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 [[Rothenberg_propriety|improper]] (incomplete) versions of [[Porcupine_family|porcupine]], [[Marvel_temperaments|negri]], etc.
{{Infobox MOS
| Periods = 1
| nLargeSteps = 1
| nSmallSteps = 4
| Equalized = 4
| Collapsed = 1
| Pattern = Lssss
| Name = pedal
}}


{| class="wikitable"
{{MOS intro}}
|-
! colspan="8" | Generator
! | Generator (s)
! | L-s
! | |L-2s|
! | Comments
|-
| | 0\1
| |
| |
| |
| |
| |
| |
| |
| style="text-align:center;" |
| |
| |
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| | 1\10
| |
| |
| style="text-align:center;" | 120
| | 600
| | 480
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| | 2\19
| |
| style="text-align:center;" | 126.32
| | 568.42
| | 442.11
| style="text-align:center;" | Negri is around here
|-
| |
| |
| |
| |
| | 1\9
| |
| |
| |
| style="text-align:center;" | 133.33
| | 533.33
| | 400
| style="text-align:center;" |
|-
| |
| |
| |
| | 1\8
| |
| |
| |
| |
| style="text-align:center;" | 150
| | 450
| | 300
| style="text-align:center;" | L/s = 4
|-
| |
| |
| |
| |
| | 2\15
| |
| |
| |
| style="text-align:center;" | 160
| | 400
| | 240
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| | 3\22
| |
| |
| style="text-align:center;" | 163.64
| | 381.82
| | 218.18
| style="text-align:center;" | Porcupine is around here
|-
| |
| |
| |
| |
| |
| |
| |
| |
| style="text-align:center;" | 1200/(4+pi)
| | 359.85
| | 191.82
| |
|-
| |
| |
| | 1\7
| |
| |
| |
| |
| |
| style="text-align:center;" | 171.43
| | 342.86
| | 171.43
| style="text-align:center;" | L/s = 3
|-
| |
| |
| |
| |
| |
| |
| |
| |
| style="text-align:center;" | <span style="display: block; text-align: center;">1200/(4+e)</span>
| | 306.915
| | 128.3
| |
|-
| |
| |
| |
| |
| | 3\20
| |
| |
| |
| style="text-align:center;" | 180
| | 300
| | 120
| |
|-
| |
| |
| |
| |
| |
| |
| |
| |
| style="text-align:center;" | <span style="display: block; text-align: center;">1200/(5+phi)</span>
| | 293.386
| | 112.064
| |
|-
| |
| |
| |
| | 2\13
| |
| |
| |
| |
| style="text-align:center;" | 184.615
| | 276.92
| | 92.31
| |
|-
| |
| | 1\6
| |
| |
| |
| |
| |
| |
| style="text-align:center;" | 200
| | 200
| | 0
| style="text-align:center;" | Boundary of propriety (generators


larger than this are strictly proper)
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.
|-
 
| |
== Modes ==
| |
{{MOS modes}}
| |
 
| |
=== Degrees ===
| |
{{MOS mode degrees}}
| |
 
| |
== Intervals ==
| |
{{MOS intervals}}
| style="text-align:center;" | 1200/(4+sqrt(3))
 
| | 153.25
== Scale tree ==
| | 56.095
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¢)
| | 3\17
|9/4=Luna/Hemithirds, Isra/Leantone
| |
|7/3=Spell
| |
|13/5=Wilson Golden 2 (181.3227¢)
| |
|10/3=Porcupine
| |
|9/2=Bleu/Jerome
| style="text-align:center;" | 211.76
|6/1=Negri}}
| | 141.18
 
| | 70.59
[[Category:5-tone scales]]
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| | 8\45
| |
| |
| style="text-align:center;" | 213.33
| | 133.33
| | 80
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| |
| style="text-align:center;" | 1200/(4+phi)
| | 132.01
| | 81.59
| style="text-align:center;" | Golden machine
|-
| |
| |
| |
| |
| |
| |
| | 13\73
| |
| style="text-align:center;" | 213.70
| | 131.51
| | 82.19
| style="text-align:center;" |
|-
| |
| |
| |
| |
| | 5\28
| |
| |
| |
| style="text-align:center;" | 214.29
| | 128.57
| | 85.71
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| |
| style="text-align:center;" | <span style="display: block; text-align: center;">1200/(8+pi)</span>
| | 122.955
| | 92.45
| |
|-
| |
| |
| | 2\11
| |
| |
| |
| |
| |
| style="text-align:center;" | 218.18
| | 109.09
| | 109.09
| style="text-align:center;" | Optimum rank range (L/s=3/2) machine
|-
| |
| |
| |
| | 3\16
| |
| |
| |
| |
| style="text-align:center;" | 225
| | 75
| | 150
| style="text-align:center;" | Gorgo is around here
|-
| |
| |
| |
| |
| | 4\21
| |
| |
| |
| style="text-align:center;" | 228.57
| | 57.14
| | 171.43
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| | 5\26
| |
| |
| style="text-align:center;" | 230.77
| | 46.15
| | 184.62
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| | 6\31
| |
| style="text-align:center;" | 232.26
| | 38.71
| | 193.55
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| | 7\36
| style="text-align:center;" | 233.33
| | 33.33
| | 200
| style="text-align:center;" | Slendric is around here
|-
| | 1\5
| |
| |
| |
| |
| |
| |
| |
| style="text-align:center;" | 240
| | 0
| | 240
| style="text-align:center;" |
|}

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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