2L 4s: Difference between revisions

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The only scale with this [[MOSScales|MOS]] pattern that's a really significant minimum of harmonic entropy is [[Diaschismic_family|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 [[Porcupine_family#Hedgehog|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).
{{Infobox MOS
| Name = malic
| Periods = 2
| nLargeSteps = 2
| nSmallSteps = 4
| Equalized = 1
| Collapsed = 0
| Pattern = LssLss
}}


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.
{{MOS intro}}


Srutal/pajara probably has the lowest harmonic entropy of all 6-note MOS scales. The near-MOS version has even lower harmonic entropy.
The only scale with this mos pattern that is 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 does not appear in this mos).


{| class="wikitable"
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.
|-
! colspan="11" | Generator
! | Cents
! | Comments
|-
| | 0\2
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | 0
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | 1\24
| |
| | 50
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | 2\46
| | 52.17
| style="text-align:center;" | Shrutar is around here
|-
| |
| |
| |
| |
| |
| |
| |
| |
| | 1\22
| |
| |
| | 54.55
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| | 1\20
| |
| |
| |
| | 60
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| | 1\18
| |
| |
| |
| |
| | 66.67
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| | 1\16
| |
| |
| |
| |
| |
| | 75
| style="text-align:center;" |
|-
| |
| |
| |
| |
| | 1\14
| |
| |
| |
| |
| |
| |
| | 85.71
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| | 2\26
| |
| |
| |
| |
| |
| | 92.31
| style="text-align:center;" | Injera is around here
|-
| |
| |
| |
| | 1\12
| |
| |
| |
| |
| |
| |
| |
| | 100
| style="text-align:center;" | L/s = 4
|-
| |
| |
| |
| |
| | 2\22
| |
| |
| |
| |
| |
| |
| | 109.09
| style="text-align:center;" | Srutal/Pajara is around here
|-
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | 600/(2+pi)
| |
|-
| |
| |
| | 1\10
| |
| |
| |
| |
| |
| |
| |
| |
| | 120
| style="text-align:center;" | L/s = 3
|-
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | 600/(2+e)
| |
|-
| |
| |
| |
| |
| | 3/28
| |
| |
| |
| |
| |
| |
| | 128.57
| |
|-
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | 600/(3+phi)
| |
|-
| |
| |
| |
| | 2/18
| |
| |
| |
| |
| |
| |
| |
| | 133.33
| |
|-
| |
| | 1\8
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | 150
| style="text-align:center;" | Boundary of propriety (generators


larger than this are proper)
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 ==
| |
{{TAMNAMS use}}
| |
 
| |
=== Intervals ===
| |
{{MOS intervals}}
| |
 
| |
=== Generator chain ===
| |
{{MOS genchain}}
| |
 
| |
=== Modes ===
| |
{{MOS mode degrees}}
| | 600/(2+sqrt(3))
 
| |
== Scale tree ==
|-
{{MOS tuning spectrum
| |
| 9/7 = [[Unidec]]
| |
| 13/8 = Golden [[hedgehog]]/[[echidna]]
| |
| 5/3 = Hedgehog (optimal around here)
| | 3\22
| 9/4 = [[Crepuscular]]
| |
| 8/3 = [[Octokaidecal]]
| |
| 7/2 = [[Pajara]]
| |
| 9/2 = [[Injera]]
| |
| 6/1 = [[Shrutar]] ↓
| |
}}
| |
 
| |
[[Category:6-tone scales]]
| | 163.64
| style="text-align:center;" | Hedgehog and echidna are both around here
|-
| |
| |
| |
| |
| |
| | 8\58
| |
| |
| |
| |
| |
| | 165.52
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | 600/(2+phi)
| style="text-align:center;" | Golden hedgehog/echidna
|-
| |
| |
| |
| |
| |
| |
| | 13\94
| |
| |
| |
| |
| | 165.96
| style="text-align:center;" |
|-
| |
| |
| |
| |
| | 5\36
| |
| |
| |
| |
| |
| |
| | 166.67
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | 600/(2+pi/2)
| |
|-
| |
| |
| | 2\14
| |
| |
| |
| |
| |
| |
| |
| |
| | 171.43
| style="text-align:center;" | Optimum rank range (L/s=3/2)
|-
| | 1\6
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | 200
| style="text-align:center;" |
|}

Latest revision as of 09:33, 15 September 2026

↖ 1L 3s ↑ 2L 3s 3L 3s ↗
← 1L 4s 2L 4s 3L 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 ¢)
View • Talk • Edit

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 is 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 does not 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 interval regions.

Intervals

Intervals of 2L 4s
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

Generator chain of 2L 4s
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

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 Unidec
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
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 (optimal 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 Crepuscular
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 Octokaidecal
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 Pajara
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
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
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