6L 16s

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↖5L 15s ↑6L 15s 7L 15s↗
←5L 16s6L 16s 7L 16s→
↙5L 17s ↓6L 17s 7L 17s↘
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└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LssLsssLsssLssLsssLsss
sssLsssLssLsssLsssLssL
Equave 2/1 (1200.0¢)
Period 1\2 (600.0¢)
Step size ranges
Large 1\22 to 1\6 (54.5¢ to 200.0¢)
Small 0\6 to 1\22 (0.0¢ to 54.5¢)
Generator size
Bright 7\22 to 2\6 (381.8¢ to 400.0¢)
Dark 1\6 to 4\22 (200.0¢ to 218.2¢)
TAMNAMS information
Descends from 6L 4s (lemon)
Related MOS scales
Parent 6L 10s
Sister 16L 6s
Daughters 22L 6s
6L 22s
Equal tunings
Equalized (L:s = 1:1) 7\22 (381.8¢)
Supersoft (L:s = 4:3) 23\72 (383.3¢)
Soft (L:s = 3:2) 16\50 (384.0¢)
Semisoft (L:s = 5:3) 25\78 (384.6¢)
Basic (L:s = 2:1) 9\28 (385.7¢)
Semihard (L:s = 5:2) 20\62 (387.1¢)
Hard (L:s = 3:1) 11\34 (388.2¢)
Superhard (L:s = 4:1) 13\40 (390.0¢)
Collapsed (L:s = 1:0) 2\6 (400.0¢)

6L 16s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 6 large steps and 16 small steps, with a period of 3 large steps and 8 small steps that repeats every 600.0¢, or twice every octave. 6L 16s is a grandchild scale of 6L 4s, expanding it by 12 tones. Generators that produce this scale range from 381.8¢ to 400¢, or from 200¢ to 218.2¢.

It has a small major third as a generator instead of the medium to large major third which generates 3L 8s. With the half-octave equivalence, the third inverts to a 'diatonic' whole tone of no more than 4/22edo (218.182 cents).

Scale tree and tuning spectrum of 6L 16s
Generator (in steps of edo) Cents Step ratio Comments
Bright Dark L:s Hardness
7\22 381.818 218.182 1:1 1.000 Equalized 6L 16s
37\116 382.759 217.241 6:5 1.200
30\94 382.979 217.021 5:4 1.250
53\166 383.133 216.867 9:7 1.286
23\72 383.333 216.667 4:3 1.333 Supersoft 6L 16s
62\194 383.505 216.495 11:8 1.375
39\122 383.607 216.393 7:5 1.400
55\172 383.721 216.279 10:7 1.429
16\50 384.000 216.000 3:2 1.500 Soft 6L 16s
57\178 384.270 215.730 11:7 1.571
41\128 384.375 215.625 8:5 1.600
66\206 384.466 215.534 13:8 1.625
25\78 384.615 215.385 5:3 1.667 Semisoft 6L 16s
59\184 384.783 215.217 12:7 1.714
34\106 384.906 215.094 7:4 1.750
43\134 385.075 214.925 9:5 1.800
9\28 385.714 214.286 2:1 2.000 Basic 6L 16s
Scales with tunings softer than this are proper
38\118 386.441 213.559 9:4 2.250
29\90 386.667 213.333 7:3 2.333
49\152 386.842 213.158 12:5 2.400
20\62 387.097 212.903 5:2 2.500 Semihard 6L 16s
51\158 387.342 212.658 13:5 2.600
31\96 387.500 212.500 8:3 2.667
42\130 387.692 212.308 11:4 2.750
11\34 388.235 211.765 3:1 3.000 Hard 6L 16s
35\108 388.889 211.111 10:3 3.333
24\74 389.189 210.811 7:2 3.500
37\114 389.474 210.526 11:3 3.667
13\40 390.000 210.000 4:1 4.000 Superhard 6L 16s
28\86 390.698 209.302 9:2 4.500
15\46 391.304 208.696 5:1 5.000
17\52 392.308 207.692 6:1 6.000
2\6 400.000 200.000 1:0 → ∞ Collapsed 6L 16s