4L 3s

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4L 3s refers to the structure of moment of symmetry scales with generators ranging from 1\4edo (one degree of 4edo, 300¢) to 2\7edo (two degrees of 7edo, or approx. 342.857¢). The spectrum looks like this:

Generator Tetrachord g in cents 2g 3g 4g Comments
1\4 1 0 1 300 600 900 0
9\35 8 1 8 308.571 617.143 925.714 34.286
8\31 7 1 7 309.677 619.355 929.023 38.71 Myna is around here
7\27 6 1 6 311.111 622.222 933.333 44.444
6\23 5 1 5 313.043 626.087 939.13 52.174
5\19 4 1 4 315.789 631.579 947.368 63.158 L/s = 4
9\34 7 2 7 317.647 634.294 951.941 70.588 Hanson/Keemun is around here
pi 1 pi 319.272 638.545 957.817 77.089 L/s = pi
4\15 3 1 3 320 640 960 80 L/s = 3
e 1 e 321.6245 641.249 964.874 86.498 L/s = e
11\41 8 3 8 321.951 643.902 965.854 87.805
29\108 21 8 21 322.222 644.444 966.667 88.889
18\67 13 5 13 322.388 644.776 967.364 89.522
7\26 5 2 5 323.077 646.154 969.231 92.308 Orgone is around here
3\11 2 1 2 327.273 654.545 981.818 109.091 Boundary of propriety (generators
larger than this are proper)
√3 1 √3 330.217 660.434 990.651 120.868
8\29 5 3 5 331.034 662.069 993.013 124.138
21\76 13 8 13 331.579 663.158 994.739 126.316
34\123 21 13 21 331.707 663.415 995.122 126.829 Unnamed golden temperament
13\47 8 5 8 331.915 663.83 995.745 127.66
pi 2 pi 332.3165 664.633 996.9495 129.266
5\18 3 2 3 333.333 666.667 1000 133.333 Optimum rank range (L/s=3/2)
7\25 4 3 4 336 672 1008 144
9\32 5 4 5 337.5 675 1012.5 150 Sixix
11\39 6 5 6 338.462 676.923 1015.385 153.846 Sixix
13\46 7 6 7 339.13 678.261 1017.391 156.522 (17/14)^3=9/5
15\53 8 7 8 339.623 679.245 1018.868 158.491 Amity is around here
2\7 1 1 1 342.857 685.714 1028.571 171.429

There are two notable harmonic entropy minima: hanson/keemun, in which the generator is 6/5 and 6 of them make a 3/1, and myna, in which the generator is also 6/5 but now 10 of them make a 6/1 (so no 4/3's or 3/2's appear in this scale).