3.5.11 subgroup: Difference between revisions
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== Temperaments == | == Temperaments == | ||
=== Equal temperaments === | === Equal temperaments === | ||
In the [[3.5.7 subgroup]], [[13edt]] is extremely good for its size, and in the [[3.7.11 subgroup]], [[22edt]] is even more good for its size. In contrast, the 3.5.11 subgroup does not have any outstanding very small EDTs like this. Some EDTs that do relatively well in the 3.5.11 subgroup are [[11edt]], [[17edt]], [[28edt]], [[32edt]], [[60edt]] and [[71edt]]. [[11edt]] is a simple but low-accuracy system with a decent [[11/9]] but with [[5/3]] flat by 19.8 cents. The 11-form is important to several of the rank-2 temperaments in this subgroup, which is interesting since 11edt is stretched [[7edo]], so | In the [[3.5.7 subgroup]], [[13edt]] is extremely good for its size, and in the [[3.7.11 subgroup]], [[22edt]] is even more good for its size. In contrast, the 3.5.11 subgroup does not have any outstanding very small EDTs like this. Some EDTs that do relatively well in the 3.5.11 subgroup are [[11edt]], [[17edt]], [[28edt]], [[32edt]], [[60edt]] and [[71edt]]. [[11edt]] is a simple but low-accuracy system with a decent [[11/9]] but with [[5/3]] flat by 19.8 cents. The 11-form is important to several of the rank-2 temperaments in this subgroup, which is interesting since 11edt is stretched [[7edo]], so those temperaments have [[MOS scale]]s which are diatonic-like in terms of melodic properties and interval classification, but not harmonic properties. [[28edt]] is a good smaller option and might be considered as an analog of [[12edo]], with a nearly-pure [[5/3]] but [[11/9]] off by 11.4 cents. [[71edt]] is excellent accuracy for its size (being the lowest in Sintel [[badness]]) and gives [[microtempering]] on this subgroup with errors under a cent, but is obviously quite large. | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||