A Theory of Evolving Tonality

acoustic dimension atonal scale 12 auxiliary degrees black keys centitones characteristic Chinese musical chromatic scale complicated consonances and dissonances consonant chord construction diagram diatonic scale dimension Dyad equally tempered EXAMPLE expressed five regular degrees former Fourths HALF STEP WHOLE half steps harmonic combinations infra infra-diatonic scale infra-Fifth infra-modes infra-tempered intonation infra-Thirds instance inversions latter major minor major major Third melodies minor major minor minor supra mode modern composers musical art musical practice musical system natural Fifths notation notes octave overtones pentatonic scale perf perfect principle Pythagorean comma Pythagorean intonation ratio regard regular and auxiliary represented scale 5+2 scale 7+5 Scriabin semitones series of natural Siamese STEP HALF STEP STEP WHOLE STEP steps and half structure sub-infra-diatonic scale supra-diatonic Hexad supra-diatonic scale Supra-Eighth supra-mode supra-tempered intonation Supra-Tonality theoretical Third tion tonal system Triad tuned twelve-tone vibration-fractions WHOLE STEP HALF WHOLE STEP WHOLE whole tone whole-step chord