80th-octave temperaments: Difference between revisions
Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
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== Mercury == | == Mercury == | ||
Named after the 80th element, defined as the 320 & 2000 temperament. 7 periods are mapped to ~[[17/16]], 11 periods are mapped to ~[[11/10]]. | Named after the 80th element, defined as the 320 & 2000 temperament. 7 periods are mapped to ~[[17/16]], 11 periods are mapped to ~[[11/10]]. | ||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 9801/9800, 67392/67375, 1399680/1399489, {{monzo|14 -8 -8 5 2 -1}} | |||
{{mapping|legend=1| 80 3 161 -23 252 197 | 0 5 1 10 1 4 }} | |||
Mapping generators: ~9295/9216, ~2304/1859 | |||
Optimal tuning (CTE): ~2304/1859 = 371.385 | |||
{{Optimal ET sequence|legend=1|320, 2000, 4320}} | |||
=== 17-limit === | |||
Subgroup: 2.3.5.7.11.13.17 | |||
Comma list: 9801/9800, 12376/12375, 67392/67375, 4230144/4229225, 494534656/494515125 | |||
{{mapping|legend=1| 80 3 161 -23 252 197 327 | 0 5 1 10 1 4 0 }} | |||
Mapping generators: ~459/455, ~1859/1500 | |||
Optimal tuning (CTE): ~2275/1836 = 371.386 | |||
{{Optimal ET sequence|legend=1|320, 2000, 4320}} | |||
=== 19-limit === | === 19-limit === | ||
Subgroup: 2.3.5.7.11.13.17.19 | Subgroup: 2.3.5.7.11.13.17.19 | ||
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Mapping: [{{val|80 3 161 -23 252 197 327 117}}, {{val|0 5 1 10 1 4 0 9}}] | Mapping: [{{val|80 3 161 -23 252 197 327 117}}, {{val|0 5 1 10 1 4 0 9}}] | ||
Mapping generators: ~459/455, ~2275/1836 | Mapping generators: ~459/455, ~2275/1836 | ||
Optimal tuning (CTE): ~2275/1836 = 371.386 | Optimal tuning (CTE): ~2275/1836 = 371.386 | ||