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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
'''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.
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-10-12 09:22:31 UTC</tt>.<br>
: The original revision id was <tt>595001456</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">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. Below is.a list of MOS families which present it completely (however smearily) using a generator of 845.3 to 951.0 cents:


[[Sub-Arcturus|Mini chromatic]]
{{tdlink|No-twos subgroup temperaments #Arcturus}}
[[Anti-Arcturus|Anti-chromatic]]


||||||||||||||~ Generator ||~ cents ||~ L ||~ s ||~ 2g ||~ Notes ||
== Etymology ==
||= 6\13 ||=   ||=   ||=   ||=  ||=  ||=  ||= 877.825 ||= 146.304 ||= 0.00 ||= 1755.651 ||= L=1 s=0 ||
This temperament is named after the star {{w|Arcturus}}, following a series of non-octave temperaments that are named after stars.  
||=  ||=  ||=  ||=  ||=  ||=  ||= 43\93 ||= 879.399 ||= 143.158 ||= 20.451 ||= 1758.797 ||= L=7 s=1 ||
{{todo|add etymology|inline=1|text=Add name (person who coined the term) and year (when it was coined).}}
||=  ||=  ||=  ||=  ||=  ||= 37\80 ||=  ||= 879.654 ||= 142.647 ||= 23.774 ||= 1759.38 ||= L=6 s=1 ||
||=  ||=  ||=  ||=  ||=  ||=  ||= 68\147 ||= 879.816 ||= 142.323 ||= 25.877 ||= 1759.632 ||=  ||
||=  ||=  ||=  ||=  ||= 31\67 ||=  ||=  ||= 880.009 ||= 141.937 ||= 28.387 ||= 1760.081 ||= L=5 s=1 ||
||=  ||=  ||=  ||=  ||=  ||=  ||= 87\188 ||= 880.16 ||= 141.634 ||= 30.35 ||= 1760.32 ||=  ||
||=  ||=  ||=  ||=  ||=  ||= 56\121 ||=  ||= 880.243 ||= 141.468 ||= 31.437 ||= 1760.487 ||=  ||
||=  ||=  ||=  ||=  ||=  ||=  ||= 81\175 ||= [[tel/880.3335|880.3335]] ||= 141.288 ||= 32.605 ||= 1760.667 ||=  ||
||=  ||=  ||=  ||= 25\54 ||=  ||=  ||=  ||= 880.535 ||= 140.886 ||= 35.221 ||= 1761.069 ||= L=4 s=1 ||
||=  ||=  ||=  ||=  ||=  ||=  ||= 94\203 ||= 880.708 ||= [[tel/140.5385|140.5385]] ||= 37.477 ||= 1761.4165 ||=  ||
||=  ||=  ||=  ||=  ||=  ||= 69\149 ||=  ||= 880.711 ||= 140.413 ||= 38.294 ||= 1761.542 ||=  ||
||=  ||=  ||=  ||=  ||=  ||=  ||= 113\244 ||= 880.823 ||= 140.308 ||= 38.9745 ||= 1761.647 ||=  ||
||=  ||=  ||=  ||=  ||= 44\95 ||=  ||=  ||= [[tel/880.9055|880.9055]] ||= 140.144 ||= 40.041 ||= 1761.811 ||= L=7 s=2 ||
||=  ||=  ||=  ||=  ||=  ||=  ||= 107\231 ||= 880.992 ||= 139.971 ||= 41.168 ||= 1761.984 ||=  ||
||=  ||=  ||=  ||=  ||=  ||= 63\136 ||=  ||= 881.053 ||= 139.85 ||= 41.955 ||= 1762.105 ||=  ||
||=  ||=  ||=  ||=  ||=  ||=  ||= 82\177 ||= 881.132 ||= 139.692 ||= 42.982 ||= 1762.263 ||=  ||
||=  ||=  ||= 19\41 ||=  ||=  ||=  ||=  ||= 881.394 ||= 139.167 ||= 46.389 ||= 1762.788 ||= L=3 s=1 ||
||=  ||=  ||=  ||=  ||=  ||=  ||= 89\192 ||= 881.635 ||= 138.684 ||= 49.53 ||= 1763.271 ||=  ||
||=  ||=  ||=  ||=  ||=  ||= 70\151 ||=  ||= 881.701 ||= 138.553 ||= 50.383 ||= 1763.402 ||=  ||
||=  ||=  ||=  ||=  ||=  ||=  ||= 121\261 ||= 881.794 ||= [[tel/138.4565|138.4565]] ||= 51.01 ||= 1763.4985 ||=  ||
||=  ||=  ||=  ||=  ||= 51\110 ||=  ||=  ||= [[tel/881.8155|881.8155]] ||= 138.324 ||= 51.8715 ||= 1763.631 ||=  ||
||=  ||=  ||=  ||=  ||=  ||=  ||= 134\289 ||= 881.875 ||= 138.204 ||= 52.649 ||= 1763.751 ||=  ||
||=  ||=  ||=  ||=  ||=  ||= 83\179 ||=  ||= 881.912 ||= 138.131 ||= 53.172 ||= 1763.824 ||=  ||
||=  ||=  ||=  ||=  ||=  ||=  ||= 115\248 ||= 881.955 ||= 138.045 ||= 53.684 ||= 1763.91 ||=  ||
||=  ||=  ||=  ||= 32\69 ||=  ||=  ||=  ||= 882.066 ||= 137.823 ||= 55.129 ||= 1764.132 ||= L=5 s=2 ||
||=  ||=  ||=  ||=  ||=  ||=  ||= 109\235 ||= 882.183 ||= 137.588 ||= 56.654 ||= 1764.367 ||=  ||
||=  ||=  ||=  ||=  ||=  ||= 77\166 ||=  ||= 882.232 ||= 137.491 ||= 57.288 ||= 1764.464 ||=  ||
||=  ||=  ||=  ||=  ||=  ||=  ||= 122\263 ||= 882.276 ||= 137.404 ||= 57.854 ||= 1764.551 ||=  ||
||=  ||=  ||=  ||=  ||= 45\97 ||=  ||=  ||= 882.35 ||= [[tel/137.2545|137.2545]] ||= 58.823 ||= 1764.7005 ||= L=7 s=3 ||
||=  ||=  ||=  ||=  ||=  ||=  ||= 103\222 ||= 882.439 ||= 137.078 ||= 59.972 ||= 1764.877 ||=  ||
||=  ||=  ||=  ||=  ||=  ||= 58\125 ||=  ||= 882.507 ||= 136.941 ||= 60.863 ||= 1765.014 ||=  ||
||=  ||=  ||=  ||=  ||=  ||=  ||= 71\153 ||= 882.607 ||= 136.742 ||= 62.155 ||= 1765.213 ||=  ||
||=  ||= 13\28 ||=  ||=  ||=  ||=  ||=  ||= [[tel/883.0505|883.0505]] ||= 135.854 ||= 67.93 ||= 1766.101 ||= L=2 s=1 ||
||=  ||=  ||=  ||=  ||=  ||=  ||= 72\155 ||= 883.489 ||= [[tel/134.9775|134.9775]] ||= 73.624 ||= 1766.9775 ||=  ||
||=  ||=  ||=  ||=  ||=  ||= 59\127 ||=  ||= 883.585 ||= 134.784 ||= 74.88 ||= 1767.171 ||=  ||
||=  ||=  ||=  ||=  ||=  ||=  ||= 105\226 ||= 883.652 ||= 134.652 ||= 75.742 ||= 1767.303 ||=  ||
||=  ||=  ||=  ||=  ||= 46\99 ||=  ||=  ||= 883.737 ||= 134.482 ||= 76.847 ||= 1767.473 ||= L=7 s=4 ||
||=  ||=  ||=  ||=  ||=  ||=  ||= 125\269 ||= 883.808 ||= 134.339 ||= 77.775 ||= 1767.616 ||=  ||
||=  ||=  ||=  ||=  ||=  ||= 79\170 ||=  ||= 883.85 ||= 134.256 ||= 78.316 ||= 1767.699 ||=  ||
||=  ||=  ||=  ||=  ||=  ||=  ||= 112\241 ||= 883.896 ||= 134.163 ||= 78.919 ||= 1767.792 ||=  ||
||=  ||=  ||=  ||= 33\71 ||=  ||=  ||=  ||= 884.007 ||= 133.94 ||= 80.364 ||= 1768.0145 ||= L=5 s=3 ||
||=  ||=  ||=  ||=  ||=  ||=  ||= 119\256 ||= 884.112 ||= 133.731 ||= 81.725 ||= 1768.224 ||=  ||
||=  ||=  ||=  ||=  ||=  ||= 86\185 ||=  ||= 884.152 ||= 133.651 ||= 82.247 ||= 1768.304 ||=  ||
||=  ||=  ||=  ||=  ||=  ||=  ||= 139\299 ||= 884.186 ||= 133.582 ||= 82.694 ||= 1768.373 ||= Golden Arcturus is near here ||
||=  ||=  ||=  ||=  ||= 53\114 ||=  ||=  ||= 884.24 ||= [[tel/133.4705|133.4705]] ||= 83.419 ||= 1768.4845 ||=  ||
||=  ||=  ||=  ||=  ||=  ||=  ||= 126\271 ||= 884.303 ||= 133.347 ||= 84.219 ||= 1768.608 ||=  ||
||=  ||=  ||=  ||=  ||=  ||= 73\157 ||=  ||= [[tel/884.3485|884.3485]] ||= 133.258 ||= 84.8005 ||= 1768.697 ||=  ||
||=  ||=  ||=  ||=  ||=  ||=  ||= 93\200 ||= 884.409 ||= 133.137 ||= 85.588 ||= 1768.818 ||=  ||
||=  ||=  ||= 20\43 ||=  ||=  ||=  ||=  ||= 884.63 ||= [[tel/132.6945|132.6945]] ||= 88.463 ||= 1769.2605 ||= L=3 s=2 ||
||=  ||=  ||=  ||=  ||=  ||=  ||= 87\187 ||= 884.867 ||= [[tel/132.2215|132.2215]] ||= 91.538 ||= 1769.7335 ||=  ||
||=  ||=  ||=  ||=  ||=  ||= 67\144 ||=  ||= 884.937 ||= 132.08 ||= 92.456 ||= 1769.875 ||=  ||
||=  ||=  ||=  ||=  ||=  ||=  ||= 114\245 ||= 884.991 ||= 131.972 ||= 93.157 ||= 1769.983 ||=  ||
||=  ||=  ||=  ||=  ||= 47\101 ||=  ||=  ||= 885.068 ||= 131.819 ||= 94.156 ||= 1770.136 ||= L=7 s=5 ||
||=  ||=  ||=  ||=  ||=  ||=  ||= 121\260 ||= 885.141 ||= 131.674 ||= 95.098 ||= 1770.281 ||=  ||
||=  ||=  ||=  ||=  ||=  ||= 74\159 ||=  ||= 885.187 ||= 131.582 ||= 95.696 ||= 1770.373 ||=  ||
||=  ||=  ||=  ||=  ||=  ||=  ||= 101\217 ||= 885.242 ||= [[tel/131.4715|131.4715]] ||= 96.4125 ||= 1770.4835 ||=  ||
||=  ||=  ||=  ||= 27\58 ||=  ||=  ||=  ||= 885.393 ||= 131.169 ||= 98.377 ||= 1770.786 ||= L=4 s=3 ||
||=  ||=  ||=  ||=  ||=  ||=  ||= 88\189 ||= 885.566 ||= 130.822 ||= [[tel/100.6325|100.6325]] ||= 1771.133 ||=  ||
||=  ||=  ||=  ||=  ||=  ||= 61\131 ||=  ||= 885.643 ||= 130.669 ||= 101.631 ||= 1771.286 ||=  ||
||=  ||=  ||=  ||=  ||=  ||=  ||= 95\204 ||= 885.714 ||= 130.526 ||= 102.556 ||= 1771.429 ||=  ||
||=  ||=  ||=  ||=  ||= 34\73 ||=  ||=  ||= 885.842 ||= 130.271 ||= 104.217 ||= 1771.684 ||= L=5 s=4 ||
||=  ||=  ||=  ||=  ||=  ||=  ||= 75\161 ||= 886.004 ||= 129.947 ||= [[tel/106.3205|106.3205]] ||= 1772.008 ||=  ||
||=  ||=  ||=  ||=  ||=  ||= 41\88 ||=  ||= 886.138 ||= 129.679 ||= 108.065 ||= 1772.276 ||= L=6 s=5 ||
||=  ||=  ||=  ||=  ||=  ||=  ||= 48\103 ||= 886.348 ||= 129.259 ||= [[tel/110.7935|110.7935]] ||= 1772.696 ||= L=7 s=6 ||
||= 7\15 ||=  ||=  ||=  ||=  ||=  ||=  ||= 887.579 ||||= 126.797 ||= 1775.158 ||= L=1 s=1 ||


[[Super-Arcturus 15L 2s|Mini enharmonic]]
== Chords ==
[[Super-Arcturus 17L 2s|Enharmonic]]
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.
[[Trans-Arcturus enneadecatonic|Anti-enharmonic]]</pre></div>
<h4>Original HTML content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Arcturus&lt;/title&gt;&lt;/head&gt;&lt;body&gt;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. Below is.a list of MOS families which present it completely (however smearily) using a generator of 845.3 to 951.0 cents:&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Sub-Arcturus"&gt;Mini chromatic&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Anti-Arcturus"&gt;Anti-chromatic&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;


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


&lt;table class="wiki_table"&gt;
{| class="wikitable" style="text-align: center;"
    &lt;tr&gt;
|-
        &lt;th colspan="7"&gt;Generator&lt;br /&gt;
! colspan="7" | Generator
&lt;/th&gt;
! Cents<br>Hekts
        &lt;th&gt;cents&lt;br /&gt;
! L
&lt;/th&gt;
! s
        &lt;th&gt;L&lt;br /&gt;
! 2g
&lt;/th&gt;
! Notes
        &lt;th&gt;s&lt;br /&gt;
|-
&lt;/th&gt;
| 6\13
        &lt;th&gt;2g&lt;br /&gt;
|
&lt;/th&gt;
|
        &lt;th&gt;Notes&lt;br /&gt;
|
&lt;/th&gt;
|
    &lt;/tr&gt;
|
    &lt;tr&gt;
|
        &lt;td style="text-align: center;"&gt;6\13&lt;br /&gt;
| 877.825<br>600
&lt;/td&gt;
| 146.304<br>100
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
| 0
&lt;/td&gt;
| 1755.651<br>1200
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
| {{nowrap|L {{=}} 1|s {{=}} 0}}
&lt;/td&gt;
|-
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
|
&lt;/td&gt;
|
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
|
&lt;/td&gt;
|
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
|
&lt;/td&gt;
|
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
| 43\93
&lt;/td&gt;
| 879.399<br>601.075
        &lt;td style="text-align: center;"&gt;877.825&lt;br /&gt;
| 143.158<br>97.8495
&lt;/td&gt;
| 20.451<br>13.9785
        &lt;td style="text-align: center;"&gt;146.304&lt;br /&gt;
| 1758.797<br>1202.151
&lt;/td&gt;
| {{nowrap|L {{=}} 7|s {{=}} 1}}
        &lt;td style="text-align: center;"&gt;0.00&lt;br /&gt;
|-
&lt;/td&gt;
|
        &lt;td style="text-align: center;"&gt;1755.651&lt;br /&gt;
|
&lt;/td&gt;
|
        &lt;td style="text-align: center;"&gt;L=1 s=0&lt;br /&gt;
|
&lt;/td&gt;
|
    &lt;/tr&gt;
| 37\80
    &lt;tr&gt;
|
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
| 879.654<br>601.25
&lt;/td&gt;
| 142.647<br>97.5
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
| 23.774<br>16.25
&lt;/td&gt;
| 1759.38<br>1202.5
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
| {{nowrap|L {{=}} 6|s {{=}} 1}}
&lt;/td&gt;
|-
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
|
&lt;/td&gt;
|
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
|
&lt;/td&gt;
|
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
|
&lt;/td&gt;
|
        &lt;td style="text-align: center;"&gt;43\93&lt;br /&gt;
| 68\147
&lt;/td&gt;
| 879.816<br>601.3605
        &lt;td style="text-align: center;"&gt;879.399&lt;br /&gt;
| 142.323<br>97.279
&lt;/td&gt;
| 25.877<br>17.687
        &lt;td style="text-align: center;"&gt;143.158&lt;br /&gt;
| 1759.632<br>1202.721
&lt;/td&gt;
|
        &lt;td style="text-align: center;"&gt;20.451&lt;br /&gt;
|-
&lt;/td&gt;
|
        &lt;td style="text-align: center;"&gt;1758.797&lt;br /&gt;
|
&lt;/td&gt;
|
        &lt;td style="text-align: center;"&gt;L=7 s=1&lt;br /&gt;
|
&lt;/td&gt;
| 31\67
    &lt;/tr&gt;
|
    &lt;tr&gt;
|
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
| 880.009<br>601.4925
&lt;/td&gt;
| 141.937<br>97.015
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
| 28.387<br>19.403
&lt;/td&gt;
| 1760.081<br>1202.985
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
| {{nowrap|L {{=}} 5|s {{=}} 1}}
&lt;/td&gt;
|-
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
|
&lt;/td&gt;
|
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
|
&lt;/td&gt;
|
        &lt;td style="text-align: center;"&gt;37\80&lt;br /&gt;
|
&lt;/td&gt;
|
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
| 87\188
&lt;/td&gt;
| 880.16<br>601.596
        &lt;td style="text-align: center;"&gt;879.654&lt;br /&gt;
| 141.634<br>96.8085
&lt;/td&gt;
| 30.35<br>20.745
        &lt;td style="text-align: center;"&gt;142.647&lt;br /&gt;
| 1760.32<br>1203.191
&lt;/td&gt;
|
        &lt;td style="text-align: center;"&gt;23.774&lt;br /&gt;
|-
&lt;/td&gt;
|
        &lt;td style="text-align: center;"&gt;1759.38&lt;br /&gt;
|
&lt;/td&gt;
|
        &lt;td style="text-align: center;"&gt;L=6 s=1&lt;br /&gt;
|
&lt;/td&gt;
|
    &lt;/tr&gt;
| 56\121
    &lt;tr&gt;
|
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
| 880.243<br>601.653
&lt;/td&gt;
| 141.468<br>96.694
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
| 31.437<br>21.488
&lt;/td&gt;
| 1760.487<br>1203.306
        &lt;td style="
|
|-
|
|
|
|
|
|
| 81\175
| 880.3335<br>601.714
| 141.288<br>96.571
| 32.605<br>22.286
| 1760.667<br>1203.429
|
|-
|
|
|
| 25\54
|
|
|
| 880.535<br>601.852
| 140.886<br>96.296
| 35.221<br>24.074
| 1761.069<br>1203.704
| {{nowrap|L {{=}} 4|s {{=}} 1}}
|-
|
|
|
|
|
|
| 94\203
| 880.708<br>601.97
| 140.5385<br>96.059
| 37.477<br>25.616
| 1761.4165<br>1203.971
|
|-
|
|
|
|
|
| 69\149
|
| 880.711<br>602.013
| 140.413<br>95.973
| 38.294<br>26.1745
 


&lt;br /&gt;
== Scales ==
&lt;a class="wiki_link" href="/Super-Arcturus%2015L%202s"&gt;Mini enharmonic&lt;/a&gt;&lt;br /&gt;
* {{mos scalesig|9L 2s<3/1>|link=1}} (mini chromatic, aka sub-Arcturus)
&lt;a class="wiki_link" href="/Super-Arcturus%2017L%202s"&gt;Enharmonic&lt;/a&gt;&lt;br /&gt;
* {{mos scalesig|11L 2s<3/1>|link=1}} (anti-chromatic, aka anti-Arcturus)
&lt;a class="wiki_link" href="/Trans-Arcturus%20enneadecatonic"&gt;Anti-enharmonic&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
* {{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)
 
[[Category:Arcturus| ]] <!-- main article -->
[[Category:Rank-2 temperaments]]
[[Category:Non-octave temperaments]]
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