User:Dummy index/Semitritave

Interval information

Expression	[math]\displaystyle{ (3/1)^(1/2) }[/math]
Monzo	[0 1/2⟩
Size in cents	950.9775¢
Name	semitritave
Special properties	reduced

Interval

Semitritave, semitwelfth, square root of 3:1, 951.1 cents, is an candidate for "practically merciful intonation", because it's [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.

Pseudooctave

Semitritave is available for pseudooctave. Differ from acoustic phi or natave, two equave makes 3:1, well-known equave.

2*N-edt

Every even-numbered EDT has semitritave interval. 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.

• 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...