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 ¢)

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

Scale degrees of the modes of 3L 6s

UDP	Cyclic order	Step pattern	Scale degree (cherdegree)
			0	1	2	3	4	5	6	7	8	9
6|0(3)	1	LssLssLss	Perf.	Aug.	Perf.	Perf.	Aug.	Perf.	Perf.	Aug.	Perf.	Perf.
3|3(3)	3	sLssLssLs	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.	Perf.
0|6(3)	2	ssLssLssL	Perf.	Perf.	Dim.	Perf.	Perf.	Dim.	Perf.	Perf.	Dim.	Perf.

Intervals

Intervals of 3L 6s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-cherstep	Perfect 0-cherstep	P0chs	0	0.0 ¢
1-cherstep	Perfect 1-cherstep	P1chs	s	0.0 ¢ to 133.3 ¢
	Augmented 1-cherstep	A1chs	L	133.3 ¢ to 400.0 ¢
2-cherstep	Diminished 2-cherstep	d2chs	2s	0.0 ¢ to 266.7 ¢
	Perfect 2-cherstep	P2chs	L + s	266.7 ¢ to 400.0 ¢
3-cherstep	Perfect 3-cherstep	P3chs	L + 2s	400.0 ¢
4-cherstep	Perfect 4-cherstep	P4chs	L + 3s	400.0 ¢ to 533.3 ¢
	Augmented 4-cherstep	A4chs	2L + 2s	533.3 ¢ to 800.0 ¢
5-cherstep	Diminished 5-cherstep	d5chs	L + 4s	400.0 ¢ to 666.7 ¢
	Perfect 5-cherstep	P5chs	2L + 3s	666.7 ¢ to 800.0 ¢
6-cherstep	Perfect 6-cherstep	P6chs	2L + 4s	800.0 ¢
7-cherstep	Perfect 7-cherstep	P7chs	2L + 5s	800.0 ¢ to 933.3 ¢
	Augmented 7-cherstep	A7chs	3L + 4s	933.3 ¢ to 1200.0 ¢
8-cherstep	Diminished 8-cherstep	d8chs	2L + 6s	800.0 ¢ to 1066.7 ¢
	Perfect 8-cherstep	P8chs	3L + 5s	1066.7 ¢ to 1200.0 ¢
9-cherstep	Perfect 9-cherstep	P9chs	3L + 6s	1200.0 ¢

External links

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