5L 20s

5L 20s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 20 small steps, with a period of 1 large step and 4 small steps that repeats every 240.0 ¢, or 5 times every octave. 5L 20s is a great-grandchild scale of 5L 5s, expanding it by 15 tones. Generators that produce this scale range from 192 ¢ to 240 ¢, or from 0 ¢ to 48 ¢.

↖ 4L 19s	↑ 5L 19s	6L 19s ↗
← 4L 20s	5L 20s	6L 20s →
↙ 4L 21s	↓ 5L 21s	6L 21s ↘

Scale structure
Step pattern	LssssLssssLssssLssssLssss ssssLssssLssssLssssLssssL
Equave	2/1 (1200.0 ¢)
Period	1\5 (240.0 ¢)
Generator size
Bright	4\25 to 1\5 (192.0 ¢ to 240.0 ¢)
Dark	0\5 to 1\25 (0.0 ¢ to 48.0 ¢)
TAMNAMS information
Related to	5L 5s (pentawood)
With tunings	4:1 to 1:0 (ultrahard)
Related MOS scales
Parent	5L 15s
Sister	20L 5s
Daughters	25L 5s, 5L 25s
Neutralized	10L 15s
2-Flought	30L 20s, 5L 45s
Equal tunings
Equalized (L:s = 1:1)	4\25 (192.0 ¢)
Supersoft (L:s = 4:3)	13\80 (195.0 ¢)
Soft (L:s = 3:2)	9\55 (196.4 ¢)
Semisoft (L:s = 5:3)	14\85 (197.6 ¢)
Basic (L:s = 2:1)	5\30 (200.0 ¢)
Semihard (L:s = 5:2)	11\65 (203.1 ¢)
Hard (L:s = 3:1)	6\35 (205.7 ¢)
Superhard (L:s = 4:1)	7\40 (210.0 ¢)
Collapsed (L:s = 1:0)	1\5 (240.0 ¢)
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Modes

Modes of 5L 20s

UDP	Cyclic order	Step pattern
20|0(5)	1	LssssLssssLssssLssssLssss
15|5(5)	5	sLssssLssssLssssLssssLsss
10|10(5)	4	ssLssssLssssLssssLssssLss
5|15(5)	3	sssLssssLssssLssssLssssLs
0|20(5)	2	ssssLssssLssssLssssLssssL

Intervals

Intervals of 5L 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 48.0 ¢
	Augmented 1-mosstep	A1ms	L	48.0 ¢ to 240.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 96.0 ¢
	Major 2-mosstep	M2ms	L + s	96.0 ¢ to 240.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0 ¢ to 144.0 ¢
	Major 3-mosstep	M3ms	L + 2s	144.0 ¢ to 240.0 ¢
4-mosstep	Diminished 4-mosstep	d4ms	4s	0.0 ¢ to 192.0 ¢
	Perfect 4-mosstep	P4ms	L + 3s	192.0 ¢ to 240.0 ¢
5-mosstep	Perfect 5-mosstep	P5ms	L + 4s	240.0 ¢
6-mosstep	Perfect 6-mosstep	P6ms	L + 5s	240.0 ¢ to 288.0 ¢
	Augmented 6-mosstep	A6ms	2L + 4s	288.0 ¢ to 480.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	L + 6s	240.0 ¢ to 336.0 ¢
	Major 7-mosstep	M7ms	2L + 5s	336.0 ¢ to 480.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	L + 7s	240.0 ¢ to 384.0 ¢
	Major 8-mosstep	M8ms	2L + 6s	384.0 ¢ to 480.0 ¢
9-mosstep	Diminished 9-mosstep	d9ms	L + 8s	240.0 ¢ to 432.0 ¢
	Perfect 9-mosstep	P9ms	2L + 7s	432.0 ¢ to 480.0 ¢
10-mosstep	Perfect 10-mosstep	P10ms	2L + 8s	480.0 ¢
11-mosstep	Perfect 11-mosstep	P11ms	2L + 9s	480.0 ¢ to 528.0 ¢
	Augmented 11-mosstep	A11ms	3L + 8s	528.0 ¢ to 720.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	2L + 10s	480.0 ¢ to 576.0 ¢
	Major 12-mosstep	M12ms	3L + 9s	576.0 ¢ to 720.0 ¢
13-mosstep	Minor 13-mosstep	m13ms	2L + 11s	480.0 ¢ to 624.0 ¢
	Major 13-mosstep	M13ms	3L + 10s	624.0 ¢ to 720.0 ¢
14-mosstep	Diminished 14-mosstep	d14ms	2L + 12s	480.0 ¢ to 672.0 ¢
	Perfect 14-mosstep	P14ms	3L + 11s	672.0 ¢ to 720.0 ¢
15-mosstep	Perfect 15-mosstep	P15ms	3L + 12s	720.0 ¢
16-mosstep	Perfect 16-mosstep	P16ms	3L + 13s	720.0 ¢ to 768.0 ¢
	Augmented 16-mosstep	A16ms	4L + 12s	768.0 ¢ to 960.0 ¢
17-mosstep	Minor 17-mosstep	m17ms	3L + 14s	720.0 ¢ to 816.0 ¢
	Major 17-mosstep	M17ms	4L + 13s	816.0 ¢ to 960.0 ¢
18-mosstep	Minor 18-mosstep	m18ms	3L + 15s	720.0 ¢ to 864.0 ¢
	Major 18-mosstep	M18ms	4L + 14s	864.0 ¢ to 960.0 ¢
19-mosstep	Diminished 19-mosstep	d19ms	3L + 16s	720.0 ¢ to 912.0 ¢
	Perfect 19-mosstep	P19ms	4L + 15s	912.0 ¢ to 960.0 ¢
20-mosstep	Perfect 20-mosstep	P20ms	4L + 16s	960.0 ¢
21-mosstep	Perfect 21-mosstep	P21ms	4L + 17s	960.0 ¢ to 1008.0 ¢
	Augmented 21-mosstep	A21ms	5L + 16s	1008.0 ¢ to 1200.0 ¢
22-mosstep	Minor 22-mosstep	m22ms	4L + 18s	960.0 ¢ to 1056.0 ¢
	Major 22-mosstep	M22ms	5L + 17s	1056.0 ¢ to 1200.0 ¢
23-mosstep	Minor 23-mosstep	m23ms	4L + 19s	960.0 ¢ to 1104.0 ¢
	Major 23-mosstep	M23ms	5L + 18s	1104.0 ¢ to 1200.0 ¢
24-mosstep	Diminished 24-mosstep	d24ms	4L + 20s	960.0 ¢ to 1152.0 ¢
	Perfect 24-mosstep	P24ms	5L + 19s	1152.0 ¢ to 1200.0 ¢
25-mosstep	Perfect 25-mosstep	P25ms	5L + 20s	1200.0 ¢

Scale tree

Scale tree and tuning spectrum of 5L 20s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
4\25						192.000	48.000	1:1	1.000	Equalized 5L 20s
					21\130	193.846	46.154	6:5	1.200
				17\105		194.286	45.714	5:4	1.250
					30\185	194.595	45.405	9:7	1.286
			13\80			195.000	45.000	4:3	1.333	Supersoft 5L 20s
					35\215	195.349	44.651	11:8	1.375
				22\135		195.556	44.444	7:5	1.400
					31\190	195.789	44.211	10:7	1.429
		9\55				196.364	43.636	3:2	1.500	Soft 5L 20s
					32\195	196.923	43.077	11:7	1.571
				23\140		197.143	42.857	8:5	1.600
					37\225	197.333	42.667	13:8	1.625
			14\85			197.647	42.353	5:3	1.667	Semisoft 5L 20s
					33\200	198.000	42.000	12:7	1.714
				19\115		198.261	41.739	7:4	1.750
					24\145	198.621	41.379	9:5	1.800
	5\30					200.000	40.000	2:1	2.000	Basic 5L 20s Scales with tunings softer than this are proper
					21\125	201.600	38.400	9:4	2.250
				16\95		202.105	37.895	7:3	2.333
					27\160	202.500	37.500	12:5	2.400
			11\65			203.077	36.923	5:2	2.500	Semihard 5L 20s
					28\165	203.636	36.364	13:5	2.600
				17\100		204.000	36.000	8:3	2.667
					23\135	204.444	35.556	11:4	2.750
		6\35				205.714	34.286	3:1	3.000	Hard 5L 20s
					19\110	207.273	32.727	10:3	3.333
				13\75		208.000	32.000	7:2	3.500
					20\115	208.696	31.304	11:3	3.667
			7\40			210.000	30.000	4:1	4.000	Superhard 5L 20s
					15\85	211.765	28.235	9:2	4.500
				8\45		213.333	26.667	5:1	5.000
					9\50	216.000	24.000	6:1	6.000
1\5						240.000	0.000	1:0	→ ∞	Collapsed 5L 20s