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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]]
Retrieved from "https://en.xen.wiki/w/5L_1s"