Dualistic Forms

This article explores some of the consequences of Riemann's harmonic dualism that were not pursued by Riemann himself. The question of musical forms is one that Riemann intriguingly leaves unresolved—despite the fact that he is considered a formalist theorist, his ideas about musical form remain comparatively underdeveloped. The root of the problem is assumed to be related to the skepticism with which harmonic dualism is widely regarded. In exploring the idea of a dualistically based concept of form, the article takes Riemannian ideas further than Riemann did and (re-)constructs a Riemannian theory of forms based on the concept of harmonic symmetries.

Dualism · Epistemology · Harmonic · Physics · Pure mathematics · Quantum mechanics · Riemann hypothesis · Skepticism · Historical and Literary Studies · History and Theory of Mathematics · Mathematics · Musicology and Musical Analysis · Philosophy

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