3L 13s

↖ 2L 12s	↑ 3L 12s	4L 12s ↗
← 2L 13s	3L 13s	4L 13s →
↙ 2L 14s	↓ 3L 14s	4L 14s ↘

┌╥┬┬┬┬╥┬┬┬┬╥┬┬┬┬┬┐ │║││││║││││║││││││ ││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LssssLssssLsssss sssssLssssLssssL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	5\16 to 1\3 (375.0 ¢ to 400.0 ¢)
Dark	2\3 to 11\16 (800.0 ¢ to 825.0 ¢)
TAMNAMS information
Related to	3L 7s (sephiroid)
With tunings	3:1 to 1:0 (hard)
Related MOS scales
Parent	3L 10s
Sister	13L 3s
Daughters	16L 3s, 3L 16s
Neutralized	6L 10s
2-Flought	19L 13s, 3L 29s
Equal tunings
Equalized (L:s = 1:1)	5\16 (375.0 ¢)
Supersoft (L:s = 4:3)	16\51 (376.5 ¢)
Soft (L:s = 3:2)	11\35 (377.1 ¢)
Semisoft (L:s = 5:3)	17\54 (377.8 ¢)
Basic (L:s = 2:1)	6\19 (378.9 ¢)
Semihard (L:s = 5:2)	13\41 (380.5 ¢)
Hard (L:s = 3:1)	7\22 (381.8 ¢)
Superhard (L:s = 4:1)	8\25 (384.0 ¢)
Collapsed (L:s = 1:0)	1\3 (400.0 ¢)

3L 13s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 13 small steps, repeating every octave. 3L 13s is a grandchild scale of 3L 7s, expanding it by 6 tones. Generators that produce this scale range from 375 ¢ to 400 ¢, or from 800 ¢ to 825 ¢. This MOS, having its large steps separated by intervals of 4s, 4s and 5s; is the quasi-enharmonic scale of Magic temperament. It is also the smallest MOS which is ideal for composing melodies in Magic temperament, owing to the fact that the optimal generator range for it is the range where Magic temperament is tuned most accurately (6/19edo to 7/22edo); and is generated by a small major third no smaller than 5/16edo (375 cents).

Modes

Modes of 3L 13s

UDP	Cyclic order	Step pattern
15|0	1	LssssLssssLsssss
14|1	6	LssssLsssssLssss
13|2	11	LsssssLssssLssss
12|3	16	sLssssLssssLssss
11|4	5	sLssssLsssssLsss
10|5	10	sLsssssLssssLsss
9|6	15	ssLssssLssssLsss
8|7	4	ssLssssLsssssLss
7|8	9	ssLsssssLssssLss
6|9	14	sssLssssLssssLss
5|10	3	sssLssssLsssssLs
4|11	8	sssLsssssLssssLs
3|12	13	ssssLssssLssssLs
2|13	2	ssssLssssLsssssL
1|14	7	ssssLsssssLssssL
0|15	12	sssssLssssLssssL