Three Asymmetric Divisions of the Octave (1996)
6 days ago
- #asymmetric divisions
- #microtonal music
- #tuning theory
- Historical tuning theory has focused on integer divisions of the octave, ensuring symmetry and exact octave intervals.
- Traditional tunings include the equally tempered scale and divisions like 19, 31, and 53 equal steps.
- Symmetric divisions include redundant interval pairs (e.g., perfect fifth and fourth), leading to octave over-representation.
- An experiment explores non-integer, fractional divisions, losing octave symmetry but potentially discovering more consonant scales.
- Three asymmetric divisions were discovered: Alpha (15.385 steps/octave), Beta (18.809 steps/octave), and Gamma (34.188 steps/octave).
- Alpha offers pure harmonies and exotic melodic motions but lacks exact octaves.
- Beta resembles 19-tone Equal but with better harmonies, though it lacks harmonic seventh chords found in Alpha.
- Gamma is smoother than Alpha and Beta, nearly indistinguishable from Just tuning, but requires a specialized keyboard.
- Alpha splits the minor third exactly in half, a unique musical property not found in Western music.
- Beta splits the perfect fourth similarly to the 19-tone Equal division.
- These tunings were overlooked historically due to their asymmetry but offer rich musical possibilities.