Xenharmonic Wiki

User:Moremajorthanmajor/Greater whole tone scale: Difference between revisions

← Older editNewer edit →
VisualWikitext
Line 1: Line 1:
'''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.
'''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.


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.
Line 7: Line 7:
== Scale tree ==
== Scale tree ==
{| class="wikitable center-all"
{| class="wikitable center-all"
! colspan="8" | Generator
! Generator
! Normalized Cents (septave)
! Normalized Cents (septave)
! Cents
! Cents
Line 15: Line 15:
! Comments
! Comments
|-
|-
| 1\6 || || || || || || || || 171.429 || 200.000 || 1 || 1 || 1.000 ||  
| 1\6 || 171.429 || 200.000 || 1 || 1 || 1.000 ||  
|-
|-
|
|
|
|
|
|
|
|9\53
|9\53
|177.049
|177.049
Line 32: Line 25:
|
|
|-
|-
|
|
|
|
|
|
|8\47
|8\47
|
|177.778
|177.778
|204.255
|204.255
Line 47: Line 33:
|
|
|-
|-
|
|
|
|
|
|7\41
|7\41
|
|
|178.723
|178.723
|204.878
|204.878
Line 62: Line 41:
|
|
|-
|-
|
|
|
|
|
|
|13\76
|13\76
|
|179.310
|179.310
|205.263
|205.263
Line 77: Line 49:
|
|
|-
|-
| || || || || 6\35 || || || || 180.000 || 205.714 || 6 || 5 || 1.200 ||  
| 6\35|| 180.000 || 205.714 || 6 || 5 || 1.200 ||  
|-
|-
| || || || 5\29 || || || || || 181.818 || 206.897 || 5 || 4 || 1.250 ||  
| 5\29|| 181.818 || 206.897 || 5 || 4 || 1.250 ||  
|-
|-
| || || || || || 14\81 || || || 182.609 || 207.407 || 14 || 11 || 1.273 ||  
| 14\81|| 182.609 || 207.407 || 14 || 11 || 1.273 ||  
|-  
|-  
| || || || || 9\52 || || || || 183.051 || 207.692 || 9 || 7 || 1.286 ||  
| 9\52|| 183.051 || 207.692 || 9 || 7 || 1.286 ||  
|-
|-
| || || 4\23 || || || || || || 184.615 || 208.696 || 4 || 3 || 1.333 ||
| 4\23|| 184.615 || 208.696 || 4 || 3 || 1.333 ||
|-
|-
| || || || || 11\63 || || || ||185.915 || 209.524||11||8|| 1.375||
| 11\63||185.915 || 209.524||11||8|| 1.375||
|-
|-
| || || ||7\40|| || || || ||186.667|| 210.000||7||5|| 1.400||
| 7\40||186.667|| 210.000||7||5|| 1.400||
|-
|-
|  || || || ||10\57|| || || ||187.500 || 210.528|| 10||7||1.428||
| 10\57 ||187.500 || 210.528|| 10||7||1.428||
|-
|-
| || || || || ||13\74 ||  || ||187.952||210.811||13||9|| 1.444||
| 13\74||187.952||210.811||13||9|| 1.444||
|-
|-
| || || || || || ||16\91|| ||188.235||210.989||16||11 ||1.4545||
| 16\91||188.235||210.989||16||11 ||1.4545||
|-
|-
| ||3\17|| || || || || || || 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 || || ||190.909||212.658 ||14 || 9|| 1.556||
| 14\79||190.909||212.658 ||14 || 9|| 1.556||
|-
|-
| || || ||  || 11\62|| || || ||191.304|| 212.903||11 ||7||1.571||
| 11\62||191.304|| 212.903||11 ||7||1.571||
|-
|-
| || || ||8\45 ||  ||  ||  || ||192.000||213.333||8 || 5||1.600||
| 8\45||192.000||213.333||8 || 5||1.600||
|-
|-
| || || || ||13\73|| || || || 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|| ||  ||  || ||  || 193.548||214.286||5||3||1.667 || Ionianic-Machine
| 5\28|| 193.548||214.286||5||3||1.667 || Ionianic-Machine
|-
|-
| || || || || 12\67|| || || || 194.595||214.925 ||12||7||1.714||
| 12\67|| 194.595||214.925 ||12||7||1.714||
|-
|-
| ||  || ||7\39|| || || || ||195.349||215.385||7||4 || 1.750||
| 7\39||195.349||215.385||7||4 || 1.750||
|-
|-
|  || || || ||9\50|| || || ||196.364||216.000 ||9||5||1.800 ||
| 9\50 ||196.364||216.000 ||9||5||1.800 ||
|-
|-
| ||  || || || ||11\61|| || || 197.015||216.393||11 ||6||1.833 ||
| 11\61|| 197.015||216.393||11 ||6||1.833 ||
|-  
|-  
| || || || || ||  || 13\72|| ||197.468||216.667 ||13||7||1.857||
| 13\72||197.468||216.667 ||13||7||1.857||
|-   
|-   
| ||  ||  || ||  || ||  || 15\83||197.802|197.802||216.867||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||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 || 202.247||219.512||15|| 7||2.143||
|-
|-
|  || || || || || ||13\71|| ||202.597||219.718||13||6 || 2.167||
| 13\71 ||202.597||219.718||13||6 || 2.167||
|-
|-
| || || || || ||11\60|| || ||203.077 ||220.000 ||11|| 5|| 2.200||
| 11\60||203.077 ||220.000 ||11|| 5|| 2.200||
|-
|-
|  ||  || ||  || 9\49 || || ||  ||203.774||220.408 || 9||4||2.250||
| 9\49 ||203.774||220.408 || 9||4||2.250||
|-
|-
| || || ||7\38|| || || ||  ||204.878 ||221.053||7 || 3||2.333||
| 7\38||204.878 ||221.053||7 || 3||2.333||
|-
|-
| || || || ||12\65 || || || ||205.714||221.538||12|| 5||2.400 ||
| 12\65||205.714||221.538||12|| 5||2.400 ||
|-
|-
| || ||5\27|| ||  || || || ||206.897||222.222||5||2||2.500 ||
| 5\27||206.897||222.222||5||2||2.500 ||
|-
|-
|  || ||  || || ||18\97|| || ||207.692 || 222.680 ||18||7|| 2.571||
| 18\97 ||207.692 || 222.680 ||18||7|| 2.571||
|-
|-
| || || ||  ||13\70|| || || ||208.000||222.857||13||5||2.600||Unnamed golden tuning
| 13\70||208.000||222.857||13||5||2.600||Unnamed golden tuning
|-
|-
| ||  || || 8\43|| || || || ||208.697||223.256||8||3||2.667||
| 8\43||208.697||223.256||8||3||2.667||
|-
|-
|  || || || ||11\59||  ||  ||  || 209.524|| 223.729||11||4||2.750||
| 11\59 || 209.524|| 223.729||11||4||2.750||
|-
|-
| || || ||  ||  ||14\75 || || ||210.000||224.000||14||5 ||3.000||
| 14\75||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||211.765||225.000||3||1||3.000||L/s = 3/1, Ionianic-clyndro
|-
|-
| || || || || || || 16\85 || ||213.333||225.882||16|| 5|| 3.200||
|22\117
|212.903
|225.641
|22
|7
|3.143
|
|-
|19\101
|213.084
|225.743
|19
|6
|3.167
|
|-
| 16\85||213.333||225.882||16|| 5|| 3.200||
|-  
|-  
| || || || || ||13\69||  ||  ||213.698||226.087||13 || 4|| 3.250||
| 13\69||213.698||226.087||13 || 4|| 3.250||
|-
|-
|  ||  || || ||10\53|| || || ||214.857 ||226.415|| 10 ||3||3.333||
| 10\53 ||214.857 ||226.415|| 10 ||3||3.333||
|-
|-
| || || ||7\37 ||  || || || ||215.385||227.027||7||2||3.500||Ionianic-Laconic
| 7\37||215.385||227.027||7||2||3.500||Ionianic-Laconic
|-
|-
|  ||  || || ||11\58 ||  ||  ||  ||216.393||227.586||11||3 || 3.667||
| 11\58 ||216.393||227.586||11||3 || 3.667||
|-
|-
| ||  ||  ||  ||  || 15\79 ||  || ||216.867||227.848||15||4||3.750||
| 15\79||216.867||227.848||15||4||3.750||
|-
|-
|  || || || || ||  || 19\100|| ||217.143 || 228.000 || 19||5||3.800||
| 19\100 ||217.143 || 228.000 || 19||5||3.800||
|-
|-
| || ||4\21|| || || || || ||218.182||228.571||4||1||4.000||Ionianic-Gorgo
| 4\21||218.182||228.571||4||1||4.000||Ionianic-Gorgo
|-
|-
|  || ||  || || ||13\68|| || ||219.718||229.412 || 13||3||4.333 ||
| 13\68 ||219.718||229.412 || 13||3||4.333 ||
|-
|-
|  ||  || || ||9\47|| || ||  ||220.408||229.787||9||2||4.500||
| 9\47 ||220.408||229.787||9||2||4.500||
|-
|-
|  || ||  || || ||14\73|| || ||221.053 || 230.137||14||3||4.667||
| 14\73 ||221.053 || 230.137||14||3||4.667||
|-
|-
| || || ||5\26 ||  || ||  ||  ||222.222||230.769||5||1 || 5.000||Ionianic-Gidorah
| 5\26||222.222||230.769||5||1 || 5.000||Ionianic-Gidorah
|-
|-
| || || || || || ||11\57 || || 223.729|| 231.579 || 11||2||5.500 ||
| 11\57|| 223.729|| 231.579 || 11||2||5.500 ||
|-  
|-  
|  || || || || ||  ||  ||17\88||224.179||231.818 || 17||3||5.667||
| 17\88 ||224.179||231.818 || 17||3||5.667||
|-   
|-   
|  || || || || 6\31|| || || ||225.000||232.258||6||1||6.000 || Ionianic-Slendric↓
| 6\31 ||225.000||232.258||6||1||6.000 || Ionianic-Slendric↓
|-
|-
|
|
|
|
|
|
|13\67
|13\67
|
| 226.087
| 226.087
|232.839
|232.839
Line 194: Line 191:
|
|
|-
|-
|
|
|
|
|
|7\36
|7\36
|
|
|227.027
|227.027
| 233.333
| 233.333
Line 209: Line 199:
|
|
|-
|-
|
|
|
|
|
|
|8\41
|8\41
|
| 228.571
| 228.571
| 234.146
| 234.146
Line 224: Line 207:
|
|
|-
|-
|
|
|
|
|
|
|
|9\46
|9\46
|229.787
|229.787
Line 239: Line 215:
|
|
|-
|-
|1\5|| || || || || || || ||240.000|| 240.000||1||0||→ inf||
|1\5||240.000|| 240.000||1||0||→ inf||
|}
|}


Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/Greater_whole_tone_scale"