5L 6s

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This pattern, with a generator between 2\11 (218.182 cents) and 1\5 (240), has multiple significant harmonic entropy minima, but they are all improper. The only saving grace for it is that is has harmonic entropy minima where the ratio between the large and small steps is optimal for melody, and that the generator for these scales is less than 6 cents flat of 8/7. The saving grace of the more lopsided scales is that a syntonic fifth is three generators up from the root.

1\5 240
9\46 234.783
17\87 234.483 Rodan is around here
8\41 234.146
15\77 233.766 Slendric is around here
7\36 233.333
13\67 232.836
6\31 232.258 Cynder/mothra is around here
11\57 231.579
5\26 230.769
9\47 229.787
228.944
4\21 228.571
227.75
11\58 227.586
29\153 227.451
76\401 227.431
47\248 227.419
18\95 227.368
7\37 227.027
3\16 225 Boundary of propriety

(smaller generators are proper)

223.692
8\43 223.256
21\113 223.009
55\296 222.973
89\479 222.9645
34\183 222.951
13\70 222.857
222.6765
5\27 222.222
7\38 221.035
9\49 220.408
11\60 220
13\71 219.718
15\82 219.512
17\93 219.355
2\11 218.182 Machine is around here