Squares: Difference between revisions

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{{Infobox Regtemp

| Title = Skwares; Squares

| Subgroups = 2.3.7, 2.3.7.11, 2.3.5.7.11

| Comma basis = [[19683/19208]] (2.3.7); <br> [[99/98]], [[243/242]] (2.3.7.11); <br> [[81/80]], [[99/98]], [[121/120]] (11-limit)

| Edo join 1 = 31 | Edo join 2 = 45

| Generator = 9/7 | Generator tuning = 426.0 | Optimization method = CWE

| MOS scales = [[3L 2s]], [[3L 5s]], [[3L 8s]], [[3L 11s]], [[14L 3s]]

| Mapping = 1; -4 -16 -9 -10

| Pergen = (P8, P11/4)

| Odd limit 1 = (2.3.7) 7 | Mistuning 1 = 4.7 | Complexity 1 = 11

| Odd limit 2 = 11 | Mistuning 2 = 10.8 | Complexity 2 = 17

}}

At its most basic level, '''squares''' can be thought of as a [[2.3.7 subgroup|2.3.7-subgroup]] temperament (sometimes called ''skwares''), generated by a flat [[~]][[9/7]] such that four of them stack to the perfect eleventh, [[8/3]], therefore [[tempering out]] the comma [[19683/19208]]. However, it is more natural to think of the temperament first as [[2.3.7.11 subgroup]], tempering out [[99/98]] so as to identify the generator with [[14/11]] in addition to 9/7 and so that two generators stack to the undecimal neutral sixth, [[18/11]], two of which are then identified with 8/3 due to tempering out [[243/242]]. This can also be thought of as an octavization of the 3.7.11-subgroup [[mintaka]] temperament by identifying [[2/1]] with a false octave corresponding to 99/49~243/121, in a manner similar to [[sensi]]'s relation to [[BPS]].

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+{{Infobox Regtemp
+| Title = Skwares;&nbsp;Squares
+| Subgroups = 2.3.7, 2.3.7.11, 2.3.5.7.11
+| Comma basis = [[19683/19208]] (2.3.7); <br> [[99/98]], [[243/242]] (2.3.7.11); <br> [[81/80]], [[99/98]], [[121/120]] (11-limit)
+| Edo join 1 = 31 | Edo join 2 = 45
+| Generator = 9/7 | Generator tuning = 426.0 | Optimization method = CWE
+| MOS scales = [[3L 2s]], [[3L 5s]], [[3L 8s]], [[3L 11s]], [[14L 3s]]
+| Mapping = 1; -4 -16 -9 -10
+| Pergen = (P8, P11/4)
+| Odd limit 1 = (2.3.7) 7 | Mistuning 1 = 4.7 | Complexity 1 = 11
+| Odd limit 2 = 11 | Mistuning 2 = 10.8 | Complexity 2 = 17
+}}
 At its most basic level, '''squares''' can be thought of as a [[2.3.7 subgroup|2.3.7-subgroup]] temperament (sometimes called ''skwares''), generated by a flat [[~]][[9/7]] such that four of them stack to the perfect eleventh, [[8/3]], therefore [[tempering out]] the comma [[19683/19208]]. However, it is more natural to think of the temperament first as [[2.3.7.11 subgroup]], tempering out [[99/98]] so as to identify the generator with [[14/11]] in addition to 9/7 and so that two generators stack to the undecimal neutral sixth, [[18/11]], two of which are then identified with 8/3 due to tempering out [[243/242]]. This can also be thought of as an octavization of the 3.7.11-subgroup [[mintaka]] temperament by identifying [[2/1]] with a false octave corresponding to 99/49~243/121, in a manner similar to [[sensi]]'s relation to [[BPS]].