Galileo's Abandoned Project on Acoustic Instruments at the Medici Court

Ludovico Cardi da Cigoli to Galileo, 24 February 1613, in Galilei Galileo Favaro Antonio , Le opere di Galileo Galilei, 4th edn (20 vols, Florence, 1968), xi, 484–5.

Daniello Antonini to Galileo, 1 October 1612, in Galileo and Favaro , op. cit. (ref. 1), xi, 406.

Aristotle , The physics, transl. by Wicksteed Philip H. Cornford Francis M. (Cambridge, MA, 1934), in Aristotle in twenty-three volumes, iv—v, II, 8; 199 a 15–17. For an introduction to the Aristotelian concepts of art and nature, see Wolfgang Schadewaldt, Die Begriffe ‘Natur’ und ‘Technik’ bei den Griechen, Hellas und Hesperien: Gesammelte Schriften zur Antike und Literatur (Zürich, 1960), 907–19; Bartels Klaus , Der Begriff Techne bei Aristoteles, in Flashar Helmut Gaiser Konrad (eds), Synusia: Festgabe für Wolfgang Schadewaldt zum 15. März 1965 (Pfullingen, 1965), 275–87; and Schiefsky M. , Art and nature in ancient mechanics, in Bensaude-Vincent B. Newman W. (eds), The artifcial and the natural: An evolving polarity (Cambridge, MA, 2007), 67–108. For a critical approach to the view expressed by the previous authors, see Schummer Joachim , “Aristotle on technology and nature”, Philosophia naturalis, xxxviii (2001), 2001–20.

During the early modern period the conception of art as the completion or imitation of nature became less and less dominant and finally this process concluded with a more central relocation of the human being in the realm of nature. For an introduction to such encompassing cultural and philosophical changes, see Blumenberg Hans , “‘Nachahmung der Natur’: Zur Vorgeschichte der Idee des schöpferischen Menschen”, Studium generale, x (1957), 266–82. This kind of process can also be analysed from the perspective of the process of ‘transformation of ancient science’ during the early modern period. The structure of this process is being analysed as part of a project funded by the German Research Center (DFG), Transformations of Antiquity. As in the case of this present work, the research carried out as part of such a project focuses on single material objects. For a study concerning the cantilever model and its relation to the process of emergence of the theory of resistance of materials, see Valleriani Matteo , “The transformation of Aristotle's Mechanical Questions: A bridge between the Italian Renaissance architects and Galileo's first New Science”, Annals of science, lxvi (2009), 2009–208. For studies concerning pneumatic devices, see Valleriani Matteo , From condensation to compression: How Renaissance Italian engineers approached Hero's pneumatics, in Böhme Hartmu Rapp Christof Rösler Wolfgan (eds), Übersetzung und Transformation (Berlin, 2007), 333–54; and Valleriani Matteo , Il ruolo della pneumatica antica durante il Rinascimento: L'esempio dell'organo idraulico nel giardino di Pratolino, in Calzona Arturo Lamberini Daniela (eds), La civiltà delle acque dal Medioevo al Rinascimento (2 vols, Ingenium, Florence, 2010), ii, 613–32.

Up until the appearance of electrical devices, no history of hearing instruments from Antiquity had been written, and for what concerns the modern developments of these instruments, some works, not originating in the field of the history of science, have been published on the basis of the strict relation between hearing instruments and deafness. The secondary literature at our disposal on this subject, therefore, results mostly from the collaboration between companies that produced and are producing these devices. Other quite isolated research has been undertaken by hospitals and academic departments for otorhinolaryngology, which are obviously not concerned with an investigation of the commercially irrelevant prehistory of the auricle. Classical books along this line of research are Pollack Michael C. , Amplification for the hearing-impaired (New York, 1975), and Berger Kenneth Walter , Hearing aid: Operation and development (Milan, 1974).

For a survey on ancient theories of sound, their relations to practical realizations and the experimental method, see Hunt Frederick V. , Origins in acoustics: The science of sound from Antiquity to the age of Newton (New Haven and London, 1978), 9–42. Since the dominant conception of sound at the beginning of the sixteenth century was Aristotelian, this article will disregard all other ancient conceptions and focus only on the scientific work that took place during the seventeenth century.

Feldmann Harald , Die geschichtliche Entwicklung der Hörprüfungsmethoden (Stuttgart, 1960).

Berger , op. cit. (ref. 5), 8.

della Porta Giovan Battista , Magiae naturalis libri XX (Naples, 1589).

Porta Della , op. cit. (ref. 9), 296–7.

Porta Della , op. cit. (ref. 9), 269–70. see also Van Helden Albert , “The invention of the telescope”, Transactions of the American Philosophical Society, lxvii/4 (1977), 1–67. Della Porta claimed the paternity of the invention of the telescope in 1609 by writing directly to Federico Cesi: Giovan Battista della Porta to Federico Cesi, 28 August 1609, in Galileo Favaro , op. cit. (ref. 1), x, 201. In this letter, however, della Porta quotes the ninth chapter of his De refractione optices parte libri nouem (Naples, 1593). Della Porta was clearly mistaken and probably wanted to mention the eighth chapter, which deals with the rules governing the functioning of mirrors. Although this knowledge plays a relevant role in understanding the innovative technological process that led to the appearance of the telescope, della Porta in this work did not even mention the possibility of combining a concave and a convex lens. For more details, see Dupré Sven , Die Ursprünge des Teleskops, in Renn Jürge Staude Jakob Valleriani Matteo (eds), Galilei und die Anderen (Heidelberg, 2009), 32–42. See also Ilardi Vincent , Renaissance vision from spectacles to telescopes (Philadelphia, 2007).

Porta Della , op. cit. (ref. 9), 297: “Forma igitur instrumenti auditus oportet sit ampla, & concava & aperta, & intus cochleata, duplici de causa. Prima si soni intus rectè serrentur, oblænderent sensum, secundo quia per cochleam circumferuntur, & allisa vox per aurium anfractus, moltiplicatur, ut de echo videmus”.

Leurechon Jean van Hetten Henrik ), Récréation mathématique: Composée de plusieurs problémes plaisants et facétieux (Pont-a-Mousson, 1624). In the following, the first English translation is used: Jean Leurechon ( van Henrik Hetten ), Mathematical recreations (London, 1663).

During the early modern period the term ‘problem’ was used to denote texts and arguments or to describe isolated natural phenomena or the functioning and building procedures of instruments; they were usually short and compact in form. The use of this term was certainly related to the structure of the well-known Aristotelian text Mechanical problems. The scientific meetings among the Jesuits, for example, were called meetings to “recite a problem”. On various occasions, Galileo also announced his intention to write “collections of problems”. For more details, see Valleriani Matteo , Galileo engineer (Dordrecht, 2010), 132.

Leurechon , op. cit. (ref. 13, 1663), 87–8.

Bacon Francis , Sylva sylvarum or a natural history in ten centuries (London, 1627), 73.

The analogy between the ear trumpet and the telescope is valid only to a certain extent within the Aristotelian framework, for sound is not produced by the objects from which it is dispersed, as light is produced by the stars: Sound is produced by a blow between two bodies. As will be shown in the next section, the Aristotelian conception of the nature of sound is weakened by this difference.

An analysis of the relation between the human hand and the tools to be operated within the frame of activity defined in Aristotelian terms (such as techné) can be found in Bartels , op. cit. (ref. 3), 275–87.

Aristotle , On the soul , in Hett W. S. (ed.), On the soul. Parva naturalia. On breath (Cambridge, MA, 1936), in Aristotle in twenty-three volumes, viii, 8–203, III, 2; 425 b 27–9.

Aristotle , On the soul (ref. 19), III, 2; 426 a 5–8.

Aristotle, On the soul (ref. 19), III, 2; 426 a 16–20. For an introduction to Aristotle's theory of sensible qualities, see Stuart Ganson Todd , “What's wrong with the Aristotelian theory of sensible qualities?”, Phronesis, xlii (1997), 263–82.

Aristotle , On the soul (ref. 19), III, 12; 434 b 30–435 a 1.

Stuart . op. cit. (ref. 21), 273.

Aristotle, The physics (ref. 3), VIII, 10; 267 a 2–10.

Pseudo-Aristotle, On things heard, in Goold George P. , Minor works (Cambridge, MA, 1980), in Aristotle in twenty-three volumes, xiv, 50–79, pp. 57–9. This text is generally believed to have been written by Aristotle's pupils. Because of the lack of a critical edition, the history of the transmission of this text is still unknown.

Biancani Giuseppe , Sphaera mundi, seu Cosmographia demonstrativa ac facili methodo tradita (Bologna, 1620), 432.

Ausonio's own copy seems to be lost. However, it was copied several times between the end of the sixteenth and the beginning of the seventeenth century. Galileo, for example, prepared a copy between 1592 and 1601, which is now preserved at the Biblioteca Nazionale Centrale of Florence and published in Galileo Favaro , op. cit. (ref. 1), iii, Parte seconda, 865–71. Giovanni Antonio Magini, a mathematician in Bologna, copied and published a slightly altered version of Ausonio's manuscript in Magini Giovanni Antonio , Theorica speculi concavi sphaerici (Bologna, 1602) and, finally, discussed the same phenomenon more expansively in Magini Giovanni Antonio , Breve instruttione sopra l'apparenze: Et mirabili effetti dello specchio concavo sferico (Bologna, 1611). For the relevance of Ausonio's text, see also Dupré Sven , “Mathematical instruments and the theory of the concave spherical mirror: Galileo's optics beyond art and science”, Nuncius, xv (2000), 2000–88, and especially Sven Dupré, “Ausonio's mirrors and Galileo's lenses: The telescope of the sixteenth-century practical optical knowledge”, Galilaeana, ii (2005), 2005–80.

Mersenne Marin , Harmonie universelle contenant la théorie et la pratique de la music. Paris, 1636 (3 vols), Paris, (1986).

At the beginning of the seventeenth century, optics was undergoing a remarkable development. A relevant role in this process was played by the works of Kepler: Kepler Johannes , Ad Vitellionem Paralipomena, quibus Astronomiae pars optica traditur; potissimum de artificiosa observatione et aestimatione diametrorum deliquiorumque Solis & Lunae (Frankfurt, 1604), Dissertatio cum Nuncio Sidereo (Prague, 1610), and Dioptrice (Augsburg, 1611).

The original text reads: “… car il s'en trouue plusieurs qui croyent que le Son n'est rien, s'il n'est entendu …, i'estime que le Son n'est pas moins reel deuant qu'il soit entendu….” Author's translation. Mersenne , op. cit. (ref. 28), 1.

Author's translation. The original text reads: “un mouuement de l'air exterieur ou interieur capable d'estre ouy.” Italics in the original. Mersenne , op. cit. (ref. 28), 2.

Mersenne explained his view on these aspects in Propositions VI and VII of the first book: Ibid., 11–14.

No early work on the functioning of musical instruments and, especially, about the way they amplify sound is known to date. Research based completely on primary sources is required, eventually investigating the practical knowledge in which Mersenne's reflections are rooted.

Galilei Galileo , Discorsi e dimostrazioni matematiche intorno à due nuove scienze (Leiden, 1638). Reprinted in Galilei Favaro , op. cit. (ref. 1), viii, 39–318.

Galileo had already briefly touched upon the issue of the nature of sound in 1623 in Il saggiatore. On this occasion, Galileo clearly refuted the Aristotelian conception of sound as a sensible quality and advanced the idea that sound, like heat, can be considered as movements in air. For more details, see Galilei Galileo , Il saggiatore (Rome, 1623), reprinted in Galileo Favaro , op. cit. (ref. 1), vi, 197–372, pp. 346–50. In the first of the four Days of which the 1638 Discorsi is constituted, Galileo considered several acoustic phenomena, especially those related to vibration frequencies. He gave a compact exposition of the results of his experiments on the following topics related to acoustics, listed here in modern terms: The relation of pitch to frequency, consonance and dissonance, the correspondence between frequency ratios and musical intervals, vibratory resonance, sympathetic vibrations, and the quantitative dependence of the frequency of vibration of a string on its length, diameter, density and tension. For Galileo's exposition, see Galileo Favaro , op. cit. (ref. 1), viii, 141–50. On the relevance of Galileo's experiments to the history of acoustics, see Hunt , op. cit. (ref. 6), 80–2. Galileo's interest in harmonics and acoustics should not be dated to the time of the publication of the Discorsi. Particularly in reference to the correspondence between frequency ratios and musical intervals, Galileo's investigations had been reported by Galileo himself to Federico Cesi, patron of the Accademia dei Lincei, back in 1619. For more details, see for example, Federico Cesi to Giovanni Faber, 14 January 1619, in Galileo Favaro , op. cit. (ref. 1), xii, 436.

“Quod spectat ad motum aëris ipsius à corpore usque sonante versùs aurem tendentis, id permirum est, quæcumque sit tandem sive vehementia, sive remissio, quo à sonante exagitatur, translationem eius per spatium esse semper æqui-velocem.” From Gassendi Pierre , Petri Gassendi Opera omnia (Leiden, 1658; reprinted Stuttgart-Bad Cannstatt, 1964), i, 417–18 (Petri Gassendi Syntagma philosophicum, Petri Gassendi Syntagmatis philosophici pars secunda, quae est phisica, Phisicae sectio prima de rebus naturae universe, Liber sextus de qualitatibus rerum, Caput X De sono).

For an introduction to the work of the Accademia del Cimento, see Middleton W. E. Knowles , The experimenters (Baltimore and London, 1971), and Boschiero Luciano , Experiment and natural philosophy in seventeenth-century Tuscany: The history of the Accademia del Cimento (Dordrecht, 2007).

Daston Lorraine , “Unruly weather: Natural law confronts natural variability”, in Daston Lorraine Stoilleis Michael (eds), Natural law and laws of nature in early modern Europe: Jurisprudence, theology, moral, and natural philosophy (Farnham, 2008), 233–48.

In this present work the second edition is used: Saggi di naturali esperienze, 2nd edn (Florence, 1691). For the section dedicated to the movements of sound, see pp. 241–5.

Ibid., 243–4.

For more details, see Boschiero , op. cit. (ref. 37), 52–5.

Favaro Antonio , Amici e corrispondenti di Galileo (3 vols, Florence, 1983), ii, 1043.

BNCF, Mss Galileiani, Cimento, iv, car. 261. See also Favaro , op. cit. (ref. 42), ii, 1043, ref. 1.

Favaro suggested that this investigation by Viviani was somehow related to or even inspired by the work of Aproino, Galileo's pupil and colleague. As will be shown, however, this is quite improbable, for in the end, Aproino suggested building the ear trumpet by using a hyperbolic curve on their longitudinal section, rather than a parabolic curve. Moreover, Aproino was a pupil of Galileo during his time in Padua, whereas Viviani was a pupil only towards the end of Galileo's life.

For an introduction to Athanasius Kircher's life and work, see Stolzenberg Daniel (ed.), The great art of knowing: The baroque encyclopedia of Athanasius Kircher (Stanford, 2001).

Kircher Athanasius , Musurgia universalis sive ars magna consoni et dissoni (Rome, 1650).

The original text reads: “… ita maximas quoque vires obtinet.” From Kircher, op. cit. (ref. 46), ii, 277.

Kircher Athanasius , Athanasii Kircheri Phonurgia nova, sive, Conjugium mechanico-physicum artis & natvra paranympha phonosophia concinnatum (Campidona, 1673), 158.

An interesting biographical work on Samuel Morland is Dickinson H. W. , Sir Samuel Morland: Diplomat and inventor, 1625–1695 (Cambridge, 1970).

Morland Samuel , Tuba stentoro-phonica (London, 1671).

Morland , op. cit. (ref. 50), 1.

Despite their similarity, speaking and ear trumpets work on the basis of different principles and Morland investigated the behaviour of sound lines only in reference to sound exiting the speaking trumpet. From the physical point of view, however, at the end of the seventeenth century the difference between the ear and speaking trumpets was not yet recognized, as the theory of receivers in theoretical acoustics is relatively recent. For more details, see Euler Leonhard , Leonhardi Euleri Commentationes mechanicae: Ad theoriam corporum fluidorum pertinentes, volumen posterius , in Truesdell Clifford A. , Leonhardi Euleri Opera omnia (77 vols, Leipzig, 1955), Section 2, Book 13, vol. ii, pp. XIXff.

Morland , op. cit. (ref. 50), 5, italics in original.

Laurent de Chartres Cassegrain , “Report of a letter received from N. Cassegrain de Chartres”, Journal des sçavans, 1672, supplement, 2 May 1672, 124–31.

Hunt , op. cit. (ref. 6), 127–8.

Galileo testified to Aproino's affiliation to his school in the sixth chapter of his Discorsi (ref. 34). Galileo's Discorsi was originally conceived as being constituted of six sections, each of them defined as a Day (of discussion). The last two Days, however, were never completed and their manuscripts were first published by Antonio Favaro in Galileo and Favaro , op. cit. (ref. 1), viii, 319–46. At the beginning of the Sixth Day, Simplicio, one of the speakers in the dialogue, is said to be absent because it had been too difficult for him to understand the topics of the first five Days. Sagredo, another speaker, thus introduces Aproino as a new speaker, a person possibly equipped with a more acute mind.

Daniello Antonini is quoted at the beginning of the Sixth Day of the Discorsi as well.

Favaro , op. cit. (ref. 42), ii, 730.

Paolo Aproino to Galileo, 27 July 1613, in Galileo Favaro , op. cit. (ref. 1), xi, 540–4, author's italics. The translation of the complete letter is appended below.

Galileo to Belisario Vinta, 7 May 1610, Ibid., x, 348–53, author's italics.

See ref. 59.

Paolo Aproino to Galileo, 26 January 1613, in Galileo and Favaro, op. cit. (ref. 1), xi, 470–1.

Paolo Aproino to Galileo, 25 May 1613, Ibid., xi, 513–14.

Paolo Aproino to Galileo, 1 June 1613, Ibid., xi, 517–19. The translation of the complete letter is appended below.

See ref. 59.

Rondolet Guillaume , Universae aquatilium historiae pars altera, cum vero ipsorum imaginibus (Leiden, 1555).

Rondolet's History was republished four years later as a sort of appendix to a much larger work by the same author: Rondolet Guillaume , Libri de piscibus marinis (Leiden, 1559). In the first part of this later work, which Aproino did not know, there is a chapter describing ears and explaining how they work. Rondolet stated that (i) the more rigid the flesh of which the ear is constituted, the more the sound resounds; (ii) the inside of the ear has revolutions which causes it to resemble the cochlea, so that the sound can resound better, as in the case of the echo; and (iii) those who have an impaired sense of hearing can be helped with the auricola built by imitating nature! For more details, see pp. 49–50 of his work.

Rondolet , op. cit. (ref. 66), 81–3. The buccinum is already mentioned by Pliny. In ancient times, the bucina was an instrument used during the classical Roman period. It was a trumpet employed during military campaigns, for example, or to mark the time intervals between day and night in Rome. Classical Latin literature contains many mentions of the bucina. One example is Ovid , Metamorphoses, 1.335. For Pliny's description of the nautilus, see Pliny Rackam H. , Natural history (Cambridge, MA, 1952; reprinted 1983), iii, Book 9, 232–33.

According to Aproino's narration, he never thought of applying a cut seashell to help the hard of hearing.

Clearly , no one would have been surprised at this phenomenon during the seventeenth century and what Aproino wrote are clearly the rhetorical passages for an introduction to a treatise presenting the ear trumpet.

See ref. 59.

Boethius , De institutione musica libri quinque , in Friedlein Gottfried (ed.), De institutione arithmetica libri duo. De institutione musica libri quinque (Leipzig, 1867).

Boethius , op. cit. (ref. 72), esp. p. 200.

The first biography of Maurolicus appeared as early as 1613: Francesco Barone della Foresta , Vita dell'Abbate del Parto D. Francesco (Messina, 1613).

Maurolicus Franciscus , Musicae traditiones, Opuscola mathematica (Venice, 1575).

Ibid., 145–60.

It is very difficult to provide an unambiguous translation of Maurolicus's statement. The complete original sentence reads: “Quod in tibijs, tubis, atque cannis, aer flatu, aut follibus impulsus ac per foramina illisus, reciproco ac tremebundo motu, angustias laterum reverberans efficit.” From Maurolicus , op. cit. (ref. 76), 146.

Vitruvius Marcus Pollio Barbaro Daniele , I dieci libri dell'architettura di M. Vitruvio (Venice, 1567; reprinted Milan, 1997), 243–7.

Pezzi Alfonso , “Considerazioni sull'acustica delle sale” (Alma Mater Studiorum Università di Bologna, Facoltà d'Ingegneria, 2003). On the efficiency of Vitruvius's vasa, see Desarnaulds Victor Loerincik Yves Carvalho Antonio P. O. , “Efficiency of 13th-century acoustic ceramic pots in two Swiss churches” (paper presented at the Noise-Con 2001, Portland Maine, 29–31 October 2001).

See ref. 59.

Aproino was not really sure about the opening of the second trumpet and indicated to Galileo that it was between 23 and 25 degrees.

It is likely that Aproino's story about Rondolet's book during his holiday is made up since it is known from other sources that the idea of providing the court with an ear trumpet was Galileo's. However, it is still relevant that Aproino intended to present his project as originating from investigations using current scientific methods that were based on the principle of imitation of nature. This principle, moreoever, is also reflected by the word Aproino uses for ground noise: bucinamento, which is clearly related to the Latin denotation of the nautilus and of the mentioned classic trumpet built to resemble it.

See ref. 59.

See ref. 59.

The textual description of the method is in ibid. For the art of the trumpet-makers, see Barclay Robert , The art of the trumpet-maker: The materials, tools and techniques of the seventeenth and eighteenth centuries in Nuremberg (Oxford, 1996).

The scientific and social aspects of the debate that ended with Galileo's publication of his Floating bodies in 1612 is analysed in Biagioli Mario , Galileo courtier (Chicago, 1993), and in Shea William R. , Galileo's intellectual revolution: Middle period, 1610–1632 (New York, 1972).

Galileo promised but never gave a theoretical explanation of the functioning of the telescope. Instead he demonstrated to the greatest possible number of people that it worked. For more details, see Biagioli Mario , Galileo's instruments of credit (Chicago, 2006), 81ff.

For the normative aspects of the role of the court in the scientific practice of the Renaissance I thank the profound insights of an anonymous reviewer.

An extensive study of Galileo's profile as an engineer in Padua has been published in Valleriani , op. cit. (ref. 14).

See ref. 59.

For an in-depth study of Galileo as an engineer and engineer-scientist, see Valleriani , op. cit. (ref. 14); Valleriani Matteo , “Galileo in the role of the caster's assistant: The 1634 bell of the Torre del Mangia in Siena”, Galileana, v (2008), 89–112; Valleriani Matteo , “A view on Galileo's ‘Ricordi Autografi’: Galileo practitioner in Padua”, in Montesinos Jose Solís Carlos (eds), Largo campo di filosofare (La Orotava, 2001), 281–92; and Renn Jürgen Valleriani Matteo , “Galileo and the challenge of the Arsenal”, Nuncius, xvi (2001), 2001–503.

In 1675, for example, Newton mentioned an ear trumpet that he considered longitudinally shaped with a gradual curvature compounded by the curve of a cone and the curve of a hyperbole. For more details, see Newton to Oldenburg, 30 November 1675, in Newton Isaac , The correspondence of Isaac Newton (7 vols, Cambridge, 1959–77), i, 359–60. From the end of the seventeenth century on, practical acoustics resulted more and more from the impressive development of applied theoretical acoustics after Newton's time. For a survey on the theoretical developments in acoustics during the eighteenth century, which touches upon the works of Daniel Bernoulli, Joseph Louis Lagrange and Leonhard Euler, see Euler Leonhard , op. cit. (ref. 52), pp. XIX–LXXII.

A similar result was achieved in the context of a study concerning the thermoscope. For more details, see Valleriani , op. cit. (ref. 14), 155–90.

Rondolet , op. cit. (ref. 66).