20th-octave temperaments: Difference between revisions
okay I'll fill in the lower limit versions of calcium later once I have time since I have school, the remarkable fact is how high it goes |
→Calcium: added more calcium dimensions |
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==Calcium== | ==Calcium== | ||
A highly precise and high-limit 2000 & 2460 temperament, named after the 20th element following the convention of naming some fractional-octave temperaments after chemical elements. | A highly precise and high-limit 2000 & 2460 temperament, named after the 20th element following the convention of naming some fractional-octave temperaments after chemical elements. | ||
=== 17-limit === | |||
Subgroup: 2.3.5.7.11.13.17 | |||
Comma list: 9801/9800, 12376/12375, 37180/37179, 123201/123200, 903168/903125 | |||
Mapping: [{{val|20 3 12 -73 -37 8 10 62}}, {{val|0 10 12 45 37 23 25 8}}] | |||
Mapping generators: ~88/85, ~243/220 | |||
Optimal tuning (CTE): ~243/220 = 172.196 | |||
=== 19-limit === | |||
Subgroup: 2.3.5.7.11.13.17.19 | |||
Comma list: 9801/9800, 12376/12375, 89376/89375, 104976/104975, 123201/123200, 1549184/1549125 | |||
Mapping: [{{val|20 3 12 -73 -37 8 10 62}}, {{val|0 10 12 45 37 23 25 8}}] | |||
Mapping generators: ~88/85, ~169/153 | |||
Optimal tuning (CTE): ~169/153 = 172.196 | |||
Vals: 460, 2000, 2460 | |||
===23-limit=== | ===23-limit=== | ||
Subgroup: 2.3.5.7.11.13.17.19.23 | Subgroup: 2.3.5.7.11.13.17.19.23 | ||
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Mapping: [{{val|20 3 12 -73 -37 8 10 62 145}}, {{val|0 10 12 45 37 23 25 8 -19}}] | Mapping: [{{val|20 3 12 -73 -37 8 10 62 145}}, {{val|0 10 12 45 37 23 25 8 -19}}] | ||
Mapping generators: ~88/85, ~11875/10752 | Mapping generators: ~88/85, ~11875/10752 | ||