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
Brightest mode LssLssLss
Equave (cents) 2/1 (1200.0¢)
Period (cents) 1\3edo (400.0¢)
Generator ranges
Bright 2\9 (266.7¢) to 1\3 (400.0¢)
Dark 0\3 (0.0¢) to 1\9 (133.3¢)
TAMNAMS information
Name tcherepnin
Prefix cher-
Abbrev. ch
Related scales
Parent 3L 3s
Sister 6L 3s
Daughters 9L 3s, 3L 9s
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¢.

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

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