User:FloraC/Temperament extension issues: Difference between revisions

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 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:

@@ 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 92: / 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: