In two letters to the famous musician Cipriano de Rore, Giovanni Battista Benedetti discussed topics related to music theory. The letters were published in Diversarumspeculationummathematicarum & physicarum liber in 1585. In them, Benedetti clearly proved that the pitch of a note in a polyphonic piece can rise or fall by a syntonic comma when performed with just intonation; he also proposed a form of temperament to avoid the problem, formulated the law of vibrating strings, and suggested that the pitches of notes can be related to the frequency of their air pulses. The letters were read and commented upon by scholars immediately following Benedetti, and continue to be the subject of in-depth studies by historians of music and science. Despite their relevance, there is no systematic study of them. Only some parts have been commented on by various historians, following their interests but without a unified view. Most importantly, no complete English translation has been proposed with a faithful transcription of the Latin text. The present work, divided into two parts, the first a commentary on all the salient aspects, the second the translation and semi-diplomatic transcription, intends to fill the gap.
References
[1]
Barbieri, P. (2001). Galileo’s Coincidence Theory of Consonances, from Nicomachus to Sauveur. Recercare, 13, 201-232.
[2]
Barker, A. (1989). Greek Musical Writings(2 vols). Cambridge University Press.
[3]
Beeckman, I. (1939-1953). Journal tenu par Isaac Beeckman de 1604 à 1634 (4vols). M. Nijhoff.
[4]
Benedetti, G. B. (1585). Diversarumspeculationummathematicarum & physicarum liber. Bevilaqua.
[5]
Blackwood, E. (1529). The Structure of Recognizable Diatonic Tunings. Princeton University Press.
[6]
Boethius (1948). De institutione musica. In M. R. Choen (Ed.), A Source Book in Greek Science (pp. 291-294). McGraw-Hill.
[7]
Bordiga, G. (1985). Giovanni Battista Benedetti. Filosofo e matematico Veneziano del secolo XVI. Istituto Veneto di Scienze, Lettere e Arti.
[8]
Capecchi, D. (2018). The Path to Post-Galilean Epistemology. Springer
[9]
Capecchi, G., & Capecchi, D (2022). Between Acoustics and Music. Two Letters of Giovanni Battista Benedetti to Cipriano de Rore. In P. Bussotti, D. Capecchi, & P. Tucci (Eds), SISFA 42nd Annual Conference, (pp. 231-238). Pisa University Press.
[10]
Cardano, G. (1568). Opera omnia (10 vols). Huguetan & Rovaud.
[11]
Choen, H. F. (1987). Benedetti’s Views on Musical Science and Their Background in Contemporary Venetian Culture. In Istituto Veneto di Scienze, Lettere e Arti (Ed.), Cultura, scienze e tecnichenella Venezia del Cinquecento (pp. 301-310). Istituto Veneto di Scienze, Lettere e Arti.
[12]
De Rore, C. (1569). Il primo librodeimadrigali. Gardano.
[13]
Duffin, R. W. (2006). Just Intonation in Renaissance Theory and Practice. Music Theory Online, 12, 1-16. https://doi.org/10.30535/mto.12.3.1
[14]
Duffin, R. W. (2017). Cipriano De Rore, Giovanni Battista Benedetti, and the Just Tuning Conundrum. Journal of the Alamire Foundation, 9, 239-266. https://doi.org/10.1484/j.jaf.5.115544
[15]
Euler, L. (1739). Tentamen novae theoriae musicae ex certissismisharmoniaeprincipiisdilucideexpositae. Academiae Scientiarum, Saint Petersburg.
[16]
Field, J. V. (1987). The Natural Philosopher as Mathematician: Benedetti’s Mathematics and the Tradition of Perspectiva. In Istituto Veneto di Scienze, Lettere e Arti (Ed.), Cultura, scienze e tecnichenella Venezia del Cinquecento (pp. 247-270). Istituto Veneto di Scienze, Lettere e Arti.
[17]
Fogliano, L. (1529). Musica theorica. De Sabio.
[18]
Galilei, G. (1638). Discorsi e dimostrazioni matematiche sopra due nuove scienze. In Favaro, A. (Ed.), Le opere di Galileo Galilei (National edition) (20 vols). Barbera.
[19]
Huygens, C. (1888-1950a). Oeuvres compl’etes de Christian Huygens (22 vols). Nijhoff.
[20]
Huygens, C. (1888-1950b). Cosmotheoros. In C. Huygens (Ed.), Oeuvres complètes de Christian Huygens (22 vols) (pp. 677-821). Nijhoff.
[21]
Keller, J., Roten, E., & Kirschenbaun, O. (2022). Just Intonation in the Renaissance. https://www.earlymusicsources.com/youtube/justintonation
[22]
Lindley, M. (1986). Heinrich Schtz: Intonazione della scala e struttura to 14/15: (Prima parte). Recercare, 14, 58-65.
[23]
Lindley, M. (2001). Just Intonation. https://www.oxfordmusiconline.com/grovemusic/view/10.1093/gmo/9781561592630.001.0001/omo-9781561592630-e0000014564
[24]
Lindley, M. (2022). An Historical Survey of Meantone Temperaments to 1620. https://www.academia.edu/1134182/An_historical_survey_of_meantone_temperaments_to_1620
[25]
Lindley, M., & Turner-Smith, R. (1993). Mathematical Models of Musical Scales. A New Approach. Verlag für systematische Musikwissenschaft.
[26]
Owens, J. A., & Schiltz, K. (1985). Cipriano de Rore: New Perspectives on His Life and Music(Edition Open Source). Brepols Publishers.
[27]
Palisca, C. V. (1985). Humanism in Italian Renaissance Musical Thought. Yale University Press.
[28]
Palisca, C. V. (1994). Studies in the History of Italian Music and Music Theory. Clarendon.
[29]
Panetta, V. J. (1987). Treatise of Harpsichord Tuning by Jean Denis. Cambridge University Press.
[30]
Roero, C. S. (1997). Giovanni Battista Benedetti and the Scientific Environment of Turin in the 16th Century. Centaurus, 39, 37-66. https://doi.org/10.1111/j.1600-0498.1997.tb00024.x
[31]
Sauveur, J. (1707). Méthodegénérale pour les systèmestempérés de musique, et du choix de celuiquon doit suivre. Mémoires de mathématique et de Physique de lAcadémie Royale des Sciences, 203-222.
[32]
Truesdell, C. A. (1960). The Rational Mechanics of Flexible or Elastic Bodies. Birkhäuser.
[33]
Walker, D.P. (1978). Studies in Musical Science in the Late Renaissance. Brill. https://doi.org/10.1163/9789004610217
[34]
Walker, J. (1996). Intonational Injustice: A Defense of Just Intonation in the Performance of Renaissance Polyphony. Music Theory Online, 2, 1-12. https://doi.org/10.30535/mto.2.6.3
[35]
Zarlino, G. (1562). Istitutioniharmoniche. Senese.
