The Mathematical Theory of Tone Systems

12-tone Equal Temperament a₁ acoustic algorithm analysis approximation Arabic Aristorenos c.f. Figure c.f. Table C(EN cents chords chromatic genus comma complex consider consonance defined Definition Denote diesis dissonance function Dorian Mode Enharmonic equation Example finite fuzzy sets gamelan Garbuzov zones geometric nets granules harmonic structures Hypodorian instruments intonation Inverted Schlesinger's ker(S keyboard lattice Lemma logx major major third maqams Math mathematical matrix mbira meantone microtonal minor sixth minor third mistuning music theory musical intervals numbers octave equivalence Pelog pentatonic perfect fifth permutations pitch pointed harmonic pointed interval structure Praetorius System problem psychoacoustic Pythagorean comma Pythagorean System ratios real numbers segmentation semitone septimal sequence seventh Slendro solution sound signal steps Subsection superparticular superparticular ratios t₁ tempered fifths tempered tone systems tetrachord Theorem timbre time-frequency atoms time-frequency plane tone systems transposition tuning uncertainty values w₁ w₂ whole tone Wigner-Ville transform Wr(t WT(t