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.
Scale properties
- This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for diatonic interval categories.
Intervals
The intervals of 2L 4s are named after the number of mossteps (L and s) they subtend. Each interval, apart from the period intervals (perfect 0-malstep, perfect 3-malstep, and perfect 6-malstep), has two varieties, or sizes, each. Interval varieties are named major and minor for the large and small sizes, respectively, and augmented, perfect, and diminished for the scale's generators.
| 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 ¢ |
Generator chain
A chain of bright generators, each a perfect 2-malstep, produces the following scale degrees. A chain of 3 bright generators from each period contains the scale degrees of one of the modes of 2L 4s. Expanding each chain to 4 scale degrees produces the modes of either 6L 2s (for soft-of-basic tunings) or 2L 6s (for hard-of-basic tunings).
| Bright gens | Scale degree | Abbrev. | Scale degree | Abbrev. |
|---|---|---|---|---|
| 3 | Augmented 0-maldegree | A0mald | Augmented 3-maldegree | A3mald |
| 2 | Augmented 1-maldegree | A1mald | Augmented 4-maldegree | A4mald |
| 1 | Perfect 2-maldegree | P2mald | Perfect 5-maldegree | P5mald |
| 0 | Perfect 0-maldegree Perfect 3-maldegree |
P0mald P3mald |
Perfect 3-maldegree Perfect 6-maldegree |
P3mald P6mald |
| −1 | Perfect 1-maldegree | P1mald | Perfect 4-maldegree | P4mald |
| −2 | Diminished 2-maldegree | d2mald | Diminished 5-maldegree | d5mald |
| −3 | Diminished 3-maldegree | d3mald | Diminished 6-maldegree | d6mald |
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 | |||||