4L 4s

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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