User:Dummy index/Semitritave: Difference between revisions

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==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.　It is strongly related to island comma, [[676/675]], via 13-limit approximant 26/15 and 45/26.

Semitritave, square [[root]] of 3:1, is an [[interseptimal]] interval. It divide [[tritave]] into two equal parts. Every even-numbered [[EDT]] has this interval.　It is strongly related to island comma, [[676/675]], via 13-limit approximant 26/15 and 45/26.

==Merciful intonation==

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* 46edt - approximately 29edo. Two "fifth," "14\23" ≈ 7/5, "13\23" ≈ 15/11. 13/11 and 15/13 are precise.

* 54edt - approximately 34edo. Two "fifth," "16\27" ≈ 18/13 and "15\27" ≈ 19/14 are precise. Together with "9\27" ≈ 6/5 and "11\27" ≈ 5/4, seems good for micro- augene<nowiki>[12]</nowiki>.

* 62edt - approximately 39edo. "Fifth" is "18\31" ≈ 11/8, and "wolf fifth" is "19\31" ≈ 7/5. By the way, "upmajor 3rd" and "downminor 3rd" approximate 17/14 and 17/15, where (17/14)*(17/15) ≈ (11/8)*([[1156/1155]]).

* 62edt - approximately 39edo. "Fifth" is "18\31" ≈ 11/8, and "wolf fifth" is "19\31" ≈ 7/5. By the way, "upmajor 3rd" and "downminor 3rd" approximate 17/14 and 17/15, where (17/14)*(17/15) = (11/8)*([[1156/1155]]).

==Memo==

[http://x31eq.com/cgi-bin/pregular.cgi?limit=3.5%2F2.11%2F8&error=5.0 3.5/2.11/8 => 24edt],

[http://x31eq.com/cgi-bin/pregular.cgi?limit=3.5.7.13&error=5.0 3.5.7.13 => 30edt],

[http://x31eq.com/cgi-bin/pregular.cgi?limit=3.5%2F2.7%2F2&error=5.0 3.5/2.7/2 => 36edt],

[http://x31eq.com/cgi-bin/pregular.cgi?limit=3.2.11.17&error=5.0 3.2.11.17 => 38edt],

[http://x31eq.com/cgi-bin/pregular.cgi?limit=3.2.11%2F5.13%2F5&error=5.0 3.2.11/5.13/5 => 46edt],

[http://x31eq.com/cgi-bin/pregular.cgi?limit=3.10.14.13%2F8.34&error=5.0 3.10.14.13/8.34 => 52edt],

[http://x31eq.com/cgi-bin/pregular.cgi?limit=3.2.5.13.17&error=5.0 3.2.5.13.17 => 54edt],

[http://x31eq.com/cgi-bin/pregular.cgi?limit=3.10.14.17.11%2F8&error=5.0 3.10.14.17.11/8 => 62edt]

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 }}
 ==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.　It is strongly related to island comma, [[676/675]], via 13-limit approximant 26/15 and 45/26.
+Semitritave, square [[root]] of 3:1, is an [[interseptimal]] interval. It divide [[tritave]] into two equal parts. Every even-numbered [[EDT]] has this interval.　It is strongly related to island comma, [[676/675]], via 13-limit approximant 26/15 and 45/26.
 ==Merciful intonation==
@@ Line 34: / Line 34: @@
 * 46edt - approximately 29edo. Two "fifth," "14\23" ≈ 7/5, "13\23" ≈ 15/11. 13/11 and 15/13 are precise.
 * 54edt - approximately 34edo. Two "fifth," "16\27" ≈ 18/13 and "15\27" ≈ 19/14 are precise. Together with "9\27" ≈ 6/5 and "11\27" ≈ 5/4, seems good for micro- augene<nowiki>[12]</nowiki>.
-* 62edt - approximately 39edo. "Fifth" is "18\31" ≈ 11/8, and "wolf fifth" is "19\31" ≈ 7/5. By the way, "upmajor 3rd" and "downminor 3rd" approximate 17/14 and 17/15, where (17/14)*(17/15) ≈ (11/8)*([[1156/1155]]).
+* 62edt - approximately 39edo. "Fifth" is "18\31" ≈ 11/8, and "wolf fifth" is "19\31" ≈ 7/5. By the way, "upmajor 3rd" and "downminor 3rd" approximate 17/14 and 17/15, where (17/14)*(17/15) = (11/8)*([[1156/1155]]).
 ==Memo==
 [http://x31eq.com/cgi-bin/pregular.cgi?limit=3.5%2F2.11%2F8&error=5.0 3.5/2.11/8 => 24edt],
+[http://x31eq.com/cgi-bin/pregular.cgi?limit=3.5.7.13&error=5.0 3.5.7.13 => 30edt],
 [http://x31eq.com/cgi-bin/pregular.cgi?limit=3.5%2F2.7%2F2&error=5.0 3.5/2.7/2 => 36edt],
 [http://x31eq.com/cgi-bin/pregular.cgi?limit=3.2.11.17&error=5.0 3.2.11.17 => 38edt],
 [http://x31eq.com/cgi-bin/pregular.cgi?limit=3.2.11%2F5.13%2F5&error=5.0 3.2.11/5.13/5 => 46edt],
+[http://x31eq.com/cgi-bin/pregular.cgi?limit=3.10.14.13%2F8.34&error=5.0 3.10.14.13/8.34 => 52edt],
 [http://x31eq.com/cgi-bin/pregular.cgi?limit=3.2.5.13.17&error=5.0 3.2.5.13.17 => 54edt],
 [http://x31eq.com/cgi-bin/pregular.cgi?limit=3.10.14.17.11%2F8&error=5.0 3.10.14.17.11/8 => 62edt]