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The minimum harmonic entropy scale with this [[MOSScales|MOS]] pattern is [[Jubilismic_clan|diminished]][8], basically the familiar [[Octatonic_scale|octatonic scale]] of 12edo.
The minimum harmonic entropy scale with this [[MOS]] pattern is [[diminished]][8], basically the familiar [[octatonic scale]] of 12edo.


There are 4 different near-MOSes such that multiples of the period are the only generic intervals with more than two specific representatives: LLsLsLss, LLsLssLs, LLssLLss, LLssLsLs. However, none are strictly proper in 12edo. (They are only proper if the generator is larger than 100 cents, which unfortunately is the wrong direction for good diminished tunings.)
There are 4 different near-MOSes such that multiples of the period are the only generic intervals with more than two specific representatives: LLsLsLss, LLsLssLs, LLssLLss, LLssLsLs. However, none are strictly proper in 12edo. (They are only proper if the generator is larger than 100 cents, which unfortunately is the wrong direction for good diminished tunings.)


{| class="wikitable"
== Scale tree ==
{| class="wikitable center-all"
! colspan="6" rowspan="2" | Generator
! colspan="2" | Cents
! rowspan="2" | L
! rowspan="2" | s
! rowspan="2" | L/s
! rowspan="2" | Comments
|-
|-
! colspan="5" | Generator
! Chroma-positive
! | Cents
! Chroma-negative
! | Comments
|-
|-
| | 0\4
| 1\8 || || || || || || 150.000 || 150.000 || 1 || 1 || 1.000 ||  
| |  
| |  
| |  
| |  
| | 0
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 6\44 || 163.636 || 136.364 || 6 || 5 || 1.200 || Fourfives↑
| |  
| |  
| |  
| | 1\24
| | 50
| |  
|-
|-
| |  
| || || || || 5\36 || || 166.667 || 133.333 || 5 || 4 || 1.250 ||
| |  
| |  
| | 1\20
| |  
| | 60
| style="text-align:center;" | L/s = 4
|-
|-
| |  
| || || || || || 9\64 || 168.750 || 105.000 || 9 || 7 || 1.286 ||  
| |  
| |  
| |  
| |  
| | 300/(1+pi)
| |  
|-
|-
| |  
| || || || 4\28 || || || 171.429 || 128.571 || 4 || 3 || 1.333 ||
| |  
| | 1\16
| |  
| |  
| | 75
| style="text-align:center;" | L/s = 3
|-
|-
| |  
| || || || || || 11\76 || 173.684 || 126.316 || 11 || 8 || 1.375 ||  
| |  
| |  
| |  
| |  
| | 300/(1+e)
| |  
|-
|-
| |  
| || || || || 7\48 || || 175.000 || 125.000 || 7 || 5 || 1.400 ||  
| |  
| |  
| |  
| | 3\44
| | 81.82
| |  
|-
|-
| |  
| || || || || || 10\68 || 176.471 || 123.529 || 10 || 7 || 1.428 ||  
| |  
| |  
| | 2\28
| |  
| | 85.71
| |  
|-
|-
| |  
| || || 3\20 || || || || 180.000 || 60.000 || 3 || 2 || 1.500 || L/s = 3/2
| | 1\12
|-
| |  
| || || || || || 11\72 || 183.333 || 116.667 || 11 || 7 || 1.571 ||
| |  
|-
| |  
| || || || || 8\52 || || 184.615 || 115.385 || 8 || 5 || 1.600 ||
| | 100
|-
| style="text-align:center;" | Diminished is around here
| || || || || || 13\84 || 185.714 || 114.286 || 13 || 8 || 1.625 || Golden diminished
 
|-
Optimum rank range (L/s=2/1) for MOS
| || || || 5\32 || || || 187.500 || 112.500 || 5 || 3 || 1.667 ||  
|-
| || || || || || 12\76 || 189.474 || 110.526 || 12 || 7 || 1.714 ||  
|-
| || || || || 7\44 || || 190.909 || 109.091 || 7 || 4 || 1.750 ||
|-
| || || || || || 9\56 || 192.857 || 107.143 || 9 || 5 || 1.800 ||
|-
| || 2\12 || || || || || 200.000 || 100.000 || 2 || 1 || 2.000 || Basic tetrawood<br>Diminished is optimal around here
|-
| || || || || || 9\52 || 207.692 || 92.308 || 9 || 4 || 2.250 ||
|-
| || || || || 7\40 || || 210.000 || 90.000 || 7 || 3 || 2.333 ||
|-
| || || || || || 12\68 || 211.765 || 88.235 || 12 || 5 || 2.400 ||
|-
| || || || 5\28 || || || 214.286 || 85.714 || 5 || 2 || 2.500 ||
|-
| || || || || || 13\72 || 216.667 || 83.333 || 13 || 5 || 2.600 || Unnamed golden tuning
|-
| || || || || 8\44 || || 218.182 || 81.818 || 8 || 3 || 2.667 ||
|-
| || || || || || 11\60 || 220.000 || 80.000 || 11 || 4 || 2.750 ||
|-
| || || 3\16 || || || || 225.000 || 75.000 || 3 || 1 || 3.000 || L/s = 3/1
|-
|-
| |  
| || || || || || 10\52 || 230.769 || 69.231 || 10 || 3 || 3.333 ||
| |  
| |  
| |  
| |  
| | 300/(1+sqrt(3))
| |  
|-
|-
| |  
| || || || || 7\36 || || 233.333 || 66.667 || 7 || 2 || 3.500 ||  
| |  
| |  
| | 3\32
| |  
| | 112.5
| style="text-align:center;" |  
|-
|-
| |  
| || || || || || 11\56 || 235.714 || 64.286 || 11 || 3 || 3.667 ||  
| |  
| |  
| |  
| | 5\52
| | 115.38
| style="text-align:center;" | Golden diminished
|-
|-
| |  
| || || || 4\20 || || || 240.000 || 60.000 || 4 || 1 || 4.000 ||
| |  
| |  
| |  
| |  
| | 300/(1+pi/2)
| |  
|-
|-
| |  
| || || || || || 9\44 || 245.455 || 54.545 || 9 || 2 || 4.500 ||  
| |  
| | 2\20
| |  
| |  
| | 120
| style="text-align:center;" |  
|-
|-
|
| || || || || 5\24 || || 250.000 || 50.000 || 5 || 1 || 5.000 ||  
|
|
|3\28
|
|128.57
|
|-
|-
|
| || || || || || 6\28 || 257.143 || 42.857 || 6 || 1 || 6.000 || Quadritikleismic↓
|
|
|
|4\36
|133.33
|
|-
|-
| | 1\8
| 1\4 || || || || || || 300.000 || 0.000 || 1 || 0 || → inf ||
| |  
| |  
| |  
| |  
| | 150
| style="text-align:center;" |  
|}
|}


[[Category:Scale theory]]
[[Category:Abstract MOS patterns]]
[[Category:Abstract MOS patterns]]
[[Category:Tetrawood]] <!-- main article -->
Retrieved from "https://en.xen.wiki/w/4L_4s"