pp. 202-203, 227 (see Note 16).
71. bis, and also erred in the numbering of his points (as noted in the transcription).