Aberschismic temperaments: Difference between revisions

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== Quintakwai ==

The ''quintakwai'' temperament (12&193) tempers out the hemifamity comma (5120/5103) and the compass comma (9765625/9680832, quinruyoyo) in the 7-limit; 1375/1372 and 4375/4356 in the 11-limit. In the 2.3.5.7.17.19 subgroup, 225/224 (the difference between 15/14 and 16/15), 256/255 (between 16/15 and 17/16), 289/288 (between 17/16 and 18/17), 324/323 (between 18/17 and 19/18), and 361/360 (between 19/18 and 20/19) are equated together, and 400/399 (between 20/19 and 21/20) is tempered out. The name ''quintakwai'' is so named because the generator is 1/5 of the [[Mirkwai clan #Kwai|kwai]] fourth (~4/3, about 497.4 cents).

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== Quinticosiennic ==

The ''quinticosiennic'' temperament (12&145) tempers out the hemifamity comma (5120/5103) and 395136/390625 (trizo-aquadbigu) in the 7-limit; 441/440 (werckisma), 896/891 (pentacircle), and 78408/78125 (lolosepgu) in the 11-limit. The word "quinticosiennic" means 5 (quintuple) × 29 (είκοσι εννέα) = 145, and so named because 1/5 of [[29edo|29EDO]] fourth, i.e. 12\145, is a possible generator.

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 == Quintakwai ==
-{{See also| 28ed5 #28ed5 as a generator }}
+{{See also| 28ed5 #Regular temperaments }}
 The ''quintakwai'' temperament (12&amp;193) tempers out the hemifamity comma (5120/5103) and the compass comma (9765625/9680832, quinruyoyo) in the 7-limit; 1375/1372 and 4375/4356 in the 11-limit. In the 2.3.5.7.17.19 subgroup, 225/224 (the difference between 15/14 and 16/15), 256/255 (between 16/15 and 17/16), 289/288 (between 17/16 and 18/17), 324/323 (between 18/17 and 19/18), and 361/360 (between 19/18 and 20/19) are equated together, and 400/399 (between 20/19 and 21/20) is tempered out. The name ''quintakwai'' is so named because the generator is 1/5 of the [[Mirkwai clan #Kwai|kwai]] fourth (~4/3, about 497.4 cents).
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 == Quinticosiennic ==
-{{See also| 16ed5/2 #16ed5/2 as a generator }}
+{{See also| 16ed5/2 #Regular temperaments }}
 The ''quinticosiennic'' temperament (12&amp;145) tempers out the hemifamity comma (5120/5103) and 395136/390625 (trizo-aquadbigu) in the 7-limit; 441/440 (werckisma), 896/891 (pentacircle), and 78408/78125 (lolosepgu) in the 11-limit. The word "quinticosiennic" means 5 (quintuple) × 29 (είκοσι εννέα) = 145, and so named because 1/5 of [[29edo|29EDO]] fourth, i.e. 12\145, is a possible generator.