No-threes subgroup temperaments: Difference between revisions

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 [[Badness]] (Sintel): 0.386
+=== Berylic ===
+Berylic tempers out the [[berylisma]] in the 2.11.37 subgroup, representing the fact that [[44/37]] is a {{w|continued fraction}} convergent to 2<sup>1/4</sup> the fourth root of 2. Beryllic is an example of a temperament which has an astronomically low [[badness]], being a very high-accuracy [[microtemperament]] with low-to-average [[complexity]] for the harmonics in its [[subgroup]]. This also makes it simultaneously supported by edo systems as low as [[16edo]] and up into the tens of thousands. The tradeoff with this temperament, not captured within the metric of badness, is that it is defined within an obscure subgroup, 2.11.37.
+If one wishes to explore harmony in this temperament, a great way is to use the 8-note [[4L 4s]] [[mos]], and use the [[32:37:44]] triad and its inversion [[296:352:407|1/(44:37:32)]] as the root chords. However, the consonance of the 37th harmonic is questionable.
+[[Subgroup]]: 2.11.37
+[[Comma list]]: 1874161/1874048
+{{Mapping|legend=2| 4 0 7 | 0 1 1 }}
+: mapping generators: ~44/37, ~11
+[[Optimal tuning]]s:
+* [[WE]]: ~44/37 = 300.0003{{c}}, ~11/8 = 551.3211{{c}}
+: [[error map]]: {{val| +0.001 +0.007 -0.017 }}
+* [[CWE]]: ~44/37 = 300.0000{{c}}, ~11/8 = 551.3237{{c}}
+: error map: {{val| 0.000 +0.006 -0.020 }}
+{{Optimal ET sequence|legend=1| 4, 16, 20, 24, 76, 100, 124, 148, 616, 764, 912, 1060, 3328, 4388, 5448 }}
+[[Badness]] (Sintel): 0.00188
 === Mavericks ===