2L 4s

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↖ 1L 3s↑ 2L 3s 3L 3s ↗
← 1L 4s2L 4s3L 4s →
↙ 1L 5s↓ 2L 5s 3L 5s ↘
┌╥┬┬╥┬┬┐
│║││║│││
││││││││
└┴┴┴┴┴┴┘
Scale structure
Step pattern LssLss
ssLssL
Equave 2/1 (1200.0¢)
Period 1\2 (600.0¢)
Generator size
Bright 2\6 to 1\2 (400.0¢ to 600.0¢)
Dark 0\2 to 1\6 (0.0¢ to 200.0¢)
TAMNAMS information
Name malic
Prefix mal-
Abbrev. mal
Related MOS scales
Parent 2L 2s
Sister 4L 2s
Daughters 6L 2s, 2L 6s
Neutralized 4L 2s
2-Flought 8L 4s, 2L 10s
Equal tunings
Equalized (L:s = 1:1) 2\6 (400.0¢)
Supersoft (L:s = 4:3) 7\20 (420.0¢)
Soft (L:s = 3:2) 5\14 (428.6¢)
Semisoft (L:s = 5:3) 8\22 (436.4¢)
Basic (L:s = 2:1) 3\8 (450.0¢)
Semihard (L:s = 5:2) 7\18 (466.7¢)
Hard (L:s = 3:1) 4\10 (480.0¢)
Superhard (L:s = 4:1) 5\12 (500.0¢)
Collapsed (L:s = 1:0) 1\2 (600.0¢)

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.

Modes

Scale degrees of the modes of 2L 4s 
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

Scale Tree and Tuning Spectrum of 2L 4s
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