1L 4s: Difference between revisions

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| Pattern = Lssss
| Pattern = Lssss
| Name = pedal
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'''1L 4s''' is the MOS pattern Lssss with small steps ranging from 0\1 (0¢) to 1\5 (one step of [[5edo]] = 240¢).
{{MOS intro}}


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.
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 ==
== Modes ==
* 4|0 Lssss
{{MOS modes}}
* 3|1 sLsss
 
* 2|2 ssLss
=== Degrees ===
* 1|3 sssLs
{{MOS mode degrees}}
* 0|4 ssssL
 
== Intervals ==
{{MOS intervals}}


== Scale tree ==
== Scale tree ==
Line 24: Line 27:
* Chroma-negative generator: 0 cents (0\1) to 240 cents (1\5)
* Chroma-negative generator: 0 cents (0\1) to 240 cents (1\5)


{| class="wikitable center-all"
{{MOS tuning spectrum
! colspan="6" | Small step <br><span style="font-size:0.85em">(chroma-negative generator)</span>
|5/4=Laconic/Gorgo|9/7=Semaja|13/8=Golden machine (213.5979¢)
! Cents
|9/4=Luna/Hemithirds, Isra/Leantone
! L
|7/3=Spell
! s
|13/5=Wilson Golden 2 (181.3227¢)
! L/s
|10/3=Porcupine
! Comments
|9/2=Bleu/Jerome
|-
|6/1=Negri}}
| 1\5 || || || || || || 240.000 || 1 || 1 || 1.000 ||
|-
| || || || || || 5\26 || 230.769 || 6 || 5 || 1.200 ||
|-
| || || || || 4\21 || || 228.571 || 5 || 4 || 1.250 || [[Laconic]]/[[gorgo]]
|-
| || || || || || 7\37 || 227.027 || 9 || 7 || 1.286 || [[Semaja]]
|-
| || || || 3\16 || || || 225.000 || 4 || 3 || 1.333 ||
|-
| || || || || || 8\43 || 223.256 || 11 || 8 || 1.375 ||
|-
| || || || || 5\27 || || 222.222 || 7 || 5 || 1.400 ||
|-
| || || || || || 7\38 || 221.053 || 10 || 7 || 1.429 ||
|-
| || || 2\11 || || || || 218.182 || 3 || 2 || 1.500 ||
|-
| || || || || || 7\39 || 215.385 || 11 || 7 || 1.571 ||
|-
| || || || || 5\28 || || 214.286 || 8 || 5 || 1.600 ||
|-
| || || || || || 8\45 || 213.333 || 13 || 8 || 1.625 || Golden [[machine]] (213.5979¢)
|-
| || || || 3\17 || || || 211.765 || 5 || 3 || 1.667 ||
|-
| || || || || || 7\40 || 210.000 || 12 || 7 || 1.714 ||
|-
| || || || || 4\23 || || 208.696 || 7 || 4 || 1.750 ||
|-
| || || || || || 5\29 || 206.897 || 9 || 5 || 1.800 ||
|-
| || 1\6 || || || || || 200.000 || 2 || 1 || 2.000 || Basic 1L 4s <br>(small steps larger than this are proper)
|-
| || || || || || 4\25 || 192.000 || 9 || 4 || 2.250 || [[Luna]]/[[hemithirds]], [[Isra]]/[[leantone]]
|-
| || || || || 3\19 || || 189.474 || 7 || 3 || 2.333 || [[Spell]]
|-
| || || || || || 5\32 || 187.500 || 12 || 5 || 2.400 ||
|-
| || || || 2\13 || || || 184.615 || 5 || 2 || 2.500 ||
|-
| || || || || || 5\33 || 181.818 || 13 || 5 || 2.600 || Wilson Golden 2 (181.3227¢)
|-
| || || || || 3\20 || || 180.000 || 8 || 3 || 2.667 ||
|-
| || || || || || 4\27 || 177.778 || 11 || 4 || 2.750 ||
|-
| || || 1\7 || || || || 171.429 || 3 || 1 || 3.000 ||
|-
| || || || || || 3\22 || 163.636 || 10 || 3 || 3.333 || [[Porcupine]]
|-
| || || || || 2\15 || || 160.000 || 7 || 2 || 3.500 ||
|-
| || || || || || 3\23 || 156.522 || 11 || 3 || 3.667 ||
|-
| || || || 1\8 || || || 150.000 || 4 || 1 || 4.000 ||
|-
| || || || || || 2\17 || 141.176 || 9 || 2 || 4.500 || [[Bleu]]/[[jerome]]
|-
| || || || || 1\9 || || 133.333 || 5 || 1 || 5.000 ||
|-
| || || || || || 1\10 || 120.000 || 6 || 1 || 6.000 || [[Negri]]
|-
| 0\1 || || || || || || 0.000 || 1 || 0 || → inf ||
|}


[[Category:5-tone scales]]
[[Category:5-tone scales]]

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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