The Jacobins: Difference between revisions

Cmloegcmluin (talk | contribs)
"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
Eliora (talk | contribs)
silicon to 14th octave temperaments per new system of organizing fractional-octave temperaments
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{{Optimal ET sequence|legend=1|31f, 91d, 1789, 3669}}, ...
{{Optimal ET sequence|legend=1|31f, 91d, 1789, 3669}}, ...
== Silicon ==
While 14edo is poor in simple harmonics, some of its multiples (such as [[224edo]] and [[742edo]]) are members of zeta edo list. The name of silicon temperament comes from the 14th element. Defined upwards to the 13-limit. When tuned in 742edo, it is generated by a [[53edo]] fifth intermingled with [[14edo]] periods.
[[Subgroup]]: 2.3.5.7
[[Comma list]]: 14348907/14336000, 56358560858112/56296884765625
[[Mapping]]: [{{val| 14 0 -145 239 }}, {{val| 0 1 8 -9 }}]
Mapping generators: ~6125/5832, ~3
[[Optimal tuning]] ([[CTE]]): ~3/2 = 701.870
{{Optimal ET sequence|legend=1| 224, 518, 742, 966, 1708, 2674 }}
[[Badness]]: 0.196
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 1240029/1239040, 2359296/2358125
Mapping: [{{val| 14 0 -145 239 115 }}, {{val| 0 1 8 -9 -3 }}]
Optimal tuning (CTE): ~3/2 = 701.872
{{Optimal ET sequence|legend=1| 224, 518, 742, 966, 1708, 4382e }}
Badness: 0.0450
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 4096/4095, 6656/6655, 9801/9800, 24192/24167
Mapping: [{{val| 14 0 -145 239 115 74 }}, {{val| 0 1 8 -9 -3 -1 }}]
Optimal tuning (CTE): ~3/2 = 701.8733
{{Optimal ET sequence|legend=1| 224, 518, 742, 966, 1708f }}
Badness: 0.0269
[[Category:Commatic realms]]
[[Category:Commatic realms]]
[[Category:Jacobin]]
[[Category:Jacobin]]