Euler’s Theories of Musical Tuning With an English Translation of Du Véritable Caractère de la Musique Moderne

Abstract

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.