2L 8s

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This is the MOS pattern of the decatonic scale of Paul Erlich and others.

The only significant harmonic entropy minimum that is proper is the decatonic scale itself (pajara[10]), in which the period is 7/5~10/7 (tempered to be the same interval), one generator down from that makes 4/3, and another generator down makes 5/4. More than a few people think this is a beautiful scale that deserves a lot of investigation and use, with some going so far as to say it's the next step up from the diatonic scale that preserves the most desirable features of diatonic melody and harmony. Paul Erlich's original paper on this scale can be found at either of these links:

http://sethares.engr.wisc.edu/paperspdf/Erlich-22.pdf

http://www.lumma.org/tuning/erlich/

Improper harmonic entropy minima include injera (which is similar to pajara except that 5/4 is now four generators up and no periods) and shrutar (which is basically pajara with the generator divided in two).

In addition to the true MOS form, LssssLssss, these scales also exist in a near-MOS form, LsssssLsss, in which the period is the only interval class with more than two flavors. In the case of the decatonic scale, LssssLssss is called the "symmetric" scale and LsssssLsss is called the "pentachordal" scale (because it has two identical "pentachords" in the same way that the diatonic scale has two identical tetrachords).

Generator Cents Comments
0\2 0
1\26 46.15
1\24 50
2\46 52.17 Shrutar is around here
1\22 54.55
1\20 60
1\18 66.67
1\16 75 L/s = 4
600/(4+pi)
1\14 85.71 L/s = 3
600/(4+e)
2\26 92.31
5\64 93.75
13\166 93.98
21\268 94.03 Golden decatonic (Injera [bad tuning])
8\102 94.12
3\38 94.74
4\50 96 Injera is around here
5\62 96.77
1\12 100 Boundary of propriety (generators

larger than this are proper)

4\46 104.35
600/(4+sqrt(3))
3\34 105.88
8\90 106.67 around here 8g=18/11
21\236 106.78
34\382 106.81 Golden decatonic (Srutal/pajara)
13\146 106.85
5\56 107.14 Srutal/pajara decatonic is around here
600/(4+pi/2)
2\22 109.09 Optimum rank range (L/s=3/2) decatonic
3\32 112.5
4\42 114.29
5\52 115.385
6\62 116.13
7\72 116.67
8\82 117.07
1\10 120