5L 1s: Difference between revisions

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{{Infobox MOS
| Name = diatonic
| Periods = 1
| nLargeSteps = 5
| nSmallSteps = 1
| Equalized = 1
| Paucitonic = 1
| Pattern = LLLLLs
| Equave = 15/8
}}
{{Infobox MOS
{{Infobox MOS
| Name = machinoid
| Name = machinoid
Line 18: Line 8:
| Pattern = LLLLLs
| Pattern = LLLLLs
}}
}}
'''5L 1s(<15/8>)''' 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|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. Other low-harmonic-entropy scales with this MOS pattern tune the seventh (septave) 1080¢ or flatter for making a quarter 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.
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== Scale tree ==
== Scale tree ==
{| class="wikitable center-all"
{| class="wikitable center-all"
! colspan="8" | Generator
! colspan="6" | Generator
! ''ed11\12''
! Normalized Cents (septave)
! Cents
! Cents
! L
! L
Line 35: Line 23:
! Comments
! Comments
|-
|-
| 1\6 || || || || || || || || ''183.333'' || 171.429 || 200.000 || 1 || 1 || 1.000 ||
| 1\6 || || || || || || 200.000 || 1 || 1 || 1.000 ||  
|-
| || || || || 6\35 || || || || ''188.571'' || 180.000 || 205.714 || 6 || 5 || 1.200 ||
|-
| || || || 5\29 || || || || || ''189.655'' || 181.818 || 206.897 || 5 || 4 || 1.250 ||
|-
| || || || || || 14\81 || || || ''190.1235''|| 182.609 || 207.407 || 14 || 11 || 1.273 ||
|-
| || || || || 9\52 || || || ||''190.385'' || 183.051 || 207.692 || 9 || 7 || 1.286 ||
|-
| || || 4\23 || || || || || || ''191.304''|| 184.615 || 208.696 || 4 || 3 || 1.333 ||
|-
| || || || || 11\63 || || || ||''192.0635'' ||185.9155 || 209.524 || 11 || 8 || 1.375 ||
|-
| || || || 7\40 || || || || ||''192.500'' ||186.667 || 210.000 || 7 || 5 || 1.400 ||
|-
| || || || || 10\57 || || || ||''192.9825'' || 187.500|| 210.528 || 10 || 7 || 1.428 ||
|-
| || || || || ||13\74 || || || ''193.243''|| 187.952|| 210.811 || 13 || 9 || 1.444 ||
|-
| || || || || || ||16\91 || || ''193.407''|| 188.235|| 210.989 || 16 || 11 || 1.4545 ||
|-
| || 3\17 || || || || || || ||''194.118''|| 189.474|| 211.765 || 3 || 2 || 1.500 || L/s = 3/2
|-
| || || || || || 14\79 || || ||''194.937'' || 190.909|| 212.658 || 14 || 9 || 1.556 ||
|-
| || || || || 11\62 || || || ||''195.161'' || 191.304|| 212.903 || 11 || 7 || 1.571 ||
|-
| || || || 8\45 || || || || || ''195.556''|| 192.000|| 213.333 || 8 || 5 || 1.600 ||  
|-
|-
| || || || || 13\73 || || || || ''195.890''||192.593 || 213.699 || 13 || 8 || 1.625 || Golden Ionianic-machine
| || || || || || 6\35 || 205.714 || 6 || 5 || 1.200 ||  
|-
|-
| || || 5\28 || || || || || ||''196.429'' ||193.548 || 214.286 || 5 || 3 || 1.667 || Machine
| || || || || 5\29 || || 206.897 || 5 || 4 || 1.250 ||  
|-
|-
| || || || || 12\67 || || || || ''197.015''|| 194.595|| 214.925 || 12 || 7 || 1.714 ||  
| || || || || || 9\52 || 207.692 || 9 || 7 || 1.286 ||  
|-
|-
| || || || 7\39 || || || || ||''197.436'' || 195.349|| 215.385 || 7 || 4 || 1.750 ||
| || || || 4\23 || || || 208.696 || 4 || 3 || 1.333 ||
|-
|-
| || || || || 9\50 || || || ||''198.000'' || 196.364|| 216.000 || 9 || 5 || 1.800 ||
| || || || || || 11\63 || 209.524 || 11 || 8 || 1.375 ||
|-
|-
| || || || || || 11\61 || || ||''198.361'' || 197.015|| 216.393 || 11 || 6 || 1.833 ||
| || || || || 7\40 || || 210.000 || 7 || 5 || 1.400 ||
|-
| || || || || || || 13\72 || ||''198.611'' || 197.468|| 216.667 || 13 || 7 || 1.857 ||
|- 
| || || || || || || || 15\83 ||''198.795'' || 197.802|| 216.8675 || 15 || 8 || 1.875 ||
|-
| 2\11 || || || || || || || || ''200.000''|| 200.000 || 218.182 || 2 || 1 || 2.000 || Basic Ionianic-machinoid
|-
|-
| || || || || || || || 15\82 ||''201.2195'' || 202.247|| 219.512 || 15 || 7 || 2.143 ||
| || || || || || 10\57 || 210.528 || 10 || 7 || 1.428 ||
|-
|-
| || || || || || || 13\71 || ||''201.4085'' || 202.597|| 219.718 || 13 || 6 || 2.167 ||
| || || 3\17 || || || || 211.765 || 3 || 2 || 1.500 || L/s = 3/2
|-
|-
| || || || || || 11\60 || || ||''201.667'' || 203.077|| 220.000 || 11 || 5 || 2.200 ||  
| || || || || || 11\62 || 212.903 || 11 || 7 || 1.571 ||
|-
|-
| || || || || 9\49 || || || ||''202.041'' || 203.774|| 220.408 || 9 || 4 || 2.250 ||
| || || || || 8\45 || || 213.333 || 8 || 5 || 1.600 ||  
|-
|-
| || || || 7\38 || || || || || ''202.632''|| 204.878|| 221.053 || 7 || 3 || 2.333 ||  
| || || || || || 13\73 || 213.699 || 13 || 8 || 1.625 || Golden machine
|-
|-
| || || || || 12\65 || || || || ''203.077''|| 205.714|| 221.538 || 12 || 5 || 2.400 ||
| || || || 5\28 || || || 214.286 || 5 || 3 || 1.667 || Machine
|-
|-
| || || 5\27 || || || || || || ''203.704''|| 206.897 || 222.222 || 5 || 2 || 2.500 ||
| || || || || || 12\67 || 214.925 || 12 || 7 || 1.714 ||  
|-
|-
| || || || || || 18\97 || || || ''204.124''|| 207.692|| 222.680 || 18 || 7 || 2.571 ||  
| || || || || 7\39 || || 215.385 || 7 || 4 || 1.750 ||
|-
|-
| || || || || 13\70 || || || || ''204.285''|| 208.000|| 222.857 || 13 || 5 || 2.600 || Unnamed golden tuning
| || || || || || 9\50 || 216.000 || 9 || 5 || 1.800 ||
|-
|-
| || || || 8\43 || || || || ||''204.651'' || 208.697 || 223.256 || 8 || 3 || 2.667 ||
| || 2\11 || || || || || 218.182 || 2 || 1 || 2.000 || Basic machinoid<br>(Generators smaller than this are proper)
|-
|-
| || || || || 11\59 || || || || ''205.085''|| 209.524|| 223.729 || 11 || 4 || 2.750 ||
| || || || || || 9\49 || 220.408 || 9 || 4 || 2.250 ||
|-
|-
| || || || || || 14\75 || || || ''205.333''|| 210.000 || 224.000 || 14 || 5 || 3.000 ||  
| || || || || 7\38 || || 221.053 || 7 || 3 || 2.333 ||  
|-
|-
| || 3\16 || || || || || || ||''206.25'' || 211.765 || 225.000 || 3 || 1 || 3.000 || L/s = 3/1, clyndro
| || || || || || 12\65 || 221.538 || 12 || 5 || 2.400 ||
|-
|-
| || || || || || || 16\85 || ||''207.059'' || 213.333 || 225.882 || 16 || 5 || 3.200 ||
| || || || 5\27 || || || 222.222 || 5 || 2 || 2.500 ||
|-
| || || || || || 13\69 || || || ''207.247''|| 213.698|| 226.087 || 13 || 4 || 3.250 ||  
|-
|-
| || || || || 10\53 || || || || ''207.547''|| 214.857|| 226.415 || 10 || 3 || 3.333 ||
| || || || || || 13\70 || 222.857 || 13 || 5 || 2.600 || Unnamed golden tuning
|-
|-
| || || || 7\37 || || || || ||''208.108'' || 215.385 || 227.027 || 7 || 2 || 3.500 || Laconic
| || || || || 8\43 || || 223.256 || 8 || 3 || 2.667 ||
|-
|-
| || || || || 11\58 || || || ||''208.621'' ||216.393 || 227.586 || 11 || 3 || 3.667 ||
| || || || || || 11\59 || 223.729 || 11 || 4 || 2.750 ||
|-
|-
| || || || || || 15\79 || || ||''208.861'' ||216.8675 || 227.848 || 15 || 4 || 3.750 ||  
| || || 3\16 || || || || 224.000 || 3 || 1 || 3.000 || L/s = 3/1, clyndro
|-
|-
| || || || || || || 19\100 || ||''209.000'' ||217.143 || 228.000 || 19 || 5 || 3.800 ||  
| || || || || || 10\53 || 226.415 || 10 || 3 || 3.333 ||
|-
|-
| || || 4\21 || || || || || || ''209.524''|| 218.182|| 228.571 || 4 || 1 || 4.000 || Gorgo
| || || || || 7\37 || || 227.027 || 7 || 2 || 3.500 || Laconic
|-
|-
| || || || || || 13\68 || || || ''210.294''|| 219.718|| 229.412 || 13 || 3 || 4.333 ||  
| || || || || || 11\58 || 227.586 || 11 || 3 || 3.667 ||
|-
|-
| || || || || 9\47 || || || ||''210.638'' || 220.408|| 229.787 || 9 || 2 || 4.500 ||
| || || || 4\21 || || || 228.571 || 4 || 1 || 4.000 || Gorgo
|-
|-
| || || || || || 14\73 || || ||''210.959'' || 221.053|| 230.137 || 14 || 3 || 4.667 ||  
| || || || || || 9\47 || 229.787 || 9 || 2 || 4.500 ||
|-
|-
| || || || 5\26 || || || || || ''211.5385''|| 222.222|| 230.769 || 5 || 1 || 5.000 || Gidorah
| || || || || 5\26 || || 230.769 || 5 || 1 || 5.000 || Gidorah
|-
|-
| || || || || || || 11\57 || || ''212.281''|| 223.729|| 231.579 || 11 || 2 || 5.500 ||
| || || || || || 6\31 || 232.258 || 6 || 1 || 6.000 || Slendric↓
|-
| || || || || || || || 17\88 || ''212.500''|| 224.179|| 231.818 || 17 || 3 || 5.667 ||
|- 
| || || || || 6\31 || || || ||''212.903'' || 225.000 || 232.258 || 6 || 1 || 6.000 || Slendric↓
|-
|-
| 1\5 || || || || || || || || ''220.000''|| 240.000 || 240.000 || 1 || 0 || → inf ||
| 1\5 || || || || || || 240.000 || 1 || 0 || → inf ||
|}
|}


[[Category:Abstract MOS patterns]]
[[Category:Abstract MOS patterns]]
[[Category:6-tone scales]]
[[Category:6-tone scales]]

Revision as of 14:44, 1 April 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.

Scale tree

Generator Cents L s L/s Comments
1\6 200.000 1 1 1.000
6\35 205.714 6 5 1.200
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 1.428
3\17 211.765 3 2 1.500 L/s = 3/2
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
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
(Generators smaller than this are proper)
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 Unnamed golden tuning
8\43 223.256 8 3 2.667
11\59 223.729 11 4 2.750
3\16 224.000 3 1 3.000 L/s = 3/1, 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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