Mathematik und Harmonie. Über den vermuteten Pythagoreismus von Leibniz
Abstract
The music theory of Leibniz was thought to be by most of the scholars a part of the Pythagorean philosophical tradition. This opinion was maintained without a founded knowledge of the Pythagorean sources nor a proper consideration of the contemporary scientific background, upon which Leibniz wrote. The purpose of this article consists of analysing to what extent the Pythagorean tradition in music theory had still an influence in a philosophical age, whose music had already thoroughly abandoned the main statements of the Pythagoreans. Questions belonging to the Pythagorean conception of music, such as the Tetraktys theory, the number proportions regarding musical intervals and the music of the spheres, are discussed here upon the background of the 17th century music theory. After that, Leibniz' considerations of these subjects turn out to be quite different from those of the Pythagorean tradition. Leibniz criticises it or translates it in an utterly modern language. He proposes a contemporary conception of harmony as an anticipation of beauty through the conjunction of the opposites, which emerges in the music theory of his time and will lead to the aesthetics substituting for the mystic. Dissonance, contrast and mistune are the new concepts to be taken into account