3L 20s

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↙ 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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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 ¢.

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

Intervals

Intervals of 3L 20s

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 52.2 ¢
	Major 1-mosstep	M1ms	L	52.2 ¢ to 400.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 104.3 ¢
	Major 2-mosstep	M2ms	L + s	104.3 ¢ to 400.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0 ¢ to 156.5 ¢
	Major 3-mosstep	M3ms	L + 2s	156.5 ¢ to 400.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	4s	0.0 ¢ to 208.7 ¢
	Major 4-mosstep	M4ms	L + 3s	208.7 ¢ to 400.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	5s	0.0 ¢ to 260.9 ¢
	Major 5-mosstep	M5ms	L + 4s	260.9 ¢ to 400.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	6s	0.0 ¢ to 313.0 ¢
	Major 6-mosstep	M6ms	L + 5s	313.0 ¢ to 400.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	7s	0.0 ¢ to 365.2 ¢
	Major 7-mosstep	M7ms	L + 6s	365.2 ¢ to 400.0 ¢
8-mosstep	Perfect 8-mosstep	P8ms	L + 7s	400.0 ¢ to 417.4 ¢
	Augmented 8-mosstep	A8ms	2L + 6s	417.4 ¢ to 800.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	L + 8s	400.0 ¢ to 469.6 ¢
	Major 9-mosstep	M9ms	2L + 7s	469.6 ¢ to 800.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	L + 9s	400.0 ¢ to 521.7 ¢
	Major 10-mosstep	M10ms	2L + 8s	521.7 ¢ to 800.0 ¢
11-mosstep	Minor 11-mosstep	m11ms	L + 10s	400.0 ¢ to 573.9 ¢
	Major 11-mosstep	M11ms	2L + 9s	573.9 ¢ to 800.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	L + 11s	400.0 ¢ to 626.1 ¢
	Major 12-mosstep	M12ms	2L + 10s	626.1 ¢ to 800.0 ¢
13-mosstep	Minor 13-mosstep	m13ms	L + 12s	400.0 ¢ to 678.3 ¢
	Major 13-mosstep	M13ms	2L + 11s	678.3 ¢ to 800.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	L + 13s	400.0 ¢ to 730.4 ¢
	Major 14-mosstep	M14ms	2L + 12s	730.4 ¢ to 800.0 ¢
15-mosstep	Diminished 15-mosstep	d15ms	L + 14s	400.0 ¢ to 782.6 ¢
	Perfect 15-mosstep	P15ms	2L + 13s	782.6 ¢ to 800.0 ¢
16-mosstep	Minor 16-mosstep	m16ms	2L + 14s	800.0 ¢ to 834.8 ¢
	Major 16-mosstep	M16ms	3L + 13s	834.8 ¢ to 1200.0 ¢
17-mosstep	Minor 17-mosstep	m17ms	2L + 15s	800.0 ¢ to 887.0 ¢
	Major 17-mosstep	M17ms	3L + 14s	887.0 ¢ to 1200.0 ¢
18-mosstep	Minor 18-mosstep	m18ms	2L + 16s	800.0 ¢ to 939.1 ¢
	Major 18-mosstep	M18ms	3L + 15s	939.1 ¢ to 1200.0 ¢
19-mosstep	Minor 19-mosstep	m19ms	2L + 17s	800.0 ¢ to 991.3 ¢
	Major 19-mosstep	M19ms	3L + 16s	991.3 ¢ to 1200.0 ¢
20-mosstep	Minor 20-mosstep	m20ms	2L + 18s	800.0 ¢ to 1043.5 ¢
	Major 20-mosstep	M20ms	3L + 17s	1043.5 ¢ to 1200.0 ¢
21-mosstep	Minor 21-mosstep	m21ms	2L + 19s	800.0 ¢ to 1095.7 ¢
	Major 21-mosstep	M21ms	3L + 18s	1095.7 ¢ to 1200.0 ¢
22-mosstep	Minor 22-mosstep	m22ms	2L + 20s	800.0 ¢ to 1147.8 ¢
	Major 22-mosstep	M22ms	3L + 19s	1147.8 ¢ to 1200.0 ¢
23-mosstep	Perfect 23-mosstep	P23ms	3L + 20s	1200.0 ¢

Scale tree

Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details: Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: {{MOS tuning spectrum | 3/2 = Example comment | 4/3 = Another example comment }} The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.

Scale tree and tuning spectrum of 3L 20s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
15\23						782.609	417.391	1:1	1.000	Equalized 3L 20s
					77\118	783.051	416.949	6:5	1.200
				62\95		783.158	416.842	5:4	1.250
					109\167	783.234	416.766	9:7	1.286
			47\72			783.333	416.667	4:3	1.333	Supersoft 3L 20s
					126\193	783.420	416.580	11:8	1.375
				79\121		783.471	416.529	7:5	1.400
					111\170	783.529	416.471	10:7	1.429
		32\49				783.673	416.327	3:2	1.500	Soft 3L 20s
					113\173	783.815	416.185	11:7	1.571
				81\124		783.871	416.129	8:5	1.600
					130\199	783.920	416.080	13:8	1.625
			49\75			784.000	416.000	5:3	1.667	Semisoft 3L 20s
					115\176	784.091	415.909	12:7	1.714
				66\101		784.158	415.842	7:4	1.750
					83\127	784.252	415.748	9:5	1.800
	17\26					784.615	415.385	2:1	2.000	Basic 3L 20s Scales with tunings softer than this are proper
					70\107	785.047	414.953	9:4	2.250
				53\81		785.185	414.815	7:3	2.333
					89\136	785.294	414.706	12:5	2.400
			36\55			785.455	414.545	5:2	2.500	Semihard 3L 20s
					91\139	785.612	414.388	13:5	2.600
				55\84		785.714	414.286	8:3	2.667
					74\113	785.841	414.159	11:4	2.750
		19\29				786.207	413.793	3:1	3.000	Hard 3L 20s
					59\90	786.667	413.333	10:3	3.333
				40\61		786.885	413.115	7:2	3.500
					61\93	787.097	412.903	11:3	3.667
			21\32			787.500	412.500	4:1	4.000	Superhard 3L 20s
					44\67	788.060	411.940	9:2	4.500
				23\35		788.571	411.429	5:1	5.000
					25\38	789.474	410.526	6:1	6.000
2\3						800.000	400.000	1:0	→ ∞	Collapsed 3L 20s