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 8: Line 18:
| 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(<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.


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. Other low-harmonic-entropy scales with this MOS pattern tune the seventh (septave) 1080¢ or flatter for making a quarter 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="6" | Generator
! colspan="8" | Generator
! ''ed11\12''
! Normalized Cents (septave)
! Cents
! Cents
! L
! L
Line 23: Line 35:
! Comments
! Comments
|-
|-
| 1\6 || || || || || || 200.000 || 1 || 1 || 1.000 ||  
| 1\6 || || || || || || || || ''183.333'' || 171.429 || 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 ||  
|-
|-
| || || || || || 6\35 || 205.714 || 6 || 5 || 1.200 ||  
| || || || || 13\73 || || || || ''195.890''||192.593 || 213.699 || 13 || 8 || 1.625 || Golden Ionianic-machine
|-
|-
| || || || || 5\29 || || 206.897 || 5 || 4 || 1.250 ||  
| || || 5\28 || || || || || ||''196.429'' ||193.548 || 214.286 || 5 || 3 || 1.667 || Machine
|-
|-
| || || || || || 9\52 || 207.692 || 9 || 7 || 1.286 ||  
| || || || || 12\67 || || || || ''197.015''|| 194.595|| 214.925 || 12 || 7 || 1.714 ||  
|-
|-
| || || || 4\23 || || || 208.696 || 4 || 3 || 1.333 ||
| || || || 7\39 || || || || ||''197.436'' || 195.349|| 215.385 || 7 || 4 || 1.750 ||
|-
|-
| || || || || || 11\63 || 209.524 || 11 || 8 || 1.375 ||
| || || || || 9\50 || || || ||''198.000'' || 196.364|| 216.000 || 9 || 5 || 1.800 ||
|-
|-
| || || || || 7\40 || || 210.000 || 7 || 5 || 1.400 ||
| || || || || || 11\61 || || ||''198.361'' || 197.015|| 216.393 || 11 || 6 || 1.833 ||
|-
| || || || || || || 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
|-
|-
| || || || || || 10\57 || 210.528 || 10 || 7 || 1.428 ||
| || || || || || || || 15\82 ||''201.2195'' || 202.247|| 219.512 || 15 || 7 || 2.143 ||
|-
|-
| || || 3\17 || || || || 211.765 || 3 || 2 || 1.500 || L/s = 3/2
| || || || || || || 13\71 || ||''201.4085'' || 202.597|| 219.718 || 13 || 6 || 2.167 ||
|-
|-
| || || || || || 11\62 || 212.903 || 11 || 7 || 1.571 ||
| || || || || || 11\60 || || ||''201.667'' || 203.077|| 220.000 || 11 || 5 || 2.200 ||  
|-
|-
| || || || || 8\45 || || 213.333 || 8 || 5 || 1.600 ||  
| || || || || 9\49 || || || ||''202.041'' || 203.774|| 220.408 || 9 || 4 || 2.250 ||
|-
|-
| || || || || || 13\73 || 213.699 || 13 || 8 || 1.625 || Golden machine
| || || || 7\38 || || || || || ''202.632''|| 204.878|| 221.053 || 7 || 3 || 2.333 ||  
|-
|-
| || || || 5\28 || || || 214.286 || 5 || 3 || 1.667 || Machine
| || || || || 12\65 || || || || ''203.077''|| 205.714|| 221.538 || 12 || 5 || 2.400 ||
|-
|-
| || || || || || 12\67 || 214.925 || 12 || 7 || 1.714 ||  
| || || 5\27 || || || || || || ''203.704''|| 206.897 || 222.222 || 5 || 2 || 2.500 ||
|-
|-
| || || || || 7\39 || || 215.385 || 7 || 4 || 1.750 ||
| || || || || || 18\97 || || || ''204.124''|| 207.692|| 222.680 || 18 || 7 || 2.571 ||  
|-
|-
| || || || || || 9\50 || 216.000 || 9 || 5 || 1.800 ||
| || || || || 13\70 || || || || ''204.285''|| 208.000|| 222.857 || 13 || 5 || 2.600 || Unnamed golden tuning
|-
|-
| || 2\11 || || || || || 218.182 || 2 || 1 || 2.000 || Basic machinoid<br>(Generators smaller than this are proper)
| || || || 8\43 || || || || ||''204.651'' || 208.697 || 223.256 || 8 || 3 || 2.667 ||
|-
|-
| || || || || || 9\49 || 220.408 || 9 || 4 || 2.250 ||
| || || || || 11\59 || || || || ''205.085''|| 209.524|| 223.729 || 11 || 4 || 2.750 ||
|-
|-
| || || || || 7\38 || || 221.053 || 7 || 3 || 2.333 ||  
| || || || || || 14\75 || || || ''205.333''|| 210.000 || 224.000 || 14 || 5 || 3.000 ||  
|-
|-
| || || || || || 12\65 || 221.538 || 12 || 5 || 2.400 ||
| || 3\16 || || || || || || ||''206.25'' || 211.765 || 225.000 || 3 || 1 || 3.000 || L/s = 3/1, clyndro
|-
|-
| || || || 5\27 || || || 222.222 || 5 || 2 || 2.500 ||
| || || || || || || 16\85 || ||''207.059'' || 213.333 || 225.882 || 16 || 5 || 3.200 ||
|-
| || || || || || 13\69 || || || ''207.247''|| 213.698|| 226.087 || 13 || 4 || 3.250 ||  
|-
|-
| || || || || || 13\70 || 222.857 || 13 || 5 || 2.600 || Unnamed golden tuning
| || || || || 10\53 || || || || ''207.547''|| 214.857|| 226.415 || 10 || 3 || 3.333 ||
|-
|-
| || || || || 8\43 || || 223.256 || 8 || 3 || 2.667 ||
| || || || 7\37 || || || || ||''208.108'' || 215.385 || 227.027 || 7 || 2 || 3.500 || Laconic
|-
|-
| || || || || || 11\59 || 223.729 || 11 || 4 || 2.750 ||
| || || || || 11\58 || || || ||''208.621'' ||216.393 || 227.586 || 11 || 3 || 3.667 ||
|-
|-
| || || 3\16 || || || || 224.000 || 3 || 1 || 3.000 || L/s = 3/1, clyndro
| || || || || || 15\79 || || ||''208.861'' ||216.8675 || 227.848 || 15 || 4 || 3.750 ||  
|-
|-
| || || || || || 10\53 || 226.415 || 10 || 3 || 3.333 ||
| || || || || || || 19\100 || ||''209.000'' ||217.143 || 228.000 || 19 || 5 || 3.800 ||  
|-
|-
| || || || || 7\37 || || 227.027 || 7 || 2 || 3.500 || Laconic
| || || 4\21 || || || || || || ''209.524''|| 218.182|| 228.571 || 4 || 1 || 4.000 || Gorgo
|-
|-
| || || || || || 11\58 || 227.586 || 11 || 3 || 3.667 ||
| || || || || || 13\68 || || || ''210.294''|| 219.718|| 229.412 || 13 || 3 || 4.333 ||  
|-
|-
| || || || 4\21 || || || 228.571 || 4 || 1 || 4.000 || Gorgo
| || || || || 9\47 || || || ||''210.638'' || 220.408|| 229.787 || 9 || 2 || 4.500 ||
|-
|-
| || || || || || 9\47 || 229.787 || 9 || 2 || 4.500 ||
| || || || || || 14\73 || || ||''210.959'' || 221.053|| 230.137 || 14 || 3 || 4.667 ||  
|-
|-
| || || || || 5\26 || || 230.769 || 5 || 1 || 5.000 || Gidorah
| || || || 5\26 || || || || || ''211.5385''|| 222.222|| 230.769 || 5 || 1 || 5.000 || Gidorah
|-
|-
| || || || || || 6\31 || 232.258 || 6 || 1 || 6.000 || Slendric↓
| || || || || || || 11\57 || || ''212.281''|| 223.729|| 231.579 || 11 || 2 || 5.500 ||
|-
| || || || || || || || 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 || || || || || || 240.000 || 1 || 0 || → inf ||
| 1\5 || || || || || || || || ''220.000''|| 240.000 || 240.000 || 1 || 0 || → inf ||
|}
|}


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

Revision as of 03:57, 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 ¢)
← 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(<15/8>) 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. Other low-harmonic-entropy scales with this MOS pattern tune the seventh (septave) 1080¢ or flatter for making a quarter 3/2.

Scales with this pattern are always proper, because there is only one small step.

Scale tree

Generator ed11\12 Normalized Cents (septave) Cents L s L/s Comments
1\6 183.333 171.429 200.000 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
5\28 196.429 193.548 214.286 5 3 1.667 Machine
12\67 197.015 194.595 214.925 12 7 1.714
7\39 197.436 195.349 215.385 7 4 1.750
9\50 198.000 196.364 216.000 9 5 1.800
11\61 198.361 197.015 216.393 11 6 1.833
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
13\71 201.4085 202.597 219.718 13 6 2.167
11\60 201.667 203.077 220.000 11 5 2.200
9\49 202.041 203.774 220.408 9 4 2.250
7\38 202.632 204.878 221.053 7 3 2.333
12\65 203.077 205.714 221.538 12 5 2.400
5\27 203.704 206.897 222.222 5 2 2.500
18\97 204.124 207.692 222.680 18 7 2.571
13\70 204.285 208.000 222.857 13 5 2.600 Unnamed golden tuning
8\43 204.651 208.697 223.256 8 3 2.667
11\59 205.085 209.524 223.729 11 4 2.750
14\75 205.333 210.000 224.000 14 5 3.000
3\16 206.25 211.765 225.000 3 1 3.000 L/s = 3/1, clyndro
16\85 207.059 213.333 225.882 16 5 3.200
13\69 207.247 213.698 226.087 13 4 3.250
10\53 207.547 214.857 226.415 10 3 3.333
7\37 208.108 215.385 227.027 7 2 3.500 Laconic
11\58 208.621 216.393 227.586 11 3 3.667
15\79 208.861 216.8675 227.848 15 4 3.750
19\100 209.000 217.143 228.000 19 5 3.800
4\21 209.524 218.182 228.571 4 1 4.000 Gorgo
13\68 210.294 219.718 229.412 13 3 4.333
9\47 210.638 220.408 229.787 9 2 4.500
14\73 210.959 221.053 230.137 14 3 4.667
5\26 211.5385 222.222 230.769 5 1 5.000 Gidorah
11\57 212.281 223.729 231.579 11 2 5.500
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
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