The Mathematical Theory of Tone Systems
CRC Press, 19. dec. 2003 - 380 sider
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.
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Tone systems and uncertainty theory
Fuzziness and sonance
Wavelets and nonspecificity
Pitch granulation and ambiguity
Mean tone systems
Well tempered systems
B Historical organs with subsemitones 14681721
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acoustic Algebra algorithm Analysis Applications Approximation basic called cents chords Chromatic comma Complex consider construction contains corresponding defined Definition Denote described Diatonic Dorian Mode Enharmonic Equal Temperament equation equivalence Example exists expressed fifth Figure fourth frequency function fuzzy gamelan genus geometric given granules Harmonia harmonic integer interesting intervals Intonation Inverted keys lattice major thirds Math mathematical meantone measure minor natural numbers observe obtain octave organ partial pentatonic perfect period Permuted pitch plane play pointed positive possible present prime problem Proof pure Pythagorean System ratios relation representatives respectively scale Schlesinger's semitone septimal sequence seventh sixth Slendro solution sound space steps structure superparticular Table temperature tetrachord Theorem theory timbre time-frequency tion tone systems transform tuning uncertainty University values various whole tone zone