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.
Tone Systems and Uncertainty Theory
Fuzziness and Sonance
Wavelets and Nonspecificity
Pitch Granulation and Ambiguity
Mean Tone Systems
Well Tempered Systems
12 and 10 Granulations
Appendix A: Extended Lists of Tone Systems
Appendix B: Catalogue of Historical Organs with Subsemitones, (1468-1721)