Abstract
More than any other scientist’s, Galileo’s work marks the transformation from Aristotelian to modern science.1 Though he made important contributions to a great variety of fields, such as observational astronomy, his work in mechanics above all provided the essential break-through. This applies in particular to his law of inertia (used for defending the Copernican theory,) and to his laws of free fall and projectile motion, published in 1638 in the Discorsi e dimostrazioni matematiche intorno à due nuove scienze attenenti alla Mecanica & i Movimenti locali (‘Discourses and Mathematical Demonstrations Concerning Two New Sciences, Pertaining to Mechanics and Motion’.) To a large extent Galileo’s work on moving bodies turned into a model for many other fields affected by the Scientific Revolution. It became exemplary in two essentially different, though related respects:
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it is mathematical in that the relationships between the parameters are quantitative, in that the proofs are geometrical, and, above all, in that the properties of falling and projected bodies are logically derived from a set of a priori postulates;
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it is experimental in that not daily experience, but nature subjected to artificial manipulation provides both the starting point and the final empirical check of the axiomatic system.
From H. Floris Cohen, Quantifying Music. The Science of Music at the First Stage of the Scientific Revolution, 1580–1650 (Dordrecht/Boston/Lancaster: D. Reidel, 1984), pp. 85–97.
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References
The literature on Galileo is virtually boundless. A penetrating account of his work in mechanics and astronomy is given by Eduard J. Dijksterhuis, The Mechanization of the World Picture, trans. C. Dikshoom (Oxford: Clarendon Press, 1961), pp. 77–123, 153–162. See also Stillman Drake in the DSB, and, by the same Author, Galileo at Work. His Scientific Biography (Chicago: University of Chicago Press, 1978). In the following I quote the Discorsi from a 1730 English translation: Mathematical Discourses concerning Two New Sciences relating to Mechanicks and Local Motion, by Thomas Weston, reprint ed. by Robert B. Lindsay, Acoustics: History and Philosophical Developments (Stroudsburg, Pa.: Hutchison and Ross, 1973); in the notes I give the Italian from Le Opere di Galilei, Edizione Nazionale a cura di A. Favaro, 20 vols. (Firenze: Barbèra, 1890–1909; reprint ed., Firenze: Barbèra, 1968 ): 8, and add references to the standard English translation by Stillman Drake, Galileo Galilei, Two New Sciences ( Madison, Wisc.: University of Wisconsin Press, 1974 ).
Mathematical Disciplines, p. 139; Drake, Two New Sciences, p. 96; Opere, 8:138: “se io ancora da cost facili e sensate esperienze trarr6 ragioni di accidenti maravigliosi in materia de i suoni… ” See for a few prior remarks of Galileo’s on music and acoustics his “Saggiatore,” Opere 6:269, 280–281, 349–350.
Mathematical Disciplines, p. 142; Drake, Two New Sciences, p. 99; Opere, 8:141: “che impossibil cosa è il farlo muover sotto altro periodo che l’unico suo naturale.”
See Cohen, Quantfying Music, pp. 29–32.
Mathematical Disciplines, p. 145; Drake, Two New Sciences, p. 100; Opere, 8:143: “ed accadendo tal volta che ‘1 tuono del bicchiere salti un’ottava più alto, nell’istesso momento ho visto ciascheduna delle dette onde dividersi in due; accidente che molto chiaramente conclude, la forma dell’ottava esser la dupla.”
Daniel P. Walker, Studies in Musical Science in the Late Renaissance (London: The Warburg Institute, and Leiden: Brill, 1978), p. 29. The first reason seems to me invalid, as Galileo’s point here is not to count the number of waves, but to show that the octave splits each wave into two.
Mathematical Disciplines, p. 146; Drake, Two New Sciences, p. 101; Opere, 8:143: “Tre sono le maniere con le quali not possiamo inacutire il tuono a una corda: l’una è lo scorciarla; l’altra, il tenderla più, o vogliam dir tirarla; il terzo è l’assottigliaria.”
Mathematical Disciplines, p. 148; Drake, Two New Sciences, p. 102; Opere, 8:144¬145: “L’invenzione fu del caso… Raschiando con uno scarpello di ferro tagliente una piastra d’ottone per levarle alcune macchie, nel muovervi sopra lo scarpello con velocità, sentii una volta e due, tra moite strisciate, fischiare e uscirne un sibilo molto gagliardo e chiaro; e guardando sopra la piastra, veddi un lungo ordine di vergolette sottili, tra di loro parallele e per egualissimi intervalli l’una dall’altra distanti.”
Mathematical Disciplines, p. 149; Drake, Two New Sciences, p. 103; Opere, 8:145: “quale veramente è la forma the si attribuisce alla diapente.”
Walker, Studies, p. 30. [NB. In a letter dated 4th of February, 1983, Professor Walker suggested to me that his argument does not conclusively disprove the possibility of Galileo’s actually having carried out the experiment, as Galileo may have used for comparison a fifth from a harpsichord tuned in mean tone temperament.]
Mathematical Disciplines, p. 151; Drake, Two New Sciences, p. 104; Opere, 8:146¬147: “La molestia di queste [sc. dissonanze] nascerà, credo io, dalle discordi pulsazioni di due diversi tuoni che sproporzionatamente colpeggiano sopra ‘I nostro timpano, e crudissime saranno le dissonanze quando i tempi delle vibrazioni fussero incommensurabili… Consonanti, e con diletto ricevute, saranno quelle coppie di suoni che verranno a percuotere con qualche ordine sopra ‘I timpano; il quai ordine ricerca, prima, che le percosse fatte dentro all’istesso tempo siano commensurabili di numero, accib che la cartilagine del timpano non abbia a star in un perpetuo tormento d’inflettersi in due diverse maniere per acconsentire ed ubbidire alle sempre discordi battiture.”
Mathematical Disciplines, p. 151; Drake, Two New Sciences, p. 104; Opere, 8:147: “sarà dunque la prima e più grata consonanza l’ottava… ”
Mathematical Disciplines, p. 152; Drake, Two New Sciences, p. 105; Opere, 8:147: “tutte l’altre sono discordi e con molestia ricevute su ‘I timpano, e giudicate dissonanti dall’udito.”
Mathematical Disciplines, p. 155; Drake, Two New Sciences, p. 107; Opere, 8:149: “fa una titillazione ed un solletico tale sopra la cartilagine del timpano, che temperando la dolcezza con uno spruzzo d’acrimonia, par che insieme soavemente baci e morda.”
Mathematical Disciplines, p. 156; Drake, Two New Sciences, p. 107; Opere, 8:149: “la quai mistione di vibrazioni è quella che, fatta dalle corde, rende all’udito l’ottava con la quinta in mezzo.”
Mathematical Disciplines, p. 156; Drake, Two New Sciences, p. 107–108; Opere, 8:150: “allora la vista si confonde nell’ordine disordinato di sregolata intrecciatura, e l’udito con noia riceve gli appulsi intemperati de i tremori dell’aria, che senze ordine o regola vanno a ferire su ‘I timpano.”
Marin Mersenne, Les nouvelles pensées de Galilée (Paris: Henry Guénon, 1638¬1639), critical ed. by Pierre Costabel and Michel-Pierre Lerner, 2 vols. (Paris: J. Vrin, 1973), 2:210. Drake, Two New Sciences, p. 107, notes that Galileo’s pupil Viviani had noticed the mistake, but apparently he corrected only the string lengths, without concluding that the experiment cannot have been performed in the way Galileo describes it.
Clifford A. Truesdell, “The Rational Mechanics of Flexible or Elastic Bodies 1638¬1788,” Leonhardi Euleri Opera Omnia, series 2, vol 11, sectio 2 (Zurich: Füssli, 1960), pp. 36–37, reaches the same conclusion from the acoustical point of view.
Cf. Drake sub voce `Benedetti’ in the DSB, pp. 607–608.
Cf. on these matters Sigalia Dostrovsky, “Early Vibration Theory: Physics and Music in the Seventeenth Century,” Archive for History of Exact Sciences, 14 (1974–1975): 181¬182, and Penelope M. Gouk, Music in the Natural Philosophy of the Early Royal Society (Ph.D. thesis, London University, Warburg Institute, 1982), chapter 1.
The two extreme positions in Alexandre Koyré, Etudes Galiléennes (Paris: Hermann, 1940) and Drake, Galileo at Work; see for a more moderate view Eduard J. Dijksterhuis, Val en worp. Een bijdrage tot de geschiedenis der mechanica van Aristoteles tot Newton (Groningen: Noordhoff, 1924), summarized in his Mechanization of the World Picture. See for an appraisal of the present state of the debate Michael Segre, “The Role of Experiment in Galileo’s Physics,” Archive for History of Exact Sciences 23 (1980), 3:227–252, passim.
Cohen, Quantifying Music, pp. 77–78, 83–85.
Author’s note, 1998: Since on completion of Quantifying Music I have more or less abandoned this particular branch of scholarship, I feel compelled to refrain from subjecting the portions here selected to a critical examination or even from working into the text facts and insights offered in reviews of the book and in other recent literature. The only alteration in my original text is the somewhat rewritten paragraph to which the present note is appended. I wish further to add that I have meanwhile changed my views on Galileo’s experiments in musical science on the strength of what Thomas Settle has told me about his own expert experiences with those experiments repeated, and that my sense of impressedness with pertinent facts adduced since by Claude V. Palisca shines through the two pages I devote to Vincenzo Galilei’s theory and practice in my book-in-progress, `How Modern Science Came into the World.’ HFC]
Ibid., p. 78.
Ibid., pp. 63–65.
Ibid., pp. 20–21.
M. Vogel, Die Zahl Sieben in der spekulativen Musiktheorie (Bonn: Ph. D. thesis, 1955) analyzes extensively the role of the intervals containing 7 in the history of musical theory; see, also, Cohen, Quantifying Music, pp. 103–111, and 225–228.
See Cohen, Quantifying Music, pp. 97–114.
Ibid., pp. 31–32.
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Cohen, H.F. (2000). Galileo Galilei. 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_10
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