User:FloraC/Temperament extension issues: Difference between revisions

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; Hemiwürschmidt

: 7-limit → 11-limit

: 11-limit → 13-limit

: 11-limit hemiwürschmidt should be decanonicalized. ~~The 7~~-limit optimum is between 99 and 130~~. The 11-limit extension shifts it~~ to somewhere ~~between~~ 130 ~~and~~ 161, and ~~is a significant drop in accuracy. Hemiwürschmidt is also described~~ as a 2.3.5.~~7.23~~-subgroup ~~temperament~~, which is ~~more natural~~.

: 13-limit hemiwürschmidt should be decanonicalized. While the 11-limit extension is a significant drop in accuracy, it doesn't shift the optimum too much (from between 99 and 130 to somewhere near 130, as 291 (= 130 + 161) isn't more accurate), and it can be reasoned based on it using the same mapping as the 2.3.5.11-subgroup version of würschmidt, the latter of which is supported by the "core" equal temps, 31, 34 and 65. The 13-limit version is where the shift of optimum becomes qualitative difference and the 31 and 99e vals are both questionable anyway.

: Proposed solution:

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: 7-limit → 11-limit

: 11-limit lunatic should be decanonicalized. Lunatic has at least three extensions: 205 & 323, 323 & 441, and 441 & 559. Perhaps, the canonicity of 441 & 559 could be argued on the basis that the 7-limit optimum is very close to 441; however, compared to the good efficiency and portability of the 7-limit temperament, this 11-limit extension is pretty mid.

: Proposed solution:

; Maquila

: 5-limit → 7-limit

: 7-limit maquila should be decanonicalized, or alternatively the 5-limit restriction should. In either case, it's a low-accuracy, high-badness extension that uses the dual-7 65edo.

: Proposed solution:

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; Würschmidt

: 5-limit → 7-limit

: 7-limit würschmidt should be decanonicalized. Almost all the notable supporting equal temperaments are dual-7: 34, 65, 96, and 127, and that speaks something about it. Würschmidt is also described as a 2.3.5.23-subgroup temperament, which is more natural.

: 7-limit würschmidt should be decanonicalized. Almost all the notable supporting equal temperaments are dual-7: 34, 65, 96, and 127, and that speaks something about it. Würschmidt is also described as a 2.3.5.11.(23)-subgroup temperament, which is more natural.

: Proposed solution:

@@ Line 44: / Line 44: @@
 ; Hemiwürschmidt
-: 7-limit → 11-limit
+: 11-limit → 13-limit
-: 11-limit hemiwürschmidt should be decanonicalized. The 7-limit optimum is between 99 and 130. The 11-limit extension shifts it to somewhere between 130 and 161, and is a significant drop in accuracy. Hemiwürschmidt is also described as a 2.3.5.7.23-subgroup temperament, which is more natural.
+: 13-limit hemiwürschmidt should be decanonicalized. While the 11-limit extension is a significant drop in accuracy, it doesn't shift the optimum too much (from between 99 and 130 to somewhere near 130, as 291 (= 130 + 161) isn't more accurate), and it can be reasoned based on it using the same mapping as the 2.3.5.11-subgroup version of würschmidt, the latter of which is supported by the "core" equal temps, 31, 34 and 65. The 13-limit version is where the shift of optimum becomes qualitative difference and the 31 and 99e vals are both questionable anyway.
 : Proposed solution:
@@ Line 56: / Line 56: @@
 : 7-limit → 11-limit
 : 11-limit lunatic should be decanonicalized. Lunatic has at least three extensions: 205 & 323, 323 & 441, and 441 & 559. Perhaps, the canonicity of 441 & 559 could be argued on the basis that the 7-limit optimum is very close to 441; however, compared to the good efficiency and portability of the 7-limit temperament, this 11-limit extension is pretty mid.
+: Proposed solution:
+; Maquila
+: 5-limit → 7-limit
+: 7-limit maquila should be decanonicalized, or alternatively the 5-limit restriction should. In either case, it's a low-accuracy, high-badness extension that uses the dual-7 65edo.
 : Proposed solution:
@@ Line 87: / Line 92: @@
 ; Würschmidt
 : 5-limit → 7-limit
-: 7-limit würschmidt should be decanonicalized. Almost all the notable supporting equal temperaments are dual-7: 34, 65, 96, and 127, and that speaks something about it. Würschmidt is also described as a 2.3.5.23-subgroup temperament, which is more natural.
+: 7-limit würschmidt should be decanonicalized. Almost all the notable supporting equal temperaments are dual-7: 34, 65, 96, and 127, and that speaks something about it. Würschmidt is also described as a 2.3.5.11.(23)-subgroup temperament, which is more natural.
 : Proposed solution: