Tone system problems were present at the dawn of mathematics and figured in the discoveries of partial differential equations and Fourier analysts. It follows that The Mathematical Theory of Tone Systems holds tone system development to be the largest technical achievement in the history of music. In scrutinizing the relevant mathematical literature, this extraordinary reference has patterned a unified theory defining the tone system in functional terms based on the principles and forms of uncertainty theory. Uses geometrical nets and measure theory to study all classes of used and theoretical tone systems, from Pythagorean tuning to superparticular pentatonics. Containing over 200 chapter examples of past and prevalent tone systems - and an appendix with hundreds more - The Mathematical Theory of Tone Systems views classical harmonic analysis vis-à-vis uncertainty-based information theory . covers dissonance functions, fuzziness, and relatedness within tone systems. explores wavelets and nonspecifioty, as well as pitch granulation and ambiguity. discusses measurements for equal temperaments along with algebraic representations of harmonic structures.

identifies acoustics algorithms, facets of meantone systems, and the anatomy of the Pythagorean whole tone. provides a formalization of well tempered tone systems. regards Pythagorean systems of India and China, African free tuning, Indonesian gamelan, Pacific Ocean tuning, and Western system trends. and considers Petzval tone systems and Huygens-Fokker tuning, tetrachords, the Euler space, and commas. Book jacket.