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Rastmic rank three clan: Difference between revisions

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=== 7-limit ===
=== 7-limit ===
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 33075/32768
[[Comma list]]: 33075/32768


[[Mapping]]: [{{val| 1 1 0 6 }}, {{val| 0 2 0 -3 }}, {{val| 0 0 1 -1 }}]
{{Mapping|legend=1| 1 1 0 6 | 0 2 0 -3 | 0 0 1 -1 }}


Mapping generators: ~2, ~128/105, ~5
: mapping generators: ~2, ~128/105, ~5


[[POTE generator]]s: ~128/105 = 350.1375, ~5/4 = 383.8665
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~128/105 = 350.1375, ~5/4 = 383.8665


{{Optimal ET sequence|legend=1| 17, 21, 24, 31, 41, 72, 281d }}
{{Optimal ET sequence|legend=1| 17, 21, 24, 31, 41, 72, 281d }}
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=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 243/242, 385/384
[[Comma list]]: 243/242, 385/384


[[Mapping]]: [{{val| 1 1 0 6 2 }}, {{val| 0 2 0 -3 5 }}, {{val| 0 0 1 -1 0 }}]
{{Mapping|legend=1| 1 1 0 6 2 | 0 2 0 -3 5 | 0 0 1 -1 0 }}


[[POTE generator]]s: ~11/9 = 349.9554, ~5/4 = 384.1048
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/9 = 349.9554, ~5/4 = 384.1048


{{Optimal ET sequence|legend=1| 17, 24, 31, 41, 72, 312bd, 384bcd, 456bcde, 528bcde, 631bcde }}
{{Optimal ET sequence|legend=1| 17, 24, 31, 41, 72, 312bd, 384bcd, 456bcde, 528bcde, 631bcde }}
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== Parahemif ==
== Parahemif ==
=== 7-limit ===
=== 7-limit ===
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 1605632/1594323
[[Comma list]]: 1605632/1594323


[[Mapping]]: [{{val| 1 1 0 -1 }}, {{val| 0 2 0 13 }}, {{val| 0 0 1 0 }}]
{{Mapping|legend=1| 1 1 0 -1 | 0 2 0 13 | 0 0 1 0 }}


Mapping generators: ~2, ~896/729, ~5
: mapping generators: ~2, ~896/729, ~5


[[POTE generator]]s: ~896/729 = 351.4846, ~5/4 = 386.9396
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~896/729 = 351.4846, ~5/4 = 386.9396


{{Optimal ET sequence|legend=1| 17c, 24, 34d, 41, 58, 99, 239, 338 }}
{{Optimal ET sequence|legend=1| 17c, 24, 34d, 41, 58, 99, 239, 338 }}
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=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 243/242, 896/891
[[Comma list]]: 243/242, 896/891


[[Mapping]]: [{{val| 1 1 0 -1 2 }}, {{val| 0 2 0 13 5 }}, {{val| 0 0 1 0 0 }}]
{{Mapping|legend=1| 1 1 0 -1 2 | 0 2 0 13 5 | 0 0 1 0 0 }}


[[POTE generator]]s: ~11/9 = 351.5347, ~5/4 = 388.0217
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/9 = 351.5347, ~5/4 = 388.0217


{{Optimal ET sequence|legend=1| 17c, 24, 34d, 41, 58, 99e }} *
{{Optimal ET sequence|legend=1| 17c, 24, 34d, 41, 58, 99e }} *
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Comma list: 144/143, 243/242, 364/363
Comma list: 144/143, 243/242, 364/363


Mapping: [{{val| 1 1 0 -1 2 4 }}, {{val| 0 2 0 13 5 -1 }}, {{val| 0 0 1 0 0 0 }}]
Mapping: {{mapping| 1 1 0 -1 2 4 | 0 2 0 13 5 -1 | 0 0 1 0 0 0 }}


POTE generators: ~11/9 = 351.6908, ~5/4 = 389.1892
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 351.6908, ~5/4 = 389.1892


{{Optimal ET sequence|legend=1| 17c, 24, 34d, 41, 58, 99ef, 157eff, 290cdeeefff }}
{{Optimal ET sequence|legend=1| 17c, 24, 34d, 41, 58, 99ef, 157eff, 290cdeeefff }}
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[[Category:Temperament clans]]
[[Category:Temperament clans]]
[[Category:Rastmic rank-3 clan| ]] <!-- main article -->
[[Category:Rastmic rank-3 clan| ]] <!-- main article -->
[[Category:Rastmic| ]] <!-- key article -->
[[Category:Rank 3]]
[[Category:Rank 3]]
Retrieved from "https://en.xen.wiki/w/Rastmic_rank_three_clan"