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}}
 
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}}
 
== 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)
 
{| class="wikitable center-all"
! colspan="6" | Small step <br><span style="font-size:0.85em">(chroma-negative generator)</span>
! Cents
! L
! s
! L/s
! Comments
|-
| 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]]
|-
|-
! colspan="8" | Generator
| || || || 3\16 || || || 225.000 || 4 || 3 || 1.333 ||
! | Generator (s)
! | L-s
! | |L-2s|
! | Comments
|-
|-
| | 0\1
| || || || || || 8\43 || 223.256 || 11 || 8 || 1.375 ||  
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| style="text-align:center;" |  
| |  
| |
| style="text-align:center;" |  
|-
|-
| |  
| || || || || 5\27 || || 222.222 || 7 || 5 || 1.400 ||  
| |  
| |  
| |  
| |
| | 1\10
| |  
| |  
| style="text-align:center;" | 120
| | 600
| | 480
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 7\38 || 221.053 || 10 || 7 || 1.429 ||  
| |  
| |  
| |  
| |  
| |
| | 2\19
| |  
| style="text-align:center;" | 126.32
| | 568.42
| | 442.11
| style="text-align:center;" | Negri is around here
|-
|-
| |  
| || || 2\11 || || || || 218.182 || 3 || 2 || 1.500 ||  
| |  
| |  
| |  
| | 1\9
| |  
| |  
| |  
| style="text-align:center;" | 133.33
| | 533.33
| | 400
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 7\39 || 215.385 || 11 || 7 || 1.571 ||  
| |  
| |  
| | 1\8
| |  
| |  
| |  
| |  
| style="text-align:center;" | 150
| | 450
| | 300
| style="text-align:center;" | L/s = 4
|-
|-
| |  
| || || || || 5\28 || || 214.286 || 8 || 5 || 1.600 ||  
| |  
| |  
| |  
| | 2\15
| |
| |  
| |  
| style="text-align:center;" | 160
| | 400
| | 240
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 8\45 || 213.333 || 13 || 8 || 1.625 || Golden [[machine]] (213.5979¢)
| |  
| |  
| |  
| |  
| | 3\22
| |  
| |  
| style="text-align:center;" | 163.64
| | 381.82
| | 218.18
| style="text-align:center;" | Porcupine is around here
|-
|-
| |  
| || || || 3\17 || || || 211.765 || 5 || 3 || 1.667 ||  
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| style="text-align:center;" | 1200/(4+pi)
| | 359.85
| | 191.82
| |  
|-
|-
| |  
| || || || || || 7\40 || 210.000 || 12 || 7 || 1.714 ||  
| |  
| | 1\7
| |  
| |  
| |  
| |  
| |  
| style="text-align:center;" | 171.43
| | 342.86
| | 171.43
| style="text-align:center;" | L/s = 3
|-
|-
| |  
| || || || || 4\23 || || 208.696 || 7 || 4 || 1.750 ||  
| |  
| |  
| |  
| |  
| |  
| |
| |  
| style="text-align:center;" | <span style="display: block; text-align: center;">1200/(4+e)</span>
| | 306.915
| | 128.3
| |  
|-
|-
| |  
| || || || || || 5\29 || 206.897 || 9 || 5 || 1.800 ||  
| |  
| |  
| |  
| | 3\20
| |
| |
| |  
| style="text-align:center;" | 180
| | 300
| | 120
| |  
|-
|-
| |  
| || 1\6 || || || || || 200.000 || 2 || 1 || 2.000 || Basic 1L 4s <br>(small steps larger than this are proper)
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| style="text-align:center;" | <span style="display: block; text-align: center;">1200/(5+phi)</span>
| | 293.386
| | 112.064
| |
|-
|-
| |  
| || || || || || 4\25 || 192.000 || 9 || 4 || 2.250 || [[Luna]]/[[hemithirds]], [[Isra]]/[[leantone]]
| |  
| |  
| | 2\13
| |  
| |  
| |
| |  
| style="text-align:center;" | 184.615
| | 276.92
| | 92.31
| |  
|-
|-
| |  
| || || || || 3\19 || || 189.474 || 7 || 3 || 2.333 || [[Spell]]
| | 1\6
| |  
| |  
| |
| |
| |  
| |  
| style="text-align:center;" | 200
| | 200
| | 0
| style="text-align:center;" | Boundary of propriety (generators
 
larger than this are strictly proper)
|-
|-
| |  
| || || || || || 5\32 || 187.500 || 12 || 5 || 2.400 ||  
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| style="text-align:center;" | 1200/(4+sqrt(3))
| | 153.25
| | 56.095
| |  
|-
|-
| |  
| || || || 2\13 || || || 184.615 || 5 || 2 || 2.500 ||  
| |  
| |  
| | 3\17
| |  
| |  
| |  
| |
| style="text-align:center;" | 211.76
| | 141.18
| | 70.59
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 5\33 || 181.818 || 13 || 5 || 2.600 || Wilson Golden 2 (181.3227¢)
| |  
| |  
| |  
| |  
| | 8\45
| |  
| |  
| style="text-align:center;" | 213.33
| | 133.33
| | 80
| style="text-align:center;" |
|-
|-
| |  
| || || || || 3\20 || || 180.000 || 8 || 3 || 2.667 ||  
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| style="text-align:center;" | 1200/(4+phi)
| | 132.01
| | 81.59
| style="text-align:center;" | Golden machine
|-
|-
| |  
| || || || || || 4\27 || 177.778 || 11 || 4 || 2.750 ||  
| |  
| |  
| |  
| |  
| |
| | 13\73
| |  
| style="text-align:center;" | 213.70
| | 131.51
| | 82.19
| style="text-align:center;" |  
|-
|-
| |  
| || || 1\7 || || || || 171.429 || 3 || 1 || 3.000 ||  
| |  
| |
| |  
| | 5\28
| |  
| |  
| |
| style="text-align:center;" | 214.29
| | 128.57
| | 85.71
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 3\22 || 163.636 || 10 || 3 || 3.333 || [[Porcupine]]
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| style="text-align:center;" | <span style="display: block; text-align: center;">1200/(8+pi)</span>
| | 122.955
| | 92.45
| |  
|-
|-
| |  
| || || || || 2\15 || || 160.000 || 7 || 2 || 3.500 ||  
| |  
| | 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\23 || 156.522 || 11 || 3 || 3.667 ||  
| |  
| |  
| | 3\16
| |  
| |  
| |  
| |  
| style="text-align:center;" | 225
| | 75
| | 150
| style="text-align:center;" | Gorgo is around here
|-
|-
| |  
| || || || 1\8 || || || 150.000 || 4 || 1 || 4.000 ||  
| |  
| |  
| |
| | 4\21
| |  
| |  
| |  
| style="text-align:center;" | 228.57
| | 57.14
| | 171.43
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 2\17 || 141.176 || 9 || 2 || 4.500 || [[Bleu]]/[[jerome]]
| |  
| |  
| |  
| |  
| | 5\26
| |  
| |
| style="text-align:center;" | 230.77
| | 46.15
| | 184.62
| style="text-align:center;" |  
|-
|-
| |  
| || || || || 1\9 || || 133.333 || 5 || 1 || 5.000 ||  
| |  
| |  
| |  
| |  
| |  
| | 6\31
| |
| style="text-align:center;" | 232.26
| | 38.71
| | 193.55
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 1\10 || 120.000 || 6 || 1 || 6.000 || [[Negri]]
| |  
| |  
| |  
| |  
| |  
| |  
| | 7\36
| style="text-align:center;" | 233.33
| | 33.33
| | 200
| style="text-align:center;" | Slendric is around here
|-
|-
| | 1\5
| 0\1 || || || || || || 0.000 || 1 || 0 || → inf ||  
| |  
| |  
| |  
| |  
| |  
| |  
| |  
| style="text-align:center;" | 240
| | 0
| | 240
| style="text-align:center;" |  
|}
|}
[[Category:5-tone scales]]

Latest revision as of 08:25, 15 December 2024

↑ 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 ¢)

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)
Small step
(chroma-negative generator) 		Cents L s L/s Comments
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
(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
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