Fractional-octave temperaments: Difference between revisions

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 Badness: 0.049316
-==== Oganesson ====
+==== Centenniamajor ====
-Named after the 118th element, since a simpler temperament was already named. 82 periods plus a generator correspond to [[13/8]].
+Named after the fact that 18 is the age of majority in most countries, and 100 (centennial) + 18 (major) = 118.
 Subgroup: 2.3.5.7.11
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 Badness: 0.122
+=== Oganesson ===
+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: 2.3.5.7.11.13
+Comma list: 4096/4095, 9801/9800, 537403776/537109375, 453874312332/453857421875
+Mapping: [{{val| 118 0 274 643 1094 499}}, {{val| 0 3 0 -5 -11 -1}}]
+Mapping generators: ~169/168, ~1124864/779625
+Optimal tuning (CTE): ~1124864/779625 = 634.009
+Vals: 354, 3776, ...
+=== 17-limit ===
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 4096/4095, 9801/9800, 34391/34375, 361250/361179, 562432/562275
+Mapping:  [{{val| 118 0 274 643 1094 499 607}}, {{val| 0 3 0 -5 -11 -1 2}}]
+Mapping generators: ~170/169, ~238/165
+Optimal tuning (CTE): ~238/165 = 634.008
+Vals: 354, 3776, ...
 [[Category:Temperament collections]]
 [[Category:Rank 2]]