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
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==Interval== | ==Interval== | ||
Semitritave, square root of 3:1 | 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 available for [[Ed5/3 through ed7/3| | Semitritave 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. | ||
Approximating it by noble number: | |||
* <math>[1; 1, 2, 1, 1, 1, ...]</math> - 942.5 cents, between 12/7 and 19/11. | |||
* <math>[1; 1, 2, 1, 2, 1, 1, 1, ...]</math> - 950.4 cents, between 45/26 and 71/41. | |||
* <math>[1; 1, 2, 1, 3, 1, 1, 1, ...]</math> - 954.6 cents, between 26/15 and 33/19. | |||
==False octave== | |||
Semitritave is available for [[Ed5/3 through ed7/3|false octave]]. Differ from [[acoustic phi]] or [[ed7/4]], two equave makes [[3/1|3:1]], well-known equave. | |||
==2*N-edt== | ==2*N-edt== | ||
Every even-numbered [[EDT]] has semitritave interval. Another preferrable intervals... | Every even-numbered [[EDT]] has semitritave interval. Treating it as equave. Another preferrable intervals... | ||
* 5edt - 380 cents major third | * 5edt - 380 cents major third | ||
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* so 30edt? | * so 30edt? | ||
To do mechanical translation from diatonic scores, "fifth" sound want to be consonance. | 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. | * 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. | * 38edt - approximately 24edo. "Fifth" is 11\19 ≈ 11/8. Can convert easily from 19edo. | ||
* 36edt - approximately [[23edo and octave stretching|stretched 23edo]]. Another candidate with "fifth" 7/5... | * 36edt - approximately [[23edo and octave stretching|stretched 23edo]]. Another candidate with "fifth" 7/5... | ||
Revision as of 14:11, 14 February 2022
| Interval information |
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...