Hemimage temperaments: Difference between revisions
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{{Val list|legend=1| 58, 118, 294, 412d, 530d }} | {{Val list|legend=1| 58, 118, 294, 412d, 530d }} | ||
[[Badness]]: 0. | [[Badness]]: 0.084317 | ||
== 11-limit == | == 11-limit == | ||
| Line 40: | Line 40: | ||
Vals: {{Val list| 58, 118, 294, 412d }} | Vals: {{Val list| 58, 118, 294, 412d }} | ||
Badness: 0. | Badness: 0.030461 | ||
= Chromat = | = Chromat = | ||
| Line 57: | Line 57: | ||
{{Val list|legend=1| 60, 99, 258, 357, 456 }} | {{Val list|legend=1| 60, 99, 258, 357, 456 }} | ||
[[Badness]]: 0. | [[Badness]]: 0.057499 | ||
= Degrees = | = Degrees = | ||
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{{Val list|legend=1| 60, 80, 140, 640b, 780b, 920b }} | {{Val list|legend=1| 60, 80, 140, 640b, 780b, 920b }} | ||
[[Badness]]: 0. | [[Badness]]: 0.106471 | ||
== 11-limit == | == 11-limit == | ||
| Line 85: | Line 85: | ||
Vals: {{Val list| 80, 140, 360, 500be, 860bde }} | Vals: {{Val list| 80, 140, 360, 500be, 860bde }} | ||
Badness: 0. | Badness: 0.046770 | ||
== 13-limit == | == 13-limit == | ||
| Line 98: | Line 98: | ||
Vals: {{Val list| 60e, 80, 140, 500be, 640be, 780be }} | Vals: {{Val list| 60e, 80, 140, 500be, 640be, 780be }} | ||
Badness: 0. | Badness: 0.032718 | ||
= Subfourth = | = Subfourth = | ||
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[[Mapping]]: [{{val| 1 0 17 4 }}, {{val| 0 4 -37 -3 }}] | [[Mapping]]: [{{val| 1 0 17 4 }}, {{val| 0 4 -37 -3 }}] | ||
{{Multival|legend=1| 4 -37 -3 -68 -16 97 }} | |||
[[POTE generator]]: ~21/16 = 475.991 | [[POTE generator]]: ~21/16 = 475.991 | ||
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{{Val list|legend=1| 58, 121, 179, 300bd, 479bcd }} | {{Val list|legend=1| 58, 121, 179, 300bd, 479bcd }} | ||
[[Badness]]: 0. | [[Badness]]: 0.140722 | ||
== 11-limit == | == 11-limit == | ||
| Line 124: | Line 126: | ||
Vals: {{Val list| 58, 121, 179e, 300bde }} | Vals: {{Val list| 58, 121, 179e, 300bde }} | ||
Badness: 0. | Badness: 0.045323 | ||
== 13-limit == | == 13-limit == | ||
| Line 137: | Line 139: | ||
Vals: {{Val list| 58, 121, 179ef, 300bdef }} | Vals: {{Val list| 58, 121, 179ef, 300bdef }} | ||
Badness: 0. | Badness: 0.023800 | ||
= Bisupermajor = | = Bisupermajor = | ||
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[[Mapping]]: [{{val| 2 1 6 1 }}, {{val| 0 8 -5 17 }}] | [[Mapping]]: [{{val| 2 1 6 1 }}, {{val| 0 8 -5 17 }}] | ||
{{Multival|legend=1| 16 -10 34 -53 9 107 }} | |||
[[POTE generator]]: ~192/175 = 162.8061 | [[POTE generator]]: ~192/175 = 162.8061 | ||
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{{Val list|legend=1| 22, 74d, 96d, 118, 140, 258, 398 }} | {{Val list|legend=1| 22, 74d, 96d, 118, 140, 258, 398 }} | ||
[[Badness]]: 0. | [[Badness]]: 0.065492 | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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Vals: {{Val list| 22, 74d, 96d, 118, 258e, 376de }} | Vals: {{Val list| 22, 74d, 96d, 118, 258e, 376de }} | ||
Badness: 0. | Badness: 0.032080 | ||
= Cotoneum = | |||
The ''cotoneum'' temperament (41&217, named by [[User:Xenllium|Xenllium]] after the Latin for "quince") tempers out the [[Quince clan|quince comma]], 823543/819200 and the [[garischisma]], 33554432/33480783. This temperament is supported by [[41edo|41]], [[176edo|176]], [[217edo|217]], and [[258edo|258]] EDOs, and can be extended to the 11-, 13-, 17-, and 19-limit by adding 441/440, 364/363, 595/594, and 343/342 to the comma list in this order. | |||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 10976/10935, 823543/819200 | |||
[[Mapping]]: [{{val|1 2 -18 -3}}, {{val|0 -1 49 14}}] | |||
{{Multival|legend=1| 1 -49 -14 -80 -25 105 }} | |||
[[POTE generator]]: ~3/2 = 702.317 | |||
{{Val list|legend=1| 41, 135c, 176, 217, 258, 475 }} | |||
[[Badness]]: 0.105632 | |||
== 11-limit == | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 441/440, 10976/10935, 16384/16335 | |||
Mapping: [{{val|1 2 -18 -3 13}}, {{val|0 -1 49 14 -23}}] | |||
POTE generator: ~3/2 = 702.303 | |||
Vals: {{Val list| 41, 176, 217 }} | |||
Badness: 0.050966 | |||
== 13-limit == | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 364/363, 441/440, 3584/3575, 10976/10935 | |||
Mapping: [{{val|1 2 -18 -3 13 29}}, {{val|0 -1 49 14 -23 -61}}] | |||
POTE generator: ~3/2 = 702.306 | |||
Vals: {{Val list| 41, 176, 217 }} | |||
Badness: 0.036951 | |||
== 17-limit == | |||
Subgroup: 2.3.5.7.11.13.17 | |||
Comma list: 364/363, 441/440, 595/594, 3584/3575, 8281/8262 | |||
Mapping: [{{val|1 2 -18 -3 13 29 41}}, {{val|0 -1 49 14 -23 -61 -89}}] | |||
POTE generator: ~3/2 = 702.307 | |||
Vals: {{Val list| 41, 176, 217 }} | |||
Badness: 0.029495 | |||
== 19-limit == | |||
Subgroup: 2.3.5.7.11.13.17.19 | |||
Comma list: 343/342, 364/363, 441/440, 595/594, 1216/1215, 1729/1728 | |||
Mapping: [{{val|1 2 -18 -3 13 29 41 -14}}, {{val|0 -1 49 14 -23 -61 -89 44}}] | |||
POTE generator: ~3/2 = 702.308 | |||
Vals: {{Val list| 41, 176, 217 }} | |||
Badness: 0.021811 | |||
[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||