Canousmic temperaments: Difference between revisions
Remove 13-limit luna I once added (not a great ext) |
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These are rank-2 temperaments that temper out the [[canousma]], 4802000/4782969 = {{monzo|4 -14 3 4}}. For the rank-3 temperament, see [[Canou family]]. | These are rank-2 temperaments that temper out the [[canousma]], 4802000/4782969 = {{monzo| 4 -14 3 4 }}. For the rank-3 temperament, see [[Canou family]]. | ||
Note that 4802000/4782969 = 2×([[10/9]])<sup>3</sup>/([[9/7]])<sup>4</sup>, these intervals tend to have lower complexity. | Note that 4802000/4782969 = 2×([[10/9]])<sup>3</sup>/([[9/7]])<sup>4</sup>, these intervals tend to have lower complexity. | ||
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= Satin = | = Satin = | ||
== 5-limit == | == 5-limit == | ||
Subgroup: 2.3.5 | |||
[[Comma list]]: {{monzo|104 -70 3}} | [[Comma list]]: {{monzo|104 -70 3}} | ||
[[Mapping]]: [{{val| 1 2 12 }}, {{val| 0 -3 -70 }}] | |||
[[POTE generator]]: ~{{monzo|-34 23 -1}} = 165.907 | [[POTE generator]]: ~{{monzo|-34 23 -1}} = 165.907 | ||
{{Val list|legend=1| 94, 217, 528, 745, 1273 }} | {{Val list|legend=1| 94, 217, 528, 745, 1273 }} | ||
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== 7-limit == | == 7-limit == | ||
Subgroup: 2.3.5.7 | |||
Mapping: [{{val| 1 2 12 -3 }}, {{val| 0 -3 -70 42 }}] | [[Comma list]]: 2100875/2097152, 4802000/4782969 | ||
[[Mapping]]: [{{val| 1 2 12 -3 }}, {{val| 0 -3 -70 42 }}] | |||
[[POTE generator]]: ~8575/7776 = 165.913 | |||
{{Val list|legend=1| 94, 217, 311, 839, 1150 }} | {{Val list|legend=1| 94, 217, 311, 839, 1150 }} | ||
Badness: 0.1972 | [[Badness]]: 0.1972 | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | |||
Comma list: 4000/3993, 19712/19683, 41503/41472 | Comma list: 4000/3993, 19712/19683, 41503/41472 | ||
Mapping: [{{val| 1 2 12 -3 13 }}, {{val| 0 -3 -70 42 -69 }}] | |||
POTE generator: ~11/10 = 165.915 | POTE generator: ~11/10 = 165.915 | ||
{{Val list|legend=1| 94, 217, 311 }} | {{Val list|legend=1| 94, 217, 311 }} | ||
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== 13-limit == | == 13-limit == | ||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 1575/1573, 2080/2079, 4096/4095, 13720/13689 | Comma list: 1575/1573, 2080/2079, 4096/4095, 13720/13689 | ||
Mapping: [{{val| 1 2 12 -3 13 -1 }}, {{val| 0 -3 -70 42 -69 34 }}] | |||
POTE generator: ~11/10 = 165.914 | POTE generator: ~11/10 = 165.914 | ||
{{Val list|legend=1| 94, 217, 311, 839e, 1150e }} | {{Val list|legend=1| 94, 217, 311, 839e, 1150e }} | ||
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== 17-limit == | == 17-limit == | ||
Subgroup: 2.3.5.7.11.13.17 | |||
Comma list: 595/594, 833/832, 1156/1155, 1575/1573, 4096/4095 | Comma list: 595/594, 833/832, 1156/1155, 1575/1573, 4096/4095 | ||
Mapping: [{{val| 1 2 12 -3 13 -1 11 }}, {{val| 0 -3 -70 42 -69 34 -50 }}] | |||
POTE generator: ~11/10 = 165.913 | POTE generator: ~11/10 = 165.913 | ||
{{Val list|legend=1| 94, 217, 311, 839e, 1150eg }} | {{Val list|legend=1| 94, 217, 311, 839e, 1150eg }} | ||
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== 19-limit == | == 19-limit == | ||
Subgroup: 2.3.5.7.11.13.17.19 | |||
Comma list: 595/594, 833/832, 969/968, 1156/1155, 1216/1215, 1575/1573 | Comma list: 595/594, 833/832, 969/968, 1156/1155, 1216/1215, 1575/1573 | ||
Mapping: [{{val| 1 2 12 -3 13 -1 11 16 }}, {{val| 0 -3 -70 42 -69 34 -50 -85 }}] | |||
POTE generator: ~11/10 = 165.913 | POTE generator: ~11/10 = 165.913 | ||
{{Val list|legend=1| 94, 217, 311, 839e, 1150eg }} | {{Val list|legend=1| 94, 217, 311, 839e, 1150eg }} | ||
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== 23-limit == | == 23-limit == | ||
Subgroup: 2.3.5.7.11.13.17.19.23 | |||
Comma list: 595/594, 760/759, 833/832, 875/874, 969/968, 1105/1104, 1156/1155 | Comma list: 595/594, 760/759, 833/832, 875/874, 969/968, 1105/1104, 1156/1155 | ||
Mapping: [{{val| 1 2 12 -3 13 -1 11 16 16 }}, {{val| 0 -3 -70 42 -69 34 -50 -85 -83 }}] | |||
POTE generator: ~11/10 = 165.914 | POTE generator: ~11/10 = 165.914 | ||
{{Val list|legend=1| 94, 217, 311, 839ei, 1150egi }} | {{Val list|legend=1| 94, 217, 311, 839ei, 1150egi }} | ||
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= Semiluna = | = Semiluna = | ||
{{see also|Luna family #Semiluna}} | {{see also|Luna family #Semiluna}} | ||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 4802000/4782969, 95703125/95551488 | [[Comma list]]: 4802000/4782969, 95703125/95551488 | ||
[[Mapping]]: [{{val| 2 8 4 23 }}, {{val| 0 -15 2 -54 }}] | |||
[[POTE generator]]: ~2187/1960 = 193.1725 | [[POTE generator]]: ~2187/1960 = 193.1725 | ||
{{Val list|legend=1| 56d, 118, 292, 410 }} | {{Val list|legend=1| 56d, 118, 292, 410 }} | ||
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== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | |||
Comma list: 5632/5625, 9801/9800, 14641/14580 | Comma list: 5632/5625, 9801/9800, 14641/14580 | ||
Mapping: [{{val| 2 8 4 23 14 }}, {{val| 0 -15 2 -54 -22 }}] | |||
POTE generator: ~121/108 = 193.1732 | POTE generator: ~121/108 = 193.1732 | ||
{{Val list|legend=1| 56d, 118, 292, 410 }} | {{Val list|legend=1| 56d, 118, 292, 410 }} | ||