4L 8s

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This is the minor chromatic scale of Diminished temperament. Its period of 300¢ (~6:5) is divided into L s s, making a universally proper scale, but the harmonic entropy minimum for it is not particularly low.

0/4 0
1/28 42.857
6/164 43.902
5/136 44.118
4/108 44.449
3/80 45
2/52 46.154
3/76 47.368
4/100 48
5/124 48.387
6/148 48.649
7/172 48.837
8/196 48.98
9/220 49.091
1/24 50
5/116 51.724
4/92 52.174
3/68 52.941
2/44 54.5455
5/108 55.556
3/64 56.25
4/84 57.143
5/104 57.692
6/124 58.0645
7/144 58.333
8/164 58.537
9/184 58.696
10/204 58.8235
11/224 58.929
12/244 59.016
300/(2+pi)
1/20 60
300/(2+e)
7/136 61.765
6/116 62.069
5/96 62.5
4/76 63.158
3/56 64.286
300/(3+phi)
5/92 65.217
2/36 66.667
7/124 67.742
5/88 68.182
3/52 69.4615
4/68 70.588
5/84 71.429
6/100 72
7/116 72.414
8/132 72.727
9/148 72.973
10/164 73.146
11/180 73.333
12/196 73.49
13/212 73.585
14/228 73.684
15/244 73.7705
16/260 73.864
17/276 73.913
18/292 73.973
19/308 74.026
1/16 75
10/156 76.923
9/140 77.143
8/124 77.419
7/108 77.778
6/92 78.261
5/76 78.947
9/136 79.412
4/60 80
300/(2+sqrt(3))
7/104 80.769
3/44 81.818
8/116 82.759
300/(2+hpi)
5/72 83.333
300/(2+pi/2)
12/172 83.721
7/100 84
2/28 85.714
11/152 86.842
9/124 87.097
7/96 87.5
5/68 88.235
8/108 88.889
11/148 89.096
3/40 90
7/92 91.304
4/52 92.308
1/12 100