3L 2s
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Scale structure
Step pattern
LLsLs
sLsLL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
3\5 to 2\3 (720.0¢ to 800.0¢)
Dark
1\3 to 2\5 (400.0¢ to 480.0¢)
Related MOS scales
Parent
2L 1s
Sister
2L 3s
Daughters
5L 3s, 3L 5s
Neutralized
1L 4s
2-Flought
8L 2s, 3L 7s
Equal tunings
Equalized (L:s = 1:1)
3\5 (720.0¢)
Supersoft (L:s = 4:3)
11\18 (733.3¢)
Soft (L:s = 3:2)
8\13 (738.5¢)
Semisoft (L:s = 5:3)
13\21 (742.9¢)
Basic (L:s = 2:1)
5\8 (750.0¢)
Semihard (L:s = 5:2)
12\19 (757.9¢)
Hard (L:s = 3:1)
7\11 (763.6¢)
Superhard (L:s = 4:1)
9\14 (771.4¢)
Collapsed (L:s = 1:0)
2\3 (800.0¢)
| ↖ 2L 1s | ↑ 3L 1s | 4L 1s ↗ |
| ← 2L 2s | 3L 2s | 4L 2s → |
| ↙ 2L 3s | ↓ 3L 3s | 4L 3s ↘ |
┌╥╥┬╥┬┐ │║║│║││ │││││││ └┴┴┴┴┴┘
sLsLL
- For the 3/2-equivalent 3L 2s pattern, see 3L 2s (fifth-equivalent).
3L 2s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 2 small steps, repeating every octave. Generators that produce this scale range from 720¢ to 800¢, or from 400¢ to 480¢. The only notable low-harmonic-entropy scale for this MOS pattern is sensi, in which two generators make a 5/3. The harmonic entropy of sensi[5] is still fairly high relative to other pentatonic scales, such as meantone. It's also improper.
Name
The TAMNAMS system applies the name antipentic as the scale utilizes opposite step sizes to the “classic” pentatonic scale (2L 3s). The name antipentic can be used regardless of the equave.
Modes
| UDP | Cyclic order |
Step pattern |
Scale degree (mosdegree) | |||||
|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | 5 | |||
| 4|0 | 1 | LLsLs | Perf. | Maj. | Aug. | Perf. | Maj. | Perf. |
| 3|1 | 4 | LsLLs | Perf. | Maj. | Perf. | Perf. | Maj. | Perf. |
| 2|2 | 2 | LsLsL | Perf. | Maj. | Perf. | Perf. | Min. | Perf. |
| 1|3 | 5 | sLLsL | Perf. | Min. | Perf. | Perf. | Min. | Perf. |
| 0|4 | 3 | sLsLL | Perf. | Min. | Perf. | Dim. | Min. | Perf. |
Scale tree
Generator ranges:
- Chroma-positive generator: 720 cents (3\5) to 800 cents (2\3)
- Chroma-negative generator: 400 cents (1\3) to 480 cents (2\5)
| Generator | Cents | L | s | L/s | Comments | |||||
|---|---|---|---|---|---|---|---|---|---|---|
| 3\5 | 720.000 | 1 | 1 | 1.000 | ||||||
| 17\28 | 728.571 | 6 | 5 | 1.200 | ||||||
| 14\23 | 730.435 | 5 | 4 | 1.250 | ||||||
| 25\41 | 731.707 | 9 | 7 | 1.286 | ||||||
| 11\18 | 733.333 | 4 | 3 | 1.333 | ||||||
| 30\49 | 734.694 | 11 | 8 | 1.375 | Semisept | |||||
| 19\31 | 735.484 | 7 | 5 | 1.400 | ||||||
| 27\44 | 736.364 | 10 | 7 | 1.429 | ||||||
| 8\13 | 738.462 | 3 | 2 | 1.500 | ||||||
| 29\47 | 740.426 | 11 | 7 | 1.571 | ||||||
| 21\34 | 741.176 | 8 | 5 | 1.600 | ||||||
| 34\55 | 741.818 | 13 | 8 | 1.625 | Golden father/petritri/aurora (741.6408¢) | |||||
| 13\21 | 742.857 | 5 | 3 | 1.667 | ||||||
| 31\50 | 744.000 | 12 | 7 | 1.714 | ||||||
| 18\29 | 744.828 | 7 | 4 | 1.750 | ||||||
| 23\37 | 745.946 | 9 | 5 | 1.800 | ||||||
| 5\8 | 750.000 | 2 | 1 | 2.000 | Basic antipentic (Generators smaller than this are proper) | |||||
| 22\35 | 754.286 | 9 | 4 | 2.250 | ||||||
| 17\27 | 755.556 | 7 | 3 | 2.333 | ||||||
| 29\46 | 756.522 | 12 | 5 | 2.400 | Sensi | |||||
| 12\19 | 757.895 | 5 | 2 | 2.500 | ||||||
| 31\49 | 759.184 | 13 | 5 | 2.600 | Golden sentry (759.4078¢) | |||||
| 19\30 | 760.000 | 8 | 3 | 2.667 | ||||||
| 26\41 | 760.976 | 11 | 4 | 2.750 | ||||||
| 7\11 | 763.636 | 3 | 1 | 3.000 | ||||||
| 23\36 | 766.667 | 10 | 3 | 3.333 | ||||||
| 16\25 | 768.000 | 7 | 2 | 3.500 | ||||||
| 25\39 | 769.231 | 11 | 3 | 3.667 | ||||||
| 9\14 | 771.429 | 4 | 1 | 4.000 | ||||||
| 20\31 | 774.194 | 9 | 2 | 4.500 | Squares/skwares | |||||
| 11\17 | 776.471 | 5 | 1 | 5.000 | ||||||
| 13\20 | 780.000 | 6 | 1 | 6.000 | ||||||
| 2\3 | 800.000 | 1 | 0 | → inf | ||||||