3L 6s

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↖ 2L 5s ↑3L 5s 4L 5s ↗
← 2L 6s3L 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 Rotational order Step pattern
6 | 0(3) 1 LssLssLss
3 | 3(3) 3 sLssLssLs
0 | 6(3) 2 ssLssLssL

Scale tree

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 August
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 Augene
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 August
4\15 320.000 80.000 3:1 3.000 Hard 3L 6s
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 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 Hemiug, hemiaug↓
1\3 400.000 0.000 1:0 → ∞ Collapsed 3L 6s

External links