Fractional-octave temperaments: Difference between revisions
→Oganesson: formatting |
→118th-octave temperaments: complete the data; normalize generators, correct mapping format; style |
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== 118th-octave temperaments == | == 118th-octave temperaments == | ||
[[118edo | [[118edo]] is accurate for harmonics 3 and 5, so various 118th-octave temperaments actually make sense. | ||
=== Parakleischis === | === Parakleischis === | ||
118edo and its multiples are members of both [[parakleismic]] and [[Schismatic family|schismic]], and from this it derives its name. | |||
Subgroup: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
[[Comma list]]: 32805/32768, 1224440064/1220703125 | [[Comma list]]: 32805/32768, 1224440064/1220703125 | ||
[[Mapping]]: [{{val|118 187 274 0}}, {{val|0 0 0 1}}] | [[Mapping]]: [{{val| 118 187 274 0 }}, {{val| 0 0 0 1 }}] | ||
[[POTE | Mapping generators: ~15625/15552, ~7 | ||
[[Optimal tuning]] ([[POTE]]): ~7/4 = 968.7235 | |||
{{Val list|legend=1| 118, 236, 354, 472, 2242, 2714b, 3186b, 3658b }} | {{Val list|legend=1| 118, 236, 354, 472, 2242, 2714b, 3186b, 3658b }} | ||
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Comma list: 9801/9800, 32805/32768, 137781/137500 | Comma list: 9801/9800, 32805/32768, 137781/137500 | ||
Mapping: [{{val|118 187 274 0 77}}, {{val|0 0 0 1 1}}] | Mapping: [{{val| 118 187 274 0 77 }}, {{val| 0 0 0 1 1 }}] | ||
POTE | Optimal tuning (POTE): ~7/4 = 968.5117 | ||
Vals: {{Val list| 118, 354, 472 }} | Vals: {{Val list| 118, 354, 472 }} | ||
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Badness: 0.049316 | Badness: 0.049316 | ||
=== Oganesson === | ==== Oganesson ==== | ||
Named after the 118th element, since a simpler temperament was already named. 82 periods plus a generator correspond to [[13/8]]. | Named after the 118th element, since a simpler temperament was already named. 82 periods plus a generator correspond to [[13/8]]. | ||
Subgroup: 2.3.5.7.11 | |||
Comma list: 32805/32768, 151263/151250, 1224440064/1220703125 | |||
Mapping: [{{val| 118 187 274 0 -420 }}, {{val| 0 0 0 2 5 }}] | |||
Mapping generators: ~15625/15552, ~405504/153125 | |||
Optimal tuning (CTE): ~202752/153125 = 484.4837 | |||
Optimal GPV sequence: {{val list| 354, 944e, 1298 }} | |||
Badness: 0.357 | |||
===== 13-limit ===== | |||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
Comma list: 1716/1715, 34398/34375 | Comma list: 1716/1715, 32805/32768, 34398/34375, 384912/384475 | ||
Mapping: [{{val| 118 187 274 0 -420 271 }}, {{val| 0 0 0 2 5 1 }}] | |||
Optimal tuning (CTE): ~8125/6144 = 484.4867 | |||
Optimal GPV sequence: {{val list| 354, 944e, 1298 }} | |||
Badness: 0.122 | |||
[[Category:Temperament collections]] | [[Category:Temperament collections]] | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||