User:MisterShafXen/1L 4s

1L 4s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 1 large step and 4 small steps, repeating every octave. Generators that produce this scale range from 960 ¢ to 1200 ¢, or from 0 ¢ to 240 ¢.

	↑ 1L 3s	2L 3s ↗
	1L 4s	2L 4s →
	↓ 1L 5s	2L 5s ↘

Scale structure
Step pattern	Lssss ssssL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	4\5 to 1\1 (960.0 ¢ to 1200.0 ¢)
Dark	0\1 to 1\5 (0.0 ¢ to 240.0 ¢)
Related MOS scales
Parent	1L 3s
Sister	4L 1s
Daughters	5L 1s, 1L 5s
Neutralized	2L 3s
2-Flought	6L 4s, 1L 9s
Equal tunings
Equalized (L:s = 1:1)	4\5 (960.0 ¢)
Supersoft (L:s = 4:3)	13\16 (975.0 ¢)
Soft (L:s = 3:2)	9\11 (981.8 ¢)
Semisoft (L:s = 5:3)	14\17 (988.2 ¢)
Basic (L:s = 2:1)	5\6 (1000.0 ¢)
Semihard (L:s = 5:2)	11\13 (1015.4 ¢)
Hard (L:s = 3:1)	6\7 (1028.6 ¢)
Superhard (L:s = 4:1)	7\8 (1050.0 ¢)
Collapsed (L:s = 1:0)	1\1 (1200.0 ¢)
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Scale properties

Intervals of 1L 4s

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 240.0 ¢
	Augmented 1-mosstep	A1ms	L	240.0 ¢ to 1200.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 480.0 ¢
	Major 2-mosstep	M2ms	L + s	480.0 ¢ to 1200.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0 ¢ to 720.0 ¢
	Major 3-mosstep	M3ms	L + 2s	720.0 ¢ to 1200.0 ¢
4-mosstep	Diminished 4-mosstep	d4ms	4s	0.0 ¢ to 960.0 ¢
	Perfect 4-mosstep	P4ms	L + 3s	960.0 ¢ to 1200.0 ¢
5-mosstep	Perfect 5-mosstep	P5ms	L + 4s	1200.0 ¢

Comparison of various tunings

L:s (edo)	A0	P1	A1	m2	M2	m3	M3	d4	P4	d5
1:1 (5edo)	0¢	240¢	240¢	480¢	480¢	720¢	720¢	960¢	960¢	1200¢
3:2 (11edo)	109¢	218¢	327¢	436¢	545¢	655¢	764¢	873¢	982¢	1091¢
2:1 (6edo)	200¢	200¢	400¢	400¢	600¢	600¢	800¢	800¢	1000¢	1000¢
3:1 (7edo)	343¢	171¢	514¢	343¢	686¢	514¢	857¢	686¢	1029¢	857¢
4:1 (8edo)	450¢	150¢	600¢	300¢	750¢	450¢	900¢	600¢	1050¢	750¢
5:1 (9edo)	533¢	133¢	667¢	267¢	800¢	400¢	933¢	533¢	1067¢	667¢
6:1 (10edo)	600¢	120¢	720¢	240¢	840¢	360¢	960¢	480¢	1080¢	600¢
7:1 (11edo)	655¢	109¢	764¢	218¢	873¢	327¢	982¢	436¢	1091¢	545¢
1:0 (1edo)	1200¢	0¢	1200¢	0¢	1200¢	0¢	1200¢	0¢	1200¢	0¢

Generator chain of 1L 4s

Bright gens	Scale degree	Abbrev.
5	Augmented 0-mosdegree	A0md
4	Augmented 1-mosdegree	A1md
3	Major 2-mosdegree	M2md
2	Major 3-mosdegree	M3md
1	Perfect 4-mosdegree	P4md
0	Perfect 0-mosdegree Perfect 5-mosdegree	P0md P5md
−1	Perfect 1-mosdegree	P1md
−2	Minor 2-mosdegree	m2md
−3	Minor 3-mosdegree	m3md
−4	Diminished 4-mosdegree	d4md
−5	Diminished 5-mosdegree	d5md

Modes of 1L 4s

UDP	Cyclic order	Step pattern
4|0	1	Lssss
3|1	5	sLsss
2|2	4	ssLss
1|3	3	sssLs
0|4	2	ssssL

Scale tree

Scale tree and tuning spectrum of 1L 4s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
4\5						960.000	240.000	1:1	1.000	Equalized 1L 4s
					21\26	969.231	230.769	6:5	1.200
				17\21		971.429	228.571	5:4	1.250
					30\37	972.973	227.027	9:7	1.286
			13\16			975.000	225.000	4:3	1.333	Supersoft 1L 4s
					35\43	976.744	223.256	11:8	1.375
				22\27		977.778	222.222	7:5	1.400
					31\38	978.947	221.053	10:7	1.429
		9\11				981.818	218.182	3:2	1.500	Soft 1L 4s
					32\39	984.615	215.385	11:7	1.571
				23\28		985.714	214.286	8:5	1.600
					37\45	986.667	213.333	13:8	1.625
			14\17			988.235	211.765	5:3	1.667	Semisoft 1L 4s
					33\40	990.000	210.000	12:7	1.714
				19\23		991.304	208.696	7:4	1.750
					24\29	993.103	206.897	9:5	1.800
	5\6					1000.000	200.000	2:1	2.000	Basic 1L 4s Scales with tunings softer than this are proper
					21\25	1008.000	192.000	9:4	2.250
				16\19		1010.526	189.474	7:3	2.333
					27\32	1012.500	187.500	12:5	2.400
			11\13			1015.385	184.615	5:2	2.500	Semihard 1L 4s
					28\33	1018.182	181.818	13:5	2.600
				17\20		1020.000	180.000	8:3	2.667
					23\27	1022.222	177.778	11:4	2.750
		6\7				1028.571	171.429	3:1	3.000	Hard 1L 4s
					19\22	1036.364	163.636	10:3	3.333
				13\15		1040.000	160.000	7:2	3.500
					20\23	1043.478	156.522	11:3	3.667
			7\8			1050.000	150.000	4:1	4.000	Superhard 1L 4s
					15\17	1058.824	141.176	9:2	4.500
				8\9		1066.667	133.333	5:1	5.000
					9\10	1080.000	120.000	6:1	6.000
1\1						1200.000	0.000	1:0	→ ∞	Collapsed 1L 4s