E33 -- Tentamen novae theoriae musicae

E33 -- Tentamen novae theoriae musicae ex certissismis harmoniae principiis dilucide expositae.

(A attempt at a new theory of music, exposed in all clearness
according to the most well-founded principles of harmony)

Summary:

According to the inscription, the original title of this book was: “Tractatus de musica.”

In addition to the “Praefatio,” it contains 14 chapters:

De sono et auditu.
De suavitate et principiis harmoniae.
De musica in genere.
De consonantiis.
De consonantiarum successione.
De seriebus consonantiarum.
De variorum intervallorum receptis appellationibus.
De generibus musicis.
De genere diatonico-chromatico.
De aliis magis compositis generibus musicis.
De consonantiis in genere diatonico-chromatico.
De modis et systematibus in genere diatonico-chromatico.
De ratione compositionis in dato modo et systemate dato.
De modorum et systematum permutatione.

Publication:

Originally published as a book by the Saint Petersburg Academy in 1739 (263 pages)
Opera Omnia: Series 3, Volume 1, pp. 197 - 427
Republished in Musique mathématique, Paris 1865, pp. I-VII, 1-215 [E33Aa]

Documents Available:

Because E33 is a lengthy book, the original document is presented here in several parts:
An excellent paper about Euler's music theory (and focusing on the Tentamen) by Patrice Bailhache at l'Université de Nantes is available in French and also in an English translation. (Professor Bailhace also has papers about the music theory of d'Alembert, Leibniz, and others available at his web site.)
Euler's other works about the theory of music include:
- E314 Conjecture de la raison de quelques dissonances généralement reçues dans la musique.
- E314 Tentamen de sono campanarum 1764.
- E457 De harmoniae veris principiis perspeculum musicum repraesentatis.
An English translation of the Tentamen was done by Charles Samuel Smith for his Ph.D. dissertation at Indiana University in June 1960, and is available at some libraries.
The Tentamen has been published in Italian by the Accademia delle Scienze di Torino: E33. The translation, along with extensive commentary, is the work of Alvise De Piero.
According to Stacy Langton at the University of San Diego, at least part of this work was translated into German by J.S. Bach's student L.C. Mizler. Whether Bach himself ever read this work is unknown.
The Euler Archive attempts to monitor current scholarship for articles and books that may be of interest to Euler Scholars. Selected references we have found that discuss or cite E33 include:
- Bailhache P., “Mersenne, Marin 'Harmonie Universelle' - Situating music between mathematics, physics, metaphysics and religion.” Etudes Philosophiques, (1-2), pp. 13-24 (Jan-Jun 1994).
- Barbieri P., “Caramuel, Juan (1606-1682) and his essay on musical logarithms and musical tuning + 17th-century theorist on tuning systems.” Muskitheorie, 2 (2), pp. 145-168 (1987).
- Barbieri P., “Tartini 3rd tone and Euler harmonic exponents - with a previously unpublished manuscript by Tartini.” Musiktheorie, 7 (3), pp. 219-234 (1992).
- Calinger R., “Leonhard Euler: The first St Petersburg years (1727-1741).” Historia Mathematica, 23 (2), pp. 121-166 (May 1996).
- Cazden N., “The definition of consonance and dissonance.” International Review of the Aesthetics and Sociology of Music, 11 (2), pp. 123-168 (1980).
- Fokker AD., “Les gammes et le temperament egal.” Acustica, 1 (1), pp. 29-35 (1951).
- Kuhn TS., “Mathematical vs experimental traditions in development of physical science.” Journal of Interdisciplinary History, 7 (1), pp. 1-31 (1976).
- Muzzulini D., “Euler, Leonhard Theory of consonance.” Musiktheorie, 9 (2), pp. 135-146 (1994).
- Parker DB., “A more natural octavian scale + derived from Euler.” Journal of Musicological Research, 6 (4), pp. 353-355 (1986).
- Schulze W., “A harmonical analog - Leibniz genealogical scheme in 'Dissertatio de arte combinatoria'.” Studia Leibnitiana, 19 (1), pp. 98-116 (1987).
- Szeider SH., “The semantics of musical scores, an approach to the mechanical composition of microtonal music.” Interface-Journal of New Music Research, 19 (2-3), pp. 175-184 (1990.
- Terhardt E., “Concept and psychoacoustic foundations of musical consonance.” Acustica, 36 (3), pp. 121-137 (1976).
- Ungeheuer G., “On the acoustics of vowel sounds in the 18th century - the Euler-Lambert correspondence and kratzenstein.” Phonetica, 40 (2), pp. 145-171 (1983).
- Wilson C., “The great inequality of Jupiter and Saturn - from Kepler to Laplace.” Archive for History of Exact Sciences, 33 (1-3), pp. 15-290 (1985).

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