No-fives subgroup temperaments: Difference between revisions
→Hectosaros leap week: Remove a period and an "and" particle from comma lists. |
+"sematology", +"reversed meantone", +"reversed mavila" |
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== Reversed meantone == | == Reversed meantone == | ||
{{ | {{Main| Reversed meantone }} | ||
Subgroup: 2.3.41 | Subgroup: 2.3.41 | ||
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{{Val list|legend=1| 5, 12, 17 }} | {{Val list|legend=1| 5, 12, 17 }} | ||
=== 2.3.7.41 subgroup === | |||
Subgroup: 2.3.7.41 | |||
[[Comma list]]: 64/63, 82/81 | |||
[[Gencom]]: [2 4/3; 64/63 82/81] | |||
[[Mapping|Sval mapping]]: [{{val| 1 2 2 7 }}, {{val| 0 -1 2 -4 }}] | |||
[[POTE generator]]: ~4/3 = 490.0323 | |||
[[TOP tuning|TOP generator]]s: ~2 = 1197.2342, ~4/3 = 488.9029 | |||
[[Optimal GPV sequence]]: {{Val list| 5, 12, 17, 22, 49 }} | |||
=== 2.3.7.11.41 subgroup === | |||
Subgroup: 2.3.7.11.41 | |||
[[Comma list]]: 64/63, 82/81, 99/98 | |||
[[Gencom]]: [2 4/3; 64/63 82/81 99/98] | |||
[[Mapping|Sval mapping]]: [{{val| 1 2 2 1 7 }}, {{val| 0 -1 2 6 -4 }}] | |||
[[POTE generator]]: ~4/3 = 492.1787 | |||
[[TOP tuning|TOP generator]]s: ~2 = 1197.9683, ~4/3 = 491.3454 | |||
[[Optimal GPV sequence]]: {{Val list| 5, 12, 17, 22, 39d }} | |||
== Magi == | == Magi == | ||
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Comma list: {{monzo|-42 -2 -5 16}}, {{monzo|10 -46 29 -5}} | Comma list: {{monzo|-42 -2 -5 16}}, {{monzo|10 -46 29 -5}} | ||
Mapping: [ | Mapping: [{{val|1 313 532 208}}, {{val|0 -439 -746 -288}}] | ||
Optimal tuning (CTE): ~1235079060111/755603996672 = 851.248 | Optimal tuning (CTE): ~1235079060111/755603996672 = 851.248 | ||
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Optimal tuning (CTE): ~6144/3757 = 851.248 | Optimal tuning (CTE): ~6144/3757 = 851.248 | ||
== Sematology == | |||
This temperament tempers out 4107/4096 and thus equates 2 [[37/32]]'s with [[4/3]]. | |||
[[Subgroup]]: 2.3.37 | |||
[[Comma list]]: 4107/4096 | |||
[[Gencom]]: [2 37/32; 4107/4096] | |||
[[Mapping]]: [{{val|1 1 5}}, {{val|0 -2 1}}] | |||
[[POTE generator]]: ~[[37/32]] = 249.075 | |||
=== 2.3.7.37 subgroup === | |||
[[Subgroup]]: 2.3.7.37 | |||
[[Comma list]]: 4107/4096, 259/256 | |||
[[Gencom]]: [2 37/32; 4107/4096 259/256] | |||
[[Mapping]]: [{{val|1 1 1 5}}, {{val|0 -2 -1 1}}] | |||
[[POTE generator]]: ~[[37/32]] = 247.782 | |||
=== 2.3.5.37 subgroup === | |||
It is difficult to extend sematology to include 5, due the 5th harmonic being quite high-complexity. | |||
[[Subgroup]]: 2.3.5.37 | |||
[[Comma list]]: 4107/4096, 17592186044416/17562397269605 | |||
[[Gencom]]: [2 37/32; 4107/4096 17592186044416/17562397269605] | |||
[[Mapping]]: [{{val|1 1 4 5}}, {{val|0 -2 -8 1}}] | |||
[[POTE generator]]: ~[[37/32]] = 251.393 | |||
=== 2.3.5.7.37 subgroup === | |||
[[Subgroup]]: 2.3.5.7.37 | |||
[[Comma list]]: 4107/4096, 17592186044416/17562397269605, 259/256 | |||
[[Gencom]]: [2 37/32; 4107/4096 17592186044416/17562397269605 259/256] | |||
[[Mapping]]: [{{val|1 1 4 1 5}}, {{val|0 -2 -8 -1 1}}] | |||
[[POTE generator]]: ~[[37/32]] = 251.204 | |||
== Reversed mavila == | |||
[[Subgroup]]: 2.3.37 | |||
[[Comma list]]: 81/74 | |||
[[Gencom]]: [2 4/3; 81/74] | |||
[[Mapping]]: [{{val|1 1 0}}, {{val|0 -1 12}}] | |||
[[POTE generator]]: ~4/3 = 521.397 | |||
[[Category:Temperament collections]] | [[Category:Temperament collections]] | ||
[[Category:Subgroup temperaments]] | [[Category:Subgroup temperaments]] | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||