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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Modes

• 3|0 Lsss
• 2|1 sLss
• 1|2 ssLs
• 0|3 sssL

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)

Small step (Chroma-negative generator)						Cents	L	s	L/s	Comments
1\4						300.000	1	1	1.000
					5\21	285.714	6	5	1.200
				4\17		282.353	5	4	1.250
					7\30	280.000	9	7	1.286
			3\13			276.923	4	3	1.333
					8\35	274.286	11	8	1.375
				5\22		272.727	7	5	1.400
					7\31	270.968	10	7	1.429	Orson/Orwell
		2\9				266.667	3	2	1.500
					7\32	262.500	11	7	1.571
				5\23		260.870	8	5	1.600
					8\37	259.459	13	8	1.625	Unnamed golden tuning (259.8508¢)
			3\14			257.143	5	3	1.667
					7\33	254.545	12	7	1.714
				4\19		252.632	7	4	1.750
					5\24	250.000	9	5	1.800	Godzilla
	1\5					240.000	2	1	2.000	Basic 1L 3s (Small steps larger than this are proper)
					4\21	228.571	9	4	2.250	Laconic/gorgo
				3\16		225.000	7	3	2.333
					5\27	222.222	12	5	2.400
			2\11			218.182	5	2	2.500
					5\28	214.286	13	5	2.600	Unnamed golden tuning (213.5979¢)
				3\17		211.765	8	3	2.667
					4\23	208.696	11	4	2.750
		1\6				200.000	3	1	3.000
					3\19	189.474	10	3	3.333	Isra/deutone
				2\13		184.615	7	2	3.500
					3\20	180.000	11	3	3.667
			1\7			171.429	4	1	4.000
					2\15	160.000	9	2	4.500	Porcupine
				1\8		150.000	5	1	5.000
					1\9	133.333	6	1	6.000
0\1						0.000	1	0	→ inf