4th-octave temperaments: Difference between revisions

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 There are nonetheless other less common temperaments which divide the octave in four.
-== Hunt 19-cycle or Saquadnu (rank-1) ==
-Associates [[19/16]] to one step of 4edo, and hence [[19/1|19th harmonic]] by octavation to 17 steps of 4edo.
-Subgroup: 2.19
+== Quad ==
+[[Subgroup]]: 2.3.5.7
-Comma list: 131072/130321
+[[Comma list]]: 9/8, 25/24
-{{Mapping|legend=2|4 17}}
+{{Mapping|legend=1| 4 6 9 0 | 0 0 0 1 }}
-: mapping generator: ~19/16 = 1\4
+{{Multival|legend=1|0 0 4 0 6 9}}
-Pure [[TE tuning]]: 299.927¢ = 1/4.00097 of the octave
+[[Optimal tuning]] ([[POTE]]): ~6/5 = 1\4, ~8/7 = 324.482
+{{Optimal ET sequence|legend=1| 4 }}
+[[Badness]]: 0.045911
-[[Support]]ing [[ET]]s: 4N, N = 1 to 60, largest: [[240edo|240]]
 == Berylic ==
 Berylic temperament tempers out the [[1874161/1874048]] comma in the 2.11.37 subgroup, representing the fact that [[44/37]] is a [[wikipedia:continued fraction|continued fraction]] convergent to the fourth root of 2.