3L 16s

↖ 2L 15s	↑ 3L 15s	4L 15s ↗
← 2L 16s	3L 16s	4L 16s →
↙ 2L 17s	↓ 3L 17s	4L 17s ↘

┌╥┬┬┬┬┬╥┬┬┬┬┬╥┬┬┬┬┬┬┐ │║│││││║│││││║│││││││ │││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
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
Related to	3L 7s (sephiroid)
With tunings	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

Scale tree

Todo: review Review entries from past page revision and enter them into the scale tree.