Abstract
The purpose of this chapter is to survey a wide and ancient tradition in order to indicate fruitful lines of research within it. This tradition, namely the Harmony of the Spheres, the musica mundana of Boethius, has hitherto been chiefly studied as a literary one, a complex of metaphors and topoi, very thoroughly and brilliantly covered by James Hutton in a long article entitled, too modestly, “Some English Poems in Praise of Music.”1 I want now to try and see when, where and in what ways musica mundana has had some importance outside literature, some reality as a part of, or influence on the following fields: ordinary music, astronomy and cosmology, astrology and magic, architecture, mathematics and early modern science.
First published as “La tradition mathématico-musicale du platonisme et les debuts de la science moderne,” in Platon et Aristote à la Renaissance (Paris: J. Vrin, 1976), pp. 249 –260, the article is printed in revised form in Walker’s Studies in Musical Science in the Late Renaissance (London: The Warburg Institute/University of London, and Leiden: E.J. Brill, 1978), pp. 1–13. On the subject see, also, Eberhard Knobloch, “Harmony and Cosmos: Mathematics serving a Teleological Understanding of the World,” Physis 32 (1995): 55–89.
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References
James Hutton, “Some English Poems in Praise of Music,” English Miscellany 2 (1951): 1–63 [now in his Essays on Renaissance Poetry, ed. Rita Guerlac (Ithaca and London: Cornell University Press, 1980), pp. 17–73]; cf. John Hollander, The Untuning of the Sky (Princeton, NJ: Princeton University Press, 1961); Ludke G. Finney, Musical Backgrounds for English Literature: 1580–1650 ( Westport, Connecticut: Greenwood Press, 1976 ).
Carl G. Jung Wolfgang Pauli, The Interpretation of Nature and the Psyche (London, 1955). [See, also, Robert Westman, “Nature, Art, and Psyche: Jung, Pauli, and the Kepler-Fludd Polemic,” in Occult and Scientific Mentalities in the Renaissance,ed. Brian Vickers (Cambridge: Cambridge University Press, 1984), pp. 177–229].
Plato, Republic,546a-d; cf. Paul Tannery, Mémoires scientifiques,ed. J.L. Heiberg H.G. Zeuthen, 17 vols. (Tolouse: E. Privat, 1912–1950), 1:12ff.; Marsilio Ficino, Opera Omnia (Basle: Ex Officina Henricpetrina, 1576), pp. 1413ff. [see, also, Michael J.B. Allen, Nuptial Arithmetic. Marsilio Ficino’s Commentary on the Fatal Number in Book VIII of Plato’s Republic (Berkeley/Los Angeles/London: University of California Press, 1994)].
Macrobius, Commentarius in Somnium Scipionis, II, i-iv
Francesco Giorgi (Zorzi) Veneto, De Harmonia Mundi cantica tria ( Venice: B. de Vitalibus, 1525 ).
Peter J. Ammann, “The Musical Theory and Philosophy of Robert Fludd,” Journal of the Warburg Courtauld Institutes 30 (1967): 198–227.
Vincent F. Hopper, Medieval Number Symbolism (New York: Columbia University, 1938); Hans Abert, Die Musikanschauung des Mittelalters (Halle: M. Niemeyer, 1905); Johan Huizinga, The Waning of the Middle Ages: A Study of the Forms of Life, Thought, and Art in France and the Netherlands in the Fourteenth and Fifteenth Century (London: E. Arnold, 1950), chapter 15.
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Hutton (see note 1 above), and Daniel P. Walker, “Musical Humanism in the Sixteenth and Early Seventeenth Centuries,” The Music Review 2 (1941): 1–13, 111–121, 220–227, 288–308 and 3 (1942): 55–71 [now in Walker’s Music, Spirit and Language in the Renaissance,ed. Penelope Gouk (London: Variorum, 1995)].
Frances A. Yates, The French Academies of the Sixteenth Century (London: The Warburg Insitute/University of London, 1947), and Musik in Geschichte und Gegenwart (=MGG), sub voce
MGG, sub voce.
Daniel P. Walker, Spiritual and Demonic Magic from Ficino to Campanella ( London: The Warburg Institute/University of London, 1958 ), pp. 14–24.
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Musique des Intermèdes de la “Pellegrina” ed. Daniel P. Walker (Paris: CNRS, 1963).
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Ibid., pp. 5–11.
Ficino, “Commentarius in Timaeum,” Opera,pp. 1456–1457; cf. Paul O. Kristeller, Supplementum Ficinianum,2 vols. (Firenze: Olschki, 1937), 1:51–54.
Walker, Studies,pp. 44–57].
Henry S. Macran, The Harmonics of Aristoxenos (Oxford: Clarendon Press, 1902), and MGG, sub voce “Aristoxenos.”
Walker, Magic,pp. 201, 231.
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Rudolf Wittkower, Architectural Principles in the Age of Humanism ( London: The Warburg Institute/University of London, 1949 ).
Ibid., pp. 90ff.
Daniele Barbaro, De Architectura libri decem, cum commentariis ( Venice: Franciscus Franciscius, 1567 ).
Paul Tannery, “Du rôle de la musique dans le développement de la mathématique pure,” in his Mémoires scientifiques,3:69–89.
Marcus Meibomius, De Proportionibus Dialogus ( Hafniae: Typis Melchioris Martzani, 1655 ).
Plato, Timaeus,34b ff. Here the harmony of the spheres is not actually mentioned, but is strongly suggested since, after the musical construction of the anima mundi,its strips are bent into an armillary sphere.
Plato, Republic,6161d ff.
Ptolemy, Harmonica,Book 1, chapter 5 [trans. Andrew Barker, Greek Musical Writings,2 vols. (Cambridge: Cambridge University Press, 1984–1989), 2:306–311].
René Descartes, Oeuvres,ed. Charles Adam Paul Tannery, 13 vols. (Paris: J. Vrin, 1974), 10:97, 99, 103.
Hellmut Ludwig, Marin Mersenne and seine Musiklehre (Berlin: Halle, 1935), pp. 40ff.
Christian Huygens, Oeuvres complètes,22 vols. (Den Haag: M. Nijhoff, 1888–1950), 1:59–60.
Ibid., 19:366–367.
To convince himself that he can hear the difference between just and Pythagorean thirds and sixths, the reader who owns a violin or `cello may make the following simple experiment. Having tuned the instrument as accurately as possible, play E on the D-string with the open G-string; then, taking care not to move your finger, play the E with the open A-string. If the major sixth has been made as sweet as possible, it will be found that the finger has to be leaned considerably forward to produce a perfect fourth. The difference between the two E’s is a comma (81:80). Then try the experiment the other way round.
John Napier, Mirifici Logarithmorum Canonis descriptio (Edinburgh: Ex officina A. Hart, 1614); a description of Napier’s logarithms was published in French in Paris in 1624: see Marin Mersenne, Correspondance,ed. Paul Tannery, 14 vols. (Paris: Presses Universitaires de France, 1945–1980), 1:314.
Walker, Studies,chapter 7].
Friedrich Waismann, Einführung in das mathematische Denken,(Munich: Deuthscher Taschenbuch-Verlag, 19703).
Alexandre Koyré, From the Closed World to the Infinite Universe ( Baltimore: Johns Hopkins Press, 1957 ).
Blaise Pascal, Pensées,ed. Léon Brunschvig, numbers 72, 206.
John Napier, A Plaine Discovery of the whole Revelation of Saint John ( Edinburgh: Ex Officina A. Hart, 1593 ).
Walker, Studies,chapter 4].
See note 8 above.
See Betty J.T. Dobbs, The Foundation of Newton ‘s Alchemy ( Cambridge: Cambridge University Press, 1975 ).
Mersenne, Correspondance,8:611.
Michel Eyquem de Montaigne, Les Essais,ed. Pierre Villey, 3 vols. (Paris: F. Alcan, 1922–1923), 2:327 (II, xii).
Matthew Shirlaw, The Theory of Harmony. An Inquiry into the Natural Principles of Harmony, with an Examination of the Chief Systems of Harmony from Rameau to thePresent (London: Novello Company, 1917; reprint ed. New York: Da Capo Press, 1969 ), p. 134.
Walker, Studies,p. 125].
Ibid., chapters 4 and 8].
Ibid., chapter 3]
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Walker, D.P. (2000). The Harmony of the Spheres. In: Gozza, P. (eds) Number to Sound. The Western Ontario Series in Philosophy of Science, vol 64. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9578-0_2
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