Abstract
The Tentamen novae theoriae musicae is a treatise in which Euler elaborated a new music theory using mathematics. The aim of this paper is to explain his theoretical system to justify the pleasure of listening to music and to analyze differences and similarities with other consonance theories.
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Notes
- 1.
G. Ernstroem, Bericht an die Eulerkommission der Schweizerschen naturforschenden Gesellshaft iber die Eulerchen Manuskripte der Petersburg Akademie, in “Jahresbericht der Deutchen Mathematiker-Vereinigung, 22”, 1913, p. 197.
- 2.
See [8] p. 7.
- 3.
This is the essay Grosse General-Bass-Schuule, published in 1731 in Hamburg and also cited in Tentamen.
- 4.
Carl Philipp Emanuel Bach (1714–1788), composer, p. 45 [21].
- 5.
Johann Joachim Quantz (1697–1773), composer and music theorist, p. 715 [21].
- 6.
Carl Heinreich Graun (1701–1759), Johann Gottlieb Graun (1702 o 1703–1771), composers, p. 360 [21].
- 7.
Johann Sebastian Bach (1685–1750), composer, pa. 46 [21].
- 8.
Baldassarre Galuppi (1706–1785), known as Buranello, Master of the Ducal Chapel of San Marco in Venice, stayed there from 1756 to 1768, p. 333 [21].
- 9.
Giuseppe Tartini (1692–1770), composer, violinist and music theorist, p. 880 [21].
- 10.
Jean-Philippe Rameau (1683–1764), composer and music theorist, p. 725 [21].
- 11.
L. Euler, Tentamen, chap. X, par.19.
- 12.
R. Descartes, emph Compendium Musicae, Utrecht, 1650, ed. mod. Abregé de musique, Édition nouvelle, in traduction, presentation and notes by Fr. de Buzon, Paris, Presses Universitaires de France, 1987. Cf. p. 55: “Media ad finem, vel soni affectiones duae sunt praecipue: nempe huius differentiae, in ratione durationis vel temporis, et in ratione intensionis circa acutum aut grave”.
- 13.
We observe that throughout the work, Euler speaks of sound but never of sound waves.
- 14.
This is clearly the frequency of the sound wave.
- 15.
De Piero hypothesizes that what Euler defines barbarians are populations living outside Europe.
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Cannas, S., Polo, M. (2022). Euler’s “Tentamen”: Historical and Mathematical Aspects on the Consonance Theory. In: Montiel, M., Agustín-Aquino, O.A., Gómez, F., Kastine, J., Lluis-Puebla, E., Milam, B. (eds) Mathematics and Computation in Music. MCM 2022. Lecture Notes in Computer Science(), vol 13267. Springer, Cham. https://doi.org/10.1007/978-3-031-07015-0_6
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