2L 4s
| ↖ 1L 3s | ↑ 2L 3s | 3L 3s ↗ |
| ← 1L 4s | 2L 4s | 3L 4s → |
| ↙ 1L 5s | ↓ 2L 5s | 3L 5s ↘ |
┌╥┬┬╥┬┬┐ │║││║│││ ││││││││ └┴┴┴┴┴┴┘
ssLssL
2L 4s, named malic in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 2 large steps and 4 small steps, with a period of 1 large step and 2 small steps that repeats every 600.0¢, or twice every octave. Generators that produce this scale range from 400¢ to 600¢, or from 0¢ to 200¢.
The only scale with this MOS pattern that's a really significant minimum of harmonic entropy is srutal/pajara, in which the period plus the generator is 3/2. Other scales include shrutar, in which the generator is half of that (about a quartertone), so 3/2 is a period plus two generators; and hedgehog, in which two generators make a 6/5, and 4/3 would be three generators (except that it doesn't appear in this MOS).
In addition to the true MOS with pattern LssLss, all these scales also come in a near-MOS version, LsLsss, in which the period is the only generic interval that has more than two specific representatives.
Srutal/pajara probably has the lowest harmonic entropy of all 6-note MOS scales. The near-MOS version has even lower harmonic entropy.
Intervals
| Intervals | Steps subtended |
Range in cents | ||
|---|---|---|---|---|
| Generic | Specific | Abbrev. | ||
| 0-malstep | Perfect 0-malstep | P0mals | 0 | 0.0¢ |
| 1-malstep | Perfect 1-malstep | P1mals | s | 0.0¢ to 200.0¢ |
| Augmented 1-malstep | A1mals | L | 200.0¢ to 600.0¢ | |
| 2-malstep | Diminished 2-malstep | d2mals | 2s | 0.0¢ to 400.0¢ |
| Perfect 2-malstep | P2mals | L + s | 400.0¢ to 600.0¢ | |
| 3-malstep | Perfect 3-malstep | P3mals | L + 2s | 600.0¢ |
| 4-malstep | Perfect 4-malstep | P4mals | L + 3s | 600.0¢ to 800.0¢ |
| Augmented 4-malstep | A4mals | 2L + 2s | 800.0¢ to 1200.0¢ | |
| 5-malstep | Diminished 5-malstep | d5mals | L + 4s | 600.0¢ to 1000.0¢ |
| Perfect 5-malstep | P5mals | 2L + 3s | 1000.0¢ to 1200.0¢ | |
| 6-malstep | Perfect 6-malstep | P6mals | 2L + 4s | 1200.0¢ |
Modes
| UDP | Cyclic order |
Step pattern |
Scale degree (maldegree) | ||||||
|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | |||
| 4|0(2) | 1 | LssLss | Perf. | Aug. | Perf. | Perf. | Aug. | Perf. | Perf. |
| 2|2(2) | 3 | sLssLs | Perf. | Perf. | Perf. | Perf. | Perf. | Perf. | Perf. |
| 0|4(2) | 2 | ssLssL | Perf. | Perf. | Dim. | Perf. | Perf. | Dim. | Perf. |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 2\6 | 400.000 | 200.000 | 1:1 | 1.000 | Equalized 2L 4s | |||||
| 11\32 | 412.500 | 187.500 | 6:5 | 1.200 | ||||||
| 9\26 | 415.385 | 184.615 | 5:4 | 1.250 | ||||||
| 16\46 | 417.391 | 182.609 | 9:7 | 1.286 | ||||||
| 7\20 | 420.000 | 180.000 | 4:3 | 1.333 | Supersoft 2L 4s | |||||
| 19\54 | 422.222 | 177.778 | 11:8 | 1.375 | ||||||
| 12\34 | 423.529 | 176.471 | 7:5 | 1.400 | ||||||
| 17\48 | 425.000 | 175.000 | 10:7 | 1.429 | ||||||
| 5\14 | 428.571 | 171.429 | 3:2 | 1.500 | Soft 2L 4s Optimum rank range | |||||
| 18\50 | 432.000 | 168.000 | 11:7 | 1.571 | ||||||
| 13\36 | 433.333 | 166.667 | 8:5 | 1.600 | ||||||
| 21\58 | 434.483 | 165.517 | 13:8 | 1.625 | Golden hedgehog/echidna | |||||
| 8\22 | 436.364 | 163.636 | 5:3 | 1.667 | Semisoft 2L 4s Hedgehog and echidna are around here | |||||
| 19\52 | 438.462 | 161.538 | 12:7 | 1.714 | ||||||
| 11\30 | 440.000 | 160.000 | 7:4 | 1.750 | ||||||
| 14\38 | 442.105 | 157.895 | 9:5 | 1.800 | ||||||
| 3\8 | 450.000 | 150.000 | 2:1 | 2.000 | Basic 2L 4s Scales with tunings softer than this are proper | |||||
| 13\34 | 458.824 | 141.176 | 9:4 | 2.250 | ||||||
| 10\26 | 461.538 | 138.462 | 7:3 | 2.333 | ||||||
| 17\44 | 463.636 | 136.364 | 12:5 | 2.400 | ||||||
| 7\18 | 466.667 | 133.333 | 5:2 | 2.500 | Semihard 2L 4s | |||||
| 18\46 | 469.565 | 130.435 | 13:5 | 2.600 | ||||||
| 11\28 | 471.429 | 128.571 | 8:3 | 2.667 | ||||||
| 15\38 | 473.684 | 126.316 | 11:4 | 2.750 | ||||||
| 4\10 | 480.000 | 120.000 | 3:1 | 3.000 | Hard 2L 4s | |||||
| 13\32 | 487.500 | 112.500 | 10:3 | 3.333 | ||||||
| 9\22 | 490.909 | 109.091 | 7:2 | 3.500 | Srutal/Pajara is around here | |||||
| 14\34 | 494.118 | 105.882 | 11:3 | 3.667 | ||||||
| 5\12 | 500.000 | 100.000 | 4:1 | 4.000 | Superhard 2L 4s | |||||
| 11\26 | 507.692 | 92.308 | 9:2 | 4.500 | Injera is around here | |||||
| 6\14 | 514.286 | 85.714 | 5:1 | 5.000 | ||||||
| 7\16 | 525.000 | 75.000 | 6:1 | 6.000 | Shrutar ↓ | |||||
| 1\2 | 600.000 | 0.000 | 1:0 | → ∞ | Collapsed 2L 4s | |||||