3L 2s
Jump to navigation
Jump to search
Step pattern
LLsLs
sLsLL
Equave
2/1 (1200.0 ¢)
Period
2/1 (1200.0 ¢)
Bright
3\5 to 2\3 (720.0 ¢ to 800.0 ¢)
Dark
1\3 to 2\5 (400.0 ¢ to 480.0 ¢)
Parent
2L 1s
Sister
2L 3s
Daughters
5L 3s, 3L 5s
Neutralized
1L 4s
2-Flought
8L 2s, 3L 7s
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 ↘ |
┌╥╥┬╥┬┐ │║║│║││ │││││││ └┴┴┴┴┴┘
Scale structure
sLsLL
Generator size
Related MOS scales
Equal tunings
- 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[5]. 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.
Intervals
| Intervals | Steps subtended |
Range in cents | ||
|---|---|---|---|---|
| Generic | Specific | Abbrev. | ||
| 0-mosstep | Perfect 0-mosstep | P0ms | 0 | 0.0 ¢ |
| 1-mosstep | Minor 1-mosstep | m1ms | s | 0.0 ¢ to 240.0 ¢ |
| Major 1-mosstep | M1ms | L | 240.0 ¢ to 400.0 ¢ | |
| 2-mosstep | Perfect 2-mosstep | P2ms | L + s | 400.0 ¢ to 480.0 ¢ |
| Augmented 2-mosstep | A2ms | 2L | 480.0 ¢ to 800.0 ¢ | |
| 3-mosstep | Diminished 3-mosstep | d3ms | L + 2s | 400.0 ¢ to 720.0 ¢ |
| Perfect 3-mosstep | P3ms | 2L + s | 720.0 ¢ to 800.0 ¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | 2L + 2s | 800.0 ¢ to 960.0 ¢ |
| Major 4-mosstep | M4ms | 3L + s | 960.0 ¢ to 1200.0 ¢ | |
| 5-mosstep | Perfect 5-mosstep | P5ms | 3L + 2s | 1200.0 ¢ |
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 ¢ (3\5) to 800 ¢ (2\3)
- Chroma-negative generator: 400 ¢ (1\3) to 480 ¢ (2\5)
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 3\5 | 720.000 | 480.000 | 1:1 | 1.000 | Equalized 3L 2s | |||||
| 17\28 | 728.571 | 471.429 | 6:5 | 1.200 | ||||||
| 14\23 | 730.435 | 469.565 | 5:4 | 1.250 | ||||||
| 25\41 | 731.707 | 468.293 | 9:7 | 1.286 | ||||||
| 11\18 | 733.333 | 466.667 | 4:3 | 1.333 | Supersoft 3L 2s | |||||
| 30\49 | 734.694 | 465.306 | 11:8 | 1.375 | Semisept | |||||
| 19\31 | 735.484 | 464.516 | 7:5 | 1.400 | ||||||
| 27\44 | 736.364 | 463.636 | 10:7 | 1.429 | ||||||
| 8\13 | 738.462 | 461.538 | 3:2 | 1.500 | Soft 3L 2s | |||||
| 29\47 | 740.426 | 459.574 | 11:7 | 1.571 | ||||||
| 21\34 | 741.176 | 458.824 | 8:5 | 1.600 | ||||||
| 34\55 | 741.818 | 458.182 | 13:8 | 1.625 | Golden father/petritri/aurora (741.6408 ¢) | |||||
| 13\21 | 742.857 | 457.143 | 5:3 | 1.667 | Semisoft 3L 2s | |||||
| 31\50 | 744.000 | 456.000 | 12:7 | 1.714 | ||||||
| 18\29 | 744.828 | 455.172 | 7:4 | 1.750 | ||||||
| 23\37 | 745.946 | 454.054 | 9:5 | 1.800 | ||||||
| 5\8 | 750.000 | 450.000 | 2:1 | 2.000 | Basic 3L 2s Scales with tunings softer than this are proper | |||||
| 22\35 | 754.286 | 445.714 | 9:4 | 2.250 | ||||||
| 17\27 | 755.556 | 444.444 | 7:3 | 2.333 | ||||||
| 29\46 | 756.522 | 443.478 | 12:5 | 2.400 | Sensi
13/5 = Golden sentry (759.4078 ¢) | |||||
| 12\19 | 757.895 | 442.105 | 5:2 | 2.500 | Semihard 3L 2s | |||||
| 31\49 | 759.184 | 440.816 | 13:5 | 2.600 | ||||||
| 19\30 | 760.000 | 440.000 | 8:3 | 2.667 | ||||||
| 26\41 | 760.976 | 439.024 | 11:4 | 2.750 | ||||||
| 7\11 | 763.636 | 436.364 | 3:1 | 3.000 | Hard 3L 2s | |||||
| 23\36 | 766.667 | 433.333 | 10:3 | 3.333 | ||||||
| 16\25 | 768.000 | 432.000 | 7:2 | 3.500 | ||||||
| 25\39 | 769.231 | 430.769 | 11:3 | 3.667 | ||||||
| 9\14 | 771.429 | 428.571 | 4:1 | 4.000 | Superhard 3L 2s | |||||
| 20\31 | 774.194 | 425.806 | 9:2 | 4.500 | Squares/skwares | |||||
| 11\17 | 776.471 | 423.529 | 5:1 | 5.000 | ||||||
| 13\20 | 780.000 | 420.000 | 6:1 | 6.000 | ||||||
| 2\3 | 800.000 | 400.000 | 1:0 | → ∞ | Collapsed 3L 2s | |||||