How can I notate my own temperament?
Posted: Thu Nov 04, 2021 12:03 pm
I made my own temperament of the 12-tone system. Its objective was to, while maintaining versatility of 12edo, express different characteristics for different keys.
My sketch was to, for each notes, give the geometric mean of some septimal just ratios. As such, I'd say it's a "pseudo-septimal" tuning.
Yet I'm unsure what commas this tuning tempers out. If this temperament were to be notated in sagittal, how?
My sketch was to, for each notes, give the geometric mean of some septimal just ratios. As such, I'd say it's a "pseudo-septimal" tuning.
- C = 1/1 = 0¢
C♯/D♭ = (25/24 * 21/20 * 16/15 * 15/14)^¼ = (5/4)^¼ ≈ 97¢
D = (35/32 * 10/9 * 28/25 * 9/8 * 8/7)^⅕ = (7/4)^⅕ ≈ 194¢
D♯/E♭ = (7/6 * 25/21 * 6/5)^⅓ = (5/3)^⅓ ≈ 295¢
E = (60/49 * 49/40 * 5/4 * 32/25 * 9/7)^⅕ = (108/35)^⅕ ≈ 390¢
F = (64/49 * 21/16 * 4/3 * 49/36 * 48/35)^⅕ = (64/15)^⅕ ≈ 502¢
F♯/G♭ = (2/1)^½ = 600¢
(And their octave complement will give the rest)
Yet I'm unsure what commas this tuning tempers out. If this temperament were to be notated in sagittal, how?