3L 16s

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↖ 2L 15s ↑ 3L 15s 4L 15s ↗
← 2L 16s 3L 16s 4L 16s →
↙ 2L 17s ↓ 3L 17s 4L 17s ↘ 
┌╥┬┬┬┬┬╥┬┬┬┬┬╥┬┬┬┬┬┬┐
│║│││││║│││││║│││││││
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└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsssssLsssssLssssss
ssssssLsssssLsssssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 6\19 to 1\3 (378.9 ¢ to 400.0 ¢)
Dark 2\3 to 13\19 (800.0 ¢ to 821.1 ¢)
TAMNAMS information
Descends from 3L 7s (sephiroid)
Ancestor's step ratio range 4:1 to 1:0 (ultrahard)
Related MOS scales
Parent 3L 13s
Sister 16L 3s
Daughters 19L 3s, 3L 19s
Neutralized 6L 13s
2-Flought 22L 16s, 3L 35s
Equal tunings
Equalized (L:s = 1:1) 6\19 (378.9 ¢)
Supersoft (L:s = 4:3) 19\60 (380.0 ¢)
Soft (L:s = 3:2) 13\41 (380.5 ¢)
Semisoft (L:s = 5:3) 20\63 (381.0 ¢)
Basic (L:s = 2:1) 7\22 (381.8 ¢)
Semihard (L:s = 5:2) 15\47 (383.0 ¢)
Hard (L:s = 3:1) 8\25 (384.0 ¢)
Superhard (L:s = 4:1) 9\28 (385.7 ¢)
Collapsed (L:s = 1:0) 1\3 (400.0 ¢)

3L 16s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 16 small steps, repeating every octave. 3L 16s is a great-grandchild scale of 3L 7s, expanding it by 9 tones. Generators that produce this scale range from 378.9 ¢ to 400 ¢, or from 800 ¢ to 821.1 ¢.

This scale is associated with magic temperament, where 5 bright generators maps to 3/1 and the generator is a flat 5/4, and würschmidt temperament, where 8 bright generators map to 6/1 and the generator is a slightly sharp 5/4.

Modes

Modes of 3L 16s
UDP Cyclic
order		 Step
pattern
18|0 1 LsssssLsssssLssssss
17|1 7 LsssssLssssssLsssss
16|2 13 LssssssLsssssLsssss
15|3 19 sLsssssLsssssLsssss
14|4 6 sLsssssLssssssLssss
13|5 12 sLssssssLsssssLssss
12|6 18 ssLsssssLsssssLssss
11|7 5 ssLsssssLssssssLsss
10|8 11 ssLssssssLsssssLsss
9|9 17 sssLsssssLsssssLsss
8|10 4 sssLsssssLssssssLss
7|11 10 sssLssssssLsssssLss
6|12 16 ssssLsssssLsssssLss
5|13 3 ssssLsssssLssssssLs
4|14 9 ssssLssssssLsssssLs
3|15 15 sssssLsssssLsssssLs
2|16 2 sssssLsssssLssssssL
1|17 8 sssssLssssssLsssssL
0|18 14 ssssssLsssssLsssssL

Intervals

Intervals of 3L 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 63.2 ¢
Major 1-mosstep M1ms L 63.2 ¢ to 400.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 126.3 ¢
Major 2-mosstep M2ms L + s 126.3 ¢ to 400.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 189.5 ¢
Major 3-mosstep M3ms L + 2s 189.5 ¢ to 400.0 ¢
4-mosstep Minor 4-mosstep m4ms 4s 0.0 ¢ to 252.6 ¢
Major 4-mosstep M4ms L + 3s 252.6 ¢ to 400.0 ¢
5-mosstep Minor 5-mosstep m5ms 5s 0.0 ¢ to 315.8 ¢
Major 5-mosstep M5ms L + 4s 315.8 ¢ to 400.0 ¢
6-mosstep Diminished 6-mosstep d6ms 6s 0.0 ¢ to 378.9 ¢
Perfect 6-mosstep P6ms L + 5s 378.9 ¢ to 400.0 ¢
7-mosstep Minor 7-mosstep m7ms L + 6s 400.0 ¢ to 442.1 ¢
Major 7-mosstep M7ms 2L + 5s 442.1 ¢ to 800.0 ¢
8-mosstep Minor 8-mosstep m8ms L + 7s 400.0 ¢ to 505.3 ¢
Major 8-mosstep M8ms 2L + 6s 505.3 ¢ to 800.0 ¢
9-mosstep Minor 9-mosstep m9ms L + 8s 400.0 ¢ to 568.4 ¢
Major 9-mosstep M9ms 2L + 7s 568.4 ¢ to 800.0 ¢
10-mosstep Minor 10-mosstep m10ms L + 9s 400.0 ¢ to 631.6 ¢
Major 10-mosstep M10ms 2L + 8s 631.6 ¢ to 800.0 ¢
11-mosstep Minor 11-mosstep m11ms L + 10s 400.0 ¢ to 694.7 ¢
Major 11-mosstep M11ms 2L + 9s 694.7 ¢ to 800.0 ¢
12-mosstep Minor 12-mosstep m12ms L + 11s 400.0 ¢ to 757.9 ¢
Major 12-mosstep M12ms 2L + 10s 757.9 ¢ to 800.0 ¢
13-mosstep Perfect 13-mosstep P13ms 2L + 11s 800.0 ¢ to 821.1 ¢
Augmented 13-mosstep A13ms 3L + 10s 821.1 ¢ to 1200.0 ¢
14-mosstep Minor 14-mosstep m14ms 2L + 12s 800.0 ¢ to 884.2 ¢
Major 14-mosstep M14ms 3L + 11s 884.2 ¢ to 1200.0 ¢
15-mosstep Minor 15-mosstep m15ms 2L + 13s 800.0 ¢ to 947.4 ¢
Major 15-mosstep M15ms 3L + 12s 947.4 ¢ to 1200.0 ¢
16-mosstep Minor 16-mosstep m16ms 2L + 14s 800.0 ¢ to 1010.5 ¢
Major 16-mosstep M16ms 3L + 13s 1010.5 ¢ to 1200.0 ¢
17-mosstep Minor 17-mosstep m17ms 2L + 15s 800.0 ¢ to 1073.7 ¢
Major 17-mosstep M17ms 3L + 14s 1073.7 ¢ to 1200.0 ¢
18-mosstep Minor 18-mosstep m18ms 2L + 16s 800.0 ¢ to 1136.8 ¢
Major 18-mosstep M18ms 3L + 15s 1136.8 ¢ to 1200.0 ¢
19-mosstep Perfect 19-mosstep P19ms 3L + 16s 1200.0 ¢

Scale tree

Scale tree and tuning spectrum of 3L 16s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
6\19 378.947 821.053 1:1 1.000 Equalized 3L 16s
31\98 379.592 820.408 6:5 1.200
25\79 379.747 820.253 5:4 1.250
44\139 379.856 820.144 9:7 1.286
19\60 380.000 820.000 4:3 1.333 Supersoft 3L 16s
51\161 380.124 819.876 11:8 1.375 Witchcraft
32\101 380.198 819.802 7:5 1.400
45\142 380.282 819.718 10:7 1.429
13\41 380.488 819.512 3:2 1.500 Soft 3L 16s
Magic is around here
46\145 380.690 819.310 11:7 1.571
33\104 380.769 819.231 8:5 1.600
53\167 380.838 819.162 13:8 1.625 Necromancy
Golden magic (380.8191 ¢)
20\63 380.952 819.048 5:3 1.667 Semisoft 3L 16s
47\148 381.081 818.919 12:7 1.714
27\85 381.176 818.824 7:4 1.750
34\107 381.308 818.692 9:5 1.800
7\22 381.818 818.182 2:1 2.000 Basic 3L 16s
Scales with tunings softer than this are proper
29\91 382.418 817.582 9:4 2.250
22\69 382.609 817.391 7:3 2.333
37\116 382.759 817.241 12:5 2.400 Marveltri is around here
15\47 382.979 817.021 5:2 2.500 Semihard 3L 16s
38\119 383.193 816.807 13:5 2.600 Unnamed golden tuning (383.2314 ¢)
23\72 383.333 816.667 8:3 2.667
31\97 383.505 816.495 11:4 2.750
8\25 384.000 816.000 3:1 3.000 Hard 3L 16s
25\78 384.615 815.385 10:3 3.333
17\53 384.906 815.094 7:2 3.500
26\81 385.185 814.815 11:3 3.667
9\28 385.714 814.286 4:1 4.000 Superhard 3L 16s
19\59 386.441 813.559 9:2 4.500 Sulis
10\31 387.097 812.903 5:1 5.000 Grendel/Würschmidt
11\34 388.235 811.765 6:1 6.000
1\3 400.000 800.000 1:0 → ∞ Collapsed 3L 16s
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