6L 6s: Difference between revisions

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This is the bi-equal chromatic scale of [[Hexe]] temperament. It has a generator of up to the familiar semitone of 12edo (100¢) and two closed circles of minor sevenths representing the 2.9 subgroup separated thereby.
This is the bi-equal chromatic scale of [[Hexe]] temperament. It has a generator of up to the familiar semitone of 12edo (100¢) and two closed circles of minor sevenths representing the 2.9 subgroup separated thereby.


{| 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
|-
|-
| | 0/6
! Chroma-positive
| |
! Chroma-negative
| |
| |
| | <span style="font-size: 12.8000001907349px;">0</span>
|-
|-
| | 1/36
| 1\12 || || || || || || 100.000 || 100.000 || 1 || 1 || 1.000 ||
| |  
| |  
| |  
| | <span style="font-size: 12.8000001907349px;">33.333</span>
|-
|-
| |  
| || || || || || 6\66 || 109.091 || 90.909 || 6 || 5 || 1.200 || Semimist↑
| | <span style="font-size: 12.8000001907349px;">4/138</span>
| |  
| |  
| | 34.783
|-
|-
| |  
| || || || || 5\54 || || 111.111 || 88.889 || 5 || 4 || 1.250 || Hexe is optimal around here
| | <span style="font-size: 12.8000001907349px;">3/102</span>
| |  
| |  
| | 35.294
|-
|-
| |  
| || || || || || 9\96 || 112.500 || 87.500 || 9 || 7 || 1.286 ||
| |  
| | <span style="font-size: 12.8000001907349px;">5/168</span>
| |  
| | 35.714
|-
|-
| |  
| || || || 4\42 || || || 114.286 || 85.714 || 4 || 3 || 1.333 ||
| | 2/66
| |  
| |  
| | <span style="font-size: 12.8000001907349px;">36.364</span>
|-
|-
| |  
| || || || || || 11\114 || 115.789 || 84.211 || 11 || 8 || 1.375 ||
| |  
| | <span style="font-size: 12.8000001907349px;">5/162</span>
| |  
| | 37.037
|-
|-
| |  
| || || || || 7\72 || || 116.667 || 83.333 || 7 || 5 || 1.400 ||
| | <span style="font-size: 12.8000001907349px;">3/96</span>
| |  
| |  
| | 37.5
|-
|-
| |  
| || || || || || 10\102 || 117.647 || 98.824 || 10 || 7 || 1.428 ||
| | <span style="font-size: 12.8000001907349px;">4/126</span>
| |  
| |  
| | 38.095
|-
|-
| |  
| || || 3\30 || || || || 120.000 || 80.000 || 3 || 2 || 1.500 || L/s = 3/2
| | 5/156
| |  
| |  
| | 38.4615
|-
|-
| |  
| || || || || || 11\108 || 122.222 || 77.778 || 11 || 7 || 1.571 ||
| | 6/186
| |  
| |  
| | 38.71
|-
|-
| | 1/30
| || || || || 8\78 || || 123.077 || 76.923 || 8 || 5 || 1.600 ||
| |  
| |  
| |  
| | <span style="font-size: 12.8000001907349px;">40</span>
|-
|-
| |  
| || || || || || 13\126 || 123.810 || 76.190 || 13 || 8 || 1.625 || Unnamed golden tuning
| | 5/144
| |  
| |  
| | 41.667
|-
|-
| |  
| || || || 5\48 || || || 125.000 || 75.000 || 5 || 3 || 1.667 ||
| | <span style="font-size: 12.8000001907349px;">4/114</span>
| |  
| |  
| | 42.105
|-
|-
| |  
| || || || || || 12\114 || 126.316 || 73.684 || 12 || 7 || 1.714 ||  
| |  
| | 7/198
| |  
| | 42.424
|-
|-
| |  
| || || || || 7\66 || || 127.273 || 72.727 || 7 || 4 || 1.750 ||
| | <span style="font-size: 12.8000001907349px;">3/84</span>
| |  
| |  
| | 42.857
|-
|-
| |  
| || || || || || 9\84 || 128.571 || 71.429 || 9 || 5 || 1.800 ||
| |  
| |  
| | 8/222
| | 43.243
|-
|-
| |  
| || 2\18 || || || || || 133.333 || 66.667 || 2 || 1 || 2.000 || Basic 6L 6s
| |  
| | <span style="font-size: 12.8000001907349px;">5/138</span>
| |  
| | 43.478
|-
|-
| |  
| || || || || || 9\78 || 138.462 || 61.538 || 9 || 4 || 2.250 ||
| |  
| |  
| | 7/192
| | 43.75
|-
|-
| |  
| || || || || 7\60 || || 140.000 || 60.000 || 7 || 3 || 2.333 ||
| | 2/54
| |  
| |  
| | <span style="font-size: 12.8000001907349px;">44.444</span>
|-
|-
| |  
| || || || || || 12\102 || 141.176 || 58.824 || 12 || 5 || 2.400 ||
| |  
| |  
| | 7/186
| | 45.384
|-
|-
| |  
| || || || 5\42 || || || 142.857 || 57.143 || 5 || 2 || 2.500 ||
| |  
| | <span style="font-size: 12.8000001907349px;">5/132</span>
| |  
| | 45.4545
|-
|-
| |  
| || || || || || 13\108 || 144.444 || 55.556 || 13 || 5 || 2.600 || Unnamed golden tuning
| |  
| |  
| | 8/210
| | 45.714
|-
|-
| |  
| || || || || 8\66 || || 145.455 || 54.545 || 8 || 3 || 2.667 ||
| | <span style="font-size: 12.8000001907349px;">3/78</span>
| |  
| |  
| | 46.154
|-
|-
| |  
| || || || || || 11\90 || 146.667 || 53.333 || 11 || 4 || 2.750 ||
| |  
| | 7/180
| |  
| | 46.333
|-
|-
| |  
| || || 3\24 || || || || 150.000 || 50.000 || 3 || 1 || 3.000 || L/s = 3/1
| | <span style="font-size: 12.8000001907349px;">4/102</span>
| |  
| |  
| | 47.118
|-
|-
| |  
| || || || || || 10\78 || 153.846 || 46.154 || 10 || 3 || 3.333 ||
| | <span style="font-size: 12.8000001907349px;">5/126</span>
| |  
| |  
| | 47.619
|-
|-
| |  
| || || || || 7\54 || || 155.556 || 44.444 || 7 || 2 || 3.500 ||  
| | 6/150
| |  
| |  
| | 48
|-
|-
| |  
| || || || || || 11\84 || 157.143 || 42.857 || 11 || 3 || 3.667 ||
| | 7/174
| |  
| |  
| | 48.276
|-
|-
| |  
| || || || 4\30 || || || 160.000 || 40.000 || 4 || 1 || 4.000 ||
| | 8/198
| |  
| |  
| | 48.485
|-
|-
| |  
| || || || || || 9\66 || 163.636 || 36.364 || 9 || 2 || 4.500 ||
| | 9/222
| |  
| |  
| | 48.649
|-
|-
| |  
| || || || || 5\36 || || 166.667 || 33.333 || 5 || 1 || 5.000 ||
| | 10/246
| |  
| |  
| | 48.7805
|-
|-
| |  
| || || || || || 6\42 || 171.429 || 28.571 || 6 || 1 || 6.000 ||
| | 11/270
| |  
| |  
| | 48.889
|-
|-
| |
| 1\6 || || || || || || 200.000 || 0.000 || 1 || 0 || → inf ||
| | 12/294
| |
| |
| | 49.082
|-
| |
| |
| |
| |
| | 200/(1+pi)
|-
| | 1/24
| |
| |
| |
| | <span style="font-size: 12.8000001907349px;">50</span>
|-
| |
| |
| |
| |
| | 200/(1+e)
|-
| |
| | 7/162
| |
| |
| | 51.852
|-
| |
| | 6/138
| |
| |
| | 52.174
|-
| |
| | 5/114
| |
| |
| | 52.632
|-
| |
| | <span style="font-size: 12.8000001907349px;">4/90</span>
| |
| |
| | 53.333
|-
| |
| |
| | 7/156
| |
| | 53.846
|-
| |
| | <span style="font-size: 12.8000001907349px;">3/66</span>
| |
| |
| | 54.5455
|-
| |
| |
| |
| | 8/174
| | 55.1724
|-
| |
| |
| |
| |
| | 200/(2+phi)
|-
| |
| |
| | <span style="font-size: 12.8000001907349px;">5/108</span>
| |
| | 55.556
|-
| |
| |
| |
| | 7/150
| | 56
|-
| |
| | 2/42
| |
| |
| | <span style="font-size: 12.8000001907349px;">57.143</span>
|-
| |
| |
| |
| | 7/144
| | <span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">58.333</span>
|-
| |
| |
| | <span style="font-size: 12.8000001907349px;">5/102</span>
| |
| | 58.225
|-
| |
| |
| |
| | 8/162
| | 59.189
|-
| |
| | <span style="font-size: 12.8000001907349px;">3/60</span>
| |
| |
| | 60
|-
| |
| |
| | 7/138
| |
| | 60.87
|-
| |
| | <span style="font-size: 12.8000001907349px;">4/78</span>
| |
| |
| | 61.5385
|-
| |
| | 5/96
| |
| |
| | 62.5
|-
| |
| | 6/114
| |
| |
| | 63,158
|-
| |
| | 7/132
| |
| |
| | 63.727
|-
| |
| | 8/150
| |
| |
| | 64
|-
| |
| | 9/168
| |
| |
| | 64.286
|-
| |
| | 10/186
| |
| |
| | 64,516
|-
| |
| | 11/204
| |
| |
| | 64.706
|-
| |
| | 12/222
| |
| |
| | 64.865
|-
| |
| | 13/240
| |
| |
| | 65
|-
| | 1/18
| |
| |
| |
| | <span style="font-size: 12.8000001907349px;">66,667</span>
|-
| |
| | 18/318
| |
| |
| | 67.9245
|-
| |
| | 17/300
| |
| |
| | 68
|-
| |
| | 16/282
| |
| |
| | 68.085
|-
| |
| | 15/264
| |
| |
| | 68.182
|-
| |
| | 14/246
| |
| |
| | 68.293
|-
| |
| | 13/228
| |
| |
| | 68.421
|-
| |
| | 12/210
| |
| |
| | 68.571
|-
| |
| | 11/192
| |
| |
| | 68.75
|-
| |
| | 10/174
| |
| |
| | 68.9655
|-
| |
| | 9/156
| |
| |
| | 69.231
|-
| |
| | 8/138
| |
| |
| | 69.565
|-
| |
| | 7/120
| |
| |
| | 70
|-
| |
| | 6/102
| |
| |
| | 70.588
|-
| |
| | <span style="font-size: 12.8000001907349px;">5/84</span>
| |
| |
| | 71.286
|-
| |
| |
| | 9/150
| |
| | 72
|-
| |
| | <span style="font-size: 12.8000001907349px;">4/66</span>
| |
| |
| | 72.364
|-
| |
| |
| |
| |
| | 200/(1+sqrt(3))
|-
| |
| |
| | <span style="font-size: 12.8000001907349px;">7/114</span>
| |
| | 73.368
|-
| |
| | 3/48
| |
| |
| | <span style="font-size: 12.8000001907349px;">75</span>
|-
| |
| |
| | <span style="font-size: 12.8000001907349px;">8/126</span>
| |
| | 76.1905
|-
| |  
| |  
| |  
| |  
| | 200/(1+phi)
|-
| |
| | <span style="font-size: 12.8000001907349px;">5/78</span>
| |
| |
| | 76.923
|-
| |
| |
| | <span style="font-size: 12.8000001907349px;">12/186</span>
| |
| | 77.419
|-
| |
| | <span style="font-size: 12.8000001907349px;">7/108</span>
| |
| |
| | 77.778
|-
| |
| |
| |
| |
| | 200/(1+pi/2)
|-
| |
| | <span style="font-size: 12.8000001907349px;">9/138</span>
| |
| |
| | 78.261
|-
| |
| | 11/168
| |
| |
| | 78.571
|-
| |
| | 13/198
| |
| |
| | 78.788
|-
| | 2/30
| |
| |
| |
| | <span style="font-size: 12.8000001907349px;">80</span>
|-
| |
| | <span style="font-size: 12.8000001907349px;">9/132</span>
| |
| |
| | 81.818
|-
| |
| | <span style="font-size: 12.8000001907349px;">7/102</span>
| |
| |
| | 81.765
|-
| |
| |
| | <span style="font-size: 12.8000001907349px;">12/174</span>
| |
| | 82.759
|-
| |
| | 5/72
| |
| |
| | <span style="font-size: 12.8000001907349px;">83.333</span>
|-
| |
| |
| | <span style="font-size: 12.8000001907349px;">13/186</span>
| |
| | 83.871
|-
| |
| | <span style="font-size: 12.8000001907349px;">8/114</span>
| |
| |
| | 84.2105
|-
| |
| | <span style="font-size: 12.8000001907349px;">11/156</span>
| |
| |
| | 84.5385
|-
| | 3/42
| |
| |
| |
| | <span style="font-size: 12.8000001907349px;">85.714</span>
|-
| | 1/12
| |
| |  
| |  
| | 100
|}
|}


[[Category:Scales]]
[[Category:Abstract MOS patterns]]
[[Category:Abstract MOS patterns]]

Revision as of 14:32, 16 October 2021

This is the bi-equal chromatic scale of Hexe temperament. It has a generator of up to the familiar semitone of 12edo (100¢) and two closed circles of minor sevenths representing the 2.9 subgroup separated thereby.

Scale tree

Generator Cents L s L/s Comments
Chroma-positive Chroma-negative
1\12 100.000 100.000 1 1 1.000
6\66 109.091 90.909 6 5 1.200 Semimist↑
5\54 111.111 88.889 5 4 1.250 Hexe is optimal around here
9\96 112.500 87.500 9 7 1.286
4\42 114.286 85.714 4 3 1.333
11\114 115.789 84.211 11 8 1.375
7\72 116.667 83.333 7 5 1.400
10\102 117.647 98.824 10 7 1.428
3\30 120.000 80.000 3 2 1.500 L/s = 3/2
11\108 122.222 77.778 11 7 1.571
8\78 123.077 76.923 8 5 1.600
13\126 123.810 76.190 13 8 1.625 Unnamed golden tuning
5\48 125.000 75.000 5 3 1.667
12\114 126.316 73.684 12 7 1.714
7\66 127.273 72.727 7 4 1.750
9\84 128.571 71.429 9 5 1.800
2\18 133.333 66.667 2 1 2.000 Basic 6L 6s
9\78 138.462 61.538 9 4 2.250
7\60 140.000 60.000 7 3 2.333
12\102 141.176 58.824 12 5 2.400
5\42 142.857 57.143 5 2 2.500
13\108 144.444 55.556 13 5 2.600 Unnamed golden tuning
8\66 145.455 54.545 8 3 2.667
11\90 146.667 53.333 11 4 2.750
3\24 150.000 50.000 3 1 3.000 L/s = 3/1
10\78 153.846 46.154 10 3 3.333
7\54 155.556 44.444 7 2 3.500
11\84 157.143 42.857 11 3 3.667
4\30 160.000 40.000 4 1 4.000
9\66 163.636 36.364 9 2 4.500
5\36 166.667 33.333 5 1 5.000
6\42 171.429 28.571 6 1 6.000
1\6 200.000 0.000 1 0 → inf
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