15L 2s (3/1-equivalent): Difference between revisions

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This MOS, which uses a moderately sharp ~5:3 as a generator, is the closest thing to an enharmonic scale that the "proper" Arcturus temperament can provide. Of course, it is not really an Arcturus scale in the strictest sense of what Arcturus tempering entails, but its 9th is still a reasonably good 5:3.
{{Infobox MOS}}
{{MOS intro}}
 
== Modes ==
{{MOS modes}}
 
== Intervals ==
{{MOS intervals}}
 
== Tuning spectrum ==
This [[MOS]], which uses a moderately sharp ~5:3 as a [[generator]], is the closest thing to an [[enharmonic]] scale that the "proper" [[Arcturus]] temperament can provide. Of course, it is not really an Arcturus scale in the strictest sense of what Arcturus tempering entails, but its 9th is still a reasonably good 5:3.


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{| class="wikitable"
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| style="text-align:center;" | 887.579
606.667
| style="text-align:center;" | 126.797
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86.667
| style="text-align:center;" | 0.00
| style="text-align:center;" | 0.00
| style="text-align:center;" | 1775.158
| style="text-align:center;" | 1775.158
1213.667
| style="text-align:center;" | L=1 s=0
| style="text-align:center;" | L=1 s=0
|-
|-
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| style="text-align:center;" | 50\107
| style="text-align:center;" | 50\107
| style="text-align:center;" | 888.764
| style="text-align:center;" | 888.764
607.477
| style="text-align:center;" | 124.427
| style="text-align:center;" | 124.427
85.047
| style="text-align:center;" | 17.775
| style="text-align:center;" | 17.775
12.1495
| style="text-align:center;" | 1777.528
| style="text-align:center;" | 1777.528
1214.953
| style="text-align:center;" | L=7 s=1
| style="text-align:center;" | L=7 s=1
|-
|-
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 888.957
| style="text-align:center;" | 888.957
607.609
| style="text-align:center;" | 124.0405
| style="text-align:center;" | 124.0405
84.783
| style="text-align:center;" | 20.673
| style="text-align:center;" | 20.673
14.13
| style="text-align:center;" | 1777.9145
| style="text-align:center;" | 1777.9145
1215.217
| style="text-align:center;" | L=6 s=1
| style="text-align:center;" | L=6 s=1
|-
|-
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| style="text-align:center;" | 79\169
| style="text-align:center;" | 79\169
| style="text-align:center;" | 889.08
| style="text-align:center;" | 889.08
607.692
| style="text-align:center;" | 123.796
| style="text-align:center;" | 123.796
84.615
| style="text-align:center;" | 22.508
| style="text-align:center;" | 22.508
15.385
| style="text-align:center;" | 1778.159
| style="text-align:center;" | 1778.159
1215.385
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 889.226
| style="text-align:center;" | 889.226
607.792
| style="text-align:center;" | 123.504
| style="text-align:center;" | 123.504
84.416
| style="text-align:center;" | 24.701
| style="text-align:center;" | 24.701
16.883
| style="text-align:center;" | 1778.451
| style="text-align:center;" | 1778.451
1215.584
| style="text-align:center;" | L=5 s=1
| style="text-align:center;" | L=5 s=1
|-
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| style="text-align:center;" | 101\216
| style="text-align:center;" | 101\216
| style="text-align:center;" | 889.34
| style="text-align:center;" | 889.34
607.87
| style="text-align:center;" | 123.275
| style="text-align:center;" | 123.275
84.259
| style="text-align:center;" | 26.416
| style="text-align:center;" | 26.416
18.056
| style="text-align:center;" | 1778.68
| style="text-align:center;" | 1778.68
1215.741
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|-
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 889.403
| style="text-align:center;" | 889.403
607.914
| style="text-align:center;" | 123.148
| style="text-align:center;" | 123.148
84.173
| style="text-align:center;" | 27.366
| style="text-align:center;" | 27.366
18.705
| style="text-align:center;" | 1778.807
| style="text-align:center;" | 1778.807
1215.827
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| style="text-align:center;" | 94\201
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| style="text-align:center;" | 889.4715
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607.96
| style="text-align:center;" | 123.012
| style="text-align:center;" | 123.012
84.08
| style="text-align:center;" | 28.387
| style="text-align:center;" | 28.387
194.403
| style="text-align:center;" | 1778.943
| style="text-align:center;" | 1778.943
1215.92
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|-
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 889.624
| style="text-align:center;" | 889.624
608.0645
| style="text-align:center;" | 122.707
| style="text-align:center;" | 122.707
83.871
| style="text-align:center;" | 30.677
| style="text-align:center;" | 30.677
20.968
| style="text-align:center;" | 1779.248
| style="text-align:center;" | 1779.248
1216.129
| style="text-align:center;" | L=4 s=1
| style="text-align:center;" | L=4 s=1
|-
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| style="text-align:center;" | 109\233
| style="text-align:center;" | 109\233
| style="text-align:center;" | 889.756
| style="text-align:center;" | 889.756
608.1545
| style="text-align:center;" | 122.4435
| style="text-align:center;" | 122.4435
83.691
| style="text-align:center;" | 32.652
| style="text-align:center;" | 32.652
22.318
| style="text-align:center;" | 1779.5115
| style="text-align:center;" | 1779.5115
1216.309
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 889.8035
| style="text-align:center;" | 889.8035
608.187
| style="text-align:center;" | 122.348
| style="text-align:center;" | 122.348
83.626
| style="text-align:center;" | 33.368
| style="text-align:center;" | 33.368
22.807
| style="text-align:center;" | 1779.607
| style="text-align:center;" | 1779.607
1216.374
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| style="text-align:center;" | 131\280
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| style="text-align:center;" | 889.843
| style="text-align:center;" | 889.843
608.214
| style="text-align:center;" | 122.2685
| style="text-align:center;" | 122.2685
83.571
| style="text-align:center;" | 33.9635
| style="text-align:center;" | 33.9635
23.214
| style="text-align:center;" | 1779.6865
| style="text-align:center;" | 1779.6865
1216.429
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 889.906
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608.257
| style="text-align:center;" | 122.144
| style="text-align:center;" | 122.144
83.486
| style="text-align:center;" | 34.899
| style="text-align:center;" | 34.899
23.853
| style="text-align:center;" | 1779.811
| style="text-align:center;" | 1779.811
1216.514
| style="text-align:center;" | L=7 s=2
| style="text-align:center;" | L=7 s=2
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| style="text-align:center;" | 124\265
| style="text-align:center;" | 124\265
| style="text-align:center;" | 889.971
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608.302
| style="text-align:center;" | 122.012
| style="text-align:center;" | 122.012
83.396
| style="text-align:center;" | 35.886
| style="text-align:center;" | 35.886
24.528
| style="text-align:center;" | 1779.943
| style="text-align:center;" | 1779.943
1216.604
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 890.017
| style="text-align:center;" | 890.017
608.333
| style="text-align:center;" | 121.92
| style="text-align:center;" | 121.92
83.333
| style="text-align:center;" | 36.576
| style="text-align:center;" | 36.576
25
| style="text-align:center;" | 1780.035
| style="text-align:center;" | 1780.035
1216.667
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| style="text-align:center;" | 95\203
| style="text-align:center;" | 95\203
| style="text-align:center;" | 890.0775
| style="text-align:center;" | 890.0775
| style="text-align:center;" | 121.80
608.374
| style="text-align:center;" | 121.8
83.251
| style="text-align:center;" | 37.477
| style="text-align:center;" | 37.477
25.616
| style="text-align:center;" | 1780.155
| style="text-align:center;" | 1780.155
1216.749
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 890.277
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608.511
| style="text-align:center;" | 121.401
| style="text-align:center;" | 121.401
82.988
| style="text-align:center;" | 40.467
| style="text-align:center;" | 40.467
27.66
| style="text-align:center;" | 1780.554
| style="text-align:center;" | 1780.554
1217.012
| style="text-align:center;" | L=3 s=1
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| style="text-align:center;" | 103\220
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| style="text-align:center;" | 890.461
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608.636
| style="text-align:center;" | 121.0335
| style="text-align:center;" | 121.0335
82.727
| style="text-align:center;" | 43.226
| style="text-align:center;" | 43.226
29.5455
| style="text-align:center;" | 1780.9215
| style="text-align:center;" | 1780.9215
1217.273
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 890.511
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608.6705
| style="text-align:center;" | 120.934
| style="text-align:center;" | 120.934
82.659
| style="text-align:center;" | 43.976
| style="text-align:center;" | 43.976
30.058
| style="text-align:center;" | 1781.021
| style="text-align:center;" | 1781.021
1217.341
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| style="text-align:center;" | 140\299
| style="text-align:center;" | 140\299
| style="text-align:center;" | 890.5475
| style="text-align:center;" | 890.5475
608.696
| style="text-align:center;" | 120.86
| style="text-align:center;" | 120.86
82.609
| style="text-align:center;" | 44.528
| style="text-align:center;" | 44.528
30.435
| style="text-align:center;" | 1781.095
| style="text-align:center;" | 1781.095
1217.391
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 890.598
| style="text-align:center;" | 890.598
608.73
| style="text-align:center;" | 120.759
| style="text-align:center;" | 120.759
82.54
| style="text-align:center;" | 45.285
| style="text-align:center;" | 45.285
30.952
| style="text-align:center;" | 1781.196
| style="text-align:center;" | 1781.196
1217.46
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| style="text-align:center;" | 155\331
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608.761
| style="text-align:center;" | 120.668
| style="text-align:center;" | 120.668
82.477
| style="text-align:center;" | 45.969
| style="text-align:center;" | 45.969
27.492
| style="text-align:center;" | 1781.287
| style="text-align:center;" | 1781.287
1217.523
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 890.672
| style="text-align:center;" | 890.672
608.7805
| style="text-align:center;" | 120.612
| style="text-align:center;" | 120.612
82.439
| style="text-align:center;" | 46.389
| style="text-align:center;" | 46.389
31.707
| style="text-align:center;" | 1781.343
| style="text-align:center;" | 1781.343
1217.561
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| style="text-align:center;" | 133\284
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| style="text-align:center;" | 890.704
| style="text-align:center;" | 890.704
608.803
| style="text-align:center;" | 120.546
| style="text-align:center;" | 120.546
82.394
| style="text-align:center;" | 46.879
| style="text-align:center;" | 46.879
32.042
| style="text-align:center;" | 1781.409
| style="text-align:center;" | 1781.409
1217.606
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 890.789
| style="text-align:center;" | 890.789
608.861
| style="text-align:center;" | 120.377
| style="text-align:center;" | 120.377
82.2785
| style="text-align:center;" | 48.151
| style="text-align:center;" | 48.151
32.911
| style="text-align:center;" | 1781.578
| style="text-align:center;" | 1781.578
1217.7215
| style="text-align:center;" | L=5 s=2
| style="text-align:center;" | L=5 s=2
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| style="text-align:center;" | 126\269
| style="text-align:center;" | 126\269
| style="text-align:center;" | 890.879
| style="text-align:center;" | 890.879
608.922
| style="text-align:center;" | 120.198
| style="text-align:center;" | 120.198
82.156
| style="text-align:center;" | 49.493
| style="text-align:center;" | 49.493
33.829
| style="text-align:center;" | 1781.757
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1217.844
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 890.916
| style="text-align:center;" | 890.916
608.947
| style="text-align:center;" | 120.1235
| style="text-align:center;" | 120.1235
82.105
| style="text-align:center;" | 50.0515
| style="text-align:center;" | 50.0515
34.2105
| style="text-align:center;" | 1781.8315
| style="text-align:center;" | 1781.8315
1217.895
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| style="text-align:center;" | 890.949
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608.97
| style="text-align:center;" | 120.057
| style="text-align:center;" | 120.057
82.03
| style="text-align:center;" | 50.55
| style="text-align:center;" | 50.55
34.5515
| style="text-align:center;" | 1781.898
| style="text-align:center;" | 1781.898
1217.94
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 891.006
| style="text-align:center;" | 891.006
609.009
| style="text-align:center;" | 119.943
| style="text-align:center;" | 119.943
81.982
| style="text-align:center;" | 51.404
| style="text-align:center;" | 51.404
35.135
| style="text-align:center;" | 1782.012
| style="text-align:center;" | 1782.012
1218.018
| style="text-align:center;" | L=7 s=3
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| style="text-align:center;" | 119\254
| style="text-align:center;" | 119\254
| style="text-align:center;" | 891.073
| style="text-align:center;" | 891.073
609.055
| style="text-align:center;" | 119.808
| style="text-align:center;" | 119.808
81.89
| style="text-align:center;" | 52.416
| style="text-align:center;" | 52.416
35.827
| style="text-align:center;" | 1782.147
| style="text-align:center;" | 1782.147
1218.11
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 891.126
| style="text-align:center;" | 891.126
609.091
| style="text-align:center;" | 119.7035
| style="text-align:center;" | 119.7035
81.818
| style="text-align:center;" | 53.2015
| style="text-align:center;" | 53.2015
36.364
| style="text-align:center;" | 1782.2515
| style="text-align:center;" | 1782.2515
1218.182
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| style="text-align:center;" | 82\175
| style="text-align:center;" | 82\175
| style="text-align:center;" | 891.202
| style="text-align:center;" | 891.202
609.143
| style="text-align:center;" | 119.5515
| style="text-align:center;" | 119.5515
81.714
| style="text-align:center;" | 54.342
| style="text-align:center;" | 54.342
37.143
| style="text-align:center;" | 1782.4035
| style="text-align:center;" | 1782.4035
1218.286
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 891.541
| style="text-align:center;" | 891.541
609.375
| style="text-align:center;" | 118.872
| style="text-align:center;" | 118.872
81.25
| style="text-align:center;" | 59.436
| style="text-align:center;" | 59.436
40.625
| style="text-align:center;" | 1783.083
| style="text-align:center;" | 1783.083
1218.375
| style="text-align:center;" | L=2 s=1
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| style="text-align:center;" | 83\177
| style="text-align:center;" | 83\177
| style="text-align:center;" | 891.877
| style="text-align:center;" | 891.877
| style="text-align:center;" | 118.20
609.6045
| style="text-align:center;" | 118.2
80.791
| style="text-align:center;" | 64.473
| style="text-align:center;" | 64.473
44.068
| style="text-align:center;" | 1783.754
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1219.209
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| style="text-align:center;" |  
| style="text-align:center;" | 891.951
| style="text-align:center;" | 891.951
609.655
| style="text-align:center;" | 118.052
| style="text-align:center;" | 118.052
80.69
| style="text-align:center;" | 65.585
| style="text-align:center;" | 65.585
44.828
| style="text-align:center;" | 1783.903
| style="text-align:center;" | 1783.903
1219.31
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| style="text-align:center;" | 121\258
| style="text-align:center;" | 121\258
| style="text-align:center;" | 892.002
| style="text-align:center;" | 892.002
609.69
| style="text-align:center;" | 117.951
| style="text-align:center;" | 117.951
80.62
| style="text-align:center;" | 66.347
| style="text-align:center;" | 66.347
45.349
| style="text-align:center;" | 1784.004
| style="text-align:center;" | 1784.004
1219.38
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 486: Line 639:
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 892.067
| style="text-align:center;" | 892.067
609.7345
| style="text-align:center;" | 117.82
| style="text-align:center;" | 117.82
80.531
| style="text-align:center;" | 67.326
| style="text-align:center;" | 67.326
46.018
| style="text-align:center;" | 1784.135
| style="text-align:center;" | 1784.135
1219.469
| style="text-align:center;" | L=7 s=4
| style="text-align:center;" | L=7 s=4
|-
|-
Line 499: Line 656:
| style="text-align:center;" | 144\307
| style="text-align:center;" | 144\307
| style="text-align:center;" | 892.122
| style="text-align:center;" | 892.122
609.772
| style="text-align:center;" | 117.71
| style="text-align:center;" | 117.71
80.456
| style="text-align:center;" | 68.148
| style="text-align:center;" | 68.148
46.58
| style="text-align:center;" | 1784.244
| style="text-align:center;" | 1784.244
1219.544
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 512: Line 673:
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 892.154
| style="text-align:center;" | 892.154
609.794
| style="text-align:center;" | 117.647
| style="text-align:center;" | 117.647
80.412
| style="text-align:center;" | 68.627
| style="text-align:center;" | 68.627
46.907
| style="text-align:center;" | 1784.308
| style="text-align:center;" | 1784.308
1219.588
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 525: Line 690:
| style="text-align:center;" | 129\275
| style="text-align:center;" | 129\275
| style="text-align:center;" | 892.19
| style="text-align:center;" | 892.19
609.818
| style="text-align:center;" | 117.575
| style="text-align:center;" | 117.575
80.364
| style="text-align:center;" | 69.162
| style="text-align:center;" | 69.162
47.273
| style="text-align:center;" | 1784.38
| style="text-align:center;" | 1784.38
1219.636
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 538: Line 707:
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 892.275
| style="text-align:center;" | 892.275
609.8765
| style="text-align:center;" | 117.405
| style="text-align:center;" | 117.405
80.247
| style="text-align:center;" | 70.443
| style="text-align:center;" | 70.443
48.148
| style="text-align:center;" | 1784.55
| style="text-align:center;" | 1784.55
1219.743
| style="text-align:center;" | L=5 s=3
| style="text-align:center;" | L=5 s=3
|-
|-
Line 551: Line 724:
| style="text-align:center;" | 137\292
| style="text-align:center;" | 137\292
| style="text-align:center;" | 892.356
| style="text-align:center;" | 892.356
609.9315
| style="text-align:center;" | 117.244
| style="text-align:center;" | 117.244
80.137
| style="text-align:center;" | 71.649
| style="text-align:center;" | 71.649
48.973
| style="text-align:center;" | 1784.711
| style="text-align:center;" | 1784.711
1219.863
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 564: Line 741:
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 892.3865
| style="text-align:center;" | 892.3865
609.953
| style="text-align:center;" | 117.182
| style="text-align:center;" | 117.182
80.095
| style="text-align:center;" | 72.112
| style="text-align:center;" | 72.112
49.289
| style="text-align:center;" | 1784.773
| style="text-align:center;" | 1784.773
1219.905
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 575: Line 756:
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 157\341
| style="text-align:center;" | 160\341
| style="text-align:center;" | 892.413
| style="text-align:center;" | 892.413
609.971
| style="text-align:center;" | 117.129
| style="text-align:center;" | 117.129
80.059
| style="text-align:center;" | 72.509
| style="text-align:center;" | 72.509
49.56
| style="text-align:center;" | 1784.826
| style="text-align:center;" | 1784.826
1219.941
| style="text-align:center;" | Golden Super-Arcturus[17] is near here
| style="text-align:center;" | Golden Super-Arcturus[17] is near here
|-
|-
Line 590: Line 775:
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 892.456
| style="text-align:center;" | 892.456
610
| style="text-align:center;" | 117.043
| style="text-align:center;" | 117.043
80
| style="text-align:center;" | 73.152
| style="text-align:center;" | 73.152
50
| style="text-align:center;" | 1784.912
| style="text-align:center;" | 1784.912
1220
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 603: Line 792:
| style="text-align:center;" | 145\309
| style="text-align:center;" | 145\309
| style="text-align:center;" | 892.503
| style="text-align:center;" | 892.503
610.032
| style="text-align:center;" | 116.949
| style="text-align:center;" | 116.949
79.935
| style="text-align:center;" | 73.862
| style="text-align:center;" | 73.862
50.485
| style="text-align:center;" | 1785.006
| style="text-align:center;" | 1785.006
1220.065
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 616: Line 809:
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 892.5375
| style="text-align:center;" | 892.5375
610.056
| style="text-align:center;" | 116.88
| style="text-align:center;" | 116.88
79.888
| style="text-align:center;" | 74.378
| style="text-align:center;" | 74.378
50.838
| style="text-align:center;" | 1785.075
| style="text-align:center;" | 1785.075
1220.112
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 629: Line 826:
| style="text-align:center;" | 107\228
| style="text-align:center;" | 107\228
| style="text-align:center;" | 892.584
| style="text-align:center;" | 892.584
610.088
| style="text-align:center;" | 116.787
| style="text-align:center;" | 116.787
79.824
| style="text-align:center;" | 75.077
| style="text-align:center;" | 75.077
51.316
| style="text-align:center;" | 1785.168
| style="text-align:center;" | 1785.168
1220.176
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 642: Line 843:
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 892.754
| style="text-align:center;" | 892.754
610.204
| style="text-align:center;" | 116.446
| style="text-align:center;" | 116.446
79.592
| style="text-align:center;" | 77.63
| style="text-align:center;" | 77.63
53.06
| style="text-align:center;" | 1785.509
| style="text-align:center;" | 1785.509
1220.408
| style="text-align:center;" | L=3 s=2
| style="text-align:center;" | L=3 s=2
|-
|-
Line 655: Line 860:
| style="text-align:center;" | 100\213
| style="text-align:center;" | 100\213
| style="text-align:center;" | 892.937
| style="text-align:center;" | 892.937
610.329
| style="text-align:center;" | 116.082
| style="text-align:center;" | 116.082
79.342
| style="text-align:center;" | 78.1625
| style="text-align:center;" | 78.1625
54.93
| style="text-align:center;" | 1785.873
| style="text-align:center;" | 1785.873
1220.658
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 668: Line 877:
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 892.991
| style="text-align:center;" | 892.991
610.366
| style="text-align:center;" | 115.973
| style="text-align:center;" | 115.973
79.278
| style="text-align:center;" | 81.181
| style="text-align:center;" | 81.181
55.488
| style="text-align:center;" | 1785.982
| style="text-align:center;" | 1785.982
1220.722
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 681: Line 894:
| style="text-align:center;" | 131\279
| style="text-align:center;" | 131\279
| style="text-align:center;" | 893.033
| style="text-align:center;" | 893.033
610.394
| style="text-align:center;" | 115.89
| style="text-align:center;" | 115.89
79.2015
| style="text-align:center;" | 81.8045
| style="text-align:center;" | 81.8045
55.914
| style="text-align:center;" | 1786.065
| style="text-align:center;" | 1786.065
1220.7985
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 694: Line 911:
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 893.092
| style="text-align:center;" | 893.092
610.434
| style="text-align:center;" | 115.771
| style="text-align:center;" | 115.771
79.131
| style="text-align:center;" | 82.694
| style="text-align:center;" | 82.694
56.522
| style="text-align:center;" | 1786.184
| style="text-align:center;" | 1786.184
1220.869
| style="text-align:center;" | L=7 s=5
| style="text-align:center;" | L=7 s=5
|-
|-
Line 707: Line 928:
| style="text-align:center;" | 139\296
| style="text-align:center;" | 139\296
| style="text-align:center;" | 893.148
| style="text-align:center;" | 893.148
610.473
| style="text-align:center;" | 115.659
| style="text-align:center;" | 115.659
79.054
| style="text-align:center;" | 83.532
| style="text-align:center;" | 83.532
57.095
| style="text-align:center;" | 1786.296
| style="text-align:center;" | 1786.296
1220.946
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 720: Line 945:
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 893.183
| style="text-align:center;" | 893.183
610.497
| style="text-align:center;" | 115.558
| style="text-align:center;" | 115.558
79.0055
| style="text-align:center;" | 84.064
| style="text-align:center;" | 84.064
57.459
| style="text-align:center;" | 1786.367
| style="text-align:center;" | 1786.367
1220.9945
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 733: Line 962:
| style="text-align:center;" | 116\247
| style="text-align:center;" | 116\247
| style="text-align:center;" | 893.226
| style="text-align:center;" | 893.226
610.526
| style="text-align:center;" | 115.503
| style="text-align:center;" | 115.503
78.947
| style="text-align:center;" | 84.7025
| style="text-align:center;" | 84.7025
57.895
| style="text-align:center;" | 1786.452
| style="text-align:center;" | 1786.452
1221.053
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 746: Line 979:
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 893.3425
| style="text-align:center;" | 893.3425
610.606
| style="text-align:center;" | 115.27
| style="text-align:center;" | 115.27
78.788
| style="text-align:center;" | 86.4525
| style="text-align:center;" | 86.4525
59.091
| style="text-align:center;" | 1786.685
| style="text-align:center;" | 1786.685
1221.212
| style="text-align:center;" | L=4 s=3
| style="text-align:center;" | L=4 s=3
|-
|-
Line 759: Line 996:
| style="text-align:center;" | 101\215
| style="text-align:center;" | 101\215
| style="text-align:center;" | 893.4765
| style="text-align:center;" | 893.4765
610.697
| style="text-align:center;" | 115.002
| style="text-align:center;" | 115.002
78.605
| style="text-align:center;" | 88.463
| style="text-align:center;" | 88.463
60.465
| style="text-align:center;" | 1786.953
| style="text-align:center;" | 1786.953
1221.395
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 771: Line 1,012:
| style="text-align:center;" | 70\149
| style="text-align:center;" | 70\149
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 893.5'''36'''
| style="text-align:center;" | 893.536
610.738
| style="text-align:center;" | 114.883
| style="text-align:center;" | 114.883
78.5235
| style="text-align:center;" | 89.354
| style="text-align:center;" | 89.354
61.074
| style="text-align:center;" | 1787.072
| style="text-align:center;" | 1787.072
1221.4765
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 785: Line 1,030:
| style="text-align:center;" | 109\232
| style="text-align:center;" | 109\232
| style="text-align:center;" | 893.591
| style="text-align:center;" | 893.591
610.776
| style="text-align:center;" | 114.773
| style="text-align:center;" | 114.773
78.448
| style="text-align:center;" | 90.179
| style="text-align:center;" | 90.179
61.638
| style="text-align:center;" | 1787.182
| style="text-align:center;" | 1787.182
1221.552
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 798: Line 1,047:
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 893.69
| style="text-align:center;" | 893.69
610.843
| style="text-align:center;" | 114.576
| style="text-align:center;" | 114.576
78.313
| style="text-align:center;" | 91.6605
| style="text-align:center;" | 91.6605
62.651
| style="text-align:center;" | 1787.379
| style="text-align:center;" | 1787.379
1221.687
| style="text-align:center;" | L=5 s=4
| style="text-align:center;" | L=5 s=4
|-
|-
Line 811: Line 1,064:
| style="text-align:center;" | 86\183
| style="text-align:center;" | 86\183
| style="text-align:center;" | 893.815
| style="text-align:center;" | 893.815
610.929
| style="text-align:center;" | 114.325
| style="text-align:center;" | 114.325
78.142
| style="text-align:center;" | 93.539
| style="text-align:center;" | 93.539
63.934
| style="text-align:center;" | 1787.63
| style="text-align:center;" | 1787.63
1221.858
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 824: Line 1,081:
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 893.919
| style="text-align:center;" | 893.919
611
| style="text-align:center;" | 114.117
| style="text-align:center;" | 114.117
78
| style="text-align:center;" | 95.098
| style="text-align:center;" | 95.098
65
| style="text-align:center;" | 1787.838
| style="text-align:center;" | 1787.838
1222
| style="text-align:center;" | L=6 s=5
| style="text-align:center;" | L=6 s=5
|-
|-
Line 837: Line 1,098:
| style="text-align:center;" | 55\117
| style="text-align:center;" | 55\117
| style="text-align:center;" | 894.081
| style="text-align:center;" | 894.081
611.111
| style="text-align:center;" | 113.792
| style="text-align:center;" | 113.792
77.778
| style="text-align:center;" | 97.536
| style="text-align:center;" | 97.536
66.667
| style="text-align:center;" | 1788.163
| style="text-align:center;" | 1788.163
1222.222
| style="text-align:center;" | L=7 s=6
| style="text-align:center;" | L=7 s=6
|-
|-
Line 850: Line 1,115:
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 895.038
| style="text-align:center;" | 895.038
611.765
| colspan="2" style="text-align:center;" | 111.88
| colspan="2" style="text-align:center;" | 111.88
76.471
| style="text-align:center;" | 1790.075
| style="text-align:center;" | 1790.075
1223.529
| style="text-align:center;" | L=1 s=1
| style="text-align:center;" | L=1 s=1
|}
|}
[[Category:Abstract MOS patterns]]
[[Category:Arcturus]]
[[Category:Tritave]]

Latest revision as of 23:07, 27 February 2025

↖ 14L 1s⟨3/1⟩ ↑ 15L 1s⟨3/1⟩ 16L 1s⟨3/1⟩ ↗
← 14L 2s⟨3/1⟩ 15L 2s (3/1-equivalent) 16L 2s⟨3/1⟩ →
↙ 14L 3s⟨3/1⟩ ↓ 15L 3s⟨3/1⟩ 16L 3s⟨3/1⟩ ↘ 
┌╥╥╥╥╥╥╥╥┬╥╥╥╥╥╥╥┬┐
│║║║║║║║║│║║║║║║║││
│││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLLLLLsLLLLLLLs
sLLLLLLLsLLLLLLLL
Equave 3/1 (1902.0 ¢)
Period 3/1 (1902.0 ¢)
Generator size(edt)
Bright 9\17 to 8\15 (1006.9 ¢ to 1014.4 ¢)
Dark 7\15 to 8\17 (887.6 ¢ to 895.0 ¢)
Related MOS scales
Parent 2L 13s⟨3/1⟩
Sister 2L 15s⟨3/1⟩
Daughters 17L 15s⟨3/1⟩, 15L 17s⟨3/1⟩
Neutralized 13L 4s⟨3/1⟩
2-Flought 32L 2s⟨3/1⟩, 15L 19s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1) 9\17 (1006.9 ¢)
Supersoft (L:s = 4:3) 35\66 (1008.6 ¢)
Soft (L:s = 3:2) 26\49 (1009.2 ¢)
Semisoft (L:s = 5:3) 43\81 (1009.7 ¢)
Basic (L:s = 2:1) 17\32 (1010.4 ¢)
Semihard (L:s = 5:2) 42\79 (1011.2 ¢)
Hard (L:s = 3:1) 25\47 (1011.7 ¢)
Superhard (L:s = 4:1) 33\62 (1012.3 ¢)
Collapsed (L:s = 1:0) 8\15 (1014.4 ¢)

15L 2s⟨3/1⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 15 large steps and 2 small steps, repeating every interval of 3/1 (1902.0 ¢). Generators that produce this scale range from 1006.9 ¢ to 1014.4 ¢, or from 887.6 ¢ to 895 ¢.

Modes

Modes of 15L 2s⟨3/1⟩
UDP Cyclic
order		 Step
pattern
16|0 1 LLLLLLLLsLLLLLLLs
15|1 10 LLLLLLLsLLLLLLLLs
14|2 2 LLLLLLLsLLLLLLLsL
13|3 11 LLLLLLsLLLLLLLLsL
12|4 3 LLLLLLsLLLLLLLsLL
11|5 12 LLLLLsLLLLLLLLsLL
10|6 4 LLLLLsLLLLLLLsLLL
9|7 13 LLLLsLLLLLLLLsLLL
8|8 5 LLLLsLLLLLLLsLLLL
7|9 14 LLLsLLLLLLLLsLLLL
6|10 6 LLLsLLLLLLLsLLLLL
5|11 15 LLsLLLLLLLLsLLLLL
4|12 7 LLsLLLLLLLsLLLLLL
3|13 16 LsLLLLLLLLsLLLLLL
2|14 8 LsLLLLLLLsLLLLLLL
1|15 17 sLLLLLLLLsLLLLLLL
0|16 9 sLLLLLLLsLLLLLLLL

Intervals

Intervals of 15L 2s⟨3/1⟩
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Minor 1-mosstep m1ms s 0.0 ¢ to 111.9 ¢
Major 1-mosstep M1ms L 111.9 ¢ to 126.8 ¢
2-mosstep Minor 2-mosstep m2ms L + s 126.8 ¢ to 223.8 ¢
Major 2-mosstep M2ms 2L 223.8 ¢ to 253.6 ¢
3-mosstep Minor 3-mosstep m3ms 2L + s 253.6 ¢ to 335.6 ¢
Major 3-mosstep M3ms 3L 335.6 ¢ to 380.4 ¢
4-mosstep Minor 4-mosstep m4ms 3L + s 380.4 ¢ to 447.5 ¢
Major 4-mosstep M4ms 4L 447.5 ¢ to 507.2 ¢
5-mosstep Minor 5-mosstep m5ms 4L + s 507.2 ¢ to 559.4 ¢
Major 5-mosstep M5ms 5L 559.4 ¢ to 634.0 ¢
6-mosstep Minor 6-mosstep m6ms 5L + s 634.0 ¢ to 671.3 ¢
Major 6-mosstep M6ms 6L 671.3 ¢ to 760.8 ¢
7-mosstep Minor 7-mosstep m7ms 6L + s 760.8 ¢ to 783.2 ¢
Major 7-mosstep M7ms 7L 783.2 ¢ to 887.6 ¢
8-mosstep Perfect 8-mosstep P8ms 7L + s 887.6 ¢ to 895.0 ¢
Augmented 8-mosstep A8ms 8L 895.0 ¢ to 1014.4 ¢
9-mosstep Diminished 9-mosstep d9ms 7L + 2s 887.6 ¢ to 1006.9 ¢
Perfect 9-mosstep P9ms 8L + s 1006.9 ¢ to 1014.4 ¢
10-mosstep Minor 10-mosstep m10ms 8L + 2s 1014.4 ¢ to 1118.8 ¢
Major 10-mosstep M10ms 9L + s 1118.8 ¢ to 1141.2 ¢
11-mosstep Minor 11-mosstep m11ms 9L + 2s 1141.2 ¢ to 1230.7 ¢
Major 11-mosstep M11ms 10L + s 1230.7 ¢ to 1268.0 ¢
12-mosstep Minor 12-mosstep m12ms 10L + 2s 1268.0 ¢ to 1342.6 ¢
Major 12-mosstep M12ms 11L + s 1342.6 ¢ to 1394.8 ¢
13-mosstep Minor 13-mosstep m13ms 11L + 2s 1394.8 ¢ to 1454.4 ¢
Major 13-mosstep M13ms 12L + s 1454.4 ¢ to 1521.6 ¢
14-mosstep Minor 14-mosstep m14ms 12L + 2s 1521.6 ¢ to 1566.3 ¢
Major 14-mosstep M14ms 13L + s 1566.3 ¢ to 1648.4 ¢
15-mosstep Minor 15-mosstep m15ms 13L + 2s 1648.4 ¢ to 1678.2 ¢
Major 15-mosstep M15ms 14L + s 1678.2 ¢ to 1775.2 ¢
16-mosstep Minor 16-mosstep m16ms 14L + 2s 1775.2 ¢ to 1790.1 ¢
Major 16-mosstep M16ms 15L + s 1790.1 ¢ to 1902.0 ¢
17-mosstep Perfect 17-mosstep P17ms 15L + 2s 1902.0 ¢

Tuning spectrum

This MOS, which uses a moderately sharp ~5:3 as a generator, is the closest thing to an enharmonic scale that the "proper" Arcturus temperament can provide. Of course, it is not really an Arcturus scale in the strictest sense of what Arcturus tempering entails, but its 9th is still a reasonably good 5:3.

Generator cents L s 2g Notes
7\15 887.579

606.667

126.797

86.667

0.00 1775.158

1213.667

L=1 s=0
50\107 888.764

607.477

124.427

85.047

17.775

12.1495

1777.528

1214.953

L=7 s=1
43\92 888.957

607.609

124.0405

84.783

20.673

14.13

1777.9145

1215.217

L=6 s=1
79\169 889.08

607.692

123.796

84.615

22.508

15.385

1778.159

1215.385

36\77 889.226

607.792

123.504

84.416

24.701

16.883

1778.451

1215.584

L=5 s=1
101\216 889.34

607.87

123.275

84.259

26.416

18.056

1778.68

1215.741

65\139 889.403

607.914

123.148

84.173

27.366

18.705

1778.807

1215.827

94\201 889.4715

607.96

123.012

84.08

28.387

194.403

1778.943

1215.92

29\62 889.624

608.0645

122.707

83.871

30.677

20.968

1779.248

1216.129

L=4 s=1
109\233 889.756

608.1545

122.4435

83.691

32.652

22.318

1779.5115

1216.309

80\171 889.8035

608.187

122.348

83.626

33.368

22.807

1779.607

1216.374

131\280 889.843

608.214

122.2685

83.571

33.9635

23.214

1779.6865

1216.429

51\109 889.906

608.257

122.144

83.486

34.899

23.853

1779.811

1216.514

L=7 s=2
124\265 889.971

608.302

122.012

83.396

35.886

24.528

1779.943

1216.604

73\156 890.017

608.333

121.92

83.333

36.576

25

1780.035

1216.667

95\203 890.0775

608.374

121.8

83.251

37.477

25.616

1780.155

1216.749

22\47 890.277

608.511

121.401

82.988

40.467

27.66

1780.554

1217.012

L=3 s=1
103\220 890.461

608.636

121.0335

82.727

43.226

29.5455

1780.9215

1217.273

81\173 890.511

608.6705

120.934

82.659

43.976

30.058

1781.021

1217.341

140\299 890.5475

608.696

120.86

82.609

44.528

30.435

1781.095

1217.391

59\126 890.598

608.73

120.759

82.54

45.285

30.952

1781.196

1217.46

155\331 890.644

608.761

120.668

82.477

45.969

27.492

1781.287

1217.523

96\205 890.672

608.7805

120.612

82.439

46.389

31.707

1781.343

1217.561

133\284 890.704

608.803

120.546

82.394

46.879

32.042

1781.409

1217.606

37\79 890.789

608.861

120.377

82.2785

48.151

32.911

1781.578

1217.7215

L=5 s=2
126\269 890.879

608.922

120.198

82.156

49.493

33.829

1781.757

1217.844

89\190 890.916

608.947

120.1235

82.105

50.0515

34.2105

1781.8315

1217.895

141\301 890.949

608.97

120.057

82.03

50.55

34.5515

1781.898

1217.94

52\111 891.006

609.009

119.943

81.982

51.404

35.135

1782.012

1218.018

L=7 s=3
119\254 891.073

609.055

119.808

81.89

52.416

35.827

1782.147

1218.11

67\143 891.126

609.091

119.7035

81.818

53.2015

36.364

1782.2515

1218.182

82\175 891.202

609.143

119.5515

81.714

54.342

37.143

1782.4035

1218.286

15\32 891.541

609.375

118.872

81.25

59.436

40.625

1783.083

1218.375

L=2 s=1
83\177 891.877

609.6045

118.2

80.791

64.473

44.068

1783.754

1219.209

68\145 891.951

609.655

118.052

80.69

65.585

44.828

1783.903

1219.31

121\258 892.002

609.69

117.951

80.62

66.347

45.349

1784.004

1219.38

53\113 892.067

609.7345

117.82

80.531

67.326

46.018

1784.135

1219.469

L=7 s=4
144\307 892.122

609.772

117.71

80.456

68.148

46.58

1784.244

1219.544

91\194 892.154

609.794

117.647

80.412

68.627

46.907

1784.308

1219.588

129\275 892.19

609.818

117.575

80.364

69.162

47.273

1784.38

1219.636

38\81 892.275

609.8765

117.405

80.247

70.443

48.148

1784.55

1219.743

L=5 s=3
137\292 892.356

609.9315

117.244

80.137

71.649

48.973

1784.711

1219.863

99\211 892.3865

609.953

117.182

80.095

72.112

49.289

1784.773

1219.905

160\341 892.413

609.971

117.129

80.059

72.509

49.56

1784.826

1219.941

Golden Super-Arcturus[17] is near here
61\130 892.456

610

117.043

80

73.152

50

1784.912

1220

145\309 892.503

610.032

116.949

79.935

73.862

50.485

1785.006

1220.065

84\179 892.5375

610.056

116.88

79.888

74.378

50.838

1785.075

1220.112

107\228 892.584

610.088

116.787

79.824

75.077

51.316

1785.168

1220.176

23\49 892.754

610.204

116.446

79.592

77.63

53.06

1785.509

1220.408

L=3 s=2
100\213 892.937

610.329

116.082

79.342

78.1625

54.93

1785.873

1220.658

77\164 892.991

610.366

115.973

79.278

81.181

55.488

1785.982

1220.722

131\279 893.033

610.394

115.89

79.2015

81.8045

55.914

1786.065

1220.7985

54\115 893.092

610.434

115.771

79.131

82.694

56.522

1786.184

1220.869

L=7 s=5
139\296 893.148

610.473

115.659

79.054

83.532

57.095

1786.296

1220.946

85\181 893.183

610.497

115.558

79.0055

84.064

57.459

1786.367

1220.9945

116\247 893.226

610.526

115.503

78.947

84.7025

57.895

1786.452

1221.053

31\66 893.3425

610.606

115.27

78.788

86.4525

59.091

1786.685

1221.212

L=4 s=3
101\215 893.4765

610.697

115.002

78.605

88.463

60.465

1786.953

1221.395

70\149 893.536

610.738

114.883

78.5235

89.354

61.074

1787.072

1221.4765

109\232 893.591

610.776

114.773

78.448

90.179

61.638

1787.182

1221.552

39\83 893.69

610.843

114.576

78.313

91.6605

62.651

1787.379

1221.687

L=5 s=4
86\183 893.815

610.929

114.325

78.142

93.539

63.934

1787.63

1221.858

47\100 893.919

611

114.117

78

95.098

65

1787.838

1222

L=6 s=5
55\117 894.081

611.111

113.792

77.778

97.536

66.667

1788.163

1222.222

L=7 s=6
8\17 895.038

611.765

111.88

76.471

1790.075

1223.529

L=1 s=1
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