3L 20s

3L 20s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 20 small steps, repeating every octave. 3L 20s is related to 3L 5s, expanding it by 15 tones. Generators that produce this scale range from 782.6 ¢ to 800 ¢, or from 400 ¢ to 417.4 ¢.

↖ 2L 19s	↑ 3L 19s	4L 19s ↗
← 2L 20s	3L 20s	4L 20s →
↙ 2L 21s	↓ 3L 21s	4L 21s ↘

Scale structure
Step pattern	LssssssLsssssssLsssssss sssssssLsssssssLssssssL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	15\23 to 2\3 (782.6 ¢ to 800.0 ¢)
Dark	1\3 to 8\23 (400.0 ¢ to 417.4 ¢)
TAMNAMS information
Related to	3L 5s (checkertonic)
With tunings	6:1 to 1:0
Related MOS scales
Parent	3L 17s
Sister	20L 3s
Daughters	23L 3s, 3L 23s
Neutralized	6L 17s
2-Flought	26L 20s, 3L 43s
Equal tunings
Equalized (L:s = 1:1)	15\23 (782.6 ¢)
Supersoft (L:s = 4:3)	47\72 (783.3 ¢)
Soft (L:s = 3:2)	32\49 (783.7 ¢)
Semisoft (L:s = 5:3)	49\75 (784.0 ¢)
Basic (L:s = 2:1)	17\26 (784.6 ¢)
Semihard (L:s = 5:2)	36\55 (785.5 ¢)
Hard (L:s = 3:1)	19\29 (786.2 ¢)
Superhard (L:s = 4:1)	21\32 (787.5 ¢)
Collapsed (L:s = 1:0)	2\3 (800.0 ¢)
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This is the MOS where the small steps split 7-7-6 among the large steps. Its generator is a supermajor third no larger than 8/23edo (417.391 cents), which is almost exactly 14/11.

Modes

Modes of 3L 20s

UDP	Cyclic order	Step pattern
22|0	1	LssssssLsssssssLsssssss
21|1	16	LsssssssLssssssLsssssss
20|2	8	LsssssssLsssssssLssssss
19|3	23	sLssssssLsssssssLssssss
18|4	15	sLsssssssLssssssLssssss
17|5	7	sLsssssssLsssssssLsssss
16|6	22	ssLssssssLsssssssLsssss
15|7	14	ssLsssssssLssssssLsssss
14|8	6	ssLsssssssLsssssssLssss
13|9	21	sssLssssssLsssssssLssss
12|10	13	sssLsssssssLssssssLssss
11|11	5	sssLsssssssLsssssssLsss
10|12	20	ssssLssssssLsssssssLsss
9|13	12	ssssLsssssssLssssssLsss
8|14	4	ssssLsssssssLsssssssLss
7|15	19	sssssLssssssLsssssssLss
6|16	11	sssssLsssssssLssssssLss
5|17	3	sssssLsssssssLsssssssLs
4|18	18	ssssssLssssssLsssssssLs
3|19	10	ssssssLsssssssLssssssLs
2|20	2	ssssssLsssssssLsssssssL
1|21	17	sssssssLssssssLsssssssL
0|22	9	sssssssLsssssssLssssssL

Tuning spectrum

8/23					417.391
				33/95	416.842
			25/72		416.667
				42/121	416.529
		17/49			416.3265
					416.186
				43/124	416.129
					416.094
			26/75		416
					415.875
				35/101	415.842
	9/26				415.385
				28/81	414.815
			19/55		414.5455
					414.3605
				29/84	414.286
					414.207
		10/29			413.793
					413.594
				21/61	413.115
			11/32		412.5
				12/35	411.429
1/3					400