3L 21s

↖ 2L 20s	↑ 3L 20s	4L 20s ↗
← 2L 21s	3L 21s	4L 21s →
↙ 2L 22s	↓ 3L 22s	4L 22s ↘

┌╥┬┬┬┬┬┬┬╥┬┬┬┬┬┬┬╥┬┬┬┬┬┬┬┐ │║│││││││║│││││││║││││││││ ││││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LsssssssLsssssssLsssssss sssssssLsssssssLsssssssL
Equave	2/1 (1200.0 ¢)
Period	1\3 (400.0 ¢)
Generator size
Bright	7\24 to 1\3 (350.0 ¢ to 400.0 ¢)
Dark	0\3 to 1\24 (0.0 ¢ to 50.0 ¢)
TAMNAMS information
Related to	3L 6s (tcherepnin)
With tunings	6:1 to 1:0
Related MOS scales
Parent	3L 18s
Sister	21L 3s
Daughters	24L 3s, 3L 24s
Neutralized	6L 18s
2-Flought	27L 21s, 3L 45s
Equal tunings
Equalized (L:s = 1:1)	7\24 (350.0 ¢)
Supersoft (L:s = 4:3)	22\75 (352.0 ¢)
Soft (L:s = 3:2)	15\51 (352.9 ¢)
Semisoft (L:s = 5:3)	23\78 (353.8 ¢)
Basic (L:s = 2:1)	8\27 (355.6 ¢)
Semihard (L:s = 5:2)	17\57 (357.9 ¢)
Hard (L:s = 3:1)	9\30 (360.0 ¢)
Superhard (L:s = 4:1)	10\33 (363.6 ¢)
Collapsed (L:s = 1:0)	1\3 (400.0 ¢)

3L 21s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 21 small steps, with a period of 1 large step and 7 small steps that repeats every 400.0 ¢, or 3 times every octave. 3L 21s is related to 3L 6s, expanding it by 15 tones. Generators that produce this scale range from 350 ¢ to 400 ¢, or from 0 ¢ to 50 ¢.

Modes

Modes of 3L 21s

UDP	Cyclic order	Step pattern
21|0(3)	1	LsssssssLsssssssLsssssss
18|3(3)	8	sLsssssssLsssssssLssssss
15|6(3)	7	ssLsssssssLsssssssLsssss
12|9(3)	6	sssLsssssssLsssssssLssss
9|12(3)	5	ssssLsssssssLsssssssLsss
6|15(3)	4	sssssLsssssssLsssssssLss
3|18(3)	3	ssssssLsssssssLsssssssLs
0|21(3)	2	sssssssLsssssssLsssssssL

Intervals

Intervals of 3L 21s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0 ¢
1-mosstep	Perfect 1-mosstep	P1ms	s	0.0 ¢ to 50.0 ¢
	Augmented 1-mosstep	A1ms	L	50.0 ¢ to 400.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 100.0 ¢
	Major 2-mosstep	M2ms	L + s	100.0 ¢ to 400.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0 ¢ to 150.0 ¢
	Major 3-mosstep	M3ms	L + 2s	150.0 ¢ to 400.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	4s	0.0 ¢ to 200.0 ¢
	Major 4-mosstep	M4ms	L + 3s	200.0 ¢ to 400.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	5s	0.0 ¢ to 250.0 ¢
	Major 5-mosstep	M5ms	L + 4s	250.0 ¢ to 400.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	6s	0.0 ¢ to 300.0 ¢
	Major 6-mosstep	M6ms	L + 5s	300.0 ¢ to 400.0 ¢
7-mosstep	Diminished 7-mosstep	d7ms	7s	0.0 ¢ to 350.0 ¢
	Perfect 7-mosstep	P7ms	L + 6s	350.0 ¢ to 400.0 ¢
8-mosstep	Perfect 8-mosstep	P8ms	L + 7s	400.0 ¢
9-mosstep	Perfect 9-mosstep	P9ms	L + 8s	400.0 ¢ to 450.0 ¢
	Augmented 9-mosstep	A9ms	2L + 7s	450.0 ¢ to 800.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	L + 9s	400.0 ¢ to 500.0 ¢
	Major 10-mosstep	M10ms	2L + 8s	500.0 ¢ to 800.0 ¢
11-mosstep	Minor 11-mosstep	m11ms	L + 10s	400.0 ¢ to 550.0 ¢
	Major 11-mosstep	M11ms	2L + 9s	550.0 ¢ to 800.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	L + 11s	400.0 ¢ to 600.0 ¢
	Major 12-mosstep	M12ms	2L + 10s	600.0 ¢ to 800.0 ¢
13-mosstep	Minor 13-mosstep	m13ms	L + 12s	400.0 ¢ to 650.0 ¢
	Major 13-mosstep	M13ms	2L + 11s	650.0 ¢ to 800.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	L + 13s	400.0 ¢ to 700.0 ¢
	Major 14-mosstep	M14ms	2L + 12s	700.0 ¢ to 800.0 ¢
15-mosstep	Diminished 15-mosstep	d15ms	L + 14s	400.0 ¢ to 750.0 ¢
	Perfect 15-mosstep	P15ms	2L + 13s	750.0 ¢ to 800.0 ¢
16-mosstep	Perfect 16-mosstep	P16ms	2L + 14s	800.0 ¢
17-mosstep	Perfect 17-mosstep	P17ms	2L + 15s	800.0 ¢ to 850.0 ¢
	Augmented 17-mosstep	A17ms	3L + 14s	850.0 ¢ to 1200.0 ¢
18-mosstep	Minor 18-mosstep	m18ms	2L + 16s	800.0 ¢ to 900.0 ¢
	Major 18-mosstep	M18ms	3L + 15s	900.0 ¢ to 1200.0 ¢
19-mosstep	Minor 19-mosstep	m19ms	2L + 17s	800.0 ¢ to 950.0 ¢
	Major 19-mosstep	M19ms	3L + 16s	950.0 ¢ to 1200.0 ¢
20-mosstep	Minor 20-mosstep	m20ms	2L + 18s	800.0 ¢ to 1000.0 ¢
	Major 20-mosstep	M20ms	3L + 17s	1000.0 ¢ to 1200.0 ¢
21-mosstep	Minor 21-mosstep	m21ms	2L + 19s	800.0 ¢ to 1050.0 ¢
	Major 21-mosstep	M21ms	3L + 18s	1050.0 ¢ to 1200.0 ¢
22-mosstep	Minor 22-mosstep	m22ms	2L + 20s	800.0 ¢ to 1100.0 ¢
	Major 22-mosstep	M22ms	3L + 19s	1100.0 ¢ to 1200.0 ¢
23-mosstep	Diminished 23-mosstep	d23ms	2L + 21s	800.0 ¢ to 1150.0 ¢
	Perfect 23-mosstep	P23ms	3L + 20s	1150.0 ¢ to 1200.0 ¢
24-mosstep	Perfect 24-mosstep	P24ms	3L + 21s	1200.0 ¢

Scale tree

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