User:Dummy index/Semitritave: Difference between revisions

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==Interval==

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~~.

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.

==~~Pseudooctave~~==

==Merciful intonation==

Semitritave is available for [[Ed5/3 through ed7/3|~~pseudooctave~~]]. Differ from [[acoustic phi]] or ~~natave~~, two equave makes [[3/1|3:1]], well-known equave.

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==

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

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* so 30edt?

To do mechanical translation from diatonic scores, "fifth" sound want to be consonance. ~~[[Ed7/4|~~7/5 is better]], but it makes [[3L 2s]]. 11/8 corresponds meantone region.

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 [[23edo and octave stretching|stretched 23edo]]. Another candidate with "fifth" 7/5...

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 }}
 ==Interval==
-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.
+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.
-==Pseudooctave==
+==Merciful intonation==
-Semitritave is available for [[Ed5/3 through ed7/3|pseudooctave]]. Differ from [[acoustic phi]] or natave, two equave makes [[3/1|3:1]], well-known equave.
+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==
-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
@@ Line 19: / Line 27: @@
 * so 30edt?
-To do mechanical translation from diatonic scores, "fifth" sound want to be consonance. [[Ed7/4|7/5 is better]], but it makes [[3L 2s]]. 11/8 corresponds meantone region.
+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 [[23edo and octave stretching|stretched 23edo]]. Another candidate with "fifth" 7/5...