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 exa
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acoustic Algebra algorithm Analysis Applications Approximation Aristoxenos basic called cents chords Chromatic classic comma Complex consider construction contains corresponding defined Definition Denote described Diatonic Dorian Mode Enharmonic Equal Temperament equation equivalence Example exists expressed fact fifth Figure fourth frequency function fuzzy gamelan genus geometric given granules Harmonia harmonic integer intervals Intonation Inverted keys lattice major thirds 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 shows 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