ABSTRACT

The Mathematical Theory of Tone Systems patterns a unified theory defining the tone system in functional terms based on the principles and forms of uncertainty theory. This title uses geometrical nets and other measures to study all classes of used and theoretical tone systems, from Pythagorean tuning to superparticular pentatonics. Hundreds of exa

part |2 pages

Part I Fundamentals

chapter 1|24 pages

Tone systems and uncertainty theory

chapter 2|12 pages

Fuzziness and sonance

chapter 3|18 pages

Wavelets and nonspecificity

chapter 4|16 pages

Pitch granulation and ambiguity

4.1 Garbuzov zones: strife

part |2 pages

II Special System s

chapter 5|42 pages

Equal temperaments

chapter 6|58 pages

Mean tone systems

6.1 Pythagorean System

chapter 7|44 pages

Well tempered systems

7.1 Well temperament periods

chapter 8|42 pages

12 and 10 granulations

8.1 The major scale extensions

chapter 9|46 pages

Ptolemy System

9.1 Tetrachords