77edo: Difference between revisions

Revision as of 05:52, 3 February 2015

IMPORTED REVISION FROM WIKISPACES

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This revision was by author xenwolf and made on 2015-02-03 05:52:37 UTC.

The original revision id was 539467156.

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Original Wikitext content:

=<span style="color: #000083; font-family: 'Times New Roman',Times,serif; font-size: 113%;">77 tone Equal Temperament</span>= 

77-tET or 77-EDO divides the octave into 77 steps of size 15.5844 [[cent]]s each. With fifths less than a cent flat, major thirds a bit over three cents sharp and [[7_4|7/4s]] less flat than that, it represents an excellent tuning choice for both [[Valentine]], the 31&46 temperament, and [[Starling temperaments|starling]], the 126/125 [[planar temperament]], giving the optimal patent val for 11-limit valentine and its 13-limit extensions dwynwen and valentino, as well as [[Starling family#x7-limit%20starling-11-limit|11-limit starling]] and [[Starling family#Oxpecker|oxpecker]] temperaments. It also gives the optimal patent val for various members of the [[unicorn family]], with a [[generator]] of 4\77 instead of the 5\77 which gives valentine. These are 7-limit [[Unicorn family#Alicorn|alicorn]] and 11- and 13-limit camahueto.

77et tempers out 32805/32768 in the [[5-limit]], 126/125, 1029/1024 and 6144/6125 in the [[7-limit]], 121/120, 176/175, 385/384 and 441/440 in the [[11-limit]], and 196/195, 351/350, 352/351, 676/675 and 729/728 in the [[13-limit]].

=Intervals= 
||~ Degree ||~ Cents
Value ||~ Approximate Ratios
in the 13-limit ||
||> 0 ||> 0.000 ||= 1/1 ||
||> 1 ||> 15.584 ||= 81/80, 99/98 ||
||> 2 ||> 31.169 ||= 64/63, 49/48 ||
||> 3 ||> 46.753 ||= 33/32, 36/35 ||
||> 4 ||> 62.338 ||= 28/27, 26/25 ||
||> 5 ||> 77.922 ||= 21/20, 25/24 ||
||> 6 ||> 93.506 ||=   ||
||> 7 ||> 109.091 ||= 16/15 ||
||> 8 ||> 124.675 ||= 15/14 ||
||> 9 ||> 140.260 ||= 13/12 ||
||> 10 ||> 155.844 ||= 12/11, 11/10 ||
||> 11 ||> 171.429 ||=   ||
||> 12 ||> 187.013 ||= 10/9 ||
||> 13 ||> 202.597 ||= 9/8 ||
||> 14 ||> 218.182 ||=   ||
||> 15 ||> 233.766 ||= 8/7 ||
||> 16 ||> 249.351 ||= 15/13 ||
||> 17 ||> 264.935 ||= 7/6 ||
||> 18 ||> 280.519 ||= 33/28 ||
||> 19 ||> 296.104 ||= 32/27, 13/11 ||
||> 20 ||> 311.688 ||= 6/5 ||
||> 21 ||> 327.273 ||=   ||
||> 22 ||> 342.857 ||= 11/9, 39/32 ||
||> 23 ||> 358.442 ||= 16/13 ||
||> 24 ||> 374.026 ||= 56/45, 26/21 ||
||> 25 ||> 389.610 ||= 5/4 ||
||> 26 ||> 405.195 ||= 33/26, 81/64 ||
||> 27 ||> 420.779 ||= 14/11, 32/25 ||
||> 28 ||> 436.364 ||= 9/7 ||
||> 29 ||> 451.948 ||= 13/10 ||
||> 30 ||> 467.532 ||= 21/16 ||
||> 31 ||> 483.117 ||=   ||
||> 32 ||> 498.701 ||= 4/3 ||
||> 33 ||> 514.286 ||= 27/20 ||
||> 34 ||> 529.870 ||= 49/36 ||
||> 35 ||> 545.455 ||= 11/8, 15/11 ||
||> 36 ||> 561.039 ||= 18/13 ||
||> 37 ||> 576.623 ||= 7/5 ||
||> 38 ||> 592.208 ||= 45/32 ||
||> 39 ||> 607.792 ||= 64/45 ||
||> 40 ||> 623.377 ||= 10/7 ||
||> 41 ||> 638.961 ||= 13/9 ||
||> 42 ||> 654.545 ||= 16/11, 22/15 ||
||> 43 ||> 670.130 ||= 72/49 ||
||> 44 ||> 685.714 ||= 40/27 ||
||> 45 ||> 701.299 ||= 3/2 ||
||> 46 ||> 716.883 ||=   ||
||> 47 ||> 732.468 ||= 32/21 ||
||> 48 ||> 748.052 ||= 20/13 ||
||> 49 ||> 763.636 ||= 14/9 ||
||> 50 ||> 779.221 ||= 11/7, 25/16 ||
||> 51 ||> 794.805 ||= 52/33, 128/81 ||
||> 52 ||> 810.390 ||= 8/5 ||
||> 53 ||> 825.974 ||= 45/28, 21/13 ||
||> 54 ||> 841.558 ||= 13/8 ||
||> 55 ||> 857.143 ||= 18/11, 64/39 ||
||> 56 ||> 872.727 ||=   ||
||> 57 ||> 888.312 ||= 5/3 ||
||> 58 ||> 903.896 ||= 27/16, 22/13 ||
||> 59 ||> 919.481 ||= 56/33 ||
||> 60 ||> 935.065 ||= 12/7 ||
||> 61 ||> 950.649 ||= 26/15 ||
||> 62 ||> 966.234 ||= 7/4 ||
||> 63 ||> 981.818 ||=   ||
||> 64 ||> 997.403 ||= 16/9 ||
||> 65 ||> 1012.987 ||= 9/5 ||
||> 66 ||> 1028.571 ||=   ||
||> 67 ||> 1044.156 ||= 11/6, 20/11 ||
||> 68 ||> 1059.740 ||= 24/13 ||
||> 69 ||> 1075.325 ||= 28/15 ||
||> 70 ||> 1090.909 ||= 15/8 ||
||> 71 ||> 1106.494 ||=   ||
||> 72 ||> 1122.078 ||= 40/21, 48/25 ||
||> 73 ||> 1137.662 ||= 27/14, 25/13 ||
||> 74 ||> 1153.247 ||= 64/33, 35/18 ||
||> 75 ||> 1168.831 ||= 63/32, 96/49 ||
||> 76 ||> 1184.416 ||= 160/81, 196/99 ||
||> 77 ||> 1200.000 ||= 2/1 ||

=Linear temperaments= 
||~ Periods
per Octave ||~ Generator ||~ Temperaments ||
||> 1 ||> 1\77 ||   ||
||> 1 ||> 2\77 ||   ||
||> 1 ||> 3\77 ||   ||
||> 1 ||> 4\77 || [[Unicorn]]/alicorn/camahueto/qilin ||
||> 1 ||> 5\77 || [[Valentine]] ||
||> 1 ||> 6\77 ||   ||
||> 1 ||> 8\77 ||   ||
||> 1 ||> 9\77 || [[Tsaharuk]] ||
||> 1 ||> 10\77 ||   ||
||> 1 ||> 12\77 ||   ||
||> 1 ||> 13\77 ||   ||
||> 1 ||> 15\77 || [[Guiron]] ||
||> 1 ||> 16\77 || [[Hemischis]] ||
||> 1 ||> 17\77 ||   ||
||> 1 ||> 18\77 ||   ||
||> 1 ||> 19\77 ||   ||
||> 1 ||> 20\77 ||   ||
||> 1 ||> 23\77 || Restles ([[http://x31eq.com/cgi-bin/rt.cgi?ets=87+%26+77&limit=13|77&87]]) ||
||> 1 ||> 24\77 ||   ||
||> 1 ||> 25\77 ||   ||
||> 1 ||> 26\77 ||   ||
||> 1 ||> 27\77 ||   ||
||> 1 ||> 29\77 ||   ||
||> 1 ||> 30\77 ||   ||
||> 1 ||> 31\77 || [[Hemiseven]] ||
||> 1 ||> 32\77 || [[Hendecatonic]], [[Grackle|grackle]] ||
||> 1 ||> 34\77 || Mabila ([[http://x31eq.com/cgi-bin/rt.cgi?ets=34_43&limit=5|34&43]]) ||
||> 1 ||> 36\77 ||   ||
||> 1 ||> 37\77 ||   ||
||> 1 ||> 38\77 ||   ||
||> 7 ||> 1\77 || "[[TemperamentOrphanage|Absurdity]]" ([[http://x31eq.com/cgi-bin/rt.cgi?ets=7_84&limit=5|7&84]]) ||
||> 7 ||> 2\77 ||   ||
||> 7 ||> 3\77 ||   ||
||> 7 ||> 4\77 ||   ||
||> 7 ||> 5\77 ||   ||
||> 11 ||> 1\77 ||   ||
||> 11 ||> 2\77 ||   ||
||> 11 ||> 3\77 ||   ||

=Music= 

//[[http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/star_1-GrimaldiA+Bmod.mp3|Star 1-GrimaldiA+Bmod]]// by [[Joel Grant Taylor]]
//[[http://micro.soonlabel.com/star/20120830-77et-star.mp3|77et Star]]// by [[Chris Vaisvil]]
//[[http://soonlabel.com/xenharmonic/wp-content/uploads/2013/10/Freivald-J.-A-Seed-Planted-2nd-Version-77edo.mp3|A Seed Planted]]// A Seed Planted by Jake Freivald, in an [[http://soonlabel.com/xenharmonic/archives/1391|organ version]] of Claudi Meneghin.

Original HTML content:

<html><head><title>77edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x77 tone Equal Temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #000083; font-family: 'Times New Roman',Times,serif; font-size: 113%;">77 tone Equal Temperament</span></h1>
 <br />
77-tET or 77-EDO divides the octave into 77 steps of size 15.5844 <a class="wiki_link" href="/cent">cent</a>s each. With fifths less than a cent flat, major thirds a bit over three cents sharp and <a class="wiki_link" href="/7_4">7/4s</a> less flat than that, it represents an excellent tuning choice for both <a class="wiki_link" href="/Valentine">Valentine</a>, the 31&amp;46 temperament, and <a class="wiki_link" href="/Starling%20temperaments">starling</a>, the 126/125 <a class="wiki_link" href="/planar%20temperament">planar temperament</a>, giving the optimal patent val for 11-limit valentine and its 13-limit extensions dwynwen and valentino, as well as <a class="wiki_link" href="/Starling%20family#x7-limit%20starling-11-limit">11-limit starling</a> and <a class="wiki_link" href="/Starling%20family#Oxpecker">oxpecker</a> temperaments. It also gives the optimal patent val for various members of the <a class="wiki_link" href="/unicorn%20family">unicorn family</a>, with a <a class="wiki_link" href="/generator">generator</a> of 4\77 instead of the 5\77 which gives valentine. These are 7-limit <a class="wiki_link" href="/Unicorn%20family#Alicorn">alicorn</a> and 11- and 13-limit camahueto.<br />
<br />
77et tempers out 32805/32768 in the <a class="wiki_link" href="/5-limit">5-limit</a>, 126/125, 1029/1024 and 6144/6125 in the <a class="wiki_link" href="/7-limit">7-limit</a>, 121/120, 176/175, 385/384 and 441/440 in the <a class="wiki_link" href="/11-limit">11-limit</a>, and 196/195, 351/350, 352/351, 676/675 and 729/728 in the <a class="wiki_link" href="/13-limit">13-limit</a>.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 -->Intervals</h1>
 

<table class="wiki_table">
    <tr>
        <th>Degree<br />
</th>
        <th>Cents<br />
Value<br />
</th>
        <th>Approximate Ratios<br />
in the 13-limit<br />
</th>
    </tr>
    <tr>
        <td style="text-align: right;">0<br />
</td>
        <td style="text-align: right;">0.000<br />
</td>
        <td style="text-align: center;">1/1<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">1<br />
</td>
        <td style="text-align: right;">15.584<br />
</td>
        <td style="text-align: center;">81/80, 99/98<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">2<br />
</td>
        <td style="text-align: right;">31.169<br />
</td>
        <td style="text-align: center;">64/63, 49/48<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">3<br />
</td>
        <td style="text-align: right;">46.753<br />
</td>
        <td style="text-align: center;">33/32, 36/35<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">4<br />
</td>
        <td style="text-align: right;">62.338<br />
</td>
        <td style="text-align: center;">28/27, 26/25<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">5<br />
</td>
        <td style="text-align: right;">77.922<br />
</td>
        <td style="text-align: center;">21/20, 25/24<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">6<br />
</td>
        <td style="text-align: right;">93.506<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">7<br />
</td>
        <td style="text-align: right;">109.091<br />
</td>
        <td style="text-align: center;">16/15<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">8<br />
</td>
        <td style="text-align: right;">124.675<br />
</td>
        <td style="text-align: center;">15/14<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">9<br />
</td>
        <td style="text-align: right;">140.260<br />
</td>
        <td style="text-align: center;">13/12<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">10<br />
</td>
        <td style="text-align: right;">155.844<br />
</td>
        <td style="text-align: center;">12/11, 11/10<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">11<br />
</td>
        <td style="text-align: right;">171.429<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">12<br />
</td>
        <td style="text-align: right;">187.013<br />
</td>
        <td style="text-align: center;">10/9<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">13<br />
</td>
        <td style="text-align: right;">202.597<br />
</td>
        <td style="text-align: center;">9/8<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">14<br />
</td>
        <td style="text-align: right;">218.182<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">15<br />
</td>
        <td style="text-align: right;">233.766<br />
</td>
        <td style="text-align: center;">8/7<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">16<br />
</td>
        <td style="text-align: right;">249.351<br />
</td>
        <td style="text-align: center;">15/13<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">17<br />
</td>
        <td style="text-align: right;">264.935<br />
</td>
        <td style="text-align: center;">7/6<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">18<br />
</td>
        <td style="text-align: right;">280.519<br />
</td>
        <td style="text-align: center;">33/28<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">19<br />
</td>
        <td style="text-align: right;">296.104<br />
</td>
        <td style="text-align: center;">32/27, 13/11<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">20<br />
</td>
        <td style="text-align: right;">311.688<br />
</td>
        <td style="text-align: center;">6/5<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">21<br />
</td>
        <td style="text-align: right;">327.273<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">22<br />
</td>
        <td style="text-align: right;">342.857<br />
</td>
        <td style="text-align: center;">11/9, 39/32<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">23<br />
</td>
        <td style="text-align: right;">358.442<br />
</td>
        <td style="text-align: center;">16/13<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">24<br />
</td>
        <td style="text-align: right;">374.026<br />
</td>
        <td style="text-align: center;">56/45, 26/21<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">25<br />
</td>
        <td style="text-align: right;">389.610<br />
</td>
        <td style="text-align: center;">5/4<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">26<br />
</td>
        <td style="text-align: right;">405.195<br />
</td>
        <td style="text-align: center;">33/26, 81/64<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">27<br />
</td>
        <td style="text-align: right;">420.779<br />
</td>
        <td style="text-align: center;">14/11, 32/25<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">28<br />
</td>
        <td style="text-align: right;">436.364<br />
</td>
        <td style="text-align: center;">9/7<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">29<br />
</td>
        <td style="text-align: right;">451.948<br />
</td>
        <td style="text-align: center;">13/10<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">30<br />
</td>
        <td style="text-align: right;">467.532<br />
</td>
        <td style="text-align: center;">21/16<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">31<br />
</td>
        <td style="text-align: right;">483.117<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">32<br />
</td>
        <td style="text-align: right;">498.701<br />
</td>
        <td style="text-align: center;">4/3<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">33<br />
</td>
        <td style="text-align: right;">514.286<br />
</td>
        <td style="text-align: center;">27/20<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">34<br />
</td>
        <td style="text-align: right;">529.870<br />
</td>
        <td style="text-align: center;">49/36<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">35<br />
</td>
        <td style="text-align: right;">545.455<br />
</td>
        <td style="text-align: center;">11/8, 15/11<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">36<br />
</td>
        <td style="text-align: right;">561.039<br />
</td>
        <td style="text-align: center;">18/13<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">37<br />
</td>
        <td style="text-align: right;">576.623<br />
</td>
        <td style="text-align: center;">7/5<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">38<br />
</td>
        <td style="text-align: right;">592.208<br />
</td>
        <td style="text-align: center;">45/32<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">39<br />
</td>
        <td style="text-align: right;">607.792<br />
</td>
        <td style="text-align: center;">64/45<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">40<br />
</td>
        <td style="text-align: right;">623.377<br />
</td>
        <td style="text-align: center;">10/7<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">41<br />
</td>
        <td style="text-align: right;">638.961<br />
</td>
        <td style="text-align: center;">13/9<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">42<br />
</td>
        <td style="text-align: right;">654.545<br />
</td>
        <td style="text-align: center;">16/11, 22/15<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">43<br />
</td>
        <td style="text-align: right;">670.130<br />
</td>
        <td style="text-align: center;">72/49<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">44<br />
</td>
        <td style="text-align: right;">685.714<br />
</td>
        <td style="text-align: center;">40/27<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">45<br />
</td>
        <td style="text-align: right;">701.299<br />
</td>
        <td style="text-align: center;">3/2<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">46<br />
</td>
        <td style="text-align: right;">716.883<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">47<br />
</td>
        <td style="text-align: right;">732.468<br />
</td>
        <td style="text-align: center;">32/21<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">48<br />
</td>
        <td style="text-align: right;">748.052<br />
</td>
        <td style="text-align: center;">20/13<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">49<br />
</td>
        <td style="text-align: right;">763.636<br />
</td>
        <td style="text-align: center;">14/9<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">50<br />
</td>
        <td style="text-align: right;">779.221<br />
</td>
        <td style="text-align: center;">11/7, 25/16<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">51<br />
</td>
        <td style="text-align: right;">794.805<br />
</td>
        <td style="text-align: center;">52/33, 128/81<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">52<br />
</td>
        <td style="text-align: right;">810.390<br />
</td>
        <td style="text-align: center;">8/5<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">53<br />
</td>
        <td style="text-align: right;">825.974<br />
</td>
        <td style="text-align: center;">45/28, 21/13<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">54<br />
</td>
        <td style="text-align: right;">841.558<br />
</td>
        <td style="text-align: center;">13/8<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">55<br />
</td>
        <td style="text-align: right;">857.143<br />
</td>
        <td style="text-align: center;">18/11, 64/39<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">56<br />
</td>
        <td style="text-align: right;">872.727<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">57<br />
</td>
        <td style="text-align: right;">888.312<br />
</td>
        <td style="text-align: center;">5/3<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">58<br />
</td>
        <td style="text-align: right;">903.896<br />
</td>
        <td style="text-align: center;">27/16, 22/13<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">59<br />
</td>
        <td style="text-align: right;">919.481<br />
</td>
        <td style="text-align: center;">56/33<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">60<br />
</td>
        <td style="text-align: right;">935.065<br />
</td>
        <td style="text-align: center;">12/7<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">61<br />
</td>
        <td style="text-align: right;">950.649<br />
</td>
        <td style="text-align: center;">26/15<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">62<br />
</td>
        <td style="text-align: right;">966.234<br />
</td>
        <td style="text-align: center;">7/4<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">63<br />
</td>
        <td style="text-align: right;">981.818<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">64<br />
</td>
        <td style="text-align: right;">997.403<br />
</td>
        <td style="text-align: center;">16/9<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">65<br />
</td>
        <td style="text-align: right;">1012.987<br />
</td>
        <td style="text-align: center;">9/5<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">66<br />
</td>
        <td style="text-align: right;">1028.571<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">67<br />
</td>
        <td style="text-align: right;">1044.156<br />
</td>
        <td style="text-align: center;">11/6, 20/11<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">68<br />
</td>
        <td style="text-align: right;">1059.740<br />
</td>
        <td style="text-align: center;">24/13<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">69<br />
</td>
        <td style="text-align: right;">1075.325<br />
</td>
        <td style="text-align: center;">28/15<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">70<br />
</td>
        <td style="text-align: right;">1090.909<br />
</td>
        <td style="text-align: center;">15/8<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">71<br />
</td>
        <td style="text-align: right;">1106.494<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">72<br />
</td>
        <td style="text-align: right;">1122.078<br />
</td>
        <td style="text-align: center;">40/21, 48/25<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">73<br />
</td>
        <td style="text-align: right;">1137.662<br />
</td>
        <td style="text-align: center;">27/14, 25/13<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">74<br />
</td>
        <td style="text-align: right;">1153.247<br />
</td>
        <td style="text-align: center;">64/33, 35/18<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">75<br />
</td>
        <td style="text-align: right;">1168.831<br />
</td>
        <td style="text-align: center;">63/32, 96/49<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">76<br />
</td>
        <td style="text-align: right;">1184.416<br />
</td>
        <td style="text-align: center;">160/81, 196/99<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">77<br />
</td>
        <td style="text-align: right;">1200.000<br />
</td>
        <td style="text-align: center;">2/1<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Linear temperaments"></a><!-- ws:end:WikiTextHeadingRule:4 -->Linear temperaments</h1>
 

<table class="wiki_table">
    <tr>
        <th>Periods<br />
per Octave<br />
</th>
        <th>Generator<br />
</th>
        <th>Temperaments<br />
</th>
    </tr>
    <tr>
        <td style="text-align: right;">1<br />
</td>
        <td style="text-align: right;">1\77<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">1<br />
</td>
        <td style="text-align: right;">2\77<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">1<br />
</td>
        <td style="text-align: right;">3\77<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">1<br />
</td>
        <td style="text-align: right;">4\77<br />
</td>
        <td><a class="wiki_link" href="/Unicorn">Unicorn</a>/alicorn/camahueto/qilin<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">1<br />
</td>
        <td style="text-align: right;">5\77<br />
</td>
        <td><a class="wiki_link" href="/Valentine">Valentine</a><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">1<br />
</td>
        <td style="text-align: right;">6\77<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">1<br />
</td>
        <td style="text-align: right;">8\77<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">1<br />
</td>
        <td style="text-align: right;">9\77<br />
</td>
        <td><a class="wiki_link" href="/Tsaharuk">Tsaharuk</a><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">1<br />
</td>
        <td style="text-align: right;">10\77<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">1<br />
</td>
        <td style="text-align: right;">12\77<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">1<br />
</td>
        <td style="text-align: right;">13\77<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">1<br />
</td>
        <td style="text-align: right;">15\77<br />
</td>
        <td><a class="wiki_link" href="/Guiron">Guiron</a><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">1<br />
</td>
        <td style="text-align: right;">16\77<br />
</td>
        <td><a class="wiki_link" href="/Hemischis">Hemischis</a><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">1<br />
</td>
        <td style="text-align: right;">17\77<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">1<br />
</td>
        <td style="text-align: right;">18\77<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">1<br />
</td>
        <td style="text-align: right;">19\77<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">1<br />
</td>
        <td style="text-align: right;">20\77<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">1<br />
</td>
        <td style="text-align: right;">23\77<br />
</td>
        <td>Restles (<a class="wiki_link_ext" href="http://x31eq.com/cgi-bin/rt.cgi?ets=87+%26+77&amp;limit=13" rel="nofollow">77&amp;87</a>)<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">1<br />
</td>
        <td style="text-align: right;">24\77<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">1<br />
</td>
        <td style="text-align: right;">25\77<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">1<br />
</td>
        <td style="text-align: right;">26\77<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">1<br />
</td>
        <td style="text-align: right;">27\77<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">1<br />
</td>
        <td style="text-align: right;">29\77<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">1<br />
</td>
        <td style="text-align: right;">30\77<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">1<br />
</td>
        <td style="text-align: right;">31\77<br />
</td>
        <td><a class="wiki_link" href="/Hemiseven">Hemiseven</a><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">1<br />
</td>
        <td style="text-align: right;">32\77<br />
</td>
        <td><a class="wiki_link" href="/Hendecatonic">Hendecatonic</a>, <a class="wiki_link" href="/Grackle">grackle</a><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">1<br />
</td>
        <td style="text-align: right;">34\77<br />
</td>
        <td>Mabila (<a class="wiki_link_ext" href="http://x31eq.com/cgi-bin/rt.cgi?ets=34_43&amp;limit=5" rel="nofollow">34&amp;43</a>)<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">1<br />
</td>
        <td style="text-align: right;">36\77<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">1<br />
</td>
        <td style="text-align: right;">37\77<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">1<br />
</td>
        <td style="text-align: right;">38\77<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">7<br />
</td>
        <td style="text-align: right;">1\77<br />
</td>
        <td>&quot;<a class="wiki_link" href="/TemperamentOrphanage">Absurdity</a>&quot; (<a class="wiki_link_ext" href="http://x31eq.com/cgi-bin/rt.cgi?ets=7_84&amp;limit=5" rel="nofollow">7&amp;84</a>)<br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">7<br />
</td>
        <td style="text-align: right;">2\77<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">7<br />
</td>
        <td style="text-align: right;">3\77<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">7<br />
</td>
        <td style="text-align: right;">4\77<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">7<br />
</td>
        <td style="text-align: right;">5\77<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">11<br />
</td>
        <td style="text-align: right;">1\77<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">11<br />
</td>
        <td style="text-align: right;">2\77<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: right;">11<br />
</td>
        <td style="text-align: right;">3\77<br />
</td>
        <td><br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:6 -->Music</h1>
 <br />
<em><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/star_1-GrimaldiA+Bmod.mp3" rel="nofollow">Star 1-GrimaldiA+Bmod</a></em> by <a class="wiki_link" href="/Joel%20Grant%20Taylor">Joel Grant Taylor</a><br />
<em><a class="wiki_link_ext" href="http://micro.soonlabel.com/star/20120830-77et-star.mp3" rel="nofollow">77et Star</a></em> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br />
<em><a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/wp-content/uploads/2013/10/Freivald-J.-A-Seed-Planted-2nd-Version-77edo.mp3" rel="nofollow">A Seed Planted</a></em> A Seed Planted by Jake Freivald, in an <a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/archives/1391" rel="nofollow">organ version</a> of Claudi Meneghin.</body></html>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:Gedankenwelt|Gedankenwelt]] and made on <tt>2015-02-03 05:19:21 UTC</tt>.<br>
+: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2015-02-03 05:52:37 UTC</tt>.<br>
-: The original revision id was <tt>539465466</tt>.<br>
+: The original revision id was <tt>539467156</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>
@@ Line 8: / Line 8: @@
 <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">=&lt;span style="color: #000083; font-family: 'Times New Roman',Times,serif; font-size: 113%;"&gt;77 tone Equal Temperament&lt;/span&gt;=
--tET or 77-EDO divides the octave into 77 steps of size 15.5844 [[cent]]s each. With fifths less than a cent flat, major thirds a bit over three cents sharp and [[7_4|7/4s]] less flat than that, it represents an excellent tuning choice for both [[Starling temperaments#Valentine%20temperament|valentine]], the 31&amp;46 temperament, and [[Starling temperaments|starling]], the 126/125 [[planar temperament]], giving the optimal patent val for 11-limit valentine and its 13-limit extensions dwynwen and valentino, as well as [[Starling family#x7-limit%20starling-11-limit|11-limit starling]] and [[Starling family#Oxpecker|oxpecker]] temperaments. It also gives the optimal patent val for various members of the [[unicorn family]], with a [[generator]] of 4\77 instead of the 5\77 which gives valentine. These are 7-limit [[Unicorn family#Alicorn|alicorn]] and 11- and 13-limit camahueto.
+-tET or 77-EDO divides the octave into 77 steps of size 15.5844 [[cent]]s each. With fifths less than a cent flat, major thirds a bit over three cents sharp and [[7_4|7/4s]] less flat than that, it represents an excellent tuning choice for both [[Valentine]], the 31&amp;46 temperament, and [[Starling temperaments|starling]], the 126/125 [[planar temperament]], giving the optimal patent val for 11-limit valentine and its 13-limit extensions dwynwen and valentino, as well as [[Starling family#x7-limit%20starling-11-limit|11-limit starling]] and [[Starling family#Oxpecker|oxpecker]] temperaments. It also gives the optimal patent val for various members of the [[unicorn family]], with a [[generator]] of 4\77 instead of the 5\77 which gives valentine. These are 7-limit [[Unicorn family#Alicorn|alicorn]] and 11- and 13-limit camahueto.
 et tempers out 32805/32768 in the [[5-limit]], 126/125, 1029/1024 and 6144/6125 in the [[7-limit]], 121/120, 176/175, 385/384 and 441/440 in the [[11-limit]], and 196/195, 351/350, 352/351, 676/675 and 729/728 in the [[13-limit]].
@@ Line 145: / Line 145: @@
 <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;77edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x77 tone Equal Temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;span style="color: #000083; font-family: 'Times New Roman',Times,serif; font-size: 113%;"&gt;77 tone Equal Temperament&lt;/span&gt;&lt;/h1&gt;
   &lt;br /&gt;
--tET or 77-EDO divides the octave into 77 steps of size 15.5844 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s each. With fifths less than a cent flat, major thirds a bit over three cents sharp and &lt;a class="wiki_link" href="/7_4"&gt;7/4s&lt;/a&gt; less flat than that, it represents an excellent tuning choice for both &lt;a class="wiki_link" href="/Starling%20temperaments#Valentine%20temperament"&gt;valentine&lt;/a&gt;, the 31&amp;amp;46 temperament, and &lt;a class="wiki_link" href="/Starling%20temperaments"&gt;starling&lt;/a&gt;, the 126/125 &lt;a class="wiki_link" href="/planar%20temperament"&gt;planar temperament&lt;/a&gt;, giving the optimal patent val for 11-limit valentine and its 13-limit extensions dwynwen and valentino, as well as &lt;a class="wiki_link" href="/Starling%20family#x7-limit%20starling-11-limit"&gt;11-limit starling&lt;/a&gt; and &lt;a class="wiki_link" href="/Starling%20family#Oxpecker"&gt;oxpecker&lt;/a&gt; temperaments. It also gives the optimal patent val for various members of the &lt;a class="wiki_link" href="/unicorn%20family"&gt;unicorn family&lt;/a&gt;, with a &lt;a class="wiki_link" href="/generator"&gt;generator&lt;/a&gt; of 4\77 instead of the 5\77 which gives valentine. These are 7-limit &lt;a class="wiki_link" href="/Unicorn%20family#Alicorn"&gt;alicorn&lt;/a&gt; and 11- and 13-limit camahueto.&lt;br /&gt;
+-tET or 77-EDO divides the octave into 77 steps of size 15.5844 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s each. With fifths less than a cent flat, major thirds a bit over three cents sharp and &lt;a class="wiki_link" href="/7_4"&gt;7/4s&lt;/a&gt; less flat than that, it represents an excellent tuning choice for both &lt;a class="wiki_link" href="/Valentine"&gt;Valentine&lt;/a&gt;, the 31&amp;amp;46 temperament, and &lt;a class="wiki_link" href="/Starling%20temperaments"&gt;starling&lt;/a&gt;, the 126/125 &lt;a class="wiki_link" href="/planar%20temperament"&gt;planar temperament&lt;/a&gt;, giving the optimal patent val for 11-limit valentine and its 13-limit extensions dwynwen and valentino, as well as &lt;a class="wiki_link" href="/Starling%20family#x7-limit%20starling-11-limit"&gt;11-limit starling&lt;/a&gt; and &lt;a class="wiki_link" href="/Starling%20family#Oxpecker"&gt;oxpecker&lt;/a&gt; temperaments. It also gives the optimal patent val for various members of the &lt;a class="wiki_link" href="/unicorn%20family"&gt;unicorn family&lt;/a&gt;, with a &lt;a class="wiki_link" href="/generator"&gt;generator&lt;/a&gt; of 4\77 instead of the 5\77 which gives valentine. These are 7-limit &lt;a class="wiki_link" href="/Unicorn%20family#Alicorn"&gt;alicorn&lt;/a&gt; and 11- and 13-limit camahueto.&lt;br /&gt;
 &lt;br /&gt;
 et tempers out 32805/32768 in the &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt;, 126/125, 1029/1024 and 6144/6125 in the &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt;, 121/120, 176/175, 385/384 and 441/440 in the &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt;, and 196/195, 351/350, 352/351, 676/675 and 729/728 in the &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt;.&lt;br /&gt;

77edo: Difference between revisions

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IMPORTED REVISION FROM WIKISPACES

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