User:FloraC/Temperament extension issues: Difference between revisions
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=== Other notes === | === Other notes === | ||
* The | * The equal-temperament joins used here imply tuning ranges. | ||
== Open issues == | == Open issues == | ||
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; Diminished | ; Diminished | ||
: 7-limit → 11-limit | : 7-limit → 11-limit | ||
: 11-limit diminished should be decanonicalized. | : 11-limit diminished should be decanonicalized. 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: | : Proposed solution: 11-limit diminished → diminutive. Status: pending community reactions. | ||
; Gammic | ; Gammic | ||
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; Keemun | ; Keemun | ||
: 11-limit → 13-limit | : 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 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. | ||
: Proposed solution: | : 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. | : 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. | : 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: | |||
; Spell | |||
: 11-limit → 13-limit | |||
: 13-limit spell should be decanonicalized. 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: | : Proposed solution: | ||