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
| |
|}

Revision as of 19:51, 30 December 2018

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.


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