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3L 9s: Difference between revisions

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This MOS is always proper because its period runs '''Lsss'''. It is generated by a semitone of 1/12edo (100 cents) or less. It represents, among other chromatic scales, that of the [[Augene]] temperament.
{{Infobox MOS
| Periods = 3
| nLargeSteps = 3
| nSmallSteps = 9
| Equalized = 3
| Paucitonic = 1
| Pattern = LsssLsssLsss
}}


{| class="wikitable"
'''3L 9s''' is the MOS pattern LsssLsssLsss with small steps ranging from 0\1 (0¢) to 1\12 (one step of [[12edo]] = 100¢).
|-
 
| | 0/3
This MOS represents, among other chromatic scales, that of the [[Augene]] temperament.
| |
 
| |
== Modes ==
| | 0
* 9|0(3) LsssLsssLsss
|-
* 6|3(3) sLsssLsssLss
| | 1/24
* 3|6(3) ssLsssLsssLs
| |
* 0|9(3) sssLsssLsssL
| |
 
| | 50
== Scale tree ==
|-
Generator ranges:
| |
* Chroma-positive generator: 300 cents (3\12) to 400 cents (1\3)
| | 4/93
* Chroma-negative generator: 0 cents (0\3) to 100 cents (1\12)
| |
 
| | 51.613
{| class="wikitable center-all"
|-
! colspan="6" | Small step <br><span style="font-size:0.85em">(chroma-negative generator)</span>
| |
! Cents
| | 3/69
! L
| |
! s
| | 52.174
! L/s
|-
! Comments
| |
| | 2/45
| |
| | 53.333
|-
| |
| | 3/66
| |
| | 54.5455
|-
| |
| | 4/87
| |
| | 55.172
|-
| |
| | 5/108
| |
| | 55.556
|-
| |
| | 6/129
| |
| | 55.814
|-
| |
| | 7/150
| |
| | 56
|-
| | 1/21
| |
| |
| | 57.143
|-
| |
| | 5/102
| |
| | 58.8235
|-
| |
| | 4/81
| |
| | 59.259
|-
| |
| | 3/60
| |
| | 60
|-
| |
| | 2/39
| |
| | 61.5385
|-
| |
| |
| | 5/96
| | 62.5
|-
| |
| | 3/57
| |
| | 63.158
|-
| |
| | 4/75
| |
| | 64
|-
| |
| | 5/93
| |
| | 64.516
|-
| |
| | 6/111
| |
| | 64.865
|-
| |
| | 7/129
| |
| | 65.116
|-
| |
| |
| |
| | 400/(3+pi)
|-
| | 1/18
| |
| |
| | 66.667
|-
| |
| |
| |
| | 400/(3+e)
|-
| |
| | 9/159
| |
| | 67.9245
|-
| |
| | 8/141
| |
| | 68.085
|-
| |
| | 7/123
| |
| | 68.293
|-
| |
| | 6/105
| |
| | 68.571
|-
| |
| | 5/87
| |
| | 68.9655
|-
| |
| | 4/69
| |
| | 69.478
|-
| |
| | 3/51
| |
| | 70.588
|-
| |
| |
| |
| | 400/(4+phi)
|-
| |
| |
| | 5/84
| | 71.429
|-
| |
| | 2/33
| |
| | 72.727
|-
| |
| |
| | 7/114
| | 73.684
|-
| |
| |
| | 5/81
| | 74.074
|-
| |
| | 3/48
| |
| | 75
|-
| |
| | 4/63
| |
| | 76.1905
|-
| |
| | 5/78
| |
| | 76.923
|-
| |
| | 6/93
| |
| | 77.419
|-
|-
| |  
| 1\12 || || || || || || 100.000 || 1 || 1 || 1.000 ||
| | 7/108
| |  
| | 77.778
|-
|-
| |  
| || || || || || 5\63 || 95.238 || 6 || 5 || 1.200 || [[Misty]]/[[fog]]
| | 8/123
| |  
| | 78.049
|-
|-
| |  
| || || || || 4\51 || || 94.118 || 5 || 4 || 1.250 ||
| | 9/138
| |  
| | 78.261
|-
|-
| |  
| || || || || || 7\90 || 93.333 || 9 || 7 || 1.286 ||
| | 10/153
| |  
| | 78.431
|-
|-
| |  
| || || || 3\39 || || || 92.308 || 4 || 3 || 1.333 ||
| | 11/168
| |  
| | 78.571
|-
|-
| |  
| || || || || || 8\105 || 91.429 || 11 || 8 || 1.375 ||
| | 12/183
| |  
| | 78.6885
|-
|-
| |  
| || || || || 5\66 || || 90.909 || 7 || 5 || 1.400 ||
| | 13/198
| |  
| | 78.788
|-
|-
| |  
| || || || || || 7\93 || 90.323 || 10 || 7 || 1.429 ||
| | 14/213
| |  
| | 78.873
|-
|-
| |  
| || || 2\27 || || || || 88.889 || 3 || 2 || 1.500 || [[Augene]] is around here
| | 15/228
| |  
| | 78.947
|-
|-
| |  
| || || || || || 7\96 || 87.500 || 11 || 7 || 1.571 ||
| | 16/243
| |  
| | 79.012
|-
|-
| | 1/15
| || || || || 5\69 || || 86.957 || 8 || 5 || 1.600 ||
| |  
| |  
| | 80
|-
|-
| |  
| || || || || || 8\111 || 86.486 || 13 || 8 || 1.625 || Golden augene (86.6169¢)
| | 9/132
| |  
| | 81,818
|-
|-
| |  
| || || || 3\42 || || || 85.714 || 5 || 3 || 1.667 ||
| | 8/117
| |  
| | 82.051
|-
|-
| |  
| || || || || || 7\99 || 84.848 || 12 || 7 || 1.714 ||
| | 7/102
| |  
| | 82.353
|-
|-
| |  
| || || || || 4\57 || || 84.211 || 7 || 4 || 1.750 ||
| | 6/87
| |  
| | 82.759
|-
|-
| |  
| || || || || || 5\72 || 83.333 || 9 || 5 || 1.800 ||
| | 5/72
| |  
| | 83.333
|-
|-
| |  
| || 1\15 || || || || || 80.000 || 2 || 1 || 2.000 || Basic 3L 9s <br>(Generators larger than this are proper)
| | 4/57
| |  
| | 84.2105
|-
|-
| |  
| || || || || || 4\63 || 76.190 || 9 || 4 || 2.250 ||
| |  
| |  
| | 400/(3+sqrt(3))
|-
|-
| |  
| || || || || 3\48 || || 75.000 || 7 || 3 || 2.333 ||
| | 3/42
| |  
| | 85.714
|-
|-
| |  
| || || || || || 5\81 || 74.074 || 12 || 5 || 2.400 ||
| |  
| |  
| | 400/(3+phi)
|-
|-
| |  
| || || || 2\33 || || || 72.727 || 5 || 2 || 2.500 || [[Inflated]] is around here
| | 5/69
| |  
| | 86.9565
|-
|-
| |  
| || || || || || 5\84 || 71.429 || 13 || 5 || 2.600 || Golden inflated (71.1993¢)
| |  
| |  
| | 400/(3+pi/2)
|-
|-
| |  
| || || || || 3\51 || || 70.588 || 8 || 3 || 2.667 ||
| | 7/96
| |  
| | 87.5
|-
|-
| | 2/27
| || || || || || 4\69 || 69.565 || 11 || 4 || 2.750 ||
| |  
| |  
| | 88.889
|-
|-
| |  
| || || 1\18 || || || || 66.667 || 3 || 1 || 3.000 ||
| | 11/147
| |  
| | 89.796
|-
|-
| |  
| || || || || || 3\57 || 63.158 || 10 || 3 || 3.333 ||
| | 9/120
| |  
| | 90
|-
|-
| |  
| || || || || 2\39 || || 61.538 || 7 || 2 || 3.500 ||
| | 7/93
| |  
| | 90.323
|-
|-
| |  
| || || || || || 3\60 || 60.000 || 11 || 3 || 3.667 ||
| | 5/66
| |  
| | 90.909
|-
|-
| |  
| || || || 1\21 || || || 57.143 || 4 || 1 || 4.000 ||
| | 8/105
| |  
| | 91.429
|-
|-
| | 3/39
| || || || || || 2\45 || 53.333 || 9 || 2 || 4.500 ||
| |  
| |  
| | 92.308
|-
|-
| |  
| || || || || 1\24 || || 50.000 || 5 || 1 || 5.000 ||
| | 7/90
| |  
| | 93.333
|-
|-
| | 4/51
| || || || || || 1\27 || 44.444 || 6 || 1 || 6.000 || [[Hemiaug]]
| |  
| |  
| | 94.118
|-
|-
| | 1/12
| 0\3 || || || || || || 0 || 1 || 0 || → inf ||  
| |  
| |  
| | 100
|}
|}


[[Category:Abstract MOS patterns]]
[[Category:Abstract MOS patterns]]
[[Category:12-tone scales]]
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