User:Dummy index/Semitritave
Interval
Semitritave, square root of 3:1, is an interseptimal interval. It divide pure tritave into two equal parts. Every even-numbered EDT has this interval.
Merciful intonation
Semitritave is an candidate for "practically merciful intonation", because it is [math]\displaystyle{ [1; 1, 2, 1, 2, ...] }[/math] in continued fraction, have many gradually proximal ratios, 5/3, 7/4, 19/11, 26/15, 71/41, ..., makes rich dissonance.
Approximating it by noble number:
- [math]\displaystyle{ [1; 1, 2, 1, 1, 1, ...] }[/math] - 942.5 cents, between 12/7 and 19/11.
- [math]\displaystyle{ [1; 1, 2, 1, 2, 1, 1, 1, ...] }[/math] - 950.4 cents, between 45/26 and 71/41.
- [math]\displaystyle{ [1; 1, 2, 1, 3, 1, 1, 1, ...] }[/math] - 954.6 cents, between 26/15 and 33/19.
False octave
Semitritave is available for false octave. Differ from acoustic phi or ed7/4, two equave makes 3:1, well-known equave.
2*N-edt
Every even-numbered EDT has semitritave interval. Treating it as equave. Another preferrable intervals...
- 5edt - 380 cents major third
- 6edt - 317 cents minor third
- so 30edt?
To do mechanical translation from diatonic scores, "fifth" sound want to be consonance. 7/5 is better, but it makes 3L 2s. 11/8 corresponds meantone region. (for this purpose, ed9/5 is good answer.)
- 46edt - approximately 29edo. This have two "fifth," 14\23 ≈ 7/5, 13\23 ≈ 15/11.
- 38edt - approximately 24edo. "Fifth" is 11\19 ≈ 11/8. Can convert easily from 19edo.
- 36edt - approximately stretched 23edo. Another candidate with "fifth" 7/5...