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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: 7-limit → 11-limit

: 11-limit alphatrident should be decanonicalized. The tuning is not very representative of 7-limit alphatrident. Specifically, alphatrident has three 11-limit extensions: 176 & 229, 229 & 282, and 282 & 335d. The first and last are supported by 53 which means they are simpler, but they are not representative of the 7-limit optimum. The middle one is representative of the 7-limit optimum, but is very complex. Therefore, the situation is similar to slendric, where none of the extensions should be canon.

: Proposed solution:

; Chlorine

: 7-limit → 11-limit

: 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:

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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:

; 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:

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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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: 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: delete 13-limit secund. Secundly → 13-limit secund. Status: pending community reactions.~~

; Tertiaseptal

: 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.

: 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:

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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

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: 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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: 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 8: / Line 21: @@
 : 7-limit → 11-limit
 : 11-limit alphatrident should be decanonicalized. The tuning is not very representative of 7-limit alphatrident. Specifically, alphatrident has three 11-limit extensions: 176 & 229, 229 & 282, and 282 & 335d. The first and last are supported by 53 which means they are simpler, but they are not representative of the 7-limit optimum. The middle one is representative of the 7-limit optimum, but is very complex. Therefore, the situation is similar to slendric, where none of the extensions should be canon.
+: Proposed solution:
+; Chlorine
+: 7-limit → 11-limit
+: 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 26: / 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:
 ; 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:
@@ Line 38: / 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 56: / Line 79: @@
 : 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: delete 13-limit secund. Secundly → 13-limit secund. Status: pending community reactions.
 ; Tertiaseptal
 : 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.
+: 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 79: / 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 92: / 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 142: / 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