Fractional-octave temperaments: Difference between revisions
→Oganesson: naming a temp oganesson that I originally intended but couldn't voice clearly due to nonverbality issues that I have, the extension of parakleischis given the name centenniamajor |
→Oganesson: completion |
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Named after the 118th element. In the 13-limit, the period corresponds to [[169/168]], and in the 17-limit, it corresponds also to [[170/169]], meaning that 28561/28560 is tempered out. As opposed to being an extension of parakleischis, this has the generator that splits the third harmonic into three equal parts. | Named after the 118th element. In the 13-limit, the period corresponds to [[169/168]], and in the 17-limit, it corresponds also to [[170/169]], meaning that 28561/28560 is tempered out. As opposed to being an extension of parakleischis, this has the generator that splits the third harmonic into three equal parts. | ||
[[Subgroup]]: 2.3.5.7 | |||
[[Comma list]]: {{monzo| 30 10 -27 6 }}, {{monzo| 77 -20 -5 -12 }} | |||
[[Mapping]]: [{{val| 118 0 274 643 }}, {{val| 0 3 0 -5 }}] | |||
Mapping generators: ~2097152/2083725, ~1953125/1354752 | |||
[[Optimal tuning]] ([[CTE]]): ~1953125/1354752 = 634.0068 | |||
{{Val list|legend=1| 354, 2360, 2714, 3068, 3442, 3776, 7198cd, 10974bccdd }} | |||
[[Badness]]: 2.66 | |||
==== 11-limit ==== | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 9801/9800, {{monzo| 13 -1 4 -16 7 }}, {{monzo| 55 -7 -15 -2 -1 }} | |||
Mapping: [{{val| 118 0 274 643 1094 }}, {{val| 0 3 0 -5 -11 }}] | |||
Optimal tuning (CTE): ~1953125/1354752 = 634.0085 | |||
{{Val list|legend=1| 354, 3068e, 3442, 3776, 11682ccdde }} | |||
Badness: 0.568 | |||
==== 13-limit ==== | |||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Mapping generators: ~169/168, ~1124864/779625 | Mapping generators: ~169/168, ~1124864/779625 | ||
Optimal tuning (CTE): ~1124864/779625 = 634. | Optimal tuning (CTE): ~1124864/779625 = 634.0087 | ||
{{Val list|legend=1| 354, 3068e, 3422, 3776 }} | |||
Badness: 0.172 | |||
=== 17-limit === | === 17-limit === | ||