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'''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.
'''Arcturus''' is the [[non-octave]] [[rank]]-2 [[regular temperament]] of the 3.5.7 [[subgroup]] that [[tempering out|tempers out]] the arcturus 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 scalesig|2L 5s<3/1>|link=1}} [[MOS]] 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.
 
{{tdlink|No-twos subgroup temperaments #Arcturus}}
 
== Etymology ==
This temperament is named after the star {{w|Arcturus}}, following a series of non-octave temperaments that are named after stars.
{{todo|add etymology|inline=1|text=Add name (person who coined the term) and year (when it was coined).}}


== Chords ==
== 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.
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 ==
== 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:
Below is a list of MOS families which present it completely (however smearily) using a generator of 845.3 to 951.0{{c}}:


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


[[Super-Arcturus_15L_2s|Mini enharmonic]]
== Scales ==
 
* {{mos scalesig|9L 2s<3/1>|link=1}} (mini chromatic, aka sub-Arcturus)
[[Super-Arcturus_17L_2s|Enharmonic]]
* {{mos scalesig|11L 2s<3/1>|link=1}} (anti-chromatic, aka anti-Arcturus)
* {{mos scalesig|15L 2s<3/1>|link=1}} (mini enharmonic, aka super-Arcturus 15L 2s)
* {{mos scalesig|17L 2s<3/1>|link=1}} (enharmonic, aka super-Arcturus 17L 2s)
* {{mos scalesig|2L 17s<3/1>|link=1}} (anti-enharmonic, aka trans-Arcturus 2L 7s)


[[Trans-Arcturus_enneadecatonic|Anti-enharmonic]]
[[Category:Arcturus| ]] <!-- main article -->
[[Category:Temperaments]]
[[Category:Rank-2 temperaments]]
[[Category:Nonoctave]]
[[Category:Non-octave temperaments]]
Retrieved from "https://en.xen.wiki/w/Arcturus"