Aberschismic temperaments: Difference between revisions
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[[Comma]]: {{monzo | 39 -29 3 }} = 68719476736000/68630377364883 | [[Comma]]: {{monzo | 39 -29 3 }} = 68719476736000/68630377364883 | ||
[[Mapping]]: [ | [[Mapping]]: [{{val| 1 0 -13 }}, {{val| 0 3 29 }}] | ||
[[POTE tuning|POTE generator]]: ~59049/40960 = 634.012 | [[POTE tuning|POTE generator]]: ~59049/40960 = 634.012 | ||
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[[Badness]]: 0.046093 | [[Badness]]: 0.046093 | ||
=== 7-limit ( | === 7-limit (Trimot) === | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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Badness: 0.025861 | Badness: 0.025861 | ||
== Quinticosiennic == | |||
{{See also| 16ed5/2 #16ed5/2 as a generator }} | |||
The ''quinticosiennic'' temperament (12&145) tempers out the hemifamity comma (5120/5103) and 395136/390625 (trizo-aquadbigu) in the 7-limit; 441/440, 896/891, and 78408/78125 in the 11-limit. The name ''quinticosiennic'' means 5 (quintuple) × 29 (είκοσι εννέα, eicosi ennea) = 145, and so named because 1/5 of [[29EDO]] fourth, i.e. 12\145, is a possible generator. | |||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 5120/5103, 395136/390625 | |||
[[Mapping]]: [{{val|1 2 1 -1}}, {{val|0 -5 16 46}}] | |||
{{Multival|legend=1|5 -16 -46 -37 -87 -62}} | |||
[[POTE generator]]: ~135/128 = 99.345 | |||
{{Val list|legend=1| 12, 133, 145, 157, 302c, 459bcc }} | |||
[[Badness]]: 0.158041 | |||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 441/440, 896/891, 78408/78125 | |||
Mapping: [{{val|1 2 1 -1 -2}}, {{val|0 -5 16 46 66}}] | |||
POTE generator: ~35/33 = 99.318 | |||
Vals: {{Val list| 12, 133, 145 }} | |||
Badness: 0.080674 | |||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 196/195, 352/351, 364/363, 78408/78125 | |||
Mapping: [{{val|1 2 1 -1 -2 -3}}, {{val|0 -5 16 46 66 81}}] | |||
POTE generator: ~35/33 = 99.307 | |||
Vals: {{Val list| 12f, 133, 145 }} | |||
Badness: 0.052464 | |||
=== 17-limit === | |||
Subgroup: 2.3.5.7.11.13.17 | |||
Comma list: 196/195, 256/255, 352/351, 364/363, 3757/3750 | |||
Mapping: [{{val|1 2 1 -1 -2 -3 5}}, {{val|0 -5 16 46 66 81 -11}}] | |||
POTE generator: ~18/17 = 99.308 | |||
Vals: {{Val list| 12f, 133, 145 }} | |||
Badness: 0.037108 | |||
=== 19-limit === | |||
Subgroup: 2.3.5.7.11.13.17.19 | |||
Comma list: 196/195, 256/255, 352/351, 361/360, 364/363, 476/475 | |||
Mapping: [{{val|1 2 1 -1 -2 -3 5 4}}, {{val|0 -5 16 46 66 81 -11 3}}] | |||
POTE generator: ~18/17 = 99.303 | |||
Vals: {{Val list| 12f, 133, 145 }} | |||
Badness: 0.028440 | |||
[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||