3L 6s

3L 6s, named tcherepnin in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 6 small steps, with a period of 1 large step and 2 small steps that repeats every 400.0 ¢, or 3 times every octave. Generators that produce this scale range from 266.7 ¢ to 400 ¢, or from 0 ¢ to 133.3 ¢.

↖ 2L 5s	↑ 3L 5s	4L 5s ↗
← 2L 6s	3L 6s	4L 6s →
↙ 2L 7s	↓ 3L 7s	4L 7s ↘

Scale structure
Step pattern	LssLssLss ssLssLssL
Equave	2/1 (1200.0 ¢)
Period	1\3 (400.0 ¢)
Generator size
Bright	2\9 to 1\3 (266.7 ¢ to 400.0 ¢)
Dark	0\3 to 1\9 (0.0 ¢ to 133.3 ¢)
TAMNAMS information
Name	tcherepnin
Prefix	cher-
Abbrev.	ch
Related MOS scales
Parent	3L 3s
Sister	6L 3s
Daughters	9L 3s, 3L 9s
Neutralized	6L 3s
2-Flought	12L 6s, 3L 15s
Equal tunings
Equalized (L:s = 1:1)	2\9 (266.7 ¢)
Supersoft (L:s = 4:3)	7\30 (280.0 ¢)
Soft (L:s = 3:2)	5\21 (285.7 ¢)
Semisoft (L:s = 5:3)	8\33 (290.9 ¢)
Basic (L:s = 2:1)	3\12 (300.0 ¢)
Semihard (L:s = 5:2)	7\27 (311.1 ¢)
Hard (L:s = 3:1)	4\15 (320.0 ¢)
Superhard (L:s = 4:1)	5\18 (333.3 ¢)
Collapsed (L:s = 1:0)	1\3 (400.0 ¢)
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Modes

Modes of 3L 6s

UDP	Cyclic order	Step pattern
6|0(3)	1	LssLssLss
3|3(3)	3	sLssLssLs
0|6(3)	2	ssLssLssL

Scale tree

Generator						Cents		L	s	L/s	Comments
						Chroma-positive	Chroma-negative
2\9						266.667	133.333	1	1	1.000
					11\48	275.000	125.000	6	5	1.200
				9\39		276.923	123.077	5	4	1.250
					16\69	278.261	121.739	9	7	1.286
			7\30			280.000	120.000	4	3	1.333
					19\81	281.481	118.519	11	8	1.375
				12\51		282.353	117.647	7	5	1.400
					17\72	283.333	116.667	10	7	1.428
		5\21				285.714	114.286	3	2	1.500
					18\75	288.000	112.000	11	7	1.571
				13\54		288.889	111.111	8	5	1.600
					21\87	289.655	110.345	13	8	1.625	Unnamed golden tuning
			8\33			290.909	109.091	5	3	1.667
					19\78	292.308	107.692	12	7	1.714
				11\45		293.333	106.667	7	4	1.750
					14\57	294.737	105.263	9	5	1.800	August
	3\12					300.000	100.000	2	1	2.000	Basic tcherepnin (Generators smaller than this are proper)
					13\51	305.882	94.118	9	4	2.250
				10\39		307.692	92.308	7	3	2.333
					17\66	309.091	90.909	12	5	2.400	Augene (optimal around here)
			7\27			311.111	88.889	5	2	2.500
					18\69	313.043	86.957	13	5	2.600	Unnamed golden tuning
				11\42		314.286	85.714	8	3	2.667
					15\57	315.789	84.211	11	4	2.750	August
		4\15				320.000	80.000	3	1	3.000
					13\48	325.000	75.000	10	3	3.333	Inflated
				9\33		327.273	72.727	7	2	3.500
					14\51	329.412	70.588	11	3	3.667
			5\18			333.333	66.667	4	1	4.000
					11\39	338.462	61.538	9	2	4.500
				6\21		342.857	57.143	5	1	5.000
					7\24	350.000	50.000	6	1	6.000	Hemiug, hemiaug↓
1\3						400.000	0.000	1	0	→ inf