Du Véritable Caractère de la Musique Moderne (E315), a work almost unknown to musical scholars, is an extremely interesting document in the history of tuning systems. A tuning system is simply an arrangement of sound frequencies for use in music. A just tuning is an arrangement in which the ratios of these frequencies are all ratios of whole numbers- preferably small ones. Classically, these ratios involve only factors of 2, 3, and 5. In particular, a very fundamental chord in music of many genres, the so-called major triad, Has frequency ratios 4:5:6. Euler proposes introducing the prime 7, with a fundamental chord made up of ratios 4:5:6:7. Not only that, but he asserts that modern composers are already using such ratios, albeit in a disguised or subliminal form.
These ideas have had little lasting influence- indeed, Euler himself seems to have abandoned them later, as is pointed out in the notes to this translation. Nevertheless they are striking as an example of a certain type of logic pushed to the extreme.
Blaine, Larry G. and Ferré, Susan
"Euler’s Theories of Musical Tuning With an English Translation of Du Véritable Caractère de la Musique Moderne,"
Euleriana: 1(1), pp.112-140.
Available at: https://scholarlycommons.pacific.edu/euleriana/vol1/iss1/8