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

Modes of 3L 6s

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

External links

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