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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12-tone Equal Temperament 7-limit acoustic algorithm Analysis Archytas's Enharmonic Aristoxenos based on Archytas's Bohlen-Pierce c.f. Figure c.f. Table cents chords chromatic genus Complex consider consonance defined Definition Denote Diatonic PIS diatonic scales Didymus diesis dissonance function Dorian Mode equation Example finite fourth frequency gamelan geometric nets Harmonia harmonic form harmonic structures Hexany Hypodorian hypolydian Hypophrygian instruments Intonation Inverted Schlesinger's ker(S keyboard lattice Lemma major thirds Math mathematical matrix mbira meantone microtonal minor scales minor sixth mistuning Mixolydian music theory musical intervals numbers octave equivalence partial monounary algebra Pelog pentatonic perfect fifth Permuted Phrygian pitch Praetorius System prime problem Pythagorean comma Pythagorean System semitone septimal sequence seventh sixth Slendro solution split keys steps Subsection superparticular ratios temperature tempered fifths tempered tone systems tetrachord timbre time-frequency atoms tone systems tonic Tonos triad triadic cluster tritone Tritriadic tuning uncertainty values Vertex tetrachord whole tone Wigner-Ville transform