(A attempt at a new theory of music, exposed in all clearnessaccording 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.1.De suavitate et principiis harmoniae.2.De musica in genere.3.De consonantiis.4.De consonantiarum successione.5.De seriebus consonantiarum.6.De variorum intervallorum receptis appellationibus.7.De generibus musicis.8.De genere diatonico-chromatico.9.De aliis magis compositis generibus musicis.10.De consonantiis in genere diatonico-chromatico.11.De modis et systematibus in genere diatonico-chromatico.12.De ratione compositionis in dato modo et systemate dato.13.De modorum et systematum permutatione.14.

Publication:

Originally published as a book by the Saint Petersburg Academy in 1739 (263 pages)Opera Omnia: Series 3, Volume 1, pp. 197 - 427Republished 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:Front material and pages 1-79Pages 80-168Pages 169-199Pages 200-End of bookfinal page

Note: Due to technical difficulties, the final page is temporarily available only as a separate file.

An excellent paper about Euler's music theory (and focusing on the Tentamen) by Patrice Bailhache atl'Université de Nantes is available in French and also in an English translation. (Professor Bailhace alsohas 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 atIndiana 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. Thetranslation, 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 intoGerman 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 toEuler Scholars. Selected references we have found that discuss or cite E33 include:

E33 -- Tentamen novae theoriae musicae http://eulerarchive.maa.org/pages/E033.html

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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 unpublishedmanuscript 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 Aestheticsand 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 ofInterdisciplinary 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 MusicologicalResearch, 6 (4), pp. 353-355 (1986).Schulze W., “A harmonical analog - Leibniz genealogical scheme in 'Dissertatio de artecombinatoria'.” Studia Leibnitiana, 19 (1), pp. 98-116 (1987).Szeider SH., “The semantics of musical scores, an approach to the mechanical composition ofmicrotonal 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-Lambertcorrespondence and kratzenstein.” Phonetica, 40 (2), pp. 145-171 (1983).Wilson C., “The great inequality of Jupiter and Saturn - from Kepler to Laplace.” Archive for Historyof Exact Sciences, 33 (1-3), pp. 15-290 (1985).

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