# 4L 4s

The minimum harmonic entropy scale with this MOS pattern is diminished[8], basically the familiar octatonic scale of 12edo.

There are 4 different near-MOSes such that multiples of the period are the only generic intervals with more than two specific representatives: LLsLsLss, LLsLssLs, LLssLLss, LLssLsLs. However, none are strictly proper in 12edo. (They are only proper if the generator is larger than 100 cents, which unfortunately is the wrong direction for good diminished tunings.)

Generator | Cents | Comments | ||||
---|---|---|---|---|---|---|

0\4 | 0 | |||||

1\24 | 50 | |||||

1\20 | 60 | L/s = 4 | ||||

300/(1+pi) | ||||||

1\16 | 75 | L/s = 3 | ||||

300/(1+e) | ||||||

3\44 | 81.82 | |||||

2\28 | 85.71 | |||||

1\12 | 100 | Diminished is around here
Optimum rank range (L/s=2/1) for MOS | ||||

300/(1+sqrt(3)) | ||||||

3\32 | 112.5 | |||||

5\52 | 115.38 | Golden diminished | ||||

300/(1+pi/2) | ||||||

2\20 | 120 | |||||

3\28 | 128.57 | |||||

4\36 | 133.33 | |||||

1\8 | 150 |