User:Dummy index/Semitritave: Difference between revisions
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Expression
[math]\displaystyle{ (3/1)^(1/2) }[/math]
Monzo
[0 1/2⟩
Size in cents
950.9775¢
Name
semitritave
Special properties
reduced
Dummy index (talk | contribs) Created page with "{{Infobox Interval | Icon = | Ratio = (3/1)^(1/2) | Monzo = 0 1/2 | Cents = 950.97750 | Name = semitritave }} ==Interval== Semitritave, semitwelfth, square root of 3:1, 951.1..." |
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==Interval== | ==Interval== | ||
Semitritave | Semitritave, square root of 3:1, 951.1 cents, is an candidate for "practically [[merciful intonation]]", because it is <math>[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== | ==Pseudooctave== | ||
Revision as of 11:19, 13 February 2022
| Interval information |
Interval
Semitritave, square root of 3:1, 951.1 cents, 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.
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...