Xenharmonic Wiki

62edo

Revision as of 17:59, 29 December 2016 by Wikispaces>xenwolf (**Imported revision 602901646 - Original comment: **)

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author xenwolf and made on 2016-12-29 17:59:39 UTC.
The original revision id was 602901646.
The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

=<span style="color: #edd637; font-family: 'Times New Roman',Times,serif; font-size: 113%;">62 tone equal temperament</span>= 

62edo divides the octave into 62 equal parts of 19.35484 cents each. 62 = 2 * 31 and the patent val is a contorted 31edo through the 11-limit; in the 13-limit it tempers out 169/168, 1188/1183, 847/845 and 676/675. It provides the optimal patent val for [[31 comma temperaments#Gallium|gallium]], [[Starling temperaments#Valentine%20temperament-Semivalentine|semivalentine]] and [[Meantone family#Septimal%20meantone-Unidecimal%20meantone%20aka%20Huygens-Hemimeantone|hemimeantone]] temperaments.

Using the 35\62 generator, which leads to the <62 97 143 173| val, 62edo is also an excellent tuning for septimal mavila temperament; alternatively <62 97 143 172| supports hornbostel.

===**62-EDO Intervals**=== 

|| **ARMODUE NOMENCLATURE 8;3 RELATION** ||
|| * **Ɨ** = Thick (1/8-tone up)
* **‡** = Semisharp (1/4-tone up)
* **b** = Flat (5/8-tone down)
* **◊** = Node (sharp/flat blindspot 1/2-tone)
* **#** = Sharp (5/8-tone up)
* **v** = Semiflat (1/4-tone down)
* **⌐** = Thin (1/8-tone down) ||

||~ [[Degree]] ||~ Size ([[cent|Cents]]) ||~ Armodue notation ||~ Approximate intervals ||
||=  0 ||>    0.0000 ||= 1 ||   ||
||=  1 ||>   19.3548 ||= 1Ɨ ||   ||
||=  2 ||>   38.7097 ||= 1‡ (9#) ||   ||
||=  3 ||>   58.0645 ||= 2b ||   ||
||=  4 ||>   77.4194 ||= 1◊2 ||   ||
||=  5 ||>   96.7742 ||= 1# ||   ||
||=  6 ||>  116.1290 ||= 2v ||   ||
||=  7 ||>  135.4839 ||= 2⌐ ||   ||
||=  8 ||>  154.8387 ||= 2 ||   ||
||=  9 ||>  174.1935 ||= 2Ɨ ||   ||
||= 10 ||>  193.5484 ||= 2‡ ||   ||
||= 11 ||>  212.9032 ||= 3b || · ||
||= 12 ||>  232.2581 ||= 2◊3 ||   ||
||= 13 ||>  251.6129 ||= 2# ||   ||
||= 14 ||>  270.9677 ||= 3v ||   ||
||= 15 ||>  290.3226 ||= 3⌐ ||   ||
||= 16 ||>  309.6774 ||= 3 ||   ||
||= 17 ||>  329.0323 ||= 3Ɨ ||   ||
||= 18 ||>  348.3871 ||= 3‡ ||   ||
||= 19 ||>  367.7419 ||= 4b || · ||
||= 20 ||>  387.0968 ||= 3◊4 ||   ||
||= 21 ||>  406.4516 ||= 3# ||   ||
||= 22 ||>  425.8065 ||= 4v (5b) ||   ||
||= 23 ||>  445.1613 ||= 4⌐ ||   ||
||= 24 ||>  464.5161 ||= 4 ||   ||
||= 25 ||>  483.8710 ||= 4Ɨ (5v) ||   ||
||= 26 ||>  503.2258 ||= 5⌐ (4‡) ||   ||
||= 27 ||>  522.5806 ||= 5 || · ||
||= 28 ||>  541.9355 ||= 5Ɨ ||   ||
||= 29 ||>  561.2903 ||= 5‡ (4#) ||   ||
||= 30 ||>  580.6452 ||= 6b ||   ||
||= 31 ||>  600.0000 ||= 5◊6 ||   ||
||= 32 ||>  619.3548 ||= 5# ||   ||
||= 33 ||>  638.7097 ||= 6v ||   ||
||= 34 ||>  658.0645 ||= 6⌐ ||   ||
||= 35 ||>  677.4194 ||= 6 || · ||
||= 36 ||>  696.7742 ||= 6Ɨ ||   ||
||= 37 ||>  716.1290 ||= 6‡ ||   ||
||= 38 ||>  735.4839 ||= 7b ||   ||
||= 39 ||>  754.8387 ||= 6◊7 ||   ||
||= 40 ||>  774.1935 ||= 6# ||   ||
||= 41 ||>  793.5484 ||= 7v ||   ||
||= 42 ||>  812.9032 ||= 7⌐ ||   ||
||= 43 ||>  832.2581 ||= 7 || · ||
||= 44 ||>  851.6129 ||= 7Ɨ ||   ||
||= 45 ||>  870.9677 ||= 7‡ ||   ||
||= 46 ||>  890.3226 ||= 8b ||   ||
||= 47 ||>  909.6774 ||= 7◊8 ||   ||
||= 48 ||>  929.0323 ||= 7# ||   ||
||= 49 ||>  948.3871 ||= 8v ||   ||
||= 50 ||>  967.7419 ||= 8⌐ ||   ||
||= 51 ||>  987.0968 ||= 8 || · ||
||= 52 ||> 1006.4516 ||= 8Ɨ ||   ||
||= 53 ||> 1025.8065 ||= 8‡ ||   ||
||= 54 ||> 1045.1613 ||= 9b ||   ||
||= 55 ||> 1064.5161 ||= 8◊9 ||   ||
||= 56 ||> 1083.8710 ||= 8# ||   ||
||= 57 ||> 1103.2258 ||= 9v (1b) ||   ||
||= 58 ||> 1122.5806 ||= 9⌐ ||   ||
||= 59 ||> 1141.9355 ||= 9 ||   ||
||= 60 ||> 1161.2903 ||= 9Ɨ (1v) ||   ||
||= 61 ||> 1180.6452 ||= 1⌐ (9‡) ||   ||
||= 62 ||> 1200.0000 ||= 1 ||   ||

Original HTML content:

<html><head><title>62edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x62 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #edd637; font-family: 'Times New Roman',Times,serif; font-size: 113%;">62 tone equal temperament</span></h1>
 <br />
62edo divides the octave into 62 equal parts of 19.35484 cents each. 62 = 2 * 31 and the patent val is a contorted 31edo through the 11-limit; in the 13-limit it tempers out 169/168, 1188/1183, 847/845 and 676/675. It provides the optimal patent val for <a class="wiki_link" href="/31%20comma%20temperaments#Gallium">gallium</a>, <a class="wiki_link" href="/Starling%20temperaments#Valentine%20temperament-Semivalentine">semivalentine</a> and <a class="wiki_link" href="/Meantone%20family#Septimal%20meantone-Unidecimal%20meantone%20aka%20Huygens-Hemimeantone">hemimeantone</a> temperaments.<br />
<br />
Using the 35\62 generator, which leads to the &lt;62 97 143 173| val, 62edo is also an excellent tuning for septimal mavila temperament; alternatively &lt;62 97 143 172| supports hornbostel.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x62 tone equal temperament--62-EDO Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 --><strong>62-EDO Intervals</strong></h3>
 <br />


<table class="wiki_table">
    <tr>
        <td><strong>ARMODUE NOMENCLATURE 8;3 RELATION</strong><br />
</td>
    </tr>
    <tr>
        <td><ul><li><strong>Ɨ</strong> = Thick (1/8-tone up)</li><li><strong>‡</strong> = Semisharp (1/4-tone up)</li><li><strong>b</strong> = Flat (5/8-tone down)</li><li><strong>◊</strong> = Node (sharp/flat blindspot 1/2-tone)</li><li><strong>#</strong> = Sharp (5/8-tone up)</li><li><strong>v</strong> = Semiflat (1/4-tone down)</li><li><strong>⌐</strong> = Thin (1/8-tone down)</li></ul></td>
    </tr>
</table>

<br />


<table class="wiki_table">
    <tr>
        <th><a class="wiki_link" href="/Degree">Degree</a><br />
</th>
        <th>Size (<a class="wiki_link" href="/cent">Cents</a>)<br />
</th>
        <th>Armodue notation<br />
</th>
        <th>Approximate intervals<br />
</th>
    </tr>
    <tr>
        <td style="text-align: center;">0<br />
</td>
        <td style="text-align: right;">0.0000<br />
</td>
        <td style="text-align: center;">1<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">1<br />
</td>
        <td style="text-align: right;">19.3548<br />
</td>
        <td style="text-align: center;">1Ɨ<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">2<br />
</td>
        <td style="text-align: right;">38.7097<br />
</td>
        <td style="text-align: center;">1‡ (9#)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">3<br />
</td>
        <td style="text-align: right;">58.0645<br />
</td>
        <td style="text-align: center;">2b<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">4<br />
</td>
        <td style="text-align: right;">77.4194<br />
</td>
        <td style="text-align: center;">1◊2<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">5<br />
</td>
        <td style="text-align: right;">96.7742<br />
</td>
        <td style="text-align: center;">1#<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">6<br />
</td>
        <td style="text-align: right;">116.1290<br />
</td>
        <td style="text-align: center;">2v<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">7<br />
</td>
        <td style="text-align: right;">135.4839<br />
</td>
        <td style="text-align: center;">2⌐<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">8<br />
</td>
        <td style="text-align: right;">154.8387<br />
</td>
        <td style="text-align: center;">2<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">9<br />
</td>
        <td style="text-align: right;">174.1935<br />
</td>
        <td style="text-align: center;">2Ɨ<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">10<br />
</td>
        <td style="text-align: right;">193.5484<br />
</td>
        <td style="text-align: center;">2‡<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">11<br />
</td>
        <td style="text-align: right;">212.9032<br />
</td>
        <td style="text-align: center;">3b<br />
</td>
        <td>·<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">12<br />
</td>
        <td style="text-align: right;">232.2581<br />
</td>
        <td style="text-align: center;">2◊3<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">13<br />
</td>
        <td style="text-align: right;">251.6129<br />
</td>
        <td style="text-align: center;">2#<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">14<br />
</td>
        <td style="text-align: right;">270.9677<br />
</td>
        <td style="text-align: center;">3v<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">15<br />
</td>
        <td style="text-align: right;">290.3226<br />
</td>
        <td style="text-align: center;">3⌐<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">16<br />
</td>
        <td style="text-align: right;">309.6774<br />
</td>
        <td style="text-align: center;">3<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">17<br />
</td>
        <td style="text-align: right;">329.0323<br />
</td>
        <td style="text-align: center;">3Ɨ<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">18<br />
</td>
        <td style="text-align: right;">348.3871<br />
</td>
        <td style="text-align: center;">3‡<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">19<br />
</td>
        <td style="text-align: right;">367.7419<br />
</td>
        <td style="text-align: center;">4b<br />
</td>
        <td>·<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">20<br />
</td>
        <td style="text-align: right;">387.0968<br />
</td>
        <td style="text-align: center;">3◊4<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">21<br />
</td>
        <td style="text-align: right;">406.4516<br />
</td>
        <td style="text-align: center;">3#<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">22<br />
</td>
        <td style="text-align: right;">425.8065<br />
</td>
        <td style="text-align: center;">4v (5b)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">23<br />
</td>
        <td style="text-align: right;">445.1613<br />
</td>
        <td style="text-align: center;">4⌐<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">24<br />
</td>
        <td style="text-align: right;">464.5161<br />
</td>
        <td style="text-align: center;">4<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">25<br />
</td>
        <td style="text-align: right;">483.8710<br />
</td>
        <td style="text-align: center;">4Ɨ (5v)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">26<br />
</td>
        <td style="text-align: right;">503.2258<br />
</td>
        <td style="text-align: center;">5⌐ (4‡)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">27<br />
</td>
        <td style="text-align: right;">522.5806<br />
</td>
        <td style="text-align: center;">5<br />
</td>
        <td>·<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">28<br />
</td>
        <td style="text-align: right;">541.9355<br />
</td>
        <td style="text-align: center;">5Ɨ<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">29<br />
</td>
        <td style="text-align: right;">561.2903<br />
</td>
        <td style="text-align: center;">5‡ (4#)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">30<br />
</td>
        <td style="text-align: right;">580.6452<br />
</td>
        <td style="text-align: center;">6b<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">31<br />
</td>
        <td style="text-align: right;">600.0000<br />
</td>
        <td style="text-align: center;">5◊6<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">32<br />
</td>
        <td style="text-align: right;">619.3548<br />
</td>
        <td style="text-align: center;">5#<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">33<br />
</td>
        <td style="text-align: right;">638.7097<br />
</td>
        <td style="text-align: center;">6v<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">34<br />
</td>
        <td style="text-align: right;">658.0645<br />
</td>
        <td style="text-align: center;">6⌐<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">35<br />
</td>
        <td style="text-align: right;">677.4194<br />
</td>
        <td style="text-align: center;">6<br />
</td>
        <td>·<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">36<br />
</td>
        <td style="text-align: right;">696.7742<br />
</td>
        <td style="text-align: center;">6Ɨ<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">37<br />
</td>
        <td style="text-align: right;">716.1290<br />
</td>
        <td style="text-align: center;">6‡<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">38<br />
</td>
        <td style="text-align: right;">735.4839<br />
</td>
        <td style="text-align: center;">7b<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">39<br />
</td>
        <td style="text-align: right;">754.8387<br />
</td>
        <td style="text-align: center;">6◊7<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">40<br />
</td>
        <td style="text-align: right;">774.1935<br />
</td>
        <td style="text-align: center;">6#<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">41<br />
</td>
        <td style="text-align: right;">793.5484<br />
</td>
        <td style="text-align: center;">7v<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">42<br />
</td>
        <td style="text-align: right;">812.9032<br />
</td>
        <td style="text-align: center;">7⌐<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">43<br />
</td>
        <td style="text-align: right;">832.2581<br />
</td>
        <td style="text-align: center;">7<br />
</td>
        <td>·<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">44<br />
</td>
        <td style="text-align: right;">851.6129<br />
</td>
        <td style="text-align: center;">7Ɨ<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">45<br />
</td>
        <td style="text-align: right;">870.9677<br />
</td>
        <td style="text-align: center;">7‡<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">46<br />
</td>
        <td style="text-align: right;">890.3226<br />
</td>
        <td style="text-align: center;">8b<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">47<br />
</td>
        <td style="text-align: right;">909.6774<br />
</td>
        <td style="text-align: center;">7◊8<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">48<br />
</td>
        <td style="text-align: right;">929.0323<br />
</td>
        <td style="text-align: center;">7#<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">49<br />
</td>
        <td style="text-align: right;">948.3871<br />
</td>
        <td style="text-align: center;">8v<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">50<br />
</td>
        <td style="text-align: right;">967.7419<br />
</td>
        <td style="text-align: center;">8⌐<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">51<br />
</td>
        <td style="text-align: right;">987.0968<br />
</td>
        <td style="text-align: center;">8<br />
</td>
        <td>·<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">52<br />
</td>
        <td style="text-align: right;">1006.4516<br />
</td>
        <td style="text-align: center;">8Ɨ<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">53<br />
</td>
        <td style="text-align: right;">1025.8065<br />
</td>
        <td style="text-align: center;">8‡<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">54<br />
</td>
        <td style="text-align: right;">1045.1613<br />
</td>
        <td style="text-align: center;">9b<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">55<br />
</td>
        <td style="text-align: right;">1064.5161<br />
</td>
        <td style="text-align: center;">8◊9<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">56<br />
</td>
        <td style="text-align: right;">1083.8710<br />
</td>
        <td style="text-align: center;">8#<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">57<br />
</td>
        <td style="text-align: right;">1103.2258<br />
</td>
        <td style="text-align: center;">9v (1b)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">58<br />
</td>
        <td style="text-align: right;">1122.5806<br />
</td>
        <td style="text-align: center;">9⌐<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">59<br />
</td>
        <td style="text-align: right;">1141.9355<br />
</td>
        <td style="text-align: center;">9<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">60<br />
</td>
        <td style="text-align: right;">1161.2903<br />
</td>
        <td style="text-align: center;">9Ɨ (1v)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">61<br />
</td>
        <td style="text-align: right;">1180.6452<br />
</td>
        <td style="text-align: center;">1⌐ (9‡)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">62<br />
</td>
        <td style="text-align: right;">1200.0000<br />
</td>
        <td style="text-align: center;">1<br />
</td>
        <td><br />
</td>
    </tr>
</table>

</body></html>
Retrieved from "https://en.xen.wiki/index.php?title=62edo&oldid=9755"