# 4L 2s

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 |