Tentamen novae theoriae musicae

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Tentamen novae theoriae musicae ex certissimis harmoniae principiis dilucide expositae is a music theory work by the mathematician Leonhard Euler (1707–1783), which was published in 1739.

meaning

Originally the work was entitled Tractatus de musica . Euler had almost finished it as a handwritten work in May 1731 as a compulsory work for the Russian Academy of Sciences . In his tentam he published mathematical calculations on special musical phenomena: he gave the pitch of a string defined in length and weight , which is tensed with a specific force . He also calculated the change in the pitch of a pipe with changing temperatures and changing air pressure.

In his special music-theoretical system, Euler did not arrange the sounds according to the traditional contrasting categories consonance - dissonance , but presented them in continuously successive stages. In this respect, his system is forward-looking.

His method of specifying a single mathematical basic formula for all important music-theoretical phenomena was sharply criticized by Lorenz Christoph Mizler in the comments on his German partial translation with regard to its principles. Mizler agreed with Euler in principle that a “doctrine of the degrees of comfort” ( gradus suavitatis ) of whatever nature was of great importance. However, the reviewer and translator created an alternative table to the table presented by the mathematician and demonstrated some inaccuracies.

construction

Mizler's German translations are also given

Title: An attempt at a new theory of music for the right reasons of harmony clearly presented by Leonhard Euler

  • Praefatio - preface
  • 1. De sono et auditu [Of sound and hearing]
  • 2. De suavitate et principiis harmoniae [On the convenience and the first reasons of harmony]
  • 3. De musica in genere [Of music in general]
  • 4. De consonantiis [Of consonances]
  • 5. De consonantiarum successione [From the succession of consonances]
  • 6. De seriebus consonantiarum [Of the ranks of the consonances]
  • 7. De variorum intervallorum receptis appellationibus [From the names of different intervals introduced]
  • 8. De generibus musicis [Of the musical families]
  • 9. De genere diatonico-chromatico [Of the diatonic-chromatic sex]
  • 10. De aliis magis compositis generibus musicis [Of other more complex musical families]
  • 11. De consonantiis in genere diatonico-chromatico [Of the consonances in the diatonic-chromatic sex]
  • 12. De modis et systematibus in genere diatonico-chromatico [Of the tone types (Modis) and systematics in the diatonic-chromatic sex]
  • 13. De ratione compositionis in dato modo et systemate dato [Of the composition in a given tone type and system]
  • 14. De modorum et systematum permutatione [On the change in tone types and systematics]

See also

literature

  • Lorenz Christoph Mizler : Short review, in: Reliable news from the current state of science. Leipzig 1741, 22nd part, pp. 722-751. Source Online (Compare Mizler's above-mentioned detailed review in the Musical Library .)
  • Charles Samuel Smith : Leonhard Euler's Tentamen novae theoriae musicae. A Translation and Commentary. Indiana 1960.
  • Lutz Felbick : Lorenz Christoph Mizler de Kolof - student of Bach and Pythagorean "Apostle of Wolffian Philosophy". (University of Music and Theater "Felix Mendelssohn Bartholdy" Leipzig - Writings, Volume 5), Georg-Olms-Verlag, Hildesheim 2012, ISBN 978-3-487-14675-1 .
  • Lutz Felbick : Lexicon article on Euler, Leonhard: Tentamen novae theoriae musicae, St. Petersburg 1739. In: Lexikon Schriften über Musik, Vol. 1 Music theory from antiquity to the present , ed. by Hartmut Grimm / Melanie Wald-Fuhrmann / Ullrich Scheideler / Felix Wörner (Max Planck Institute for Empirical Aesthetics), Kassel 2017, pp. 131-133.

Web links

Individual evidence

  1. ↑ Mizler's partial translation and commentary in different parts of the Musical Library : Chapter 1: Mus. Bibl. Vol. 3, I, pp. 77-136; Chapter 2: Mus. Bibl. Vol. 3, II, pp. 305-346; Chapter 3: Mus. Bibl. Vol. 3, III, pp. 539-558; Chapter 4: Mus. Bibl. Vol. 4, I, pp. 69-103. Orientation aid for the online editions of the Musical Library . ( Memento of the original from April 13, 2013 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. @1@ 2Template: Webachiv / IABot / www.mizler.de