3L 6s
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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¢)
| ↖ 2L 5s | ↑ 3L 5s | 4L 5s ↗ |
| ← 2L 6s | 3L 6s | 4L 6s → |
| ↙ 2L 7s | ↓ 3L 7s | 4L 7s ↘ |
┌╥┬┬╥┬┬╥┬┬┐ │║││║││║│││ │││││││││││ └┴┴┴┴┴┴┴┴┴┘
ssLssLssL
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).
Intervals
| 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¢ |
Modes
| 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. |
Scale tree
| 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
- Piano Encyclopedia, on Tcherepnin's 9-note scale: https://pianoencyclopedia.com/scales/tcherepnin-nine-note-mode-i/