5L 1s: Difference between revisions

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This scale is always proper
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| Pattern = LLLLLs
| Pattern = LLLLLs
}}
}}
'''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
Line 25: Line 37:
| 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 ||  
Line 37: Line 49:
| || || || || 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 ||
Line 45: Line 57:
| || || || || 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
Line 65: Line 77:
| || || || 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 ||
Line 71: Line 83:
| || || || || || 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 ||
Line 92: Line 104:
[[Category:Abstract MOS patterns]]
[[Category:Abstract MOS patterns]]
[[Category:6-tone scales]]
[[Category:6-tone scales]]
[[Category:Machinoid]]

Revision as of 22:14, 2 June 2022

← 4L 1s 5L 1s 6L 1s →
↙ 4L 2s ↓ 5L 2s 6L 2s ↘ 
┌╥╥╥╥╥┬┐
│║║║║║││
││││││││
└┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLLs
sLLLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 1\6 to 1\5 (200.0 ¢ to 240.0 ¢)
Dark 4\5 to 5\6 (960.0 ¢ to 1000.0 ¢)
TAMNAMS information
Name machinoid
Prefix mech-
Abbrev. mk
Related MOS scales
Parent 1L 4s
Sister 1L 5s
Daughters 6L 5s, 5L 6s
Neutralized 4L 2s
2-Flought 11L 1s, 5L 7s
Equal tunings
Equalized (L:s = 1:1) 1\6 (200.0 ¢)
Supersoft (L:s = 4:3) 4\23 (208.7 ¢)
Soft (L:s = 3:2) 3\17 (211.8 ¢)
Semisoft (L:s = 5:3) 5\28 (214.3 ¢)
Basic (L:s = 2:1) 2\11 (218.2 ¢)
Semihard (L:s = 5:2) 5\27 (222.2 ¢)
Hard (L:s = 3:1) 3\16 (225.0 ¢)
Superhard (L:s = 4:1) 4\21 (228.6 ¢)
Collapsed (L:s = 1:0) 1\5 (240.0 ¢)

5L 1s refers to MOS scales 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 slendric, in which the large step is 8/7 and three of them make a 3/2.

Scales with this pattern are always 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

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)
Generator Cents L s L/s Comments
1\6 200.000 1 1 1.000
6\35 205.714 6 5 1.200 Quadrimage↑
5\29 206.897 5 4 1.250
9\52 207.692 9 7 1.286
4\23 208.696 4 3 1.333
11\63 209.524 11 8 1.375
7\40 210.000 7 5 1.400
10\57 210.528 10 7 1.429
3\17 211.765 3 2 1.500
11\62 212.903 11 7 1.571
8\45 213.333 8 5 1.600
13\73 213.699 13 8 1.625 Golden machine (213.5979¢)
5\28 214.286 5 3 1.667 Machine
12\67 214.925 12 7 1.714
7\39 215.385 7 4 1.750
9\50 216.000 9 5 1.800
2\11 218.182 2 1 2.000 Basic machinoid
9\49 220.408 9 4 2.250
7\38 221.053 7 3 2.333
12\65 221.538 12 5 2.400
5\27 222.222 5 2 2.500
13\70 222.857 13 5 2.600 Golden kumonga (222.9668¢)
8\43 223.256 8 3 2.667
11\59 223.729 11 4 2.750
3\16 224.000 3 1 3.000 Clyndro
10\53 226.415 10 3 3.333
7\37 227.027 7 2 3.500 Laconic
11\58 227.586 11 3 3.667
4\21 228.571 4 1 4.000 Gorgo
9\47 229.787 9 2 4.500
5\26 230.769 5 1 5.000 Gidorah
6\31 232.258 6 1 6.000 Slendric↓
1\5 240.000 1 0 → inf
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