Arcturus: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,262 edits
m Added 2 categories
CompactStar (talk | contribs)
autopatrolled
5,084 edits
Replaced content with "'''Arcturus''' is a no-twos temperament which tempers out the comma 15625/15309. Having an ~5:3 as a generator, this temperament is the application of the Pythagorean prin..."
Tag: Replaced
Line 11: Line 11:
[[Anti-Arcturus|Anti-chromatic]]
[[Anti-Arcturus|Anti-chromatic]]


{| class="wikitable"
{{Scale tree|11L 2s|depth=6}}
|-
! colspan="7" | Generator
! | cents
hekts
! | L
! | s
! | 2g
! | Notes
|-
| style="text-align:center;" | 6\13
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 877.825
600
| style="text-align:center;" | 146.304
100
| style="text-align:center;" | 0
| style="text-align:center;" | 1755.651
1200
| style="text-align:center;" | L=1 s=0
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 43\93
| style="text-align:center;" | 879.399
601.075
| style="text-align:center;" | 143.158
97.8495
| style="text-align:center;" | 20.451
13.9785
| style="text-align:center;" | 1758.797
1202.151
| style="text-align:center;" | L=7 s=1
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 37\80
| style="text-align:center;" |
| style="text-align:center;" | 879.654
601.25
| style="text-align:center;" | 142.647
97.5
| style="text-align:center;" | 23.774
16.25
| style="text-align:center;" | 1759.38
1202.5
| style="text-align:center;" | L=6 s=1
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 68\147
| style="text-align:center;" | 879.816
601.3605
| style="text-align:center;" | 142.323
97.279
| style="text-align:center;" | 25.877
17.687
| style="text-align:center;" | 1759.632
1202.721
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 31\67
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 880.009
601.4925
| style="text-align:center;" | 141.937
97.015
| style="text-align:center;" | 28.387
19.403
| style="text-align:center;" | 1760.081
1202.985
| style="text-align:center;" | L=5 s=1
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 87\188
| style="text-align:center;" | 880.16
601.596
| style="text-align:center;" | 141.634
96.8085
| style="text-align:center;" | 30.35
20.745
| style="text-align:center;" | 1760.32
1203.191
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 56\121
| style="text-align:center;" |
| style="text-align:center;" | 880.243
601.653
| style="text-align:center;" | 141.468
96.694
| style="text-align:center;" | 31.437
21.488
| style="text-align:center;" | 1760.487
1203.306
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 81\175
| style="text-align:center;" | 880.3335
601.714
| style="text-align:center;" | 141.288
96.571
| style="text-align:center;" | 32.605
22.286
| style="text-align:center;" | 1760.667
1203.429
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 25\54
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 880.535
601.852
| style="text-align:center;" | 140.886
96.296
| style="text-align:center;" | 35.221
24.074
| style="text-align:center;" | 1761.069
1203.704
| style="text-align:center;" | L=4 s=1
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 94\203
| style="text-align:center;" | 880.708
601.97
| style="text-align:center;" | 140.5385
96.059
| style="text-align:center;" | 37.477
25.616
| style="text-align:center;" | 1761.4165
1203.971
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 69\149
| style="text-align:center;" |
| style="text-align:center;" | 880.711
602.013
| style="text-align:center;" | 140.413
95.973
| style="text-align:center;" | 38.294
26.1745
| style="text-align:center;" | 1761.542
1204.027
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 113\244
| style="text-align:center;" | 880.823
602.049
| style="text-align:center;" | 140.308
95.902
| style="text-align:center;" | 38.9745
26.639
| style="text-align:center;" | 1761.647
1204.098
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 44\95
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 880.9055
602.105
| style="text-align:center;" | 140.144
95.7895
| style="text-align:center;" | 40.041
27.368
| style="text-align:center;" | 1761.811
1204.2105
| style="text-align:center;" | L=7 s=2
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 107\231
| style="text-align:center;" | 880.992
602.1645
| style="text-align:center;" | 139.971
95.671
| style="text-align:center;" | 41.168
28.1385
| style="text-align:center;" | 1761.984
1204.329.
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 63\136
| style="text-align:center;" |
| style="text-align:center;" | 881.053
602.206
| style="text-align:center;" | 139.85
95.588
| style="text-align:center;" | 41.955
28.6765
| style="text-align:center;" | 1762.105
1204.412
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 82\177
| style="text-align:center;" | 881.132
602.26
| style="text-align:center;" | 139.692
95.48
| style="text-align:center;" | 42.982
22.034
| style="text-align:center;" | 1762.263
1204.52
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 19\41
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 881.394
602.439
| style="text-align:center;" | 139.167
95.122
| style="text-align:center;" | 46.389
31.707
| style="text-align:center;" | 1762.788
1204.878
| style="text-align:center;" | L=3 s=1
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 89\192
| style="text-align:center;" | 881.635
602.604
| style="text-align:center;" | 138.684
94.792
| style="text-align:center;" | 49.53
33.854
| style="text-align:center;" | 1763.271
1205.208
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 70\151
| style="text-align:center;" |
| style="text-align:center;" | 881.701
602.649
| style="text-align:center;" | 138.553
94.702
| style="text-align:center;" | 50.383
25.828
| style="text-align:center;" | 1763.402
1205.298
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 121\261
| style="text-align:center;" | 881.794
602.682
| style="text-align:center;" | 138.4565
89.655
| style="text-align:center;" | 51.01
34.866
| style="text-align:center;" | 1763.4985
1205.362
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 51\110
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 881.8155
602.727
| style="text-align:center;" | 138.324
94.5455
| style="text-align:center;" | 51.8715
35.4545
| style="text-align:center;" | 1763.631
1205.4545
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 134\289
| style="text-align:center;" | 881.875
602.768
| style="text-align:center;" | 138.204
94.464
| style="text-align:center;" | 52.649
35.986
| style="text-align:center;" | 1763.751
1205.536
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 83\179
| style="text-align:center;" |
| style="text-align:center;" | 881.912
602.793
| style="text-align:center;" | 138.131
94.413
| style="text-align:center;" | 53.172
36.313
| style="text-align:center;" | 1763.824
1205.586
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 115\248
| style="text-align:center;" | 881.955
602.823
| style="text-align:center;" | 138.045
94.355
| style="text-align:center;" | 53.684
36.6935
| style="text-align:center;" | 1763.91
1205.645
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 32\69
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 882.066
602.899
| style="text-align:center;" | 137.823
94.203
| style="text-align:center;" | 55.129
37.681
| style="text-align:center;" | 1764.132
1205.797
| style="text-align:center;" | L=5 s=2
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 109\235
| style="text-align:center;" | 882.183
602.979
| style="text-align:center;" | 137.588
94.043
| style="text-align:center;" | 56.654
38.723
| style="text-align:center;" | 1764.367
1205.957
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 77\166
| style="text-align:center;" |
| style="text-align:center;" | 882.232
603.012
| style="text-align:center;" | 137.491
93.976
| style="text-align:center;" | 57.288
39.157
| style="text-align:center;" | 1764.464
1206.024
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 122\263
| style="text-align:center;" | 882.276
603.042
| style="text-align:center;" | 137.404
93.916
| style="text-align:center;" | 57.854
39.544
| style="text-align:center;" | 1764.551
1206.084
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 45\97
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 882.35
603.093
| style="text-align:center;" | 137.2545
93.814
| style="text-align:center;" | 58.823
40.206
| style="text-align:center;" | 1764.7005
1203.185
| style="text-align:center;" | L=7 s=3
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 103\222
| style="text-align:center;" | 882.439
603.153
| style="text-align:center;" | 137.078
93.694
| style="text-align:center;" | 59.972
40.991
| style="text-align:center;" | 1764.877
1206.306
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 58\125
| style="text-align:center;" |
| style="text-align:center;" | 882.507
603.2
| style="text-align:center;" | 136.941
93.6
| style="text-align:center;" | 60.863
41.6
| style="text-align:center;" | 1765.014
1206.4
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 71\153
| style="text-align:center;" | 882.607
603.268
| style="text-align:center;" | 136.742
93.464
| style="text-align:center;" | 62.155
42.484
| style="text-align:center;" | 1765.213
1206.536
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" | 13\28
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 883.0505
603.571
| style="text-align:center;" | 135.854
92.857
| style="text-align:center;" | 67.93
46.429
| style="text-align:center;" | 1766.101
1207.143
| style="text-align:center;" | L=2 s=1
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 72\155
| style="text-align:center;" | 883.489
603.871
| style="text-align:center;" | 134.9775
92.258
| style="text-align:center;" | 73.624
50.323
| style="text-align:center;" | 1766.9775
1207.742
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 59\127
| style="text-align:center;" |
| style="text-align:center;" | 883.585
603.937
| style="text-align:center;" | 134.784
92.126
| style="text-align:center;" | 74.88
51.181
| style="text-align:center;" | 1767.171
1207.574
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 105\226
| style="text-align:center;" | 883.652
603.982
| style="text-align:center;" | 134.652
92.035
| style="text-align:center;" | 75.742
51.77
| style="text-align:center;" | 1767.303
1207.964
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 46\99
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 883.737
604.04
| style="text-align:center;" | 134.482
91.919
| style="text-align:center;" | 76.847
52.525
| style="text-align:center;" | 1767.473
1208.081
| style="text-align:center;" | L=7 s=4
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 125\269
| style="text-align:center;" | 883.808
604.089
| style="text-align:center;" | 134.339
91.822
| style="text-align:center;" | 77.775
53.16
| style="text-align:center;" | 1767.616
1208.178
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 79\170
| style="text-align:center;" |
| style="text-align:center;" | 883.85
604.118
| style="text-align:center;" | 134.256
91.765
| style="text-align:center;" | 78.316
53.529
| style="text-align:center;" | 1767.699
1208.235
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 112\241
| style="text-align:center;" | 883.896
604.149
| style="text-align:center;" | 134.163
91.701
| style="text-align:center;" | 78.919
53.942
| style="text-align:center;" | 1767.792
1208.299
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 33\71
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 884.007
604.225
| style="text-align:center;" | 133.94
91.549
| style="text-align:center;" | 80.364
54.93
| style="text-align:center;" | 1768.0145
1208.451
| style="text-align:center;" | L=5 s=3
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 119\256
| style="text-align:center;" | 884.112
604.297
| style="text-align:center;" | 133.731
91.406
| style="text-align:center;" | 81.725
55.859
| style="text-align:center;" | 1768.224
1208.594
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 86\185
| style="text-align:center;" |
| style="text-align:center;" | 884.152
604.324
| style="text-align:center;" | 133.651
91.351
| style="text-align:center;" | 82.247
56.216
| style="text-align:center;" | 1768.304
1208.649
| style="text-align:center;" |  
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 139\299
| style="text-align:center;" | 884.186
604.348
| style="text-align:center;" | 133.582
91.304
| style="text-align:center;" | 82.694
56.522
| style="text-align:center;" | 1768.373
1208.696
| style="text-align:center;" | Golden Arcturus is near here
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 53\114
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 884.24
604.386
| style="text-align:center;" | 133.4705
91.228
| style="text-align:center;" | 83.419
57.0175
| style="text-align:center;" | 1768.4845
1208.772
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 126\271
| style="text-align:center;" | 884.303
604.428
| style="text-align:center;" | 133.347
91.144
| style="text-align:center;" | 84.219
57.565
| style="text-align:center;" | 1768.608
1208.856
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 73\157
| style="text-align:center;" |
| style="text-align:center;" | 884.3485
604.459
| style="text-align:center;" | 133.258
91.083
| style="text-align:center;" | 84.8005
57.962
| style="text-align:center;" | 1768.697
1208.917
| style="text-align:center;" |5/3-Pythagorean is near here
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 93\200
| style="text-align:center;" | 884.409
604.5
| style="text-align:center;" | 133.137
91
| style="text-align:center;" | 85.588
58.5
| style="text-align:center;" | 1768.818
1209
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 20\43
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 884.63
604.651
| style="text-align:center;" | 132.6945
90.698
| style="text-align:center;" | 88.463
60.465
| style="text-align:center;" | 1769.2605
1209.302
| style="text-align:center;" | L=3 s=2
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 87\187
| style="text-align:center;" | 884.867
604.813
| style="text-align:center;" | 132.2215
90.374
| style="text-align:center;" | 91.538
62.567
| style="text-align:center;" | 1769.7335
1209.626
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 67\144
| style="text-align:center;" |
| style="text-align:center;" | 884.937
604.861
| style="text-align:center;" | 132.08
90.278
| style="text-align:center;" | 92.456
63.194
| style="text-align:center;" | 1769.875
1209.722
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 114\245
| style="text-align:center;" | 884.991
604.898
| style="text-align:center;" | 131.972
90.204
| style="text-align:center;" | 93.157
52.6735
| style="text-align:center;" | 1769.983
1209.896
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 47\101
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 885.068
604.9505
| style="text-align:center;" | 131.819
90.099
| style="text-align:center;" | 94.156
64.356
| style="text-align:center;" | 1770.136
1209.901
| style="text-align:center;" | L=7 s=5
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 121\260
| style="text-align:center;" | 885.141
605
| style="text-align:center;" | 131.674
90
| style="text-align:center;" | 95.098
65
| style="text-align:center;" | 1770.281
1210
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 74\159
| style="text-align:center;" |
| style="text-align:center;" | 885.187
605.031
| style="text-align:center;" | 131.582
89.937
| style="text-align:center;" | 95.696
65.409
| style="text-align:center;" | 1770.373
1210.063
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 101\217
| style="text-align:center;" | 885.242
605.069
| style="text-align:center;" | 131.4715
89.862
| style="text-align:center;" | 96.4125
65.899
| style="text-align:center;" | 1770.4835
1210.138
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 27\58
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 885.393
605.172
| style="text-align:center;" | 131.169
89.655
| style="text-align:center;" | 98.377
67.241
| style="text-align:center;" | 1770.786
1210.345
| style="text-align:center;" | L=4 s=3
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 88\189
| style="text-align:center;" | 885.566
605.291
| style="text-align:center;" | 130.822
89.418
| style="text-align:center;" | 100.6325
68.783
| style="text-align:center;" | 1771.133
1210.582
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 61\131
| style="text-align:center;" |
| style="text-align:center;" | 885.643
605.3435
| style="text-align:center;" | 130.669
89.313
| style="text-align:center;" | 101.631
69.466
| style="text-align:center;" | 1771.286
1210.687
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 95\204
| style="text-align:center;" | 885.714
605.392
| style="text-align:center;" | 130.526
89.216
| style="text-align:center;" | 102.556
70.098
| style="text-align:center;" | 1771.429
1210.784
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 34\73
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 885.842
605.4795
| style="text-align:center;" | 130.271
89.041
| style="text-align:center;" | 104.217
71.233
| style="text-align:center;" | 1771.684
1210.959
| style="text-align:center;" | L=5 s=4
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 75\161
| style="text-align:center;" | 886.004
605.59
| style="text-align:center;" | 129.947
88.82
| style="text-align:center;" | 106.3205
72.671
| style="text-align:center;" | 1772.008
1211.18
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 41\88
| style="text-align:center;" |
| style="text-align:center;" | 886.138
605.682
| style="text-align:center;" | 129.679
88.636
| style="text-align:center;" | 108.065
73.864
| style="text-align:center;" | 1772.276
1211.364
| style="text-align:center;" | L=6 s=5
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 48\103
| style="text-align:center;" | 886.348
605.825
| style="text-align:center;" | 129.259
88.3495
| style="text-align:center;" | 110.7935
75.728
| style="text-align:center;" | 1772.696
1211.6505
| style="text-align:center;" | L=7 s=6
|-
| style="text-align:center;" | 7\15
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 887.579
606.667
| colspan="2" style="text-align:center;" | 126.797
86.667
| style="text-align:center;" | 1775.158
1213.333
| style="text-align:center;" | L=1 s=1
|}


[[Super-Arcturus_15L_2s|Mini enharmonic]]
[[Super-Arcturus_15L_2s|Mini enharmonic]]

Revision as of 01:53, 7 June 2023

Arcturus is a no-twos temperament which tempers out the comma 15625/15309. Having an ~5:3 as a generator, this temperament is the application of the Pythagorean principle of tuning a stack of the next higher prime number and then factoring out powers of the equivalence to tritave composition. However, a heptatonic MOS (2L 5s) will not suffice to produce an understandable rendition of it because a very close ~5:3 generates a L:s ratio between 4:1 and 5:1, which is beginning to get too lopsided to still be a complete presentation of a temperament.

Chords

Arcturus contains the triad 5:7:9 (used in Bohlen-Pierce harmony) and the triad 27:35:45 which divides 5/3 into two nearly-equal parts.

Tuning spectrum

Below is a list of MOS families which present it completely (however smearily) using a generator of 845.3 to 951.0 cents:

Mini chromatic

Anti-chromatic

Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details:
Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: 
{{MOS tuning spectrum
| 3/2 = Example comment
| 4/3 = Another example comment
}}


The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.


Scale tree and tuning spectrum of 11L 2s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
7\13 646.154 553.846 1:1 1.000 Equalized 11L 2s
48\89 647.191 552.809 7:6 1.167
41\76 647.368 552.632 6:5 1.200
75\139 647.482 552.518 11:9 1.222
34\63 647.619 552.381 5:4 1.250
95\176 647.727 552.273 14:11 1.273
61\113 647.788 552.212 9:7 1.286
88\163 647.853 552.147 13:10 1.300
27\50 648.000 552.000 4:3 1.333 Supersoft 11L 2s
101\187 648.128 551.872 15:11 1.364
74\137 648.175 551.825 11:8 1.375
121\224 648.214 551.786 18:13 1.385
47\87 648.276 551.724 7:5 1.400
114\211 648.341 551.659 17:12 1.417
67\124 648.387 551.613 10:7 1.429
87\161 648.447 551.553 13:9 1.444
20\37 648.649 551.351 3:2 1.500 Soft 11L 2s
93\172 648.837 551.163 14:9 1.556
73\135 648.889 551.111 11:7 1.571
126\233 648.927 551.073 19:12 1.583
53\98 648.980 551.020 8:5 1.600
139\257 649.027 550.973 21:13 1.615
86\159 649.057 550.943 13:8 1.625
119\220 649.091 550.909 18:11 1.636
33\61 649.180 550.820 5:3 1.667 Semisoft 11L 2s
112\207 649.275 550.725 17:10 1.700
79\146 649.315 550.685 12:7 1.714
125\231 649.351 550.649 19:11 1.727
46\85 649.412 550.588 7:4 1.750
105\194 649.485 550.515 16:9 1.778
59\109 649.541 550.459 9:5 1.800
72\133 649.624 550.376 11:6 1.833
13\24 650.000 550.000 2:1 2.000 Basic 11L 2s
Scales with tunings softer than this are proper
71\131 650.382 549.618 11:5 2.200
58\107 650.467 549.533 9:4 2.250
103\190 650.526 549.474 16:7 2.286
45\83 650.602 549.398 7:3 2.333
122\225 650.667 549.333 19:8 2.375
77\142 650.704 549.296 12:5 2.400
109\201 650.746 549.254 17:7 2.429
32\59 650.847 549.153 5:2 2.500 Semihard 11L 2s
115\212 650.943 549.057 18:7 2.571
83\153 650.980 549.020 13:5 2.600
134\247 651.012 548.988 21:8 2.625
51\94 651.064 548.936 8:3 2.667
121\223 651.121 548.879 19:7 2.714
70\129 651.163 548.837 11:4 2.750
89\164 651.220 548.780 14:5 2.800
19\35 651.429 548.571 3:1 3.000 Hard 11L 2s
82\151 651.656 548.344 13:4 3.250
63\116 651.724 548.276 10:3 3.333
107\197 651.777 548.223 17:5 3.400
44\81 651.852 548.148 7:2 3.500
113\208 651.923 548.077 18:5 3.600
69\127 651.969 548.031 11:3 3.667
94\173 652.023 547.977 15:4 3.750
25\46 652.174 547.826 4:1 4.000 Superhard 11L 2s
81\149 652.349 547.651 13:3 4.333
56\103 652.427 547.573 9:2 4.500
87\160 652.500 547.500 14:3 4.667
31\57 652.632 547.368 5:1 5.000
68\125 652.800 547.200 11:2 5.500
37\68 652.941 547.059 6:1 6.000
43\79 653.165 546.835 7:1 7.000
6\11 654.545 545.455 1:0 → ∞ Collapsed 11L 2s

Mini enharmonic

Enharmonic

Anti-enharmonic

Retrieved from "https://en.xen.wiki/index.php?title=Arcturus&oldid=115857"