The Mathematical Theory of Tone Systems: 1st Edition (Hardback) book cover

The Mathematical Theory of Tone Systems

1st Edition

By Jan Haluska

CRC Press

380 pages

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Hardback: 9780824747145
pub: 2003-12-19
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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 examples of past and prevalent tone systems are featured. Topics include Fuzziness and Sonance, Wavelets and Nonspecificity, Pitch Granulation and Ambiguity, Equal Temperaments, Mean Tone Systems.

Well Tempered Systems, Ptolemy Systems, and more. Appendices include extended lists of tone systems and a catalogue of historical organs with subsemitones.

Table of Contents

Tone Systems and Uncertainty Theory

Fuzziness and Sonance

Wavelets and Nonspecificity

Pitch Granulation and Ambiguity

Equal Temperaments

Mean Tone Systems

Well Tempered Systems

12 and 10 Granulations

Ptolemy System


Appendix A: Extended Lists of Tone Systems

Appendix B: Catalogue of Historical Organs with Subsemitones, (1468-1721)


About the Series

Chapman & Hall/CRC Pure and Applied Mathematics

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