17L 2s (3/1-equivalent): Difference between revisions

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m Modes intervals
 
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Using a generator as which is as sharp as possible for an 'ordinary' ~5:3, this MOS is the most complex parent scale for an Arcturus-like temperament. It is also the most complex parent MOS for a temperament where two generators make an "ordinary" ~14:5 (the simplest is the proper Arcturus scale).
{{Infobox MOS}}
{{MOS intro}}


Using a [[generator]] as which is as sharp as possible for an 'ordinary' ~5:3, this [[MOS]] is the most complex parent scale for an [[Arcturus]]-like temperament. It is also the most complex parent MOS for a temperament where two generators make an "ordinary" ~14:5 (the simplest is the proper Arcturus scale).
== Modes ==
{{MOS modes}}
== Intervals ==
{{MOS intervals}}
== Scale tree ==
{| class="wikitable"
{| class="wikitable"
|-
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 895.038
| style="text-align:center;" | 895.038
611.765
| style="text-align:center;" | 111.88
| style="text-align:center;" | 111.88
76.471
| style="text-align:center;" | 0.00
| style="text-align:center;" | 0.00
| style="text-align:center;" | 1790.075
| style="text-align:center;" | 1790.075
1223.529
| style="text-align:center;" | L=1 s=0
| style="text-align:center;" | L=1 s=0
|-
|-
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| style="text-align:center;" | 57\121
| style="text-align:center;" | 57\121
| style="text-align:center;" | 895.962
| style="text-align:center;" | 895.962
612.397
| style="text-align:center;" | 110.0305
| style="text-align:center;" | 110.0305
75.207
| style="text-align:center;" | 15.719
| style="text-align:center;" | 15.719
10.744
| style="text-align:center;" | 1791.925
| style="text-align:center;" | 1791.925
1224.793
| 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;" | 896.113
| style="text-align:center;" | 896.113
612.5
| style="text-align:center;" | 109.728
| style="text-align:center;" | 109.728
75
| style="text-align:center;" | 18.288
| style="text-align:center;" | 18.288
12.5
| style="text-align:center;" | 1792.227
| style="text-align:center;" | 1792.227
1225
| style="text-align:center;" | L=6 s=1
| style="text-align:center;" | L=6 s=1
|-
|-
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| style="text-align:center;" | 90\191
| style="text-align:center;" | 90\191
| style="text-align:center;" | 896.209
| style="text-align:center;" | 896.209
612.565
| style="text-align:center;" | 109.537
| style="text-align:center;" | 109.537
74.869
| style="text-align:center;" | 19.916
| style="text-align:center;" | 19.916
13.913
| style="text-align:center;" | 1792.418
| style="text-align:center;" | 1792.418
1225.131
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 896.324
| style="text-align:center;" | 896.324
612.644
| style="text-align:center;" | 109.308
| style="text-align:center;" | 109.308
74.713
| style="text-align:center;" | 21.862
| style="text-align:center;" | 21.862
14.9425
| style="text-align:center;" | 1792.647
| style="text-align:center;" | 1792.647
1225.287
| style="text-align:center;" | L=5 s=1
| style="text-align:center;" | L=5 s=1
|-
|-
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| style="text-align:center;" | 115\244
| style="text-align:center;" | 115\244
| style="text-align:center;" | 896.413
| style="text-align:center;" | 896.413
612.705
| style="text-align:center;" | 109.129
| style="text-align:center;" | 109.129
74.59
| style="text-align:center;" | 23.385
| style="text-align:center;" | 23.385
15.984
| style="text-align:center;" | 1792.826
| style="text-align:center;" | 1792.826
1225.41
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 896.463
| style="text-align:center;" | 896.463
612.739
| style="text-align:center;" | 109.029
| style="text-align:center;" | 109.029
74.522
| style="text-align:center;" | 24.229
| style="text-align:center;" | 24.229
16.5605
| style="text-align:center;" | 1792.926
| style="text-align:center;" | 1792.926
1225.478
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
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| style="text-align:center;" | 107\227
| style="text-align:center;" | 107\227
| style="text-align:center;" | 896.516
| style="text-align:center;" | 896.516
612.775
| style="text-align:center;" | 108.9225
| style="text-align:center;" | 108.9225
74.449
| style="text-align:center;" | 25.136
| style="text-align:center;" | 25.136
17.181
| style="text-align:center;" | 1793.032
| style="text-align:center;" | 1793.032
1225.551
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 896.636
| style="text-align:center;" | 896.636
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| style="text-align:center;" | 108.683
| style="text-align:center;" | 108.683
74.286
| style="text-align:center;" | 27.171
| style="text-align:center;" | 27.171
18.571
| style="text-align:center;" | 1793.272
| style="text-align:center;" | 1793.272
1225.714
| style="text-align:center;" | L=4 s=1
| style="text-align:center;" | L=4 s=1
|-
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| style="text-align:center;" | 124\263
| style="text-align:center;" | 124\263
| style="text-align:center;" | 896.739
| style="text-align:center;" | 896.739
612.928
| style="text-align:center;" | 108.4765
| style="text-align:center;" | 108.4765
74.1445
| style="text-align:center;" | 28.927
| style="text-align:center;" | 28.927
19.772
| style="text-align:center;" | 1793.478
| style="text-align:center;" | 1793.478
1225.8555
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|-
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 896.777
| style="text-align:center;" | 896.777
612.953
| style="text-align:center;" | 108.402
| style="text-align:center;" | 108.402
74.093
| style="text-align:center;" | 33.368
| style="text-align:center;" | 33.368
20.207
| style="text-align:center;" | 1793.553
| style="text-align:center;" | 1793.553
1225.907
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| style="text-align:center;" | 149\316
| style="text-align:center;" | 149\316
| style="text-align:center;" | 896.808
| style="text-align:center;" | 896.808
612.975
| style="text-align:center;" | 108.339
| style="text-align:center;" | 108.339
74.051
| style="text-align:center;" | 30.094
| style="text-align:center;" | 30.094
20.57
| style="text-align:center;" | 1793.616
| style="text-align:center;" | 1793.616
1225.949
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| style="text-align:center;" |  
|-
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 896.857
| style="text-align:center;" | 896.857
613.008
| style="text-align:center;" | 108.241
| style="text-align:center;" | 108.241
73.984
| style="text-align:center;" | 30.926
| style="text-align:center;" | 30.926
21.138
| style="text-align:center;" | 1793.714
| style="text-align:center;" | 1793.714
1226.016
| style="text-align:center;" | L=7 s=2
| style="text-align:center;" | L=7 s=2
|-
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| style="text-align:center;" | 141\299
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| style="text-align:center;" | 896.9085
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613.0435
| style="text-align:center;" | 108.138
| style="text-align:center;" | 108.138
73.913
| style="text-align:center;" | 31.805
| style="text-align:center;" | 31.805
21.739
| style="text-align:center;" | 1793.817
| style="text-align:center;" | 1793.817
1226.087
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 896.945
| style="text-align:center;" | 896.945
613.068
| style="text-align:center;" | 108.066
| style="text-align:center;" | 108.066
73.864
| style="text-align:center;" | 32.42
| style="text-align:center;" | 32.42
22.159
| style="text-align:center;" | 1793.889
| style="text-align:center;" | 1793.889
1226.136
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| style="text-align:center;" | 108\229
| style="text-align:center;" | 108\229
| style="text-align:center;" | 896.992
| style="text-align:center;" | 896.992
613.1
| style="text-align:center;" | 107.971
| style="text-align:center;" | 107.971
73.799
| style="text-align:center;" | 33.222
| style="text-align:center;" | 33.222
22.707
| style="text-align:center;" | 1793.984
| style="text-align:center;" | 1793.984
1226.201
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 897.149
| style="text-align:center;" | 897.149
613.2075
| style="text-align:center;" | 107.658
| style="text-align:center;" | 107.658
73.585
| style="text-align:center;" | 35.886
| style="text-align:center;" | 35.886
24.528
| style="text-align:center;" | 1794.297
| style="text-align:center;" | 1794.297
1226.415
| style="text-align:center;" | L=3 s=1
| style="text-align:center;" | L=3 s=1
|-
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| style="text-align:center;" | 117\248
| style="text-align:center;" | 117\248
| style="text-align:center;" | 897.293
| style="text-align:center;" | 897.293
613.3065
| style="text-align:center;" | 107.368
| style="text-align:center;" | 107.368
73.381
| style="text-align:center;" | 38.346
| style="text-align:center;" | 38.346
26.21
| style="text-align:center;" | 1794.587
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1226.613
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| style="text-align:center;" |  
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| style="text-align:center;" | 897.333
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613.333
| style="text-align:center;" | 107.29
| style="text-align:center;" | 107.29
73.333
| style="text-align:center;" | 39.0145
| style="text-align:center;" | 39.0145
26.667
| style="text-align:center;" | 1794.665
| style="text-align:center;" | 1794.665
1226.667
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| style="text-align:center;" | 159\337
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613.353
| style="text-align:center;" | 107.232
| style="text-align:center;" | 107.232
73.294
| style="text-align:center;" | 39.5065
| style="text-align:center;" | 39.5065
27.003
| style="text-align:center;" | 1794.723
| style="text-align:center;" | 1794.723
1226.706
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 897.401
| style="text-align:center;" | 897.401
613.38
| style="text-align:center;" | 107.152
| style="text-align:center;" | 107.152
73.239
| style="text-align:center;" | 40.182
| style="text-align:center;" | 40.182
27.465
| style="text-align:center;" | 1794.803
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1226.761
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| style="text-align:center;" | 176\373
| style="text-align:center;" | 897.437
| style="text-align:center;" | 897.437
613.405
| style="text-align:center;" | 107.081
| style="text-align:center;" | 107.081
73.19
| style="text-align:center;" | 40.793
| style="text-align:center;" | 40.793
27.397
| style="text-align:center;" | 1794.874
| style="text-align:center;" | 1794.874
1226.81
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 897.459
| style="text-align:center;" | 897.459
613.42
| style="text-align:center;" | 107.036
| style="text-align:center;" | 107.036
73.16
| style="text-align:center;" | 41.168
| style="text-align:center;" | 41.168
28.1385
| style="text-align:center;" | 1794.919
| style="text-align:center;" | 1794.919
1226.84
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| style="text-align:center;" | 151\320
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| style="text-align:center;" | 897.485
| style="text-align:center;" | 897.485
613.4375
| style="text-align:center;" | 106.985
| style="text-align:center;" | 106.985
73.125
| style="text-align:center;" | 41.605
| style="text-align:center;" | 41.605
28.4375
| style="text-align:center;" | 1794.97
| style="text-align:center;" | 1794.97
1226.875
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 897.552
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613.483
| style="text-align:center;" | 106.851
| style="text-align:center;" | 106.851
73.034
| style="text-align:center;" | 42.741
| style="text-align:center;" | 42.741
29.2135
| style="text-align:center;" | 1795.104
| style="text-align:center;" | 1795.104
1226.966
| style="text-align:center;" | L=5 s=2
| style="text-align:center;" | L=5 s=2
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| style="text-align:center;" | 143\303
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| style="text-align:center;" | 897.622
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613.531
| style="text-align:center;" | 106.71
| style="text-align:center;" | 106.71
72.947
| style="text-align:center;" | 43.94
| style="text-align:center;" | 43.94
30.033
| style="text-align:center;" | 1795.245
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1227.063
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 897.652
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613.551
| style="text-align:center;" | 106.652
| style="text-align:center;" | 106.652
72.897
| style="text-align:center;" | 44.438
| style="text-align:center;" | 44.438
30.374
| style="text-align:center;" | 1795.303
| style="text-align:center;" | 1795.303
1227.103
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613.569
| style="text-align:center;" | 106.599
| style="text-align:center;" | 106.599
72.86
| style="text-align:center;" | 44.884
| style="text-align:center;" | 44.884
30.6785
| style="text-align:center;" | 1795.356
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1227.14
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 897.723
| style="text-align:center;" | 897.723
613.6
| style="text-align:center;" | 106.5095
| style="text-align:center;" | 106.5095
72.8
| style="text-align:center;" | 45.647
| style="text-align:center;" | 45.647
31.2
| style="text-align:center;" | 1795.446
| style="text-align:center;" | 1795.446
1227.2
| style="text-align:center;" | L=7 s=3
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| style="text-align:center;" | 897.776
| style="text-align:center;" | 897.776
613.636
| style="text-align:center;" | 106.403
| style="text-align:center;" | 106.403
72.727
| style="text-align:center;" | 46.551
| style="text-align:center;" | 46.551
31.818
| style="text-align:center;" | 1795.552
| style="text-align:center;" | 1795.552
1227.273
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 897.817
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613.665
| style="text-align:center;" | 106.3205
| style="text-align:center;" | 106.3205
72.671
| style="text-align:center;" | 47.2535
| style="text-align:center;" | 47.2535
32.298
| style="text-align:center;" | 1795.635
| style="text-align:center;" | 1795.635
1227.329
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| style="text-align:center;" | 93\197
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| style="text-align:center;" | 897.877
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613.706
| style="text-align:center;" | 106.2005
| style="text-align:center;" | 106.2005
72.589
| style="text-align:center;" | 48.273
| style="text-align:center;" | 48.273
32.995
| style="text-align:center;" | 1795.754
| style="text-align:center;" | 1795.754
1227.411
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| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 898.145
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613.889
| style="text-align:center;" | 105.664
| style="text-align:center;" | 105.664
72.222
| style="text-align:center;" | 52.832
| style="text-align:center;" | 52.832
36.111
| style="text-align:center;" | 1796.291
| style="text-align:center;" | 1796.291
1227.778
| style="text-align:center;" | L=2 s=1
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| style="text-align:center;" | 94\199
| style="text-align:center;" | 898.411
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614.07
| style="text-align:center;" | 105.133
| style="text-align:center;" | 105.133
71.859
| style="text-align:center;" | 57.345
| style="text-align:center;" | 57.345
39.196
| style="text-align:center;" | 1796.822
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1228.141
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| style="text-align:center;" | 898.4695
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614.11
| style="text-align:center;" | 105.016
| style="text-align:center;" | 105.016
71.779
| style="text-align:center;" | 58.342
| style="text-align:center;" | 58.342
39.877
| style="text-align:center;" | 1796.939
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1228.221
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| style="text-align:center;" | 137\290
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614.138
| style="text-align:center;" | 104.935
| style="text-align:center;" | 104.935
71.732
| style="text-align:center;" | 59.026
| style="text-align:center;" | 59.026
40.345
| style="text-align:center;" | 1797.02
| style="text-align:center;" | 1797.02
1228.276
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 486: Line 639:
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 898.561
| style="text-align:center;" | 898.561
614.173
| style="text-align:center;" | 104.832
| style="text-align:center;" | 104.832
71.654
| style="text-align:center;" | 59.904
| style="text-align:center;" | 59.904
40.945
| style="text-align:center;" | 1797.123
| style="text-align:center;" | 1797.123
1228.346
| style="text-align:center;" | L=7 s=4
| style="text-align:center;" | L=7 s=4
|-
|-
Line 499: Line 656:
| style="text-align:center;" | 163\345
| style="text-align:center;" | 163\345
| style="text-align:center;" | 898.605
| style="text-align:center;" | 898.605
614.203
| style="text-align:center;" | 104.745
| style="text-align:center;" | 104.745
71.594
| style="text-align:center;" | 60.642
| style="text-align:center;" | 60.642
41.449
| style="text-align:center;" | 1797.201
| style="text-align:center;" | 1797.201
1228.406
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 512: Line 673:
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 898.63
| style="text-align:center;" | 898.63
614.22
| style="text-align:center;" | 104.695
| style="text-align:center;" | 104.695
71.56
| style="text-align:center;" | 61.072
| style="text-align:center;" | 61.072
41.743
| style="text-align:center;" | 1797.26
| style="text-align:center;" | 1797.26
1228.44
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 525: Line 690:
| style="text-align:center;" | 146\309
| style="text-align:center;" | 146\309
| style="text-align:center;" | 898.658
| style="text-align:center;" | 898.658
614.2395
| style="text-align:center;" | 104.638
| style="text-align:center;" | 104.638
71.521
| style="text-align:center;" | 61.552
| style="text-align:center;" | 61.552
42.071
| style="text-align:center;" | 1797.317
| style="text-align:center;" | 1797.317
1228.479
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 538: Line 707:
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 898.726
| style="text-align:center;" | 898.726
614.286
| style="text-align:center;" | 104.503
| style="text-align:center;" | 104.503
71.571
| style="text-align:center;" | 62.702
| style="text-align:center;" | 62.702
42.857
| style="text-align:center;" | 1797.452
| style="text-align:center;" | 1797.452
1228.571
| style="text-align:center;" | L=5 s=3
| style="text-align:center;" | L=5 s=3
|-
|-
Line 551: Line 724:
| style="text-align:center;" | 155\328
| style="text-align:center;" | 155\328
| style="text-align:center;" | 898.79
| style="text-align:center;" | 898.79
614.329
| style="text-align:center;" | 104.376
| style="text-align:center;" | 104.376
71.3415
| style="text-align:center;" | 63.785
| style="text-align:center;" | 63.785
43.598
| style="text-align:center;" | 1797.579
| style="text-align:center;" | 1797.579
1228.6585
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 564: Line 741:
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 898.814
| style="text-align:center;" | 898.814
614.346
| style="text-align:center;" | 104.327
| style="text-align:center;" | 104.327
71.308
| style="text-align:center;" | 64.201
| style="text-align:center;" | 64.201
43.882
| style="text-align:center;" | 1797.628
| style="text-align:center;" | 1797.628
1228.692
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 577: Line 758:
| style="text-align:center;" | 181\383
| style="text-align:center;" | 181\383
| style="text-align:center;" | 898.835
| style="text-align:center;" | 898.835
614.36
| style="text-align:center;" | 104.285
| style="text-align:center;" | 104.285
71.28
| style="text-align:center;" | 64.557
| style="text-align:center;" | 64.557
44.125
| style="text-align:center;" | 1797.67
| style="text-align:center;" | 1797.67
1228.72
| style="text-align:center;" | Golden Super-Arcturus[19] is near here
| style="text-align:center;" | Golden Super-Arcturus[19] is near here
|-
|-
Line 590: Line 775:
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 898.869
| style="text-align:center;" | 898.869
614.384
| style="text-align:center;" | 104.217
| style="text-align:center;" | 104.217
71.231
| style="text-align:center;" | 65.135
| style="text-align:center;" | 65.135
44.5205
| style="text-align:center;" | 1797.738
| style="text-align:center;" | 1797.738
1228.769
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 603: Line 792:
| style="text-align:center;" | 164\347
| style="text-align:center;" | 164\347
| style="text-align:center;" | 898.901
| style="text-align:center;" | 898.901
614.409
| style="text-align:center;" | 104.142
| style="text-align:center;" | 104.142
71.182
| style="text-align:center;" | 65.774
| style="text-align:center;" | 65.774
44.957
| style="text-align:center;" | 1797.813
| style="text-align:center;" | 1797.813
1228.818
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 616: Line 809:
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 898.934
| style="text-align:center;" | 898.934
614.428
| style="text-align:center;" | 104.087
| style="text-align:center;" | 104.087
71.144
| style="text-align:center;" | 66.237
| style="text-align:center;" | 66.237
45.274
| style="text-align:center;" | 1797.868
| style="text-align:center;" | 1797.868
1228.856
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 629: Line 826:
| style="text-align:center;" | 121\256
| style="text-align:center;" | 121\256
| style="text-align:center;" | 898.971
| style="text-align:center;" | 898.971
614.453
| style="text-align:center;" | 104.013
| style="text-align:center;" | 104.013
71.094
| style="text-align:center;" | 66.866
| style="text-align:center;" | 66.866
45.703
| style="text-align:center;" | 1797.942
| style="text-align:center;" | 1797.942
1228.906
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 642: Line 843:
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 899.106
| style="text-align:center;" | 899.106
614.5455
| style="text-align:center;" | 103.743
| style="text-align:center;" | 103.743
70.909
| style="text-align:center;" | 69.162
| style="text-align:center;" | 69.162
47.273
| style="text-align:center;" | 1798.212
| style="text-align:center;" | 1798.212
1229.091
| style="text-align:center;" | L=3 s=2
| style="text-align:center;" | L=3 s=2
|-
|-
Line 655: Line 860:
| style="text-align:center;" | 113\239
| style="text-align:center;" | 113\239
| style="text-align:center;" | 899.251
| style="text-align:center;" | 899.251
614.644
| style="text-align:center;" | 103.454
| style="text-align:center;" | 103.454
70.711
| style="text-align:center;" | 71.622
| style="text-align:center;" | 71.622
48.954
| style="text-align:center;" | 1798.501
| style="text-align:center;" | 1798.501
1229.289
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 668: Line 877:
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 899.294
| style="text-align:center;" | 899.294
614.674
| style="text-align:center;" | 103.367
| style="text-align:center;" | 103.367
70.652
| style="text-align:center;" | 72.357
| style="text-align:center;" | 72.357
49.4565
| style="text-align:center;" | 1798.589
| style="text-align:center;" | 1798.589
1229.348
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 681: Line 894:
| style="text-align:center;" | 148\313
| style="text-align:center;" | 148\313
| style="text-align:center;" | 899.327
| style="text-align:center;" | 899.327
614.6965
| style="text-align:center;" | 103.301
| style="text-align:center;" | 103.301
70.607
| style="text-align:center;" | 72.918
| style="text-align:center;" | 72.918
49.84
| style="text-align:center;" | 1798.654
| style="text-align:center;" | 1798.654
1229.393
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 694: Line 911:
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 899.374
| style="text-align:center;" | 899.374
614.729
| style="text-align:center;" | 103.207
| style="text-align:center;" | 103.207
70.543
| style="text-align:center;" | 73.719
| style="text-align:center;" | 73.719
50.388
| style="text-align:center;" | 1798.748
| style="text-align:center;" | 1798.748
1229.457
| style="text-align:center;" | L=7 s=5
| style="text-align:center;" | L=7 s=5
|-
|-
Line 707: Line 928:
| style="text-align:center;" | 157\332
| style="text-align:center;" | 157\332
| style="text-align:center;" | 899.4185
| style="text-align:center;" | 899.4185
614.759
| style="text-align:center;" | 103.118
| style="text-align:center;" | 103.118
70.482
| style="text-align:center;" | 74.474
| style="text-align:center;" | 74.474
50.904
| style="text-align:center;" | 1798.837
| style="text-align:center;" | 1798.837
1229.518
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 720: Line 945:
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 899.447
| style="text-align:center;" | 899.447
614.778
| style="text-align:center;" | 103.062
| style="text-align:center;" | 103.062
70.443
| style="text-align:center;" | 74.954
| style="text-align:center;" | 74.954
51.2315
| style="text-align:center;" | 1798.893
| style="text-align:center;" | 1798.893
1229.557
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 733: Line 962:
| style="text-align:center;" | 131\277
| style="text-align:center;" | 131\277
| style="text-align:center;" | 899.4805
| style="text-align:center;" | 899.4805
614.801
| style="text-align:center;" | 102.994
| style="text-align:center;" | 102.994
70.397
| style="text-align:center;" | 75.529
| style="text-align:center;" | 75.529
51.6245
| style="text-align:center;" | 1798.961
| style="text-align:center;" | 1798.961
1229.603
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 746: Line 979:
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 899.573
| style="text-align:center;" | 899.573
614.865
| style="text-align:center;" | 102.808
| style="text-align:center;" | 102.808
70.37
| style="text-align:center;" | 77.106
| style="text-align:center;" | 77.106
52.703
| style="text-align:center;" | 1799.147
| style="text-align:center;" | 1799.147
1229.63
| style="text-align:center;" | L=4 s=3
| style="text-align:center;" | L=4 s=3
|-
|-
Line 759: Line 996:
| style="text-align:center;" | 114/241
| style="text-align:center;" | 114/241
| style="text-align:center;" | 899.68
| style="text-align:center;" | 899.68
614.938
| style="text-align:center;" | 102.595
| style="text-align:center;" | 102.595
70.1345
| style="text-align:center;" | 78.919
| style="text-align:center;" | 78.919
53.942
| style="text-align:center;" | 1799.36
| style="text-align:center;" | 1799.36
1229.8655
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 772: Line 1,013:
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" | 899.727
| style="text-align:center;" | 899.727
614.97
| style="text-align:center;" | 102.501
| style="text-align:center;" | 102.501
70.06
| style="text-align:center;" | 79.723
| style="text-align:center;" | 79.723
54.491
| style="text-align:center;" | 1799.454
| style="text-align:center;" | 1799.454
1229.94
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
Line 785: Line 1,030:
| style="text-align:center;" | 123\260
| style="text-align:center;" | 123\260
| style="text-align:center;" | 899.771
| style="text-align:center;" | 899.771
615
| style="text-align:center;" | 102.413
| style="text-align:center;" | 102.413
70
| style="text-align:center;" | 80.467
| style="text-align:center;" | 80.467
55
| style="text-align:center;" | 1799.542
| style="text-align:center;" | 1799.542
1230
| 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;" | 899.85
| style="text-align:center;" | 899.85
615.054
| style="text-align:center;" | 102.256
| style="text-align:center;" | 102.256
69.8925
| style="text-align:center;" | 81.8045
| style="text-align:center;" | 81.8045
55.914
| style="text-align:center;" | 1799.699
| style="text-align:center;" | 1799.699
1230.1075
| 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;" | 97\205
| style="text-align:center;" | 97\205
| style="text-align:center;" | 899.949
| style="text-align:center;" | 899.949
615.122
| style="text-align:center;" | 102.056
| style="text-align:center;" | 102.056
69.756
| style="text-align:center;" | 83.5005
| style="text-align:center;" | 83.5005
57.073
| style="text-align:center;" | 1799.899
| style="text-align:center;" | 1799.899
1230.244
| 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;" | 900.032
| style="text-align:center;" | 900.032
615.179
| style="text-align:center;" | 101.89
| style="text-align:center;" | 101.89
69.643
| style="text-align:center;" | 84.909
| style="text-align:center;" | 84.909
58.036
| style="text-align:center;" | 1800.065
| style="text-align:center;" | 1800.065
1230.357
| 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;" | 62\131
| style="text-align:center;" | 62\131
| style="text-align:center;" | 900.162
| style="text-align:center;" | 900.162
615.267
| style="text-align:center;" | 101.631
| style="text-align:center;" | 101.631
69.466
| style="text-align:center;" | 87.112
| style="text-align:center;" | 87.112
59.542
| style="text-align:center;" | 1800.324
| style="text-align:center;" | 1800.324
1230.534
| 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;" | 900.926
| style="text-align:center;" | 900.926
615.7895
| colspan="2" style="text-align:center;" | 100.103
| colspan="2" style="text-align:center;" | 100.103
68.421
| | 1801.852
| | 1801.852
1231.579
| style="text-align:center;" | L=1 s=1
| style="text-align:center;" | L=1 s=1
|}
|}
[[Category:Arcturus]]
[[Category:Abstract MOS patterns]]

Latest revision as of 07:47, 15 December 2024

↖ 16L 1s⟨3/1⟩ ↑ 17L 1s⟨3/1⟩ 18L 1s⟨3/1⟩ ↗
← 16L 2s⟨3/1⟩ 17L 2s (3/1-equivalent) 18L 2s⟨3/1⟩ →
↙ 16L 3s⟨3/1⟩ ↓ 17L 3s⟨3/1⟩ 18L 3s⟨3/1⟩ ↘ 
┌╥╥╥╥╥╥╥╥╥┬╥╥╥╥╥╥╥╥┬┐
│║║║║║║║║║│║║║║║║║║││
│││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLLLLLLsLLLLLLLLs
sLLLLLLLLsLLLLLLLLL
Equave 3/1 (1902.0 ¢)
Period 3/1 (1902.0 ¢)
Generator size(edt)
Bright 10\19 to 9\17 (1001.0 ¢ to 1006.9 ¢)
Dark 8\17 to 9\19 (895.0 ¢ to 900.9 ¢)
Related MOS scales
Parent 2L 15s⟨3/1⟩
Sister 2L 17s⟨3/1⟩
Daughters 19L 17s⟨3/1⟩, 17L 19s⟨3/1⟩
Neutralized 15L 4s⟨3/1⟩
2-Flought 36L 2s⟨3/1⟩, 17L 21s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1) 10\19 (1001.0 ¢)
Supersoft (L:s = 4:3) 39\74 (1002.4 ¢)
Soft (L:s = 3:2) 29\55 (1002.8 ¢)
Semisoft (L:s = 5:3) 48\91 (1003.2 ¢)
Basic (L:s = 2:1) 19\36 (1003.8 ¢)
Semihard (L:s = 5:2) 47\89 (1004.4 ¢)
Hard (L:s = 3:1) 28\53 (1004.8 ¢)
Superhard (L:s = 4:1) 37\70 (1005.3 ¢)
Collapsed (L:s = 1:0) 9\17 (1006.9 ¢)

17L 2s⟨3/1⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 17 large steps and 2 small steps, repeating every interval of 3/1 (1902.0 ¢). Generators that produce this scale range from 1001 ¢ to 1006.9 ¢, or from 895 ¢ to 900.9 ¢.

Using a generator as which is as sharp as possible for an 'ordinary' ~5:3, this MOS is the most complex parent scale for an Arcturus-like temperament. It is also the most complex parent MOS for a temperament where two generators make an "ordinary" ~14:5 (the simplest is the proper Arcturus scale).

Modes

Modes of 17L 2s⟨3/1⟩
UDP Cyclic
order		 Step
pattern
18|0 1 LLLLLLLLLsLLLLLLLLs
17|1 11 LLLLLLLLsLLLLLLLLLs
16|2 2 LLLLLLLLsLLLLLLLLsL
15|3 12 LLLLLLLsLLLLLLLLLsL
14|4 3 LLLLLLLsLLLLLLLLsLL
13|5 13 LLLLLLsLLLLLLLLLsLL
12|6 4 LLLLLLsLLLLLLLLsLLL
11|7 14 LLLLLsLLLLLLLLLsLLL
10|8 5 LLLLLsLLLLLLLLsLLLL
9|9 15 LLLLsLLLLLLLLLsLLLL
8|10 6 LLLLsLLLLLLLLsLLLLL
7|11 16 LLLsLLLLLLLLLsLLLLL
6|12 7 LLLsLLLLLLLLsLLLLLL
5|13 17 LLsLLLLLLLLLsLLLLLL
4|14 8 LLsLLLLLLLLsLLLLLLL
3|15 18 LsLLLLLLLLLsLLLLLLL
2|16 9 LsLLLLLLLLsLLLLLLLL
1|17 19 sLLLLLLLLLsLLLLLLLL
0|18 10 sLLLLLLLLsLLLLLLLLL

Intervals

Intervals of 17L 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 100.1 ¢
Major 1-mosstep M1ms L 100.1 ¢ to 111.9 ¢
2-mosstep Minor 2-mosstep m2ms L + s 111.9 ¢ to 200.2 ¢
Major 2-mosstep M2ms 2L 200.2 ¢ to 223.8 ¢
3-mosstep Minor 3-mosstep m3ms 2L + s 223.8 ¢ to 300.3 ¢
Major 3-mosstep M3ms 3L 300.3 ¢ to 335.6 ¢
4-mosstep Minor 4-mosstep m4ms 3L + s 335.6 ¢ to 400.4 ¢
Major 4-mosstep M4ms 4L 400.4 ¢ to 447.5 ¢
5-mosstep Minor 5-mosstep m5ms 4L + s 447.5 ¢ to 500.5 ¢
Major 5-mosstep M5ms 5L 500.5 ¢ to 559.4 ¢
6-mosstep Minor 6-mosstep m6ms 5L + s 559.4 ¢ to 600.6 ¢
Major 6-mosstep M6ms 6L 600.6 ¢ to 671.3 ¢
7-mosstep Minor 7-mosstep m7ms 6L + s 671.3 ¢ to 700.7 ¢
Major 7-mosstep M7ms 7L 700.7 ¢ to 783.2 ¢
8-mosstep Minor 8-mosstep m8ms 7L + s 783.2 ¢ to 800.8 ¢
Major 8-mosstep M8ms 8L 800.8 ¢ to 895.0 ¢
9-mosstep Perfect 9-mosstep P9ms 8L + s 895.0 ¢ to 900.9 ¢
Augmented 9-mosstep A9ms 9L 900.9 ¢ to 1006.9 ¢
10-mosstep Diminished 10-mosstep d10ms 8L + 2s 895.0 ¢ to 1001.0 ¢
Perfect 10-mosstep P10ms 9L + s 1001.0 ¢ to 1006.9 ¢
11-mosstep Minor 11-mosstep m11ms 9L + 2s 1006.9 ¢ to 1101.1 ¢
Major 11-mosstep M11ms 10L + s 1101.1 ¢ to 1118.8 ¢
12-mosstep Minor 12-mosstep m12ms 10L + 2s 1118.8 ¢ to 1201.2 ¢
Major 12-mosstep M12ms 11L + s 1201.2 ¢ to 1230.7 ¢
13-mosstep Minor 13-mosstep m13ms 11L + 2s 1230.7 ¢ to 1301.3 ¢
Major 13-mosstep M13ms 12L + s 1301.3 ¢ to 1342.6 ¢
14-mosstep Minor 14-mosstep m14ms 12L + 2s 1342.6 ¢ to 1401.4 ¢
Major 14-mosstep M14ms 13L + s 1401.4 ¢ to 1454.4 ¢
15-mosstep Minor 15-mosstep m15ms 13L + 2s 1454.4 ¢ to 1501.5 ¢
Major 15-mosstep M15ms 14L + s 1501.5 ¢ to 1566.3 ¢
16-mosstep Minor 16-mosstep m16ms 14L + 2s 1566.3 ¢ to 1601.6 ¢
Major 16-mosstep M16ms 15L + s 1601.6 ¢ to 1678.2 ¢
17-mosstep Minor 17-mosstep m17ms 15L + 2s 1678.2 ¢ to 1701.7 ¢
Major 17-mosstep M17ms 16L + s 1701.7 ¢ to 1790.1 ¢
18-mosstep Minor 18-mosstep m18ms 16L + 2s 1790.1 ¢ to 1801.9 ¢
Major 18-mosstep M18ms 17L + s 1801.9 ¢ to 1902.0 ¢
19-mosstep Perfect 19-mosstep P19ms 17L + 2s 1902.0 ¢

Scale tree

Generator cents L s 2g Notes
8\17 895.038

611.765

111.88

76.471

0.00 1790.075

1223.529

L=1 s=0
57\121 895.962

612.397

110.0305

75.207

15.719

10.744

1791.925

1224.793

L=7 s=1
49\104 896.113

612.5

109.728

75

18.288

12.5

1792.227

1225

L=6 s=1
90\191 896.209

612.565

109.537

74.869

19.916

13.913

1792.418

1225.131

41\87 896.324

612.644

109.308

74.713

21.862

14.9425

1792.647

1225.287

L=5 s=1
115\244 896.413

612.705

109.129

74.59

23.385

15.984

1792.826

1225.41

74\157 896.463

612.739

109.029

74.522

24.229

16.5605

1792.926

1225.478

107\227 896.516

612.775

108.9225

74.449

25.136

17.181

1793.032

1225.551

33\70 896.636

612.857

108.683

74.286

27.171

18.571

1793.272

1225.714

L=4 s=1
124\263 896.739

612.928

108.4765

74.1445

28.927

19.772

1793.478

1225.8555

91\193 896.777

612.953

108.402

74.093

33.368

20.207

1793.553

1225.907

149\316 896.808

612.975

108.339

74.051

30.094

20.57

1793.616

1225.949

58\123 896.857

613.008

108.241

73.984

30.926

21.138

1793.714

1226.016

L=7 s=2
141\299 896.9085

613.0435

108.138

73.913

31.805

21.739

1793.817

1226.087

83\176 896.945

613.068

108.066

73.864

32.42

22.159

1793.889

1226.136

108\229 896.992

613.1

107.971

73.799

33.222

22.707

1793.984

1226.201

25\53 897.149

613.2075

107.658

73.585

35.886

24.528

1794.297

1226.415

L=3 s=1
117\248 897.293

613.3065

107.368

73.381

38.346

26.21

1794.587

1226.613

92\195 897.333

613.333

107.29

73.333

39.0145

26.667

1794.665

1226.667

159\337 897.362

613.353

107.232

73.294

39.5065

27.003

1794.723

1226.706

67\142 897.401

613.38

107.152

73.239

40.182

27.465

1794.803

1226.761

176\373 897.437

613.405

107.081

73.19

40.793

27.397

1794.874

1226.81

109\231 897.459

613.42

107.036

73.16

41.168

28.1385

1794.919

1226.84

151\320 897.485

613.4375

106.985

73.125

41.605

28.4375

1794.97

1226.875

42\89 897.552

613.483

106.851

73.034

42.741

29.2135

1795.104

1226.966

L=5 s=2
143\303 897.622

613.531

106.71

72.947

43.94

30.033

1795.245

1227.063

101\214 897.652

613.551

106.652

72.897

44.438

30.374

1795.303

1227.103

160\339 897.678

613.569

106.599

72.86

44.884

30.6785

1795.356

1227.14

59\125 897.723

613.6

106.5095

72.8

45.647

31.2

1795.446

1227.2

L=7 s=3
135\286 897.776

613.636

106.403

72.727

46.551

31.818

1795.552

1227.273

76\161 897.817

613.665

106.3205

72.671

47.2535

32.298

1795.635

1227.329

93\197 897.877

613.706

106.2005

72.589

48.273

32.995

1795.754

1227.411

17\36 898.145

613.889

105.664

72.222

52.832

36.111

1796.291

1227.778

L=2 s=1
94\199 898.411

614.07

105.133

71.859

57.345

39.196

1796.822

1228.141

77\163 898.4695

614.11

105.016

71.779

58.342

39.877

1796.939

1228.221

137\290 898.51

614.138

104.935

71.732

59.026

40.345

1797.02

1228.276

60\127 898.561

614.173

104.832

71.654

59.904

40.945

1797.123

1228.346

L=7 s=4
163\345 898.605

614.203

104.745

71.594

60.642

41.449

1797.201

1228.406

103\218 898.63

614.22

104.695

71.56

61.072

41.743

1797.26

1228.44

146\309 898.658

614.2395

104.638

71.521

61.552

42.071

1797.317

1228.479

43\91 898.726

614.286

104.503

71.571

62.702

42.857

1797.452

1228.571

L=5 s=3
155\328 898.79

614.329

104.376

71.3415

63.785

43.598

1797.579

1228.6585

112\237 898.814

614.346

104.327

71.308

64.201

43.882

1797.628

1228.692

181\383 898.835

614.36

104.285

71.28

64.557

44.125

1797.67

1228.72

Golden Super-Arcturus[19] is near here
69\146 898.869

614.384

104.217

71.231

65.135

44.5205

1797.738

1228.769

164\347 898.901

614.409

104.142

71.182

65.774

44.957

1797.813

1228.818

95\201 898.934

614.428

104.087

71.144

66.237

45.274

1797.868

1228.856

121\256 898.971

614.453

104.013

71.094

66.866

45.703

1797.942

1228.906

26\55 899.106

614.5455

103.743

70.909

69.162

47.273

1798.212

1229.091

L=3 s=2
113\239 899.251

614.644

103.454

70.711

71.622

48.954

1798.501

1229.289

87\184 899.294

614.674

103.367

70.652

72.357

49.4565

1798.589

1229.348

148\313 899.327

614.6965

103.301

70.607

72.918

49.84

1798.654

1229.393

61\129 899.374

614.729

103.207

70.543

73.719

50.388

1798.748

1229.457

L=7 s=5
157\332 899.4185

614.759

103.118

70.482

74.474

50.904

1798.837

1229.518

96\203 899.447

614.778

103.062

70.443

74.954

51.2315

1798.893

1229.557

131\277 899.4805

614.801

102.994

70.397

75.529

51.6245

1798.961

1229.603

35\74 899.573

614.865

102.808

70.37

77.106

52.703

1799.147

1229.63

L=4 s=3
114/241 899.68

614.938

102.595

70.1345

78.919

53.942

1799.36

1229.8655

79\167 899.727

614.97

102.501

70.06

79.723

54.491

1799.454

1229.94

123\260 899.771

615

102.413

70

80.467

55

1799.542

1230

44\93 899.85

615.054

102.256

69.8925

81.8045

55.914

1799.699

1230.1075

L=5 s=4
97\205 899.949

615.122

102.056

69.756

83.5005

57.073

1799.899

1230.244

53\112 900.032

615.179

101.89

69.643

84.909

58.036

1800.065

1230.357

L=6 s=5
62\131 900.162

615.267

101.631

69.466

87.112

59.542

1800.324

1230.534

L=7 s=6
9\19 900.926

615.7895

100.103

68.421

1801.852

1231.579

L=1 s=1
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