User:FloraC/Temperament extension issues: Difference between revisions
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: 11-limit chlorine should be decanonized. The 612 & 935 extension isn't more complex (with the same Graham complexity in the 11-odd-limit) but is way more accurate. | : 11-limit chlorine should be decanonized. 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: | : Proposed solution: | ||
; Gammic | ; Gammic | ||
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: 13-limit hemiwürschmidt should be decanonized. 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. | : 13-limit hemiwürschmidt should be decanonized. 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: | : Proposed solution: | ||
; Lunatic | ; Lunatic | ||
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: 11-limit neptune should be decanonized. 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''. | : 11-limit neptune should be decanonized. 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: | : Proposed solution: | ||
; Parakleismic | ; Parakleismic | ||
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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. | : 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: | : Proposed solution: | ||
; Wesley | ; Wesley | ||
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: 7-limit würschmidt should be decanonized. 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. | : 7-limit würschmidt should be decanonized. 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: | : Proposed solution: | ||
; Amity family | |||
: Various dubious extensions. See [[Talk: Amity family #Extensions]]. Pending public reactions. | |||
; Schismatic family | ; Schismatic family | ||
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: 7-limit dicot should be decanonized. 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. | : 7-limit dicot should be decanonized. 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. | : Proposed solution: 7- and 11-limit dicot → mujannabic. Status: changed. | ||
; Diminished | |||
: 7-limit → 11-limit | |||
: 11-limit diminished should be decanonized. While it's natural to temper out 99/98 and 100/99 as a jubilismic temperament, the 36/35 (= S8⋅S9) in the comma list makes this less accurate since we're equating 8/7~10/9 with 11/10. Besides, it flips the optimal tuning from flat to sharp of just. Diminished could arguably be more naturally defined on 2.3.5.7.17.19. | |||
: Proposed solution: 11-limit diminished → diminutive. Status: changed. | |||
; Ennealimmal | ; Ennealimmal | ||
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: 11-limit hendecatonic should be decanonized. It's not better than 22 & 99e, known as ''cohendecatonic''. | : 11-limit hendecatonic should be decanonized. It's not better than 22 & 99e, known as ''cohendecatonic''. | ||
: Proposed solution: 11-, 13- and 17-limit hendecatonic → hendecaton. Status: changed. | : Proposed solution: 11-, 13- and 17-limit hendecatonic → hendecaton. Status: changed. | ||
; Keemun | |||
: 11-limit → 13-limit | |||
: 13-limit keemun should be decanonized. Kema, which maps 15/13 to the hemifourth (and hence prime 13 to +14 steps), is the right extension to use, as in all kleismic temperaments and all semaphoresmic temperaments. Besides, kema's equal-temperament join is 15 & 19, while the currently canonical 13-limit extension is 15f & 19, and 15 is better than 15f. Kema is additionally supported by patent 34, while the currently 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. | |||
: ''Kema'' and ''kumbaya'' are etymologically unrelated to ''keemun'', so it seems okay to rename the currently canonical 13-limit keemun to something unrelated too. | |||
: Proposed solution: 13-limit keemun → kimah. Kema → 13-limit keemun. Status: changed. | |||
; Ketchup | ; Ketchup | ||
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: 11-limit nessafof should be decanonized. 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''. | : 11-limit nessafof should be decanonized. 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. | : Proposed solution: 11-limit nessafof → fof. Status: changed. | ||
; Pajara | |||
: 11-limit → 13-limit | |||
: 13-limit pajara should be decanonized. It's way too inaccurate. Pajara should be a no-13 17-limit temperament. | |||
: Proposed solution: 13-limit pajara → paja. Status: changed. | |||
; Secund | ; Secund | ||
: 11-limit → 13-limit | : 11-limit → 13-limit | ||
: 13-limit secund should be decanonized, for the other extension is obviously way better. | : 13-limit secund should be decanonized, for the other extension is obviously way better. | ||
: Proposed solution: delete 13-limit secund. | : Proposed solution: delete 13-limit secund; secundly → 13-limit secund. Status: changed. | ||
; Sengagen | |||
: 11-limit → 13-limit | |||
: 13-limit sengagen should be decanonized. The 49f & 50 extension, which maps prime 13 to +35 steps, is simpler as all the other primes are positive (Graham complexity 58 vs 73), and nearly as accurate, compared to the currently canonical extension. This should be very clear in the badness values, where the difference is significant. But more importantly, 49f and 50 show a duality: 50 tunes 11/9 a step wider than 27/22, and 49f tunes 39/32 a step wider than 16/13, both due to the vanishment of 144/143, and then 99ef is where they all converge to the true neutral third. In this sense, 49f & 50 is the result of applying a consistent logic to primes 11 and 13, so should be more natural than 49 & 50. | |||
: Proposed solution: 13-limit sengagen → sengageny; sengage → 13-limit sengagen. Status: changed. | |||
; Spell | |||
: 11-limit → 13-limit | |||
: 13-limit spell should be decanonized. Cantrip, which maps 15/13 to the hemifourth (and hence prime 13 to +17 steps), is the right extension to use, as in all semaphoresmic temperaments. Besides, cantrip's equal-temperament join is 19 & 25e, which makes more sense than whatever the currently canonical extension is. | |||
: Proposed solution: 13-limit spell → spellcraft; cantrip → 13-limit spell. Status: changed. | |||
; Tertiaseptal | |||
: 7-limit → 11-limit | |||
: 11-limit tertiaseptal should be decanonized. 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. Tertiaseptal is also described as a no-11 13- and 17-limit temperament, which further justifies the change. | |||
: Currently, the other 11-limit extensions are called ''tertia'' and ''tertiaseptia'', which, despite the confusing form (sounds like commas rather than temps), suggests that the extension 171 & 202 might be ''septia''. | |||
: Proposed solution: 11-limit tertiaseptal → septia. Status: changed. | |||
=== Rank-3 temperaments === | === Rank-3 temperaments === | ||