Squares: Difference between revisions
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{{Infobox | {{Infobox regtemp | ||
| Title = Skwares; Squares | | Title = Skwares; Squares | ||
| Subgroups = 2.3.7, 2.3.7.11, 2.3.5.7.11 | | 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) | | 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 = 14c | Edo join 2 = 17c | | Edo join 1 = 14c | Edo join 2 = 17c | ||
| | | Mapping = 1; -4 -16 -9 -10 | ||
| Generators = 9/7 | Generators tuning = 426.0 | Optimization method = CWE | |||
| MOS scales = [[3L 2s]], [[3L 5s]], [[3L 8s]], [[3L 11s]], [[14L 3s]] | | MOS scales = [[3L 2s]], [[3L 5s]], [[3L 8s]], [[3L 11s]], [[14L 3s]] | ||
| Pergen = (P8, P11/4) | | Pergen = (P8, P11/4) | ||
| Odd limit 1 = | | 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 | | 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]]. | 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]]. | ||