1L 4s: Difference between revisions

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The only notable low-harmonic-entropy scale for this [[MOSScales|MOS]] pattern is [[Gamelismic clan|slendric or gamelismic]], in which the generator is 8/7 and three of them make a 3/2. Other scales include very [[improper]] (incomplete) versions of [[Porcupine family|porcupine]], [[Marvel temperaments#Negri|negri]], etc.
{{Infobox MOS
| Periods = 1
| nLargeSteps = 1
| nSmallSteps = 4
| Equalized = 4
| Collapsed = 1
| Pattern = Lssss
| Name = pedal
}}


{| class="wikitable center-9 center-12"
{{MOS intro}}
|-
 
! colspan="8" | Generator
The only notable low-[[harmonic entropy|harmonic-entropy]] scale for this [[MOS]] pattern is [[Gamelismic clan|slendric or gamelismic]], in which the [[generator]] is [[8/7]] and three of them make a [[3/2]]. Other scales include very [[improper]] (incomplete) versions of [[Porcupine family|porcupine]], [[Marvel temperaments #Negri|negri]], etc.
! Generator (s)
 
! L-s
== Modes ==
! <nowiki> |L-2s|</nowiki>
{{MOS modes}}
! Comments
 
|-
=== Degrees ===
| 0\1
{{MOS mode degrees}}
|
 
|
== Intervals ==
|
{{MOS intervals}}
|
 
|
== Scale tree ==
|
Generator ranges:
|
* Chroma-positive generator: 960 cents (4\5) to 1200 cents (1\1)
|
* Chroma-negative generator: 0 cents (0\1) to 240 cents (1\5)
|
 
|
{{MOS tuning spectrum
|
|5/4=Laconic/Gorgo|9/7=Semaja|13/8=Golden machine (213.5979¢)
|-
|9/4=Luna/Hemithirds, Isra/Leantone
|
|7/3=Spell
|
|13/5=Wilson Golden 2 (181.3227¢)
|
|10/3=Porcupine
|
|9/2=Bleu/Jerome
|
|6/1=Negri}}
|
 
|
[[Category:5-tone scales]]
| 1\12
| 100
| 700
| 600
|
|-
|
|
|
|
|
|
| 1\11
|
| 109.09
| 654.545
| 545.455
|
|-
|
|
|
|
|
| 1\10
|
|
| 120
| 600
| 480
|
|-
|
|
|
|
|
|
| 2\19
|
| 126.32
| 568.42
| 442.11
| Negri is around here
|-
|
|
|
|
| 1\9
|
|
|
| 133.33
| 533.33
| 400
|
|-
|
|
|
| 1\8
|
|
|
|
| 150
| 450
| 300
| L/s = 4
|-
|
|
|
|
| 2\15
|
|
|
| 160
| 400
| 240
|
|-
|
|
|
|
|
| 3\22
|
|
| 163.64
| 381.82
| 218.18
| Porcupine is around here
|-
|
|
|
|
|
|
|
|
| 1200/(4+pi)
| 359.85
| 191.82
|
|-
|
|
| 1\7
|
|
|
|
|
| 171.43
| 342.86
| 171.43
| L/s = 3
|-
|
|
|
|
|
|
|
|
| 1200/(4+e)
| 306.915
| 128.3
|
|-
|
|
|
|
| 3\20
|
|
|
| 180
| 300
| 120
|
|-
|
|
|
|
|
|
|
|
| 1200/(5+phi)
| 293.386
| 112.064
|
|-
|
|
|
| 2\13
|
|
|
|
| 184.615
| 276.92
| 92.31
|
|-
|
| 1\6
|
|
|
|
|
|
| 200
| 200
| 0
| Boundary of propriety (generators <br> larger than this are [[strictly proper]])
|-
|
|  
|
|
|
|
|
|
| 1200/(4+sqrt(3))
| 153.25
| 56.095
|
|-
|
|
|
| 3\17
|
|
|
|
| 211.76
| 141.18
| 70.59
|
|-
|
|
|
|
|
| 8\45
|
|
| 213.33
| 133.33
| 80
|
|-
|
|
|
|
|
|
|
|
| 1200/(4+phi)
| 132.01
| 81.59
| Golden machine
|-
|
|
|
|
|
|  
| 13\73
|
| 213.70
| 131.51
| 82.19
|
|-
|
|
|
|
| 5\28
|
|
|
| 214.29
| 128.57
| 85.71
|
|-
|
|
|
|
|
|
|
|
| 1200/(8+pi)
| 122.955
| 92.45
|
|-
|
|
| 2\11
|  
|
|
|
|
| 218.18
| 109.09
| 109.09
| Optimum rank range (L/s=3/2) machine
|-
|
|
|
| 3\16
|
|
|
|
| 225
| 75
| 150
| Gorgo is around here
|-
|
|
|
|
| 4\21
|
|
|
| 228.57
| 57.14
| 171.43
|
|-
|
|
|
|
|
| 5\26
|
|
| 230.77
| 46.15
| 184.62
|
|-
|
|
|
|
|
|
| 6\31
|
| 232.26
| 38.71
| 193.55
|
|-
|
|
|
|
|
|
|
| 7\36
| 233.33
| 33.33
| 200
| Slendric is around here
|-
| 1\5
|
|
|
|
|
|
|
| 240
| 0
| 240
|
|}

Latest revision as of 23:14, 5 May 2026

↑ 1L 3s 2L 3s ↗
1L 4s 2L 4s →
↓ 1L 5s 2L 5s ↘
Scale structure
Step pattern Lssss
ssssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 4\5 to 1\1 (960.0 ¢ to 1200.0 ¢)
Dark 0\1 to 1\5 (0.0 ¢ to 240.0 ¢)
Related MOS scales
Parent 1L 3s
Sister 4L 1s
Daughters 5L 1s, 1L 5s
Neutralized 2L 3s
2-Flought 6L 4s, 1L 9s
Equal tunings
Equalized (L:s = 1:1) 4\5 (960.0 ¢)
Supersoft (L:s = 4:3) 13\16 (975.0 ¢)
Soft (L:s = 3:2) 9\11 (981.8 ¢)
Semisoft (L:s = 5:3) 14\17 (988.2 ¢)
Basic (L:s = 2:1) 5\6 (1000.0 ¢)
Semihard (L:s = 5:2) 11\13 (1015.4 ¢)
Hard (L:s = 3:1) 6\7 (1028.6 ¢)
Superhard (L:s = 4:1) 7\8 (1050.0 ¢)
Collapsed (L:s = 1:0) 1\1 (1200.0 ¢)
View • Talk • Edit

1L 4s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 1 large step and 4 small steps, repeating every octave. Generators that produce this scale range from 960 ¢ to 1200 ¢, or from 0 ¢ to 240 ¢.

The only notable low-harmonic-entropy scale for this MOS pattern is slendric or gamelismic, in which the generator is 8/7 and three of them make a 3/2. Other scales include very improper (incomplete) versions of porcupine, negri, etc.

Modes

Modes of 1L 4s
UDP Cyclic
order		 Step
pattern
4|0 1 Lssss
3|1 5 sLsss
2|2 4 ssLss
1|3 3 sssLs
0|4 2 ssssL

Degrees

Scale degrees of the modes of 1L 4s
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5
4|0 1 Lssss Perf. Aug. Maj. Maj. Perf. Perf.
3|1 5 sLsss Perf. Perf. Maj. Maj. Perf. Perf.
2|2 4 ssLss Perf. Perf. Min. Maj. Perf. Perf.
1|3 3 sssLs Perf. Perf. Min. Min. Perf. Perf.
0|4 2 ssssL Perf. Perf. Min. Min. Dim. Perf.

Intervals

Intervals of 1L 4s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Perfect 1-mosstep P1ms s 0.0 ¢ to 240.0 ¢
Augmented 1-mosstep A1ms L 240.0 ¢ to 1200.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 480.0 ¢
Major 2-mosstep M2ms L + s 480.0 ¢ to 1200.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 720.0 ¢
Major 3-mosstep M3ms L + 2s 720.0 ¢ to 1200.0 ¢
4-mosstep Diminished 4-mosstep d4ms 4s 0.0 ¢ to 960.0 ¢
Perfect 4-mosstep P4ms L + 3s 960.0 ¢ to 1200.0 ¢
5-mosstep Perfect 5-mosstep P5ms L + 4s 1200.0 ¢

Scale tree

Generator ranges:

  • Chroma-positive generator: 960 cents (4\5) to 1200 cents (1\1)
  • Chroma-negative generator: 0 cents (0\1) to 240 cents (1\5)


Scale tree and tuning spectrum of 1L 4s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
4\5 960.000 240.000 1:1 1.000 Equalized 1L 4s
21\26 969.231 230.769 6:5 1.200
17\21 971.429 228.571 5:4 1.250 Laconic/Gorgo
30\37 972.973 227.027 9:7 1.286 Semaja
13\16 975.000 225.000 4:3 1.333 Supersoft 1L 4s
35\43 976.744 223.256 11:8 1.375
22\27 977.778 222.222 7:5 1.400
31\38 978.947 221.053 10:7 1.429
9\11 981.818 218.182 3:2 1.500 Soft 1L 4s
32\39 984.615 215.385 11:7 1.571
23\28 985.714 214.286 8:5 1.600
37\45 986.667 213.333 13:8 1.625 Golden machine (213.5979¢)
14\17 988.235 211.765 5:3 1.667 Semisoft 1L 4s
33\40 990.000 210.000 12:7 1.714
19\23 991.304 208.696 7:4 1.750
24\29 993.103 206.897 9:5 1.800
5\6 1000.000 200.000 2:1 2.000 Basic 1L 4s
Scales with tunings softer than this are proper
21\25 1008.000 192.000 9:4 2.250 Luna/Hemithirds, Isra/Leantone
16\19 1010.526 189.474 7:3 2.333 Spell
27\32 1012.500 187.500 12:5 2.400
11\13 1015.385 184.615 5:2 2.500 Semihard 1L 4s
28\33 1018.182 181.818 13:5 2.600 Wilson Golden 2 (181.3227¢)
17\20 1020.000 180.000 8:3 2.667
23\27 1022.222 177.778 11:4 2.750
6\7 1028.571 171.429 3:1 3.000 Hard 1L 4s
19\22 1036.364 163.636 10:3 3.333 Porcupine
13\15 1040.000 160.000 7:2 3.500
20\23 1043.478 156.522 11:3 3.667
7\8 1050.000 150.000 4:1 4.000 Superhard 1L 4s
15\17 1058.824 141.176 9:2 4.500 Bleu/Jerome
8\9 1066.667 133.333 5:1 5.000
9\10 1080.000 120.000 6:1 6.000 Negri
1\1 1200.000 0.000 1:0 → ∞ Collapsed 1L 4s
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