1L 4s: Difference between revisions

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* 0|4 ssssL
* 0|4 ssssL


== Scale Tree ==
== Scale tree ==
Generator ranges:  
Generator ranges:  
* Chroma-positive generator: 960 cents (4\5) to 1200 cents (1\1)
* Chroma-positive generator: 960 cents (4\5) to 1200 cents (1\1)
* 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-9 center-12"
{| class="wikitable center-all"
|-
! colspan="6" | Small step <br><span style="font-size:0.85em">(chroma-negative generator)</span>
! colspan="8" | Small step <br><span style="font-size:0.85em">(Chroma-negative generator)</span>
! Cents
! Cents
! L-s
! L
! <nowiki> |L-2s|</nowiki>
! s
! L/s
! Comments
! Comments
|-
|-
| 0\1
| 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 ||  
|
|
|
|
|
|
| 1\12
| 100
| 700
| 600
|
|-
|-
|
| || || || || || 8\43 || 223.256 || 11 || 8 || 1.375 ||  
|
|
|
|
|
| 1\11
|
| 109.09
| 654.545
| 545.455
|
|-
|-
|
| || || || || 5\27 || || 222.222 || 7 || 5 || 1.400 ||  
|
|
|
|
| 1\10
|
|
| 120
| 600
| 480
|
|-
|-
|
| || || || || || 7\38 || 221.053 || 10 || 7 || 1.429 ||  
|
|
|
|
|
| 2\19
|
| 126.32
| 568.42
| 442.11
| [[Negri]] is around here
|-
|-
|
| || || 2\11 || || || || 218.182 || 3 || 2 || 1.500 ||  
|
|
|
| 1\9
|
|
|
| 133.33
| 533.33
| 400
|
|-
|-
|
| || || || || || 7\39 || 215.385 || 11 || 7 || 1.571 ||  
|
|
| 1\8
|
|
|
|
| 150
| 450
| 300
|  
|-
|-
|  
| || || || || 5\28 || || 214.286 || 8 || 5 || 1.600 ||  
|  
|  
|  
| 2\15
|  
|  
|  
| 160
| 400
| 240
|
|-
|-
|  
| || || || || || 8\45 || 213.333 || 13 || 8 || 1.625 || Golden [[machine]] (213.5979¢)
|  
|  
|  
|  
| 3\22
|  
|  
| 163.64
| 381.82
| 218.18
| [[Porcupine]] is around here
|-
|-
|  
| || || || 3\17 || || || 211.765 || 5 || 3 || 1.667 ||  
|  
|  
|  
|  
|  
|  
|  
| 1200/(4+pi)
| 359.85
| 191.82
|  
|-
|-
|  
| || || || || || 7\40 || 210.000 || 12 || 7 || 1.714 ||  
|  
| 1\7
|  
|  
|  
|  
|  
| 171.43
| 342.86
| 171.43
|  
|-
|-
|  
| || || || || 4\23 || || 208.696 || 7 || 4 || 1.750 ||  
|  
|  
|  
|  
|  
|  
|  
| 1200/(4+e)
| 306.915
| 128.3
|  
|-
|-
|  
| || || || || || 5\29 || 206.897 || 9 || 5 || 1.800 ||  
|  
|  
|  
| 3\20
|  
|  
|  
| 180
| 300
| 120
|  
|-
|-
|  
| || 1\6 || || || || || 200.000 || 2 || 1 || 2.000 || Basic 1L 4s <br>(small steps larger than this are proper)
|  
|  
|  
|  
|  
|  
|  
| 1200/(5+phi)
| 293.386
| 112.064
|  
|-
|-
|  
| || || || || || 4\25 || 192.000 || 9 || 4 || 2.250 || [[Luna]]/[[hemithirds]], [[Isra]]/[[leantone]]
|  
|  
| 2\13
|  
|  
|  
|  
| 184.615
| 276.92
| 92.31
|  
|-
|-
|  
| || || || || 3\19 || || 189.474 || 7 || 3 || 2.333 || [[Spell]]
| 1\6
|  
|  
|  
|  
|  
|  
| 200
| 200
| 0
| Boundary of propriety (small steps <br>larger than this are [[strictly proper]])
|-
|-
|  
| || || || || || 5\32 || 187.500 || 12 || 5 || 2.400 ||  
|  
|  
|  
|  
|  
|  
|  
| 1200/(4+sqrt(3))
| 153.25
| 56.095
|  
|-
|-
|  
| || || || 2\13 || || || 184.615 || 5 || 2 || 2.500 ||  
|  
|  
| 3\17
|  
|  
|  
|  
| 211.76
| 141.18
| 70.59
|  
|-
|-
|  
| || || || || || 5\33 || 181.818 || 13 || 5 || 2.600 || Wilson Golden 2 (181.3227¢)
|  
|  
|  
|  
| 8\45
|  
|  
| 213.33
| 133.33
| 80
|  
|-
|-
|  
| || || || || 3\20 || || 180.000 || 8 || 3 || 2.667 ||  
|  
|  
|  
|  
|  
|  
|  
| 1200/(4+phi)
| 132.01
| 81.59
| Golden machine
|-
|-
|  
| || || || || || 4\27 || 177.778 || 11 || 4 || 2.750 ||  
|  
|  
|  
|  
|  
| 13\73
|  
| 213.70
| 131.51
| 82.19
|  
|-
|-
|  
| || || 1\7 || || || || 171.429 || 3 || 1 || 3.000 ||  
|  
|  
|  
| 5\28
|  
|  
|  
| 214.29
| 128.57
| 85.71
|  
|-
|-
|  
| || || || || || 3\22 || 163.636 || 10 || 3 || 3.333 || [[Porcupine]]
|  
|  
|  
|  
|  
|  
|  
| 1200/(8+pi)
| 122.955
| 92.45
|  
|-
|-
|  
| || || || || 2\15 || || 160.000 || 7 || 2 || 3.500 ||  
|  
| 2\11
|  
|  
|  
|  
|  
| 218.18
| 109.09
| 109.09
| Optimum rank range of machine
|-
|-
|  
| || || || || || 3\23 || 156.522 || 11 || 3 || 3.667 ||  
|  
|  
| 3\16
|  
|  
|  
|  
| 225
| 75
| 150
| [[Gorgo]] is around here
|-
|-
|  
| || || || 1\8 || || || 150.000 || 4 || 1 || 4.000 ||  
|  
|  
|  
| 4\21
|  
|  
|  
| 228.57
| 57.14
| 171.43
|  
|-
|-
|  
| || || || || || 2\17 || 141.176 || 9 || 2 || 4.500 || [[Bleu]]/[[jerome]]
|  
|  
|  
|  
| 5\26
|  
|  
| 230.77
| 46.15
| 184.62
|  
|-
|-
|  
| || || || || 1\9 || || 133.333 || 5 || 1 || 5.000 ||  
|  
|  
|  
|  
|  
| 6\31
|  
| 232.26
| 38.71
| 193.55
|  
|-
|-
|  
| || || || || || 1\10 || 120.000 || 6 || 1 || 6.000 || [[Negri]]
|  
|  
|  
|  
|  
|  
| 7\36
| 233.33
| 33.33
| 200
| [[Slendric]] is around here
|-
|-
| 1\5
| 0\1 || || || || || || 0.000 || 1 || 0 || → inf ||  
|  
|  
|  
|  
|  
|  
|  
| 240
| 0
| 240
|
|}
|}


[[Category:Scales]]
[[Category:Abstract MOS patterns]]
[[Category:Abstract MOS patterns]]
[[Category:5-tone scales]]
[[Category:5-tone scales]]

Revision as of 10:07, 20 February 2022

↑ 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 the MOS pattern Lssss with small steps ranging from 0\1 (0¢) to 1\5 (one step of 5edo = 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

  • 4|0 Lssss
  • 3|1 sLsss
  • 2|2 ssLss
  • 1|3 sssLs
  • 0|4 ssssL

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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