The Mathematical Theory of Tone SystemsCRC Press, 19 dec 2003 - 380 pagina's 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. |
Inhoudsopgave
1 | 3 |
Dissonance functions | 28 |
1 | 57 |
Equal temperaments | 75 |
Mean tone systems | 117 |
Well tempered systems | 175 |
Ptolemy System | 261 |
Appendices | 319 |
B Historical organs with subsemitones 14681721 | 369 |
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12-tone Equal Temperament 7-limit A₁ acoustic algorithm analysis Aristoxenos based on Archytas's Bohlen-Pierce c.f. Figure c.f. Table cents chords chromatic genus Complex consonance defined Definition Denote diatonic scales diesis dissonance function Dorian Mode equation Example finite fourth frequency gamelan Garbuzov geometric nets granules Harmonia harmonic structures Hexany Hypodorian hypolydian instruments integer interval structures Intonation Inverted Schlesinger's ker(S keyboard lattice Lemma logx major third Math mathematical mbira meantone microtonal minor scales Mixolydian music theory musical intervals numbers octave equivalence partial monounary algebra Pelog pentatonic perfect fifth Permuted Phrygian pitch Praetorius System prime problems psychoacoustic Pythagorean comma Pythagorean System segmentation semitone septimal sequence seventh sixth Slendro solution superparticular ratios T₁ tempered fifths tetrachord Theorem theory of tone timbre time-frequency atoms time-frequency plane tone systems Tonos triadic cluster Tritriadic tuning uncertainty values Vertex tetrachord w₁ whole tone Wigner-Ville transform Wr(t zone