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1L 11s: Difference between revisions

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This MOS, properly called the Happy dodecatonic, is not a complete scale for any "interesting" temperament―the simplest absolute harmonic entropy minimum for it is where +7 generators equals a meantone fifth, and even there it implies a val with warts for 3 and (for the most part) 5. Its generators will not be listed here as the only interesting use for it is to extend it to 13 tones, i. e. to make it into a different MOS.
This MOS, also called the "happy dodecatonic", is not a complete scale for any "interesting" temperament ― the simplest absolute harmonic entropy minimum for it is where +7 generators equals a meantone fifth, and even there it implies a val with warts for 3 and (for the most part) 5. Perhaps the only use for it is to extend it to 13 tones, i.e. to make it into a different MOS.
 
 
{| class="wikitable"
! colspan=8 | generator
! | L
! | s
! | L/s
! | gen (cents)
! | comment
|-
| | 0\1
| |
| |
| |
| |
| |
| |
| |
| | 1
| | 0
| |
| | 0.000
| |
|-
| |
| |
| |
| |
| |
| |
| | 1\18
| |
| | 7
| | 1
| | 7.000
| | 66.667
| |
|-
| |
| |
| |
| |
| |
| | 1\17
| |
| |
| | 6
| | 1
| | 6.000
| | 70.588
| |
|-
| |
| |
| |
| |
| |
| |
| | 2\33
| |
| | 11
| | 2
| | 5.500
| | 72.727
| |
|-
| |
| |
| |
| |
| | 1\16
| |
| |
| |
| | 5
| | 1
| | 5.000
| | 75.000
| |
|-
| |
| |
| |
| |
| |
| |
| | 3\47
| |
| | 14
| | 3
| | 4.667
| | 76.596
| |
|-
| |
| |
| |
| |
| |
| | 2\31
| |
| |
| | 9
| | 2
| | 4.500
| | 77.419
| |
|-
| |
| |
| |
| |
| |
| |
| | 3\46
| |
| | 13
| | 3
| | 4.333
| | 78.261
| |
|-
| |
| |
| |
| | 1\15
| |
| |
| |
| |
| | 4
| | 1
| | 4.000
| | 80.000
| |
|-
| |
| |
| |
| |
| |
| |
| | 4\59
| |
| | 15
| | 4
| | 3.750
| | 81.356
| |
|-
| |
| |
| |
| |
| |
| | 3\44
| |
| |
| | 11
| | 3
| | 3.667
| | 81.818
| |
|-
| |
| |
| |
| |
| |
| |
| | 5\73
| |
| | 18
| | 5
| | 3.600
| | 82.192
| |
|-
| |
| |
| |
| |
| | 2\29
| |
| |
| |
| | 7
| | 2
| | 3.500
| | 82.759
| |
|-
| |
| |
| |
| |
| |
| |
| | 5\72
| |
| | 17
| | 5
| | 3.400
| | 83.333
| |
|-
| |
| |
| |
| |
| |
| | 3\43
| |
| |
| | 10
| | 3
| | 3.333
| | 83.721
| |
|-
| |
| |
| |
| |
| |
| |
| | 4\57
| |
| | 13
| | 4
| | 3.250
| | 84.211
| |
|-
| |
| |
| | 1\14
| |
| |
| |
| |
| |
| | 3
| | 1
| | 3.000
| | 85.714
| |
|-
| |
| |
| |
| |
| |
| |
| | 5\69
| |
| | 14
| | 5
| | 2.800
| | 86.957
| |
|-
| |
| |
| |
| |
| |
| | 4\55
| |
| |
| | 11
| | 4
| | 2.750
| | 87.273
| |
|-
| |
| |
| |
| |
| |
| |
| | 7\96
| |
| | 19
| | 7
| | 2.714
| | 87.500
| |
|-
| |
| |
| |
| |
| | 3\41
| |
| |
| |
| | 8
| | 3
| | 2.667
| | 87.805
| | Octacot is around here
|-
| |
| |
| |
| |
| |
| | 5\68
| |
| |
| | 13
| | 5
| | 2.600
| | 88.235
| |
|-
| |
| |
| |
| |
| |
| |
| | 7\95
| |
| | 18
| | 7
| | 2.571
| | 88.421
| |
|-
| |
| |
| |
| | 2\27
| |
| |
| |
| |
| | 5
| | 2
| | 2.500
| | 88.889
| |
|-
| |
| |
| |
| |
| |
| |
| | 7\94
| |
| | 17
| | 7
| | 2.429
| | 89.362
| |
|-
| |
| |
| |
| |
| |
| | 5\67
| |
| |
| | 12
| | 5
| | 2.400
| | 89.552
| |
|-
| |
| |
| |
| |
| | 3\40
| |
| |
| |
| | 7
| | 3
| | 2.333
| | 90.000
| |
|-
| |
| |
| |
| |
| |
| |
| | 7\93
| |
| | 16
| | 7
| | 2.286
| | 90.323
| |
|-
| |
| |
| |
| |
| |
| | 4\53
| |
| |
| | 9
| | 4
| | 2.250
| | 90.566
| |
|-
| |
| |
| |
| |
| |
| |
| | 5\66
| |
| | 11
| | 5
| | 2.200
| | 90.909
| |
|-
| |
| | 1\13
| |
| |
| |
| |
| |
| |
| | 2
| | 1
| | 2.000
| | 92.308
| |
|-
| |
| |
| |
| |
| |
| |
| | 6\77
| |
| | 11
| | 6
| | 1.833
| | 93.506
| |
|-
| |
| |
| |
| |
| |
| | 5\64
| |
| |
| | 9
| | 5
| | 1.800
| | 93.750
| |
|-
| |
| |
| |
| |
| | 4\51
| |
| |
| |
| | 7
| | 4
| | 1.750
| | 94.118
| |
|-
| |
| |
| |
| |
| |
| | 7\89
| |
| |
| | 12
| | 7
| | 1.714
| | 94.382
| |
|-
| |
| |
| |
| | 3\38
| |
| |
| |
| |
| | 5
| | 3
| | 1.667
| | 94.737
| |
|-
| |
| |
| |
| |
| | 5\63
| |
| |
| |
| | 8
| | 5
| | 1.600
| | 95.238
| |
|-
| |
| |
| |
| |
| |
| | 7\88
| |
| |
| | 11
| | 7
| | 1.571
| | 95.455
| |
|-
| |
| |
| | 2\25
| |
| |
| |
| |
| |
| | 3
| | 2
| | 1.500
| | 96.000
| |
|-
| |
| |
| |
| |
| |
| | 7\87
| |
| |
| | 10
| | 7
| | 1.429
| | 96.552
| |
|-
| |
| |
| |
| |
| | 5\62
| |
| |
| |
| | 7
| | 5
| | 1.400
| | 96.774
| |
|-
| |
| |
| |
| |
| |
| | 8\99
| |
| |
| | 11
| | 8
| | 1.375
| | 96.970
| |
|-
| |
| |
| |
| | 3\37
| |
| |
| |
| |
| | 4
| | 3
| | 1.333
| | 97.297
| |
|-
| |
| |
| |
| |
| |
| | 7\86
| |
| |
| | 9
| | 7
| | 1.286
| | 97.674
| |
|-
| |
| |
| |
| |
| | 4\49
| |
| |
| |
| | 5
| | 4
| | 1.250
| | 97.959
| | Passion is around here
|-
| |
| |
| |
| |
| |
| | 5\61
| |
| |
| | 6
| | 5
| | 1.200
| | 98.361
| |
|-
| |
| |
| |
| |
| |
| |
| | 6\73
| |
| | 7
| | 6
| | 1.167
| | 98.630
| |
|-
| | 1\12
| |
| |
| |
| |
| |
| |
| |
| | 1
| | 1
| | 1.000
| | 100.000
| |
|}
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