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| Pattern = LLLLLs
| Pattern = LLLLLs
}}
}}
'''5L 1s''' refers to [[MOS scales|MOS scales]] with 5 large steps and 1 small step. When L=s we have [[6edo|6edo]], the equal-tempered "whole tone scale" of impressionistic fame. At the other end of the spectrum, we approach [[5edo|5edo]], with five equal whole tones of 240 cents. In between, we find relatively even hexatonic scales with one irregularity: a "whole tone" which is smaller than all the others — perhaps not a "whole tone" at all.
'''5L 1s''' refers to [[MOS scale]]s with 5 large steps and 1 small step. When L=s we have [[6edo|6edo]], the equal-tempered "whole tone scale" of impressionistic fame. At the other end of the spectrum, we approach [[5edo]], with five equal whole tones of 240 cents. In between, we find relatively even hexatonic scales with one irregularity: a "whole tone" which is smaller than all the others — perhaps not a "whole tone" at all.


The only notable low-harmonic-entropy scale with this MOS pattern is [[Gamelismic_clan|slendric]], in which the large step is 8/7 and three of them make a 3/2.
The only notable low-harmonic-entropy scale with this MOS pattern is [[Gamelismic clan #Slendric|slendric]], in which the large step is 8/7 and three of them make a 3/2.


Scales with this pattern are always [[Rothenberg_propriety|proper]], because there is only one small step.
Scales with this pattern are always [[Rothenberg propriety|proper]], because there is only one small step.


{| class="wikitable"
== Scale tree ==
{| class="wikitable center-all"
! colspan="6" | Generator
! Cents
! L
! s
! L/s
! Comments
|-
|-
! colspan="7" | generator
| 1\6 || || || || || || 200.000 || 1 || 1 || 1.000 ||
! | scale
! | large step (L)
! | small step (s)
! | comments
|-
|-
| style="text-align:center;" | 1\[[5edo|5]]
| || || || || || 6\35 || 205.714 || 6 || 5 || 1.200 ||  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| |  
| |  
| style="text-align:center;" | 1 1 1 1 1 0
| style="text-align:center;" | 240
| style="text-align:center;" | 0
| style="text-align:center;" |  
|-
|-
| |  
| || || || || 5\29 || || 206.897 || 5 || 4 || 1.250 ||  
| |  
| |  
| |  
| |  
| |  
| | 7\36
| style="text-align:center;" | 7 7 7 7 7 1
| style="text-align:center;" | 233.3
| style="text-align:center;" | 33.3
| style="text-align:center;" | Slendric is around here
|-
|-
| |  
| || || || || || 9\52 || 207.692 || 9 || 7 || 1.286 ||  
| |  
| |  
| |  
| |  
| | 6\31
| |  
| style="text-align:center;" | 6 6 6 6 6 1
| style="text-align:center;" | 232.3
| style="text-align:center;" | 38.7
| style="text-align:center;" |  
|-
|-
| style="text-align:center;" |  
| || || || 4\23 || || || 208.696 || 4 || 3 || 1.333 ||
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |
| style="text-align:center;" | 5\[[26edo|26]]
| |  
| |  
| style="text-align:center;" | 5 5 5 5 5 1
| style="text-align:center;" | 230.8
| style="text-align:center;" | 46.2
| style="text-align:center;" |  
|-
|-
| style="text-align:center;" |  
| || || || || || 11\63 || 209.524 || 11 || 8 || 1.375 ||
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 4\[[21edo|21]]
| style="text-align:center;" |  
| |  
| |  
| style="text-align:center;" | 4 4 4 4 4 1
| style="text-align:center;" | 228.6
| style="text-align:center;" | 57.1
| style="text-align:center;" | L/s = 4
|-
|-
| style="text-align:center;" |  
| || || || || 7\40 || || 210.000 || 7 || 5 || 1.400 ||
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 7\[[37edo|37]]
| |  
| |  
| style="text-align:center;" | 7 7 7 7 7 2
| style="text-align:center;" | 227.0
| style="text-align:center;" | 64.9
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 10\57 || 210.528 || 10 || 7 || 1.428 ||
| |  
| |  
| |  
| |  
| |  
| |  
| style="text-align:center;" | pi pi pi pi pi 1
| style="text-align:center;" | 225.6
| style="text-align:center;" | 71.8
| style="text-align:center;" | <span style="display: block; text-align: center;">L/s = pi</span>
|-
|-
| style="text-align:center;" |  
| || || 3\17 || || || || 211.765 || 3 || 2 || 1.500 || L/s = 3/2
| style="text-align:center;" |  
|-
| style="text-align:center;" | 3\[[16edo|16]]
| || || || || || 11\62 || 212.903 || 11 || 7 || 1.571 ||
| style="text-align:center;" |  
|-
| style="text-align:center;" |  
| || || || || 8\45 || || 213.333 || 8 || 5 || 1.600 ||  
| |  
|-
| |  
| || || || || || 13\73 || 213.699 || 13 || 8 || 1.625 || Golden machine
| style="text-align:center;" | 3 3 3 3 3 1
|-
| style="text-align:center;" | 225
| || || || 5\28 || || || 214.286 || 5 || 3 || 1.667 || Machine
| style="text-align:center;" | 75
| style="text-align:center;" | Gorgo is around here
 
L/s = 3
|-
|-
| |  
| || || || || || 12\67 || 214.925 || 12 || 7 || 1.714 ||  
| |  
| |  
| |  
| |  
| |  
| |  
| style="text-align:center;" | e e e e e 1
| style="text-align:center;" | 223.55
| style="text-align:center;" | 82.2
| style="text-align:center;" | <span style="display: block; text-align: center;">L/s = e</span>
|-
|-
| style="text-align:center;" |  
| || || || || 7\39 || || 215.385 || 7 || 4 || 1.750 ||
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 8\[[43edo|43]]
| |  
| |  
| style="text-align:center;" | 8 8 8 8 8 3
| style="text-align:center;" | 223.3
| style="text-align:center;" | 83.7
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 9\50 || 216.000 || 9 || 5 || 1.800 ||
| |  
| |  
| |  
| |  
| |  
| |  
| style="text-align:center;" | <span style="display: block; text-align: center;">phi+1 phi+1 phi+1 phi+1 phi+1 1</span>
| style="text-align:center;" | 223
| style="text-align:center;" | 85.2
| |  
|-
|-
| style="text-align:center;" |  
| || 2\11 || || || || || 218.182 || 2 || 1 || 2.000 || Basic machinoid<br>(Generators smaller than this are proper)
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 5\[[27edo|27]]
| style="text-align:center;" |  
| |  
| |  
| style="text-align:center;" | 5 5 5 5 5 2
| style="text-align:center;" | 222.2
| style="text-align:center;" | 88.9
| style="text-align:center;" |  
|-
|-
| style="text-align:center;" |  
| || || || || || 9\49 || 220.408 || 9 || 4 || 2.250 ||
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 7\[[38edo|38]]
| |
| |  
| style="text-align:center;" | 7 7 7 7 7 3
| style="text-align:center;" | 221.1
| style="text-align:center;" | 94.7
| style="text-align:center;" |  
|-
|-
| style="text-align:center;" |  
| || || || || 7\38 || || 221.053 || 7 || 3 || 2.333 ||  
| style="text-align:center;" | 2\[[11edo|11]]
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| |  
| |  
| style="text-align:center;" | 2 2 2 2 2 1
| style="text-align:center;" | 218.2
| style="text-align:center;" | 109.1
| style="text-align:center;" | Optimum rank range (L/s=2/1) machine
|-
|-
| style="text-align:center;" |  
| || || || || || 12\65 || 221.538 || 12 || 5 || 2.400 ||
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 7\[[39edo|39]]
| |
| |  
| style="text-align:center;" | 7 7 7 7 7 4
| style="text-align:center;" | 215.4
| style="text-align:center;" | 123.1
| style="text-align:center;" |  
|-
|-
| |  
| || || || 5\27 || || || 222.222 || 5 || 2 || 2.500 ||
| |  
| |  
| |  
| |  
| |  
| |  
| style="text-align:center;" | <span style="background-color: #ffffff;">√3 √3 √3 √3 √3 1</span>
| style="text-align:center;" | 215.2
| style="text-align:center;" | 124.2
| |  
|-
|-
| style="text-align:center;" |  
| || || || || || 13\70 || 222.857 || 13 || 5 || 2.600 || Unnamed golden tuning
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 5\[[28edo|28]]
| style="text-align:center;" |  
| |  
| |  
| style="text-align:center;" | 5 5 5 5 5 3
| style="text-align:center;" | 214.3
| style="text-align:center;" | 128.6
| style="text-align:center;" |  
|-
|-
| |  
| || || || || 8\43 || || 223.256 || 8 || 3 || 2.667 ||
| |  
| |  
| |  
| |
| | 13\73
| |  
| style="text-align:center;" | 13 13 13 13 8
| style="text-align:center;" | 213.7
| style="text-align:center;" | 131.5
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 11\59 || 223.729 || 11 || 4 || 2.750 ||
| |  
| |  
| |  
| |  
| |  
| |  
| style="text-align:center;" | phi phi phi phi phi 1
| style="text-align:center;" | 213.6
| style="text-align:center;" | 1200/(1+5phi)
| style="text-align:center;" | Golden machine
|-
|-
| style="text-align:center;" |  
| || || 3\16 || || || || 224.000 || 3 || 1 || 3.000 || L/s = 3/1, clyndro
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 8\[[45edo|45]]
| |  
| |  
| style="text-align:center;" | 8 8 8 8 8 5
| style="text-align:center;" | 213.3
| style="text-align:center;" | 133.3
| style="text-align:center;" |
|-
|-
| |  
| || || || || || 10\53 || 226.415 || 10 || 3 || 3.333 ||
| |  
| |  
| |  
| |  
| |  
| |  
| style="text-align:center;" | <span style="display: block; text-align: center;">pi pi pi pi pi 2</span>
| style="text-align:center;" | 212.9
| style="text-align:center;" | 135.5
| |  
|-
|-
| style="text-align:center;" |  
| || || || || 7\37 || || 227.027 || 7 || 2 || 3.500 || Laconic
| style="text-align:center;" |  
| style="text-align:center;" | 3\[[17edo|17]]
| style="text-align:center;" |  
| style="text-align:center;" |  
| |  
| |  
| style="text-align:center;" | 3 3 3 3 3 2
| style="text-align:center;" | 211.8
| style="text-align:center;" | 141.2
| style="text-align:center;" |  
|-
|-
| style="text-align:center;" |  
| || || || || || 11\58 || 227.586 || 11 || 3 || 3.667 ||
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 7\[[40edo|40]]
| |
| |  
| style="text-align:center;" | 7 7 7 7 7 5
| style="text-align:center;" | 210
| style="text-align:center;" | 150
| style="text-align:center;" |  
|-
|-
| style="text-align:center;" |  
| || || || 4\21 || || || 228.571 || 4 || 1 || 4.000 || Gorgo
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 4\[[23edo|23]]
| style="text-align:center;" |  
| |  
| |  
| style="text-align:center;" | 4 4 4 4 4 3
| style="text-align:center;" | 208.7
| style="text-align:center;" | 156.5
| style="text-align:center;" |  
|-
|-
| style="text-align:center;" |  
| || || || || || 9\47 || 229.787 || 9 || 2 || 4.500 ||
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 5\[[29edo|29]]
| |  
| |  
| style="text-align:center;" | 5 5 5 5 5 4
| style="text-align:center;" | 206.9
| style="text-align:center;" | 165.5
| style="text-align:center;" |  
|-
|-
|
| || || || || 5\26 || || 230.769 || 5 || 1 || 5.000 || Gidorah
|
|
|
|
|6\35
|
|6 6 6 6 6 5
|205.7
|171.4
|Whole tone scales proper begin here
|-
|-
|
| || || || || || 6\31 || 232.258 || 6 || 1 || 6.000 || Slendric↓
|
|
|
|
|
|7\41
|7 7 7 7 7 6
|204.9
|175.6
|
|-
|-
| style="text-align:center;" | 1\[[6edo|6]]
| 1\5 || || || || || || 240.000 || 1 || 0 || → inf ||
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| |  
| |  
| style="text-align:center;" | 1 1 1 1 1 1
| colspan="2" style="text-align:center;" | 200
| style="text-align:center;" |  
|}
|}


[[Category:Scales]]
[[Category:Abstract MOS patterns]]
[[Category:Abstract MOS patterns]]
[[Category:6-tone scales]]
Retrieved from "https://en.xen.wiki/w/5L_1s"