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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"><html><head><title>Arcturus</title></head><body>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:<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Sub-Arcturus">Mini chromatic</a><br />
| |
| <a class="wiki_link" href="/Anti-Arcturus">Anti-chromatic</a><br />
| |
| <br />
| |
|
| |
|
| | == 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}}: |
|
| |
|
| <table class="wiki_table">
| | {| class="wikitable" style="text-align: center;" |
| <tr>
| | |- |
| <th colspan="7">Generator<br />
| | ! colspan="7" | Generator |
| </th>
| | ! Cents<br>Hekts |
| <th>cents<br />
| | ! L |
| </th>
| | ! s |
| <th>L<br />
| | ! 2g |
| </th>
| | ! Notes |
| <th>s<br />
| | |- |
| </th>
| | | 6\13 |
| <th>2g<br />
| | | |
| </th>
| | | |
| <th>Notes<br />
| | | |
| </th>
| | | |
| </tr>
| | | |
| <tr>
| | | |
| <td style="text-align: center;">6\13<br />
| | | 877.825<br>600 |
| </td>
| | | 146.304<br>100 |
| <td style="text-align: center;"><br />
| | | 0 |
| </td>
| | | 1755.651<br>1200 |
| <td style="text-align: center;"><br />
| | | {{nowrap|L {{=}} 1|s {{=}} 0}} |
| </td>
| | |- |
| <td style="text-align: center;"><br />
| | | |
| </td>
| | | |
| <td style="text-align: center;"><br />
| | | |
| </td>
| | | |
| <td style="text-align: center;"><br />
| | | |
| </td>
| | | |
| <td style="text-align: center;"><br />
| | | 43\93 |
| </td>
| | | 879.399<br>601.075 |
| <td style="text-align: center;">877.825<br />
| | | 143.158<br>97.8495 |
| </td>
| | | 20.451<br>13.9785 |
| <td style="text-align: center;">146.304<br />
| | | 1758.797<br>1202.151 |
| </td>
| | | {{nowrap|L {{=}} 7|s {{=}} 1}} |
| <td style="text-align: center;">0.00<br />
| | |- |
| </td>
| | | |
| <td style="text-align: center;">1755.651<br />
| | | |
| </td>
| | | |
| <td style="text-align: center;">L=1 s=0<br />
| | | |
| </td>
| | | |
| </tr>
| | | 37\80 |
| <tr>
| | | |
| <td style="text-align: center;"><br />
| | | 879.654<br>601.25 |
| </td>
| | | 142.647<br>97.5 |
| <td style="text-align: center;"><br />
| | | 23.774<br>16.25 |
| </td>
| | | 1759.38<br>1202.5 |
| <td style="text-align: center;"><br />
| | | {{nowrap|L {{=}} 6|s {{=}} 1}} |
| </td>
| | |- |
| <td style="text-align: center;"><br />
| | | |
| </td>
| | | |
| <td style="text-align: center;"><br />
| | | |
| </td>
| | | |
| <td style="text-align: center;"><br />
| | | |
| </td>
| | | |
| <td style="text-align: center;">43\93<br />
| | | 68\147 |
| </td>
| | | 879.816<br>601.3605 |
| <td style="text-align: center;">879.399<br />
| | | 142.323<br>97.279 |
| </td>
| | | 25.877<br>17.687 |
| <td style="text-align: center;">143.158<br />
| | | 1759.632<br>1202.721 |
| </td>
| | | |
| <td style="text-align: center;">20.451<br />
| | |- |
| </td>
| | | |
| <td style="text-align: center;">1758.797<br />
| | | |
| </td>
| | | |
| <td style="text-align: center;">L=7 s=1<br />
| | | |
| </td>
| | | 31\67 |
| </tr>
| | | |
| <tr>
| | | |
| <td style="text-align: center;"><br />
| | | 880.009<br>601.4925 |
| </td>
| | | 141.937<br>97.015 |
| <td style="text-align: center;"><br />
| | | 28.387<br>19.403 |
| </td>
| | | 1760.081<br>1202.985 |
| <td style="text-align: center;"><br />
| | | {{nowrap|L {{=}} 5|s {{=}} 1}} |
| </td>
| | |- |
| <td style="text-align: center;"><br />
| | | |
| </td>
| | | |
| <td style="text-align: center;"><br />
| | | |
| </td>
| | | |
| <td style="text-align: center;">37\80<br />
| | | |
| </td>
| | | |
| <td style="text-align: center;"><br />
| | | 87\188 |
| </td>
| | | 880.16<br>601.596 |
| <td style="text-align: center;">879.654<br />
| | | 141.634<br>96.8085 |
| </td>
| | | 30.35<br>20.745 |
| <td style="text-align: center;">142.647<br />
| | | 1760.32<br>1203.191 |
| </td>
| | | |
| <td style="text-align: center;">23.774<br />
| | |- |
| </td>
| | | |
| <td style="text-align: center;">1759.38<br />
| | | |
| </td>
| | | |
| <td style="text-align: center;">L=6 s=1<br />
| | | |
| </td>
| | | |
| </tr>
| | | 56\121 |
| <tr>
| | | |
| <td style="text-align: center;"><br />
| | | 880.243<br>601.653 |
| </td>
| | | 141.468<br>96.694 |
| <td style="text-align: center;"><br />
| | | 31.437<br>21.488 |
| </td>
| | | 1760.487<br>1203.306 |
| <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 |
| | |
|
| |
|
| <br />
| | == Scales == |
| <a class="wiki_link" href="/Super-Arcturus%2015L%202s">Mini enharmonic</a><br />
| | * {{mos scalesig|9L 2s<3/1>|link=1}} (mini chromatic, aka sub-Arcturus) |
| <a class="wiki_link" href="/Super-Arcturus%2017L%202s">Enharmonic</a><br />
| | * {{mos scalesig|11L 2s<3/1>|link=1}} (anti-chromatic, aka anti-Arcturus) |
| <a class="wiki_link" href="/Trans-Arcturus%20enneadecatonic">Anti-enharmonic</a></body></html></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]] |
Arcturus is the non-octave rank-2 regular temperament of the 3.5.7 subgroup that 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 2L 5s⟨3/1⟩ 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.
For technical data, see No-twos subgroup temperaments #Arcturus.
Etymology
This temperament is named after the star Arcturus, following a series of non-octave temperaments that are named after stars.
|
Todo: add etymology
Add name (person who coined the term) and year (when it was coined).
|
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 ¢:
| Generator
|
Cents
Hekts
|
L
|
s
|
2g
|
Notes
|
| 6\13
|
|
|
|
|
|
|
877.825
600
|
146.304
100
|
0
|
1755.651
1200
|
L = 1, s = 0
|
|
|
|
|
|
|
|
43\93
|
879.399
601.075
|
143.158
97.8495
|
20.451
13.9785
|
1758.797
1202.151
|
L = 7, s = 1
|
|
|
|
|
|
|
37\80
|
|
879.654
601.25
|
142.647
97.5
|
23.774
16.25
|
1759.38
1202.5
|
L = 6, s = 1
|
|
|
|
|
|
|
|
68\147
|
879.816
601.3605
|
142.323
97.279
|
25.877
17.687
|
1759.632
1202.721
|
|
|
|
|
|
|
31\67
|
|
|
880.009
601.4925
|
141.937
97.015
|
28.387
19.403
|
1760.081
1202.985
|
L = 5, s = 1
|
|
|
|
|
|
|
|
87\188
|
880.16
601.596
|
141.634
96.8085
|
30.35
20.745
|
1760.32
1203.191
|
|
|
|
|
|
|
|
56\121
|
|
880.243
601.653
|
141.468
96.694
|
31.437
21.488
|
1760.487
1203.306
|
|
|
|
|
|
|
|
|
81\175
|
880.3335
601.714
|
141.288
96.571
|
32.605
22.286
|
1760.667
1203.429
|
|
|
|
|
|
25\54
|
|
|
|
880.535
601.852
|
140.886
96.296
|
35.221
24.074
|
1761.069
1203.704
|
L = 4, s = 1
|
|
|
|
|
|
|
|
94\203
|
880.708
601.97
|
140.5385
96.059
|
37.477
25.616
|
1761.4165
1203.971
|
|
|
|
|
|
|
|
69\149
|
|
880.711
602.013
|
140.413
95.973
|
38.294
26.1745
|
1761.542
1204.027
|
|
|
|
|
|
|
|
|
113\244
|
880.823
602.049
|
140.308
95.902
|
38.9745
26.639
|
1761.647
1204.098
|
|
|
|
|
|
|
44\95
|
|
|
880.9055
602.105
|
140.144
95.7895
|
40.041
27.368
|
1761.811
1204.2105
|
L = 7, s = 2
|
|
|
|
|
|
|
|
107\231
|
880.992
602.1645
|
139.971
95.671
|
41.168
28.1385
|
1761.984
1204.329.
|
|
|
|
|
|
|
|
63\136
|
|
881.053
602.206
|
139.85
95.588
|
41.955
28.6765
|
1762.105
1204.412
|
|
|
|
|
|
|
|
|
82\177
|
881.132
602.26
|
139.692
95.48
|
42.982
22.034
|
1762.263
1204.52
|
|
|
|
|
19\41
|
|
|
|
|
881.394
602.439
|
139.167
95.122
|
46.389
31.707
|
1762.788
1204.878
|
L = 3, s = 1
|
|
|
|
|
|
|
|
89\192
|
881.635
602.604
|
138.684
94.792
|
49.53
33.854
|
1763.271
1205.208
|
|
|
|
|
|
|
|
70\151
|
|
881.701
602.649
|
138.553
94.702
|
50.383
25.828
|
1763.402
1205.298
|
|
|
|
|
|
|
|
|
121\261
|
881.794
602.682
|
138.4565
89.655
|
51.01
34.866
|
1763.4985
1205.362
|
|
|
|
|
|
|
51\110
|
|
|
881.8155
602.727
|
138.324
94.5455
|
51.8715
35.4545
|
1763.631
1205.4545
|
|
|
|
|
|
|
|
|
134\289
|
881.875
602.768
|
138.204
94.464
|
52.649
35.986
|
1763.751
1205.536
|
|
|
|
|
|
|
|
83\179
|
|
881.912
602.793
|
138.131
94.413
|
53.172
36.313
|
1763.824
1205.586
|
|
|
|
|
|
|
|
|
115\248
|
881.955
602.823
|
138.045
94.355
|
53.684
36.6935
|
1763.91
1205.645
|
|
|
|
|
|
32\69
|
|
|
|
882.066
602.899
|
137.823
94.203
|
55.129
37.681
|
1764.132
1205.797
|
L = 5, s = 2
|
|
|
|
|
|
|
|
109\235
|
882.183
602.979
|
137.588
94.043
|
56.654
38.723
|
1764.367
1205.957
|
|
|
|
|
|
|
|
77\166
|
|
882.232
603.012
|
137.491
93.976
|
57.288
39.157
|
1764.464
1206.024
|
|
|
|
|
|
|
|
|
122\263
|
882.276
603.042
|
137.404
93.916
|
57.854
39.544
|
1764.551
1206.084
|
|
|
|
|
|
|
45\97
|
|
|
882.35
603.093
|
137.2545
93.814
|
58.823
40.206
|
1764.7005
1203.185
|
L = 7, s = 3
|
|
|
|
|
|
|
|
103\222
|
882.439
603.153
|
137.078
93.694
|
59.972
40.991
|
1764.877
1206.306
|
|
|
|
|
|
|
|
58\125
|
|
882.507
603.2
|
136.941
93.6
|
60.863
41.6
|
1765.014
1206.4
|
|
|
|
|
|
|
|
|
71\153
|
882.607
603.268
|
136.742
93.464
|
62.155
42.484
|
1765.213
1206.536
|
|
|
|
13\28
|
|
|
|
|
|
883.0505
603.571
|
135.854
92.857
|
67.93
46.429
|
1766.101
1207.143
|
L = 2, s = 1
|
|
|
|
|
|
|
|
72\155
|
883.489
603.871
|
134.9775
92.258
|
73.624
50.323
|
1766.9775
1207.742
|
|
|
|
|
|
|
|
59\127
|
|
883.585
603.937
|
134.784
92.126
|
74.88
51.181
|
1767.171
1207.574
|
|
|
|
|
|
|
|
|
105\226
|
883.652
603.982
|
134.652
92.035
|
75.742
51.77
|
1767.303
1207.964
|
|
|
|
|
|
|
46\99
|
|
|
883.737
604.04
|
134.482
91.919
|
76.847
52.525
|
1767.473
1208.081
|
L = 7, s = 4
|
|
|
|
|
|
|
|
125\269
|
883.808
604.089
|
134.339
91.822
|
77.775
53.16
|
1767.616
1208.178
|
|
|
|
|
|
|
|
79\170
|
|
883.85
604.118
|
134.256
91.765
|
78.316
53.529
|
1767.699
1208.235
|
|
|
|
|
|
|
|
|
112\241
|
883.896
604.149
|
134.163
91.701
|
78.919
53.942
|
1767.792
1208.299
|
|
|
|
|
|
33\71
|
|
|
|
884.007
604.225
|
133.94
91.549
|
80.364
54.93
|
1768.0145
1208.451
|
L = 5, s = 3
|
|
|
|
|
|
|
|
119\256
|
884.112
604.297
|
133.731
91.406
|
81.725
55.859
|
1768.224
1208.594
|
|
|
|
|
|
|
|
86\185
|
|
884.152
604.324
|
133.651
91.351
|
82.247
56.216
|
1768.304
1208.649
|
|
|
|
|
|
|
|
|
139\299
|
884.186
604.348
|
133.582
91.304
|
82.694
56.522
|
1768.373
1208.696
|
Golden Arcturus is near here
|
|
|
|
|
|
53\114
|
|
|
884.24
604.386
|
133.4705
91.228
|
83.419
57.0175
|
1768.4845
1208.772
|
|
|
|
|
|
|
|
|
126\271
|
884.303
604.428
|
133.347
91.144
|
84.219
57.565
|
1768.608
1208.856
|
|
|
|
|
|
|
|
73\157
|
|
884.3485
604.459
|
133.258
91.083
|
84.8005
57.962
|
1768.697
1208.917
|
5/3-Pythagorean is near here
|
|
|
|
|
|
|
|
93\200
|
884.409
604.5
|
133.137
91
|
85.588
58.5
|
1768.818
1209
|
|
|
|
|
20\43
|
|
|
|
|
884.63
604.651
|
132.6945
90.698
|
88.463
60.465
|
1769.2605
1209.302
|
L = 3, s = 2
|
|
|
|
|
|
|
|
87\187
|
884.867
604.813
|
132.2215
90.374
|
91.538
62.567
|
1769.7335
1209.626
|
|
|
|
|
|
|
|
67\144
|
|
884.937
604.861
|
132.08
90.278
|
92.456
63.194
|
1769.875
1209.722
|
|
|
|
|
|
|
|
|
114\245
|
884.991
604.898
|
131.972
90.204
|
93.157
52.6735
|
1769.983
1209.896
|
|
|
|
|
|
|
47\101
|
|
|
885.068
604.9505
|
131.819
90.099
|
94.156
64.356
|
1770.136
1209.901
|
L = 7, s = 5
|
|
|
|
|
|
|
|
121\260
|
885.141
605
|
131.674
90
|
95.098
65
|
1770.281
1210
|
|
|
|
|
|
|
|
74\159
|
|
885.187
605.031
|
131.582
89.937
|
95.696
65.409
|
1770.373
1210.063
|
|
|
|
|
|
|
|
|
101\217
|
885.242
605.069
|
131.4715
89.862
|
96.4125
65.899
|
1770.4835
1210.138
|
|
|
|
|
|
27\58
|
|
|
|
885.393
605.172
|
131.169
89.655
|
98.377
67.241
|
1770.786
1210.345
|
L = 4, s = 3
|
|
|
|
|
|
|
|
88\189
|
885.566
605.291
|
130.822
89.418
|
100.6325
68.783
|
1771.133
1210.582
|
|
|
|
|
|
|
|
61\131
|
|
885.643
605.3435
|
130.669
89.313
|
101.631
69.466
|
1771.286
1210.687
|
|
|
|
|
|
|
|
|
95\204
|
885.714
605.392
|
130.526
89.216
|
102.556
70.098
|
1771.429
1210.784
|
|
|
|
|
|
|
34\73
|
|
|
885.842
605.4795
|
130.271
89.041
|
104.217
71.233
|
1771.684
1210.959
|
L = 5, s = 4
|
|
|
|
|
|
|
|
75\161
|
886.004
605.59
|
129.947
88.82
|
106.3205
72.671
|
1772.008
1211.18
|
|
|
|
|
|
|
|
41\88
|
|
886.138
605.682
|
129.679
88.636
|
108.065
73.864
|
1772.276
1211.364
|
L = 6, s = 5
|
|
|
|
|
|
|
|
48\103
|
886.348
605.825
|
129.259
88.3495
|
110.7935
75.728
|
1772.696
1211.6505
|
L = 7, s = 6
|
| 7\15
|
|
|
|
|
|
|
887.579
606.667
|
126.797
86.667
|
1775.158
1213.333
|
L = 1, s = 1
|
Scales
