The Mathematical Theory of Tone Systems

12-tone Equal Temperament 7-limit a₁ acoustic algebra algorithm analysis Approximation Arabic Aristorenos based on Archytas's c.f. Figure c.f. Table cents chords chromatic genus comma complex consider consonance defined Definition Denote Diatonic Diatonic genus diesis dissonance function Dorian Mode Enharmonic equation Example finite frequency fuzzy sets gamelan Garbuzov Garbuzov zones geometric nets granules Hexany Hypodorian instruments intonation ker(S keyboard lattice Lemma logx major Math mathematical matrix mbira meantone microtonal minor third music theory musical intervals numbers octave equivalence partial Pelog pentatonic perfect fifth permutations Petzval's pitch pointed interval structure problem psychoacoustic Pythagorean comma Pythagorean System ratios scale segmentation semitone septimal sequence Slendro sound signal steps Subsection superparticular superparticular ratios t₁ tempered fifths tempered tone systems tetrachord Theorem timbre time-frequency atoms time-frequency plane tone systems Tritriadic tuning uncertainty values w₁ whole tone Wigner-Ville transform Wr(t WT(t