User:FloraC/Temperament extension issues: Difference between revisions

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{{Editable user page|Please add name proposals. Discussion goes to the talk page. }}

A list of issues with temperament extensions.

== Preliminaries ==

=== Objectives ===

"It's just labeling mathematical objects." I hear you say.

The goal is to make the scope of a temp name more coherent so that you need less modification and explanation to the names you use, ultimately to facilitate exploring the space of useful ideas and to reduce the friction in the communication of these ideas.

=== Terms ===

; Segment

: For rank-2 temps, refers to a tuning range of an extension, often bounded by equal temps. Segments often zigzag, i.e., the tuning of the added element changes direction as the tuning of the generator crosses a boundary, entering the range of another extension. A ''central segment'' is a range, among many, that takes the middle part of the original tuning range, and thus is most fit for a canonical extension.

=== Other notes ===

* The edo joins used here imply tuning ranges.

== Open issues ==

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: Proposed solution:

; ~~Dicot~~

; Chlorine

: 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 chlorine should be decanonicalized. The 612 & 935 extension isn't more complex (with the same Graham complexity in the 11-odd-limit) but is way more accurate.

: Proposed solution:

Line 18:

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: 7-limit → 11-limit

: 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:

; Grendel

: 11-limit → 13-limit

: 13-limit grendel should be decanonicalized. The tuning is not very representative of 11-limit grendel. Specifically, grendel has three 13-limit extensions: 121 & 152f, 152f & 183, and 183 & 214. The first and last are supported by 31 which means they are simpler, but they are not representative of the 11-limit optimum. The middle one is representative of the 11-limit optimum, but somewhat more complex than the last. Therefore, the situation is similar to slendric, where none of the extensions should be canon.

: Proposed solution:

; Hemiwürschmidt

: 7-limit → 11-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.

: Proposed solution:

; Keemun

: 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.

: 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. Its edo join is 15 & 19, while the current canonical 13-limit extension is 15f & 19, and 15 is better than 15f. Kema is additionally supported by patent 34, while the current canonical extension uses the much less accurate 34f. The mapping of prime 13 to -5 generators is inaccurate and in the opposite direction compared to primes 3, 5, and 7, making other intervals of 13 more complex.

: 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:

; 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:

; 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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: Paralytic has four notable 13-limit extensions: 99ef & 118, 99e & 118, 99ef & 118f, and 99e & 118f. Note that 99e & 118 and 99ef & 118f are the more accurate ones, supported by 217, and the other two are less accurate, but use the simpler 19e-form in the 13-limit. The 13-odd-limit Graham complexities of 99e & 118 and 99ef & 118f are 157 and 142, respectively, showing that 99e & 118 isn't simpler than 99ef & 118f; thus 13-limit paralytic needs a distinct name too.

: Paradigmic has two notable 13-limit extensions: 80 & 99e and 80 & 99ef, and like above, 80 & 99e is the simpler 19-form whereas 80 & 99ef is more accurate. 80 & 99ef also supports 13-limit parapyth, which is an extra point. It follows that 13-limit paradigmic needs a distinct name too.

~~: Proposed solution:~~

~~; Secund~~

~~: 11-limit → 13-limit~~

~~: 13-limit secund should be decanonicalized, for the other extension is obviously way better.~~

: Proposed solution:

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Line 83:

: 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:

; Wesley

: 5-limit → 7-limit

: 7-limit wesley should be decanonicalized. The tuning is not very representative of 5-limit wesley. Roman (26 & 29) is most representative, even tho it's a little more complex.

: 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:

; Schismatic family

: Various dubious extensions. ~~Will eventually collect them and add to the talk page~~.

: Various dubious extensions. See [[Talk: Schismatic family #Extensions]]. Pending public reactions.

; Tetracot family

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=== Rank-3 temperaments ===

~~; Agni~~

~~: 11-limit → 13-limit~~

~~: 13-limit agni should be decanonicalized. There's no reason to favor 31 & 72 over 41 & 72.~~

~~: Proposed solution:~~

; Artemis

: 11-limit → 13-limit

Line 67:

Line 110:

: 11-limit → 13-limit

: 13-limit big brother should be decanonicalized. See the case with artemis.

: Proposed solution:

; Freya

: 11-limit → 13-limit

: 13-limit freya should be decanonicalized. 11-limit freya has three extensions: 31 & 41 & 270, 31 & 72 & 270, and 41 & 72 & 270. 31 & 41 & 270 is a pretty neutral choice, but is also the least efficient out of all three.

: Proposed solution:

== Closed issues ==

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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

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: 11-limit nessafof should be decanonicalized. Extending nessafof to the 11-limit is complicated since both 84edo and 99edo have ambiguous interpretations (see the case with parakleismic). Currently we have catalogued the two low-complexity 15-form extensions, which makes sense. One is being called ''nessa'' so the other may simply be ''fof''.

: Proposed solution: 11-limit nessafof → fof. Status: changed.

; Secund

: 11-limit → 13-limit

: 13-limit secund should be decanonicalized, for the other extension is obviously way better.

: Proposed solution: delete 13-limit secund. Secundly → 13-limit secund. Status: changed.

=== Rank-3 temperaments ===

; Agni

: 11-limit → 13-limit

: 13-limit agni should be decanonicalized. There's no reason to favor 31 & 72 over 41 & 72, even tho the latter has a little higher badness. Proposing to rename it to pavaka, after another name of Agni.

: Proposed solution: 13-limit agni → pavaka. Status: changed.

; Aphrodite

: 11-limit → 13-limit

@@ Line 1: / Line 1: @@
-{{Editable user page|Please add ideas and name proposals. }}
+{{Editable user page|Please add name proposals. Discussion goes to the talk page. }}
 A list of issues with temperament extensions.
+== Preliminaries ==
+=== Objectives ===
+"It's just labeling mathematical objects." I hear you say.
+The goal is to make the scope of a temp name more coherent so that you need less modification and explanation to the names you use, ultimately to facilitate exploring the space of useful ideas and to reduce the friction in the communication of these ideas.
+=== Terms ===
+; Segment
+: For rank-2 temps, refers to a tuning range of an extension, often bounded by equal temps. Segments often zigzag, i.e., the tuning of the added element changes direction as the tuning of the generator crosses a boundary, entering the range of another extension. A ''central segment'' is a range, among many, that takes the middle part of the original tuning range, and thus is most fit for a canonical extension.
+=== Other notes ===
+* The edo joins used here imply tuning ranges.
 == Open issues ==
@@ Line 10: / Line 23: @@
 : Proposed solution:
-; Dicot
+; Chlorine
-: 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 chlorine should be decanonicalized. The 612 & 935 extension isn't more complex (with the same Graham complexity in the 11-odd-limit) but is way more accurate.
 : Proposed solution:
@@ Line 18: / Line 31: @@
 : 7-limit → 11-limit
 : 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:
+; Grendel
+: 11-limit → 13-limit
+: 13-limit grendel should be decanonicalized. The tuning is not very representative of 11-limit grendel. Specifically, grendel has three 13-limit extensions: 121 & 152f, 152f & 183, and 183 & 214. The first and last are supported by 31 which means they are simpler, but they are not representative of the 11-limit optimum. The middle one is representative of the 11-limit optimum, but somewhat more complex than the last. Therefore, the situation is similar to slendric, where none of the extensions should be canon.
+: Proposed solution:
+; Hemiwürschmidt
+: 7-limit → 11-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.
 : Proposed solution:
 ; Keemun
 : 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.
+: 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. Its edo join is 15 & 19, while the current canonical 13-limit extension is 15f & 19, and 15 is better than 15f. Kema is additionally supported by patent 34, while the current canonical extension uses the much less accurate 34f. The mapping of prime 13 to -5 generators is inaccurate and in the opposite direction compared to primes 3, 5, and 7, making other intervals of 13 more complex.
+: 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:
+; 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:
+; 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 35: / Line 78: @@
 : Paralytic has four notable 13-limit extensions: 99ef & 118, 99e & 118, 99ef & 118f, and 99e & 118f. Note that 99e & 118 and 99ef & 118f are the more accurate ones, supported by 217, and the other two are less accurate, but use the simpler 19e-form in the 13-limit. The 13-odd-limit Graham complexities of 99e & 118 and 99ef & 118f are 157 and 142, respectively, showing that 99e & 118 isn't simpler than 99ef & 118f; thus 13-limit paralytic needs a distinct name too.
 : Paradigmic has two notable 13-limit extensions: 80 & 99e and 80 & 99ef, and like above, 80 & 99e is the simpler 19-form whereas 80 & 99ef is more accurate. 80 & 99ef also supports 13-limit parapyth, which is an extra point. It follows that 13-limit paradigmic needs a distinct name too.
-: Proposed solution:
-; Secund
-: 11-limit → 13-limit
-: 13-limit secund should be decanonicalized, for the other extension is obviously way better.
 : Proposed solution:
@@ Line 45: / Line 83: @@
 : 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:
+; Wesley
+: 5-limit → 7-limit
+: 7-limit wesley should be decanonicalized. The tuning is not very representative of 5-limit wesley. Roman (26 & 29) is most representative, even tho it's a little more complex.
+: 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:
 ; Schismatic family
-: Various dubious extensions. Will eventually collect them and add to the talk page.
+: Various dubious extensions. See [[Talk: Schismatic family #Extensions]]. Pending public reactions.
 ; Tetracot family
@@ Line 54: / Line 102: @@
 === Rank-3 temperaments ===
-; Agni
-: 11-limit → 13-limit
-: 13-limit agni should be decanonicalized. There's no reason to favor 31 & 72 over 41 & 72.
-: Proposed solution:
 ; Artemis
 : 11-limit → 13-limit
@@ Line 67: / Line 110: @@
 : 11-limit → 13-limit
 : 13-limit big brother should be decanonicalized. See the case with artemis.
 : Proposed solution:
+; Freya
+: 11-limit → 13-limit
+: 13-limit freya should be decanonicalized. 11-limit freya has three extensions: 31 & 41 & 270, 31 & 72 & 270, and 41 & 72 & 270. 31 & 41 & 270 is a pretty neutral choice, but is also the least efficient out of all three.
+: Proposed solution:
 == Closed issues ==
@@ Line 75: / Line 123: @@
 : 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 112: / Line 165: @@
 : 11-limit nessafof should be decanonicalized. Extending nessafof to the 11-limit is complicated since both 84edo and 99edo have ambiguous interpretations (see the case with parakleismic). Currently we have catalogued the two low-complexity 15-form extensions, which makes sense. One is being called ''nessa'' so the other may simply be ''fof''.
 : Proposed solution: 11-limit nessafof → fof. Status: changed.
+; Secund
+: 11-limit → 13-limit
+: 13-limit secund should be decanonicalized, for the other extension is obviously way better.
+: Proposed solution: delete 13-limit secund. Secundly → 13-limit secund. Status: changed.
 === Rank-3 temperaments ===
+; Agni
+: 11-limit → 13-limit
+: 13-limit agni should be decanonicalized. There's no reason to favor 31 & 72 over 41 & 72, even tho the latter has a little higher badness. Proposing to rename it to pavaka, after another name of Agni.
+: Proposed solution: 13-limit agni → pavaka. Status: changed.
 ; Aphrodite
 : 11-limit → 13-limit