7L 5s

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This is the MOS pattern of the meantone chromatic scale, which is the only notable harmonic entropy minimum in this range of possible scales. In meantone, "diatonic" semitones (~16/15), such as appear in the diatonic scale, for example B-C, are larger than "chromatic" semitones (~25/24), the intervals by which flats and sharps alter pitches.

The meantone chromatic scale is proper.

Generator in cents Comments
3\7 514.286
20\47 510.638
17\40 510
31\73 509.589
14\33 509.091
39\92 508.696
25\59 508.475
36\85 508.235
507.934 L/s = pi
11\26 507.692 Flattone
41\97 507.216 Flattone
507.151 L/s = e
30\71 507.042 Flattone
506.9365 L/s = phi+1
49\116 506.897 Flattone
19\45 506.667 Flattone
46\109 506.422 Flattone
27\64 506.25 Flattone
35\83 506.024
8\19 505.263 Boundary of propriety: generators smaller than this are proper.

Meanenneadecal; L/s = 2

37\88 504.5455
504.507 Lucy Tuning
29\69 504.348
504.275 L/s = sqrt(3)
50\119 504.202
21\50 504 Meantone / Meanpop
55\131 503.817 Golden meantone
503.7855 L/s = phi
34\81 503.704 Optimal meantone is around here
47\112 503.571 Meantone / Meanpop
503.5685 L/s = pi/2
13\31 503.226 Optimal rank range (L/s = 3/2)
44\105 502.857 Meantone / Huygens
31\74 502.703 Meantone / Huygens
49\117 502.564
18\43 502.326 Meantone / Meridetone
41\98 502.041
23\55 501.818
28\67 501.493
5\12 500