3L 6s

↖ 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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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 ¢.

Name

TAMNAMS suggests the temperaement-agnostic name tcherepnin for this scale. This is named after Alexander Tcherepnin's 9-note scale which, in 12edo, is notated as C Db Eb E F G Ab A B C, forming the step pattern of HWHHWHHWH in standard notation (assuming a root of C).

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

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 3L 6s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
2\9						266.667	133.333	1:1	1.000	Equalized 3L 6s
					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	Supersoft 3L 6s
					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	1.429
		5\21				285.714	114.286	3:2	1.500	Soft 3L 6s
					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
			8\33			290.909	109.091	5:3	1.667	Semisoft 3L 6s
					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
	3\12					300.000	100.000	2:1	2.000	Basic 3L 6s Scales with tunings softer 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
			7\27			311.111	88.889	5:2	2.500	Semihard 3L 6s
					18\69	313.043	86.957	13:5	2.600
				11\42		314.286	85.714	8:3	2.667
					15\57	315.789	84.211	11:4	2.750
		4\15				320.000	80.000	3:1	3.000	Hard 3L 6s
					13\48	325.000	75.000	10:3	3.333
				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	Superhard 3L 6s
					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
1\3						400.000	0.000	1:0	→ ∞	Collapsed 3L 6s

External links

• Piano Encyclopedia, on Tcherepnin's 9-note scale: https://pianoencyclopedia.com/scales/tcherepnin-nine-note-mode-i/