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{{Infobox MOS
'''5L 1s(<major seventh>)''', also known as the greater whole tone scale, 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.
| Name = diatonic
| Periods = 1
| nLargeSteps = 5
| nSmallSteps = 1
| Equalized = 1
| Paucitonic = 1
| Pattern = LLLLLs
| Equave = 15/8
}}
{{Infobox MOS
| Name = machinoid
| Periods = 1
| nLargeSteps = 5
| nSmallSteps = 1
| Equalized = 1
| Paucitonic = 1
| 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.


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. Other low-harmonic-entropy scales with this MOS pattern tune the seventh (septave) 1050¢ or flatter for making a quarter 3/2 and between 1080¢ and 1100¢ for making a 7/2-equivalent augmented thirteenth scale.  


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
! Generator
! ''ed11\12''
! Normalized Cents (septave)
! Normalized Cents (septave)
! Cents
! Cents
Line 35: Line 15:
! Comments
! Comments
|-
|-
| 1\6 || || || || || || || || ''183.333'' || 171.429 || 200.000 || 1 || 1 || 1.000 ||  
| 1\6 || 171.429 || 200.000 || 1 || 1 || 1.000 ||  
|-
|-
| || || || || 6\35 || || || || ''188.571'' || 180.000 || 205.714 || 6 || 5 || 1.200 ||  
|9\53
|177.049
|203.774
|9
|8
|1.125
|
|-
|-
| || || || 5\29 || || || || || ''189.655'' || 181.818 || 206.897 || 5 || 4 || 1.250 ||  
|8\47
|177.778
|204.255
|8
|7
|1.143
|
|-
|-
| || || || || || 14\81 || || || ''190.1235''|| 182.609 || 207.407 || 14 || 11 || 1.273 ||  
|7\41
|178.723
|204.878
|7
|6
|1.167
|
|-
|13\76
|179.310
|205.263
|13
|11
|1.273
|
|-
| 6\35|| 180.000 || 205.714 || 6 || 5 || 1.200 ||
|-
| 5\29|| 181.818 || 206.897 || 5 || 4 || 1.250 ||
|-
| 14\81|| 182.609 || 207.407 || 14 || 11 || 1.273 ||  
|-  
|-  
| || || || || 9\52 || || || ||''190.385'' || 183.051 || 207.692 || 9 || 7 || 1.286 ||  
| 9\52|| 183.051 || 207.692 || 9 || 7 || 1.286 ||  
|-
|-
| || || 4\23 || || || || || || ''191.304''|| 184.615 || 208.696 || 4 || 3 || 1.333 ||
| 4\23|| 184.615 || 208.696 || 4 || 3 || 1.333 ||
|-
|-
| || || || || 11\63 || || || ||''192.0635'' ||185.9155 || 209.524 || 11 || 8 || 1.375 ||
| 11\63||185.915 || 209.524||11||8|| 1.375||
|-
|-
| || || || 7\40 || || || || ||''192.500'' ||186.667 || 210.000 || 7 || 5 || 1.400 ||
| 7\40||186.667|| 210.000||7||5|| 1.400||
|-
|-
| || || || || 10\57 || || || ||''192.9825'' || 187.500|| 210.528 || 10 || 7 || 1.428 ||
| 10\57 ||187.500 || 210.528|| 10||7||1.428||
|-
|-
| || || || || ||13\74 || || || ''193.243''|| 187.952|| 210.811 || 13 || 9 || 1.444 ||  
| 13\74||187.952||210.811||13||9|| 1.444||
|-
|-
| || || || || || ||16\91 || || ''193.407''|| 188.235|| 210.989 || 16 || 11 || 1.4545 ||  
| 16\91||188.235||210.989||16||11 ||1.4545||
|-
|-
| || 3\17 || || || || || || ||''194.118''|| 189.474|| 211.765 || 3 || 2 || 1.500 || L/s = 3/2
| 3\17|| 189.474 || 211.765 || 3||2||1.500||L/s = 3/2
|-
|-
| || || || || || 14\79 || || ||''194.937'' || 190.909|| 212.658 || 14 || 9 || 1.556 ||  
| 14\79||190.909||212.658 ||14 || 9|| 1.556||
|-
|-
| || || || || 11\62 || || || ||''195.161'' || 191.304|| 212.903 || 11 || 7 || 1.571 ||
| 11\62||191.304|| 212.903||11 ||7||1.571||
|-
|-
| || || || 8\45 || || || || || ''195.556''|| 192.000|| 213.333 || 8 || 5 || 1.600 ||  
| 8\45||192.000||213.333||8 || 5||1.600||
|-
|-
| || || || || 13\73 || || || || ''195.890''||192.593 || 213.699 || 13 || 8 || 1.625 || Golden Ionianic-machine
| 13\73|| 192.593||213.699 ||13 || 8|| 1.625||Golden Ionianic-machine
|-
|-
| || || 5\28 || || || || || ||''196.429'' ||193.548 || 214.286 || 5 || 3 || 1.667 || Ionianic-Machine
| 5\28|| 193.548||214.286||5||3||1.667 || Ionianic-Machine
|-
|-
| || || || || 12\67 || || || || ''197.015''|| 194.595|| 214.925 || 12 || 7 || 1.714 ||  
| 12\67|| 194.595||214.925 ||12||7||1.714||
|-
|-
| || || || 7\39 || || || || ||''197.436'' || 195.349|| 215.385 || 7 || 4 || 1.750 ||
| 7\39||195.349||215.385||7||4 || 1.750||
|-
|-
| || || || || 9\50 || || || ||''198.000'' || 196.364|| 216.000 || 9 || 5 || 1.800 ||
| 9\50 ||196.364||216.000 ||9||5||1.800 ||
|-
|-
| || || || || || 11\61 || || ||''198.361'' || 197.015|| 216.393 || 11 || 6 || 1.833 ||
| 11\61|| 197.015||216.393||11 ||6||1.833 ||
|-  
|-  
| || || || || || || 13\72 || ||''198.611'' || 197.468|| 216.667 || 13 || 7 || 1.857 ||
| 13\72||197.468||216.667 ||13||7||1.857||
|-   
|-   
| || || || || || || || 15\83 ||''198.795'' || 197.802|| 216.8675 || 15 || 8 || 1.875 ||
| 15\83|| 197.802 |197.802||216.867||15||8||1.875
|
|-
|17\94
|198.058
|217.021
|17
|9
|1.889
|
|-  
|-  
| 2\11 || || || || || || || || ''200.000''|| 200.000 || 218.182 || 2 || 1 || 2.000 || Basic Ionianic-machinoid
| 2\11 ||200.000||218.182||2||1||2.000 ||Basic Ionianic-machinoid
|-
|17\93
|201.980
|219.355
|17
|8
|2.125
|
|-
| 15\82 || 202.247||219.512||15|| 7||2.143||
|-
|-
| || || || || || || || 15\82 ||''201.2195'' || 202.247|| 219.512 || 15 || 7 || 2.143 ||
| 13\71 ||202.597||219.718||13||6 || 2.167||
|-
|-
| || || || || || || 13\71 || ||''201.4085'' || 202.597|| 219.718 || 13 || 6 || 2.167 ||
| 11\60||203.077 ||220.000 ||11|| 5|| 2.200||
|-
|-
| || || || || || 11\60 || || ||''201.667'' || 203.077|| 220.000 || 11 || 5 || 2.200 ||  
| 9\49 ||203.774||220.408 || 9||4||2.250||
|-
|-
| || || || || 9\49 || || || ||''202.041'' || 203.774|| 220.408 || 9 || 4 || 2.250 ||
| 7\38||204.878 ||221.053||7 || 3||2.333||
|-
|-
| || || || 7\38 || || || || || ''202.632''|| 204.878|| 221.053 || 7 || 3 || 2.333 ||  
| 12\65||205.714||221.538||12|| 5||2.400 ||
|-
|-
| || || || || 12\65 || || || || ''203.077''|| 205.714|| 221.538 || 12 || 5 || 2.400 ||
| 5\27||206.897||222.222||5||2||2.500 ||
|-
|-
| || || 5\27 || || || || || || ''203.704''|| 206.897 || 222.222 || 5 || 2 || 2.500 ||
| 18\97 ||207.692 || 222.680 ||18||7|| 2.571||
|-
|-
| || || || || || 18\97 || || || ''204.124''|| 207.692|| 222.680 || 18 || 7 || 2.571 ||  
| 13\70||208.000||222.857||13||5||2.600||Unnamed golden tuning
|-
|-
| || || || || 13\70 || || || || ''204.285''|| 208.000|| 222.857 || 13 || 5 || 2.600 || Unnamed golden tuning
| 8\43||208.697||223.256||8||3||2.667||
|-
|-
| || || || 8\43 || || || || ||''204.651'' || 208.697 || 223.256 || 8 || 3 || 2.667 ||
| 11\59 || 209.524|| 223.729||11||4||2.750||
|-
|-
| || || || || 11\59 || || || || ''205.085''|| 209.524|| 223.729 || 11 || 4 || 2.750 ||
| 14\75||210.000||224.000||14||5 ||3.000||
|-
|-
| || || || || || 14\75 || || || ''205.333''|| 210.000 || 224.000 || 14 || 5 || 3.000 ||  
| 3\16||211.765||225.000||3||1||3.000||L/s = 3/1, Ionianic-clyndro
|-
|-
| || 3\16 || || || || || || ||''206.25'' || 211.765 || 225.000 || 3 || 1 || 3.000 || L/s = 3/1, Ionianic-clyndro
|22\117
|212.903
|225.641
|22
|7
|3.143
|
|-
|-
| || || || || || || 16\85 || ||''207.059'' || 213.333 || 225.882 || 16 || 5 || 3.200 ||
|19\101
|213.084
|225.743
|19
|6
|3.167
|
|-
| 16\85||213.333||225.882||16|| 5|| 3.200||
|-  
|-  
| || || || || || 13\69 || || || ''207.247''|| 213.698|| 226.087 || 13 || 4 || 3.250 ||  
| 13\69||213.698||226.087||13 || 4|| 3.250||
|-
|-
| || || || || 10\53 || || || || ''207.547''|| 214.857|| 226.415 || 10 || 3 || 3.333 ||
| 10\53 ||214.857 ||226.415|| 10 ||3||3.333||
|-
|-
| || || || 7\37 || || || || ||''208.108'' || 215.385 || 227.027 || 7 || 2 || 3.500 || Ionianic-Laconic
| 7\37||215.385||227.027||7||2||3.500||Ionianic-Laconic
|-
|-
| || || || || 11\58 || || || ||''208.621'' ||216.393 || 227.586 || 11 || 3 || 3.667 ||
| 11\58 ||216.393||227.586||11||3 || 3.667||
|-
|-
| || || || || || 15\79 || || ||''208.861'' ||216.8675 || 227.848 || 15 || 4 || 3.750 ||  
| 15\79||216.867||227.848||15||4||3.750||
|-
|-
| || || || || || || 19\100 || ||''209.000'' ||217.143 || 228.000 || 19 || 5 || 3.800 ||  
| 19\100 ||217.143 || 228.000 || 19||5||3.800||
|-
|-
| || || 4\21 || || || || || || ''209.524''|| 218.182|| 228.571 || 4 || 1 || 4.000 || Ionianic-Gorgo
| 4\21||218.182||228.571||4||1||4.000||Ionianic-Gorgo
|-
|-
| || || || || || 13\68 || || || ''210.294''|| 219.718|| 229.412 || 13 || 3 || 4.333 ||  
| 13\68 ||219.718||229.412 || 13||3||4.333 ||
|-
|-
| || || || || 9\47 || || || ||''210.638'' || 220.408|| 229.787 || 9 || 2 || 4.500 ||
| 9\47 ||220.408||229.787||9||2||4.500||
|-
|-
| || || || || || 14\73 || || ||''210.959'' || 221.053|| 230.137 || 14 || 3 || 4.667 ||  
| 14\73 ||221.053 || 230.137||14||3||4.667||
|-
|-
| || || || 5\26 || || || || || ''211.5385''|| 222.222|| 230.769 || 5 || 1 || 5.000 || Ionianic-Gidorah
| 5\26||222.222||230.769||5||1 || 5.000||Ionianic-Gidorah
|-
|-
| || || || || || || 11\57 || || ''212.281''|| 223.729|| 231.579 || 11 || 2 || 5.500 ||
| 11\57|| 223.729|| 231.579 || 11||2||5.500 ||
|-  
|-  
| || || || || || || || 17\88 || ''212.500''|| 224.179|| 231.818 || 17 || 3 || 5.667 ||
| 17\88 ||224.179||231.818 || 17||3||5.667||
|-   
|-   
| || || || || 6\31 || || || ||''212.903'' || 225.000 || 232.258 || 6 || 1 || 6.000 || Ionianic-Slendric↓
| 6\31 ||225.000||232.258||6||1||6.000 || Ionianic-Slendric↓
|-
|-
| 1\5 || || || || || || || || ''220.000''|| 240.000 || 240.000 || 1 || 0 || → inf ||
|13\67
| 226.087
|232.839
|13
|2
|6.500
|
|-
|7\36
|227.027
| 233.333
|7
|1
|7.000
|
|-
|8\41
| 228.571
| 234.146
| 8
| 1
|8.000
|
|-
|9\46
|229.787
|234.783
| 9
|1
| 9.000
|
|-
|1\5||240.000|| 240.000||1||0||→ inf||
|}
|}


==See also==
[[5L 1s (11/6-equivalent)]] - simplest tuning
[[5L 1s (15/8-equivalent)]] - classical tuning
[[5L 1s (21/11-equivalent)]] - Neogothic tuning
[[5L 1s (27/14-equivalent)]] - septimal tuning
[[Category:6-tone scales]]
[[Category:6-tone scales]]
Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/Greater_whole_tone_scale"