4L 2s: Difference between revisions

4L 2s can be seen as a [[Warped diatonic|warped diatonic scale]], where one large step of diatonic (5L 2s) is removed, or as the equal-tempered whole-tone scale ([[6edo]]), but with two "whole tones" that are smaller than the others.

Scales with the true MOS pattern are always [[Rothenberg propriety|proper]], because there is only one small step per period. In addition, there are near-MOS patterns, such as LLLsLs, in which the period is the only generic interval that has more than two specific representatives. The near-MOS is only proper if the generator is smaller than 2\10 of an octave (240 cents).

== Name==

==Theory==

===Low harmonic entropy scales===

There are three scales with this [[MOSScales|MOS]] pattern that are significant minima of harmonic entropy. The first is [[antikythera]], or no-3's [[Diaschismic_family|srutal/pajara]], which is srutal/pajara without any intervals containing 3 in their prime factorization, so it becomes a 2.5.9 or 2.5.7.9 subgroup temperament. This means that the generator is twice that of srutal/pajara (210-220 cents rather than 105-110), since odd numbers of generators are only needed for intervals with 3. So this is a basically "whole tone" scale, but made uneven so some 2-step intervals are 5/4 and others are 9/7.

The second is [[Dicot_family|decimal]], in which two generators make a 4/3, and the third is [[Jubilismic_clan|Doublewide]], in which the generator is 7/6 so the period minus the generator is 6/5.