4L 2s

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There are three scales with this MOS pattern that are significant minima of harmonic entropy.

The first is antikythera, or no-3's 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 decimal, in which two generators make a 4/3, and the third is Doublewide, in which the generator is 7/6 so the period minus the generator is 6/5.

In addition to the true MOS with pattern LLsLLs, all these scales also come in a near-MOS version, LLLsLs, in which the period is the only generic interval that has more than two specific representatives. The true MOS is always proper, but the near-MOS is only proper if the generator is smaller than 2\10 of an octave (240 cents).

Generator Cents Comments
1\6 200
6\34 211.76
5\28 214.29 Antikythera is around here
4\22 218.18
3\16 225
227.56
8\42 228.57
600/(1+phi) Golden lemba
13\68 229.41
5\26 230.77
232.8
7\36 233.33 Lemba is around here
2\10 240 Boundary of propriety for near-MOS

Optimum rank range (L/s=2/1) for MOS

5\24 250 Decimal is around here
251.89
8\38 252.63
253.39 L/s = e
3\14 257.14 L/s = 3
258.81 L/s = pi
4\18 266.67 L/s = 4
5\22 272.73
6\26 276.92
7\30 280
8\34 282.35
9\38 284.21
10\42 285.71
11\46 286.96 Doublewide is around here
1\4 300