1L 3s

1L 3s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 1 large step and 3 small steps, repeating every octave. Generators that produce this scale range from 900 ¢ to 1200 ¢, or from 0 ¢ to 300 ¢.

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

Scale structure
Step pattern	Lsss sssL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	3\4 to 1\1 (900.0 ¢ to 1200.0 ¢)
Dark	0\1 to 1\4 (0.0 ¢ to 300.0 ¢)
Related MOS scales
Parent	1L 2s
Sister	3L 1s
Daughters	4L 1s, 1L 4s
Neutralized	2L 2s
2-Flought	5L 3s, 1L 7s
Equal tunings
Equalized (L:s = 1:1)	3\4 (900.0 ¢)
Supersoft (L:s = 4:3)	10\13 (923.1 ¢)
Soft (L:s = 3:2)	7\9 (933.3 ¢)
Semisoft (L:s = 5:3)	11\14 (942.9 ¢)
Basic (L:s = 2:1)	4\5 (960.0 ¢)
Semihard (L:s = 5:2)	9\11 (981.8 ¢)
Hard (L:s = 3:1)	5\6 (1000.0 ¢)
Superhard (L:s = 4:1)	6\7 (1028.6 ¢)
Collapsed (L:s = 1:0)	1\1 (1200.0 ¢)
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In South Africa, the San use a tetratonic scale which can be approximated by basic 1L 3s.

Modes

Scale degrees of the modes of 1L 3s

UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
			0	1	2	3	4
3|0	1	Lsss	Perf.	Aug.	Maj.	Perf.	Perf.
2|1	4	sLss	Perf.	Perf.	Maj.	Perf.	Perf.
1|2	3	ssLs	Perf.	Perf.	Min.	Perf.	Perf.
0|3	2	sssL	Perf.	Perf.	Min.	Dim.	Perf.

Intervals

Intervals of 1L 3s

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 300.0 ¢
	Augmented 1-mosstep	A1ms	L	300.0 ¢ to 1200.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 600.0 ¢
	Major 2-mosstep	M2ms	L + s	600.0 ¢ to 1200.0 ¢
3-mosstep	Diminished 3-mosstep	d3ms	3s	0.0 ¢ to 900.0 ¢
	Perfect 3-mosstep	P3ms	L + 2s	900.0 ¢ to 1200.0 ¢
4-mosstep	Perfect 4-mosstep	P4ms	L + 3s	1200.0 ¢

Scale tree

Generator ranges:

• Chroma-positive generator: 900 cents (3\4) to 1200 cents (1\1)
• Chroma-negative generator: 0 cents (0\1) to 300 cents (1\4)

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 1L 3s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
3\4						900.000	300.000	1:1	1.000	Equalized 1L 3s
					16\21	914.286	285.714	6:5	1.200
				13\17		917.647	282.353	5:4	1.250
					23\30	920.000	280.000	9:7	1.286
			10\13			923.077	276.923	4:3	1.333	Supersoft 1L 3s
					27\35	925.714	274.286	11:8	1.375
				17\22		927.273	272.727	7:5	1.400
					24\31	929.032	270.968	10:7	1.429
		7\9				933.333	266.667	3:2	1.500	Soft 1L 3s
					25\32	937.500	262.500	11:7	1.571
				18\23		939.130	260.870	8:5	1.600
					29\37	940.541	259.459	13:8	1.625
			11\14			942.857	257.143	5:3	1.667	Semisoft 1L 3s
					26\33	945.455	254.545	12:7	1.714
				15\19		947.368	252.632	7:4	1.750
					19\24	950.000	250.000	9:5	1.800
	4\5					960.000	240.000	2:1	2.000	Basic 1L 3s Scales with tunings softer than this are proper
					17\21	971.429	228.571	9:4	2.250
				13\16		975.000	225.000	7:3	2.333
					22\27	977.778	222.222	12:5	2.400
			9\11			981.818	218.182	5:2	2.500	Semihard 1L 3s
					23\28	985.714	214.286	13:5	2.600
				14\17		988.235	211.765	8:3	2.667
					19\23	991.304	208.696	11:4	2.750
		5\6				1000.000	200.000	3:1	3.000	Hard 1L 3s
					16\19	1010.526	189.474	10:3	3.333
				11\13		1015.385	184.615	7:2	3.500
					17\20	1020.000	180.000	11:3	3.667
			6\7			1028.571	171.429	4:1	4.000	Superhard 1L 3s
					13\15	1040.000	160.000	9:2	4.500
				7\8		1050.000	150.000	5:1	5.000
					8\9	1066.667	133.333	6:1	6.000
1\1						1200.000	0.000	1:0	→ ∞	Collapsed 1L 3s

Sources

Todo: expand