6L 16s

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↖ 5L 15s ↑ 6L 15s 7L 15s ↗
← 5L 16s 6L 16s 7L 16s →
↙ 5L 17s ↓ 6L 17s 7L 17s ↘ 
┌╥┬┬╥┬┬┬╥┬┬┬╥┬┬╥┬┬┬╥┬┬┬┐
│║││║│││║│││║││║│││║││││
││││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LssLsssLsssLssLsssLsss
sssLsssLssLsssLsssLssL
Equave 2/1 (1200.0¢)
Period 1\2 (600.0¢)
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)
Ancestor's step ratio range 3:1 to 1:0 (hard)
Related MOS scales
Parent 6L 10s
Sister 16L 6s
Daughters 22L 6s, 6L 22s
Neutralized 12L 10s
2-Flought 28L 16s, 6L 38s
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).

Modes

Modes of 6L 16s
UDP Cyclic
order		 Step
pattern
20|0(2) 1 LssLsssLsssLssLsssLsss
18|2(2) 8 LsssLssLsssLsssLssLsss
16|4(2) 4 LsssLsssLssLsssLsssLss
14|6(2) 11 sLssLsssLsssLssLsssLss
12|8(2) 7 sLsssLssLsssLsssLssLss
10|10(2) 3 sLsssLsssLssLsssLsssLs
8|12(2) 10 ssLssLsssLsssLssLsssLs
6|14(2) 6 ssLsssLssLsssLsssLssLs
4|16(2) 2 ssLsssLsssLssLsssLsssL
2|18(2) 9 sssLssLsssLsssLssLsssL
0|20(2) 5 sssLsssLssLsssLsssLssL

Intervals

Intervals of 6L 16s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0¢
1-mosstep Minor 1-mosstep m1ms s 0.0¢ to 54.5¢
Major 1-mosstep M1ms L 54.5¢ to 200.0¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0¢ to 109.1¢
Major 2-mosstep M2ms L + s 109.1¢ to 200.0¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0¢ to 163.6¢
Major 3-mosstep M3ms L + 2s 163.6¢ to 200.0¢
4-mosstep Perfect 4-mosstep P4ms L + 3s 200.0¢ to 218.2¢
Augmented 4-mosstep A4ms 2L + 2s 218.2¢ to 400.0¢
5-mosstep Minor 5-mosstep m5ms L + 4s 200.0¢ to 272.7¢
Major 5-mosstep M5ms 2L + 3s 272.7¢ to 400.0¢
6-mosstep Minor 6-mosstep m6ms L + 5s 200.0¢ to 327.3¢
Major 6-mosstep M6ms 2L + 4s 327.3¢ to 400.0¢
7-mosstep Diminished 7-mosstep d7ms L + 6s 200.0¢ to 381.8¢
Perfect 7-mosstep P7ms 2L + 5s 381.8¢ to 400.0¢
8-mosstep Minor 8-mosstep m8ms 2L + 6s 400.0¢ to 436.4¢
Major 8-mosstep M8ms 3L + 5s 436.4¢ to 600.0¢
9-mosstep Minor 9-mosstep m9ms 2L + 7s 400.0¢ to 490.9¢
Major 9-mosstep M9ms 3L + 6s 490.9¢ to 600.0¢
10-mosstep Minor 10-mosstep m10ms 2L + 8s 400.0¢ to 545.5¢
Major 10-mosstep M10ms 3L + 7s 545.5¢ to 600.0¢
11-mosstep Perfect 11-mosstep P11ms 3L + 8s 600.0¢
12-mosstep Minor 12-mosstep m12ms 3L + 9s 600.0¢ to 654.5¢
Major 12-mosstep M12ms 4L + 8s 654.5¢ to 800.0¢
13-mosstep Minor 13-mosstep m13ms 3L + 10s 600.0¢ to 709.1¢
Major 13-mosstep M13ms 4L + 9s 709.1¢ to 800.0¢
14-mosstep Minor 14-mosstep m14ms 3L + 11s 600.0¢ to 763.6¢
Major 14-mosstep M14ms 4L + 10s 763.6¢ to 800.0¢
15-mosstep Perfect 15-mosstep P15ms 4L + 11s 800.0¢ to 818.2¢
Augmented 15-mosstep A15ms 5L + 10s 818.2¢ to 1000.0¢
16-mosstep Minor 16-mosstep m16ms 4L + 12s 800.0¢ to 872.7¢
Major 16-mosstep M16ms 5L + 11s 872.7¢ to 1000.0¢
17-mosstep Minor 17-mosstep m17ms 4L + 13s 800.0¢ to 927.3¢
Major 17-mosstep M17ms 5L + 12s 927.3¢ to 1000.0¢
18-mosstep Diminished 18-mosstep d18ms 4L + 14s 800.0¢ to 981.8¢
Perfect 18-mosstep P18ms 5L + 13s 981.8¢ to 1000.0¢
19-mosstep Minor 19-mosstep m19ms 5L + 14s 1000.0¢ to 1036.4¢
Major 19-mosstep M19ms 6L + 13s 1036.4¢ to 1200.0¢
20-mosstep Minor 20-mosstep m20ms 5L + 15s 1000.0¢ to 1090.9¢
Major 20-mosstep M20ms 6L + 14s 1090.9¢ to 1200.0¢
21-mosstep Minor 21-mosstep m21ms 5L + 16s 1000.0¢ to 1145.5¢
Major 21-mosstep M21ms 6L + 15s 1145.5¢ to 1200.0¢
22-mosstep Perfect 22-mosstep P22ms 6L + 16s 1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 6L 16s
Generator(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
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