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5L 1s: Difference between revisions

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This scale is always proper
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| Pattern = LLLLLs
| Pattern = LLLLLs
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}}
'''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.
'''5L 1s''' refers to [[MOS scale]]s with 5 large steps and 1 small step. When L=s we have [[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|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.
== Modes ==
* 5|0 LLLLLs
* 4|1 LLLLsL
* 3|2 LLLsLL
* 2|3 LLsLLL
* 1|4 LsLLLL
* 0|5 sLLLLL


== Scale tree ==
== Scale tree ==
Generator ranges:
* Chroma-positive generator: 200 cents (1\6) to 240 cents (1\5)
* Chroma-negative generator: 960 cents (4\5) to 1000 cents (5\6)
{| class="wikitable center-all"
{| class="wikitable center-all"
! colspan="6" | Generator
! colspan="6" | Generator
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| 1\6 || || || || || || 200.000 || 1 || 1 || 1.000 ||  
| 1\6 || || || || || || 200.000 || 1 || 1 || 1.000 ||  
|-
|-
| || || || || || 6\35 || 205.714 || 6 || 5 || 1.200 ||  
| || || || || || 6\35 || 205.714 || 6 || 5 || 1.200 || [[Quadrimage]]↑
|-
|-
| || || || || 5\29 || || 206.897 || 5 || 4 || 1.250 ||  
| || || || || 5\29 || || 206.897 || 5 || 4 || 1.250 ||  
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| || || || || 7\40 || || 210.000 || 7 || 5 || 1.400 ||
| || || || || 7\40 || || 210.000 || 7 || 5 || 1.400 ||
|-
|-
| || || || || || 10\57 || 210.528 || 10 || 7 || 1.428 ||
| || || || || || 10\57 || 210.528 || 10 || 7 || 1.429 ||
|-
|-
| || || 3\17 || || || || 211.765 || 3 || 2 || 1.500 || L/s = 3/2
| || || 3\17 || || || || 211.765 || 3 || 2 || 1.500 ||  
|-
|-
| || || || || || 11\62 || 212.903 || 11 || 7 || 1.571 ||
| || || || || || 11\62 || 212.903 || 11 || 7 || 1.571 ||
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| || || || || 8\45 || || 213.333 || 8 || 5 || 1.600 ||  
| || || || || 8\45 || || 213.333 || 8 || 5 || 1.600 ||  
|-
|-
| || || || || || 13\73 || 213.699 || 13 || 8 || 1.625 || Golden machine
| || || || || || 13\73 || 213.699 || 13 || 8 || 1.625 || Golden [[machine]] (213.5979¢)
|-
|-
| || || || 5\28 || || || 214.286 || 5 || 3 || 1.667 || Machine
| || || || 5\28 || || || 214.286 || 5 || 3 || 1.667 || Machine
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| || || || 5\27 || || || 222.222 || 5 || 2 || 2.500 ||
| || || || 5\27 || || || 222.222 || 5 || 2 || 2.500 ||
|-
|-
| || || || || || 13\70 || 222.857 || 13 || 5 || 2.600 || Unnamed golden tuning
| || || || || || 13\70 || 222.857 || 13 || 5 || 2.600 || Golden [[kumonga]] (222.9668¢)
|-
|-
| || || || || 8\43 || || 223.256 || 8 || 3 || 2.667 ||
| || || || || 8\43 || || 223.256 || 8 || 3 || 2.667 ||
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| || || || || || 11\59 || 223.729 || 11 || 4 || 2.750 ||
| || || || || || 11\59 || 223.729 || 11 || 4 || 2.750 ||
|-
|-
| || || 3\16 || || || || 224.000 || 3 || 1 || 3.000 || L/s = 3/1, clyndro
| || || 3\16 || || || || 224.000 || 3 || 1 || 3.000 || [[Clyndro]]
|-
|-
| || || || || || 10\53 || 226.415 || 10 || 3 || 3.333 ||
| || || || || || 10\53 || 226.415 || 10 || 3 || 3.333 ||
|-
|-
| || || || || 7\37 || || 227.027 || 7 || 2 || 3.500 || Laconic
| || || || || 7\37 || || 227.027 || 7 || 2 || 3.500 || [[Laconic]]
|-
|-
| || || || || || 11\58 || 227.586 || 11 || 3 || 3.667 ||
| || || || || || 11\58 || 227.586 || 11 || 3 || 3.667 ||
|-
|-
| || || || 4\21 || || || 228.571 || 4 || 1 || 4.000 || Gorgo
| || || || 4\21 || || || 228.571 || 4 || 1 || 4.000 || [[Gorgo]]
|-
|-
| || || || || || 9\47 || 229.787 || 9 || 2 || 4.500 ||
| || || || || || 9\47 || 229.787 || 9 || 2 || 4.500 ||
|-
|-
| || || || || 5\26 || || 230.769 || 5 || 1 || 5.000 || Gidorah
| || || || || 5\26 || || 230.769 || 5 || 1 || 5.000 || [[Gidorah]]
|-
|-
| || || || || || 6\31 || 232.258 || 6 || 1 || 6.000 || Slendric↓
| || || || || || 6\31 || 232.258 || 6 || 1 || 6.000 || [[Slendric]]↓
|-
|-
| 1\5 || || || || || || 240.000 || 1 || 0 || → inf ||
| 1\5 || || || || || || 240.000 || 1 || 0 || → inf ||
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[[Category:Abstract MOS patterns]]
[[Category:Abstract MOS patterns]]
[[Category:6-tone scales]]
[[Category:6-tone scales]]
[[Category:Machinoid]]
Retrieved from "https://en.xen.wiki/w/5L_1s"