Aberschismic temperaments: Difference between revisions

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== Leapday ==

: ''For the 5-limit version of this temperament, see [[High badness temperaments #Leapday]].''

[[Leapday]] tempers out {{monzo|31 -21 1}} (trisayo) in the 5-limit. This temperament can be described as 29&46 temperament, which tempers out the hemifamity and 686/675 (senga). Alternative extension [[Porwell temperaments #Polypyth|polypyth]] (46&121) tempers out the same 5-limit comma as the leapday, but with the porwell (6144/6125) rather than the hemifamity tempered out.

~~Subgroup: 2.3.5~~

~~[[Comma list]]: 10737418240/10460353203~~

~~[[Mapping]]: [{{val| 1 0 -31 }}, {{val| 0 1 21 }}]~~

~~[[POTE generator]]: ~3/2 = 704.179~~

~~{{Val list|legend=1| 29, 46, 121, 167, 455bc, 622bbc }}~~

~~[[Badness]]: 0.523182~~

~~=== 7-limit ===~~

Subgroup: 2.3.5.7

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Badness: 0.017863

=== 19-limit ===

==== 19-limit ====

Subgroup: 2.3.5.7.11.13.17.19

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Badness: 0.017356

=== Leapling ===

==== Leapling ====

Subgroup: 2.3.5.7.11.13.17.19

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== Mystery ==

: ''For the 5-limit version of this temperament, see [[High badness temperaments #Mystery]].''

~~Subgroup: 2.3.5~~

~~[[Comma list]]: {{monzo| 46 -29 }}~~

~~[[Mapping]]: [{{val| 29 46 0 }}, {{val| 0 0 1 }}]~~

~~Mapping generators: ~531441/524288, ~5~~

~~[[POTE generator]]: ~5/4 = 387.408~~

~~{{Val list|legend=1| 29, 58, 87, 232, 319 }}~~

~~[[Badness]]: 1.020556~~

~~=== 7-limit ===~~

Subgroup: 2.3.5.7

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[[Mapping]]: [{{val| 1 0 -13 }}, {{val| 0 3 29 }}]

[[~~POTE tuning|~~POTE generator]]: ~59049/40960 = 634.012

[[POTE generator]]: ~59049/40960 = 634.012

{{Val list|legend=1| 53, 229, 282, 335, 388, 441, 1376, 1817, 2258 }}

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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).

Subgroup: 2.3.5.7

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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.

Subgroup: 2.3.5.7

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 == Leapday ==
+: ''For the 5-limit version of this temperament, see [[High badness temperaments #Leapday]].''
 [[Leapday]] tempers out {{monzo|31 -21 1}} (trisayo) in the 5-limit. This temperament can be described as 29&amp;46 temperament, which tempers out the hemifamity and 686/675 (senga). Alternative extension [[Porwell temperaments #Polypyth|polypyth]] (46&amp;121) tempers out the same 5-limit comma as the leapday, but with the porwell (6144/6125) rather than the hemifamity tempered out.
-Subgroup: 2.3.5
-[[Comma list]]: 10737418240/10460353203
-[[Mapping]]: [{{val| 1 0 -31 }}, {{val| 0 1 21 }}]
-[[POTE generator]]: ~3/2 = 704.179
-{{Val list|legend=1| 29, 46, 121, 167, 455bc, 622bbc }}
-[[Badness]]: 0.523182
-=== 7-limit ===
 Subgroup: 2.3.5.7
@@ Line 182: / Line 172: @@
 Badness: 0.017863
-=== 19-limit ===
+==== 19-limit ====
 Subgroup: 2.3.5.7.11.13.17.19
@@ Line 195: / Line 185: @@
 Badness: 0.017356
-=== Leapling ===
+==== Leapling ====
 Subgroup: 2.3.5.7.11.13.17.19
@@ Line 210: / Line 200: @@
 == Mystery ==
 {{main| Mystery }}
+: ''For the 5-limit version of this temperament, see [[High badness temperaments #Mystery]].''
-Subgroup: 2.3.5
-[[Comma list]]: {{monzo| 46 -29 }}
-[[Mapping]]: [{{val| 29 46 0 }}, {{val| 0 0 1 }}]
-Mapping generators: ~531441/524288, ~5
-[[POTE generator]]: ~5/4 = 387.408
-{{Val list|legend=1| 29, 58, 87, 232, 319 }}
-[[Badness]]: 1.020556
-=== 7-limit ===
 Subgroup: 2.3.5.7
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 [[Mapping]]: [{{val| 1 0 -13 }}, {{val| 0 3 29 }}]
-[[POTE tuning|POTE generator]]: ~59049/40960 = 634.012
+[[POTE generator]]: ~59049/40960 = 634.012
 {{Val list|legend=1| 53, 229, 282, 335, 388, 441, 1376, 1817, 2258 }}
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 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).
 Subgroup: 2.3.5.7
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 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.
 Subgroup: 2.3.5.7