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User:FloraC/Temperament extension issues: Difference between revisions

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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:  
; 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: pending community reactions.


; Lunatic
; Lunatic
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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:  
; 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: pending community reactions.
; 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: pending community reactions.


; Wesley
; Wesley
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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 → 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. Secundly → 13-limit secund. Status: changed.  
: 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
; Tertiaseptal
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