User:FloraC/Temperament extension issues: Difference between revisions

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: Proposed solution:

; ~~Dicot~~

; Diminished

: 5-limit → 7-limit

: 7-limit → 11-limit

: 7-limit ~~dicot~~ should be decanonicalized. It ~~has been clear that it~~'s ~~difficult to discuss these as~~ a ~~single temperament~~.

: 11-limit diminished should be decanonicalized. It flips the optimal tuning from flat to sharp of just.

: Proposed solution:

; Gammic

: 7-limit → 11-limit

: 11-limit gammic should be decanonicalized. It's a low-accuracy extension.

: Proposed solution:

; ~~Diminished~~

; Hemiwürschmidt

: 7-limit → 11-limit

: 11-limit ~~diminished~~ should be decanonicalized. ~~It flips the optimal tuning from flat~~ to ~~sharp of just~~.

: 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.

: Proposed solution:

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Line 28:

: 11-limit → 13-limit

: 13-limit keemun should be decanonicalized. Kema, which maps prime 13 to +14 steps, is the right extension to use, as in all kleismic temperaments.

: Proposed solution:

; Lunatic

: 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:

; Neptune

: 7-limit → 11-limit

: 11-limit neptune should be decanonicalized. It's a low-accuracy extension. Neptune is also described as a 2.3.5.7.17-subgroup temperament, which is more natural. However, the 2.3.5.7.17.31-subgroup extension is a significant drop in accuracy so that one should at least be dual-named like ''triceneptune''.

: Proposed solution:

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: 7-limit → 11-limit

: 11-limit tertiaseptal should be decanonicalized. Tertiaseptal has three 11-limit extensions: 109 & 140, 140 & 171, and 171 & 202. Perhaps, the canonicity of 171 & 202 could be argued on the basis that the 7-limit optimum is very close to 171; however, compared to the absolute supremacy of the 7-limit temperament, this 11-limit extension is plain bad. ''Tertia'' and ''tertiaseptia'' are bad-tasted names so we might wanna reconsider these names too.

: Proposed solution:

; 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.

: Proposed solution:

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: 7-limit augene should be canonicalized while 13-limit augene should be decanonicalized. Tempering out 126/125 is natural for diaschismic, augmented and diminished, and since both diaschismic and diminished have canonical 7-limit extensions, so should augmented (even tho septimal diaschismic is essentially grandfathered in). Furthermore, the 11-limit extension should remain as canon, for the 11-odd-limit diamond monotone range is the same as 9-odd-limit. The name ''augene'' may remain as an alias for this temperament, but the 13-limit extension should eventually have its name changed cuz that one is much worse.

: Proposed solution: 7-, 11-, and 13-limit augene → augmented (augene). Status: changed.

; Dicot

: 5-limit → 7-limit

: 7-limit dicot should be decanonicalized. It has been clear that it's difficult to discuss these as a single temperament. The 7-limit extension is in fact the best extension of 2.3.7-subgroup {54/49} (in the same way beep is the best extension of bug), known as ''mujannabic'', so it may inherit that name.

: Proposed solution: 7- and 11-limit dicot → mujannabic. Status: changed.

; Ennealimmal

@@ Line 10: / Line 10: @@
 : Proposed solution:
-; Dicot
+; Diminished
-: 5-limit → 7-limit
+: 7-limit → 11-limit
-: 7-limit dicot should be decanonicalized. It has been clear that it's difficult to discuss these as a single temperament.
+: 11-limit diminished should be decanonicalized. It flips the optimal tuning from flat to sharp of just.
+: Proposed solution:
+; Gammic
+: 7-limit → 11-limit
+: 11-limit gammic should be decanonicalized. It's a low-accuracy extension.
 : Proposed solution:
-; Diminished
+; Hemiwürschmidt
 : 7-limit → 11-limit
-: 11-limit diminished should be decanonicalized. It flips the optimal tuning from flat to sharp of just.
+: 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.
 : Proposed solution:
@@ Line 23: / Line 28: @@
 : 11-limit → 13-limit
 : 13-limit keemun should be decanonicalized. Kema, which maps prime 13 to +14 steps, is the right extension to use, as in all kleismic temperaments.
+: Proposed solution:
+; Lunatic
+: 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:
+; Neptune
+: 7-limit → 11-limit
+: 11-limit neptune should be decanonicalized. It's a low-accuracy extension. Neptune is also described as a 2.3.5.7.17-subgroup temperament, which is more natural. However, the 2.3.5.7.17.31-subgroup extension is a significant drop in accuracy so that one should at least be dual-named like ''triceneptune''.
 : Proposed solution:
@@ Line 45: / Line 60: @@
 : 7-limit → 11-limit
 : 11-limit tertiaseptal should be decanonicalized. Tertiaseptal has three 11-limit extensions: 109 & 140, 140 & 171, and 171 & 202. Perhaps, the canonicity of 171 & 202 could be argued on the basis that the 7-limit optimum is very close to 171; however, compared to the absolute supremacy of the 7-limit temperament, this 11-limit extension is plain bad. ''Tertia'' and ''tertiaseptia'' are bad-tasted names so we might wanna reconsider these names too.
+: Proposed solution:
+; 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.
 : Proposed solution:
@@ Line 75: / Line 95: @@
 : 7-limit augene should be canonicalized while 13-limit augene should be decanonicalized. Tempering out 126/125 is natural for diaschismic, augmented and diminished, and since both diaschismic and diminished have canonical 7-limit extensions, so should augmented (even tho septimal diaschismic is essentially grandfathered in). Furthermore, the 11-limit extension should remain as canon, for the 11-odd-limit diamond monotone range is the same as 9-odd-limit. The name ''augene'' may remain as an alias for this temperament, but the 13-limit extension should eventually have its name changed cuz that one is much worse.
 : Proposed solution: 7-, 11-, and 13-limit augene → augmented (augene). Status: changed.
+; Dicot
+: 5-limit → 7-limit
+: 7-limit dicot should be decanonicalized. It has been clear that it's difficult to discuss these as a single temperament. The 7-limit extension is in fact the best extension of 2.3.7-subgroup {54/49} (in the same way beep is the best extension of bug), known as ''mujannabic'', so it may inherit that name.
+: Proposed solution: 7- and 11-limit dicot → mujannabic. Status: changed.
 ; Ennealimmal