4L 20s

4L 20s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 20 small steps, with a period of 1 large step and 5 small steps that repeats every 300.0 ¢, or 4 times every octave. 4L 20s is related to 4L 4s, expanding it by 16 tones. Generators that produce this scale range from 250 ¢ to 300 ¢, or from 0 ¢ to 50 ¢.

↖ 3L 19s	↑ 4L 19s	5L 19s ↗
← 3L 20s	4L 20s	5L 20s →
↙ 3L 21s	↓ 4L 21s	5L 21s ↘

Scale structure
Step pattern	LsssssLsssssLsssssLsssss sssssLsssssLsssssLsssssL
Equave	2/1 (1200.0 ¢)
Period	1\4 (300.0 ¢)
Generator size
Bright	5\24 to 1\4 (250.0 ¢ to 300.0 ¢)
Dark	0\4 to 1\24 (0.0 ¢ to 50.0 ¢)
TAMNAMS information
Related to	4L 4s (tetrawood)
With tunings	5:1 to 1:0
Related MOS scales
Parent	4L 16s
Sister	20L 4s
Daughters	24L 4s, 4L 24s
Neutralized	8L 16s
2-Flought	28L 20s, 4L 44s
Equal tunings
Equalized (L:s = 1:1)	5\24 (250.0 ¢)
Supersoft (L:s = 4:3)	16\76 (252.6 ¢)
Soft (L:s = 3:2)	11\52 (253.8 ¢)
Semisoft (L:s = 5:3)	17\80 (255.0 ¢)
Basic (L:s = 2:1)	6\28 (257.1 ¢)
Semihard (L:s = 5:2)	13\60 (260.0 ¢)
Hard (L:s = 3:1)	7\32 (262.5 ¢)
Superhard (L:s = 4:1)	8\36 (266.7 ¢)
Collapsed (L:s = 1:0)	1\4 (300.0 ¢)
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Modes

Modes of 4L 20s

UDP	Cyclic order	Step pattern
20|0(4)	1	LsssssLsssssLsssssLsssss
16|4(4)	6	sLsssssLsssssLsssssLssss
12|8(4)	5	ssLsssssLsssssLsssssLsss
8|12(4)	4	sssLsssssLsssssLsssssLss
4|16(4)	3	ssssLsssssLsssssLsssssLs
0|20(4)	2	sssssLsssssLsssssLsssssL

Intervals

Intervals of 4L 20s

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 300.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 100.0 ¢
	Major 2-mosstep	M2ms	L + s	100.0 ¢ to 300.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0 ¢ to 150.0 ¢
	Major 3-mosstep	M3ms	L + 2s	150.0 ¢ to 300.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	4s	0.0 ¢ to 200.0 ¢
	Major 4-mosstep	M4ms	L + 3s	200.0 ¢ to 300.0 ¢
5-mosstep	Diminished 5-mosstep	d5ms	5s	0.0 ¢ to 250.0 ¢
	Perfect 5-mosstep	P5ms	L + 4s	250.0 ¢ to 300.0 ¢
6-mosstep	Perfect 6-mosstep	P6ms	L + 5s	300.0 ¢
7-mosstep	Perfect 7-mosstep	P7ms	L + 6s	300.0 ¢ to 350.0 ¢
	Augmented 7-mosstep	A7ms	2L + 5s	350.0 ¢ to 600.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	L + 7s	300.0 ¢ to 400.0 ¢
	Major 8-mosstep	M8ms	2L + 6s	400.0 ¢ to 600.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	L + 8s	300.0 ¢ to 450.0 ¢
	Major 9-mosstep	M9ms	2L + 7s	450.0 ¢ to 600.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	L + 9s	300.0 ¢ to 500.0 ¢
	Major 10-mosstep	M10ms	2L + 8s	500.0 ¢ to 600.0 ¢
11-mosstep	Diminished 11-mosstep	d11ms	L + 10s	300.0 ¢ to 550.0 ¢
	Perfect 11-mosstep	P11ms	2L + 9s	550.0 ¢ to 600.0 ¢
12-mosstep	Perfect 12-mosstep	P12ms	2L + 10s	600.0 ¢
13-mosstep	Perfect 13-mosstep	P13ms	2L + 11s	600.0 ¢ to 650.0 ¢
	Augmented 13-mosstep	A13ms	3L + 10s	650.0 ¢ to 900.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	2L + 12s	600.0 ¢ to 700.0 ¢
	Major 14-mosstep	M14ms	3L + 11s	700.0 ¢ to 900.0 ¢
15-mosstep	Minor 15-mosstep	m15ms	2L + 13s	600.0 ¢ to 750.0 ¢
	Major 15-mosstep	M15ms	3L + 12s	750.0 ¢ to 900.0 ¢
16-mosstep	Minor 16-mosstep	m16ms	2L + 14s	600.0 ¢ to 800.0 ¢
	Major 16-mosstep	M16ms	3L + 13s	800.0 ¢ to 900.0 ¢
17-mosstep	Diminished 17-mosstep	d17ms	2L + 15s	600.0 ¢ to 850.0 ¢
	Perfect 17-mosstep	P17ms	3L + 14s	850.0 ¢ to 900.0 ¢
18-mosstep	Perfect 18-mosstep	P18ms	3L + 15s	900.0 ¢
19-mosstep	Perfect 19-mosstep	P19ms	3L + 16s	900.0 ¢ to 950.0 ¢
	Augmented 19-mosstep	A19ms	4L + 15s	950.0 ¢ to 1200.0 ¢
20-mosstep	Minor 20-mosstep	m20ms	3L + 17s	900.0 ¢ to 1000.0 ¢
	Major 20-mosstep	M20ms	4L + 16s	1000.0 ¢ to 1200.0 ¢
21-mosstep	Minor 21-mosstep	m21ms	3L + 18s	900.0 ¢ to 1050.0 ¢
	Major 21-mosstep	M21ms	4L + 17s	1050.0 ¢ to 1200.0 ¢
22-mosstep	Minor 22-mosstep	m22ms	3L + 19s	900.0 ¢ to 1100.0 ¢
	Major 22-mosstep	M22ms	4L + 18s	1100.0 ¢ to 1200.0 ¢
23-mosstep	Diminished 23-mosstep	d23ms	3L + 20s	900.0 ¢ to 1150.0 ¢
	Perfect 23-mosstep	P23ms	4L + 19s	1150.0 ¢ to 1200.0 ¢
24-mosstep	Perfect 24-mosstep	P24ms	4L + 20s	1200.0 ¢

Scale tree

Scale tree and tuning spectrum of 4L 20s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
5\24						250.000	50.000	1:1	1.000	Equalized 4L 20s
					26\124	251.613	48.387	6:5	1.200
				21\100		252.000	48.000	5:4	1.250
					37\176	252.273	47.727	9:7	1.286
			16\76			252.632	47.368	4:3	1.333	Supersoft 4L 20s
					43\204	252.941	47.059	11:8	1.375
				27\128		253.125	46.875	7:5	1.400
					38\180	253.333	46.667	10:7	1.429
		11\52				253.846	46.154	3:2	1.500	Soft 4L 20s
					39\184	254.348	45.652	11:7	1.571
				28\132		254.545	45.455	8:5	1.600
					45\212	254.717	45.283	13:8	1.625
			17\80			255.000	45.000	5:3	1.667	Semisoft 4L 20s
					40\188	255.319	44.681	12:7	1.714
				23\108		255.556	44.444	7:4	1.750
					29\136	255.882	44.118	9:5	1.800
	6\28					257.143	42.857	2:1	2.000	Basic 4L 20s Scales with tunings softer than this are proper
					25\116	258.621	41.379	9:4	2.250
				19\88		259.091	40.909	7:3	2.333
					32\148	259.459	40.541	12:5	2.400
			13\60			260.000	40.000	5:2	2.500	Semihard 4L 20s
					33\152	260.526	39.474	13:5	2.600
				20\92		260.870	39.130	8:3	2.667
					27\124	261.290	38.710	11:4	2.750
		7\32				262.500	37.500	3:1	3.000	Hard 4L 20s
					22\100	264.000	36.000	10:3	3.333
				15\68		264.706	35.294	7:2	3.500
					23\104	265.385	34.615	11:3	3.667
			8\36			266.667	33.333	4:1	4.000	Superhard 4L 20s
					17\76	268.421	31.579	9:2	4.500
				9\40		270.000	30.000	5:1	5.000
					10\44	272.727	27.273	6:1	6.000
1\4						300.000	0.000	1:0	→ ∞	Collapsed 4L 20s

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