No-threes subgroup temperaments: Difference between revisions
→Tricesimoprimal miracloid: improve description |
documenting french decimal |
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Comma list: 1001/1000, 34420736/34328125, 5670699008/5661858125 | Comma list: 1001/1000, 34420736/34328125, 5670699008/5661858125 | ||
Mapping: [{{val| 1 1 20 -49 35 }}, {{val| 0 3 -39 119 -71 }}] | Sval Mapping: [{{val| 1 1 20 -49 35 }}, {{val| 0 3 -39 119 -71 }}] | ||
Optimal tuning (POTE): ~1664/1225 = 529.003¢ | Optimal tuning (POTE): ~1664/1225 = 529.003¢ | ||
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Subgroup: 2.5.7.11.13.17 | Subgroup: 2.5.7.11.13.17 | ||
Mapping: [{{val| 1 1 20 -49 35 42 }}, {{val| 0 3 -39 119 -71 -86 }}] | Sval Mapping: [{{val| 1 1 20 -49 35 42 }}, {{val| 0 3 -39 119 -71 -86 }}] | ||
Comma list: 1001/1000, 32768/32725, 147968/147875, 537824/537251 | Comma list: 1001/1000, 32768/32725, 147968/147875, 537824/537251 | ||
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Subgroup: 2.5.7.11.13.17.19 | Subgroup: 2.5.7.11.13.17.19 | ||
Mapping: [{{val| 1 1 20 -49 35 42 }}, {{val| 0 3 -39 119 -71 -86 }}] | Sval Mapping: [{{val| 1 1 20 -49 35 42 }}, {{val| 0 3 -39 119 -71 -86 }}] | ||
Comma list: 1001/1000, 2128/2125, 3328/3325, 16807/16796, 147968/147875 | Comma list: 1001/1000, 2128/2125, 3328/3325, 16807/16796, 147968/147875 | ||
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Comma list: 10241/10240, 5858783/5856400, 4093705/4090624, 15109493/15089800, 102942875/102834688 | Comma list: 10241/10240, 5858783/5856400, 4093705/4090624, 15109493/15089800, 102942875/102834688 | ||
Mapping: [{{val| 1 419 48 177 157 624 625 }}, {{val| 0 -461 -50 -192 -169 -685 -686 }}] | Sval Mapping: [{{val| 1 419 48 177 157 624 625 }}, {{val| 0 -461 -50 -192 -169 -685 -686 }}] | ||
Optimal tuning (CTE): ~58/31 = 1084.628 | Optimal tuning (CTE): ~58/31 = 1084.628 | ||
Vals: {{EDOs| 52, 1737, 1789 }}, ... | Vals: {{EDOs| 52, 1737, 1789 }}, ... | ||
== French decimal == | |||
Conceived upon the fact that 1789edo has an excellent 5/4, and uses it as the generator. This rings particularly true for the French attempts to decimalize a lot more things than we are used to today. Using the maximal evenness method of finding rank-2 temperaments, a 1525 & 1789 temperament is obtained. | |||
Subgroup: 2.5.7 | |||
Comma basis: 372 -159 -1 | |||
Sval mapping: [{{val| 1 2 54 -177 52}}, {{val|0 1 -159 -539 173}}] | |||
Optimal tuning (CTE): ~5/4 = 386.360 | |||
Vals: 205, 264, 469, 733, 997, 1261, 1525, 1789, ... | |||
=== 2.5.7.11 subgroup === | |||
Subgroup: 2.5.7.11 | |||
Comma basis: -49 8 17 -5, 45 -27 10 -3 | |||
Sval mapping: [{{val| 1 2 54 -177 52}}, {{val|0 1 -159 -539 173}}] | |||
Optimal tuning (CTE): ~5/4 = 386.361 | |||
Vals: 264, 733, ... | |||
=== 2.5.7.11.13 subgroup === | |||
Subgroup: 2.5.7.11.13 | |||
Comma basis: 28824005/28792192, 200126927/200000000, 6106906624/6103515625 | |||
Sval mapping: [{{val| 1 2 54 -177 52}}, {{val|0 1 -159 -539 173}}] | |||
Optimal tuning (CTE): ~5/4 = 386.361 | |||
Vals: 1525, 1789, ... | |||