60edo: Difference between revisions

Revision as of 20:31, 22 March 2014

IMPORTED REVISION FROM WIKISPACES

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This revision was by author Andrew_Heathwaite and made on 2014-03-22 20:31:12 UTC.

The original revision id was 497629112.

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

Original Wikitext content:

The 60 equal division divides the octave into 60 parts of exactly 20 cents each. Since 60 = 5 * 12, it belongs to the family of edos which contain 12edo, and like the other small edos of this kind, it tempers out the [[Pythagorean comma]], 531441/524288 = |-19 12>. In the 5-limit, it tempers out both the magic comma, 3125/3072, and the amity comma, 1600000/1594323, and supplies the optimal patent val for 5-limit magic, tempering out 3125/3072. In the 7-limit it tempers out 875/864, 245/243, 225/224 and 10976/10935, and supports magic, compton and tritonic temperaments. In the 11-limit, the 60e val scores lower in badness than the patent val, and makes for an excellent tritonic tuning. It tempers out 121/120 and 441/440, whereas the patent val tempers out 100/99, 385/384 and 540/539. The tuning of 13 is superb at half a cent flat, and the 60e val also works excellently for 13-limit tritonic. As a no-fives val, it is also excellent for the 2.3.7.11.13 [[Chromatic pairs#Bleu|bleu temperament]].

=Intervals= 
|| degrees of 60edo || cents value || approximate ratios in the 2.3.5.13 subgroup || additional ratios of 7 and 11 (assuming flat values for primes) ||
|| 0 || 0 ||   ||   ||
|| 1 || 20 ||   ||   ||
|| 2 || 40 ||   ||   ||
|| 3 || 60 ||   ||   ||
|| 4 || 80 ||   ||   ||
|| 5 || 100 ||   ||   ||
|| 6 || 120 || 16/15 ||   ||
|| 7 || 140 ||   ||   ||
|| 8 || 160 ||   || 12/11, 11/10 ||
|| 9 || 180 || 10/9 ||   ||
|| 10 || 200 || 9/8 ||   ||
|| 11 || 220 ||   ||   ||
|| 12 || 240 || 15/13 || 8/7 ||
|| 13 || 260 ||   || 7/6 ||
|| 14 || 280 ||   ||   ||
|| 15 || 300 ||   ||   ||
|| 16 || 320 ||   ||   ||
|| 17 || 340 ||   || 11/9 ||
|| 18 || 360 || 16/13 ||   ||
|| 19 || 380 ||   ||   ||
|| 20 || 400 ||   ||   ||
|| 21 || 420 ||   || 14/11 ||
|| 22 || 440 ||   || 9/7 ||
|| 23 || 460 || 13/10 ||   ||
|| 24 || 480 ||   ||   ||
|| 25 || 500 || 4/3 ||   ||
|| 26 || 520 ||   ||   ||
|| 27 || 540 ||   || 11/8, 15/11 ||
|| 28 || 560 || 18/13 ||   ||
|| 29 || 580 ||   || 7/5 ||
|| 30 || 600 ||   ||   ||
|| 31 || 620 ||   || 10/7 ||
|| 32 || 640 || 13/8 ||   ||
|| 33 || 660 ||   || 16/11, 22/15 ||
|| 34 || 680 ||   ||   ||
|| 35 || 700 || 3/2 ||   ||
|| 36 || 720 ||   ||   ||
|| 37 || 740 || 20/13 ||   ||
|| 38 || 760 ||   || 14/9 ||
|| 39 || 780 ||   || 11/7 ||
|| 40 || 800 ||   ||   ||
|| 41 || 820 ||   ||   ||
|| 42 || 840 || 13/8 ||   ||
|| 43 || 860 ||   || 18/11 ||
|| 44 || 880 ||   ||   ||
|| 45 || 900 ||   ||   ||
|| 46 || 920 ||   ||   ||
|| 47 || 940 ||   || 12/7 ||
|| 48 || 960 || 26/15 || 7/4 ||
|| 49 || 980 ||   ||   ||
|| 50 || 1000 || 16/9 ||   ||
|| 51 || 1020 || 9/5 ||   ||
|| 52 || 1040 ||   || 11/6, 20/11 ||
|| 53 || 1060 ||   ||   ||
|| 54 || 1080 || 15/8 ||   ||
|| 55 || 1100 ||   ||   ||
|| 56 || 1120 ||   ||   ||
|| 57 || 1140 ||   ||   ||
|| 58 || 1160 ||   ||   ||
|| 59 || 1180 ||   ||   ||
|| 60 || 1200 ||   ||   ||


=Compositions= 
[[http://eceserv0.ece.wisc.edu/%7Esethares/mp3s/rojqoq.html|Rojqoq (So-Called Peace)]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Sethares/Rojqoq.mp3|play]] by William Sethares
[[http://youtu.be/1rrgmP9VYQU|Skating On Thin Ice]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Perry/Skating%20On%20Thin%20Ice.mp3|play]]
[[http://youtu.be/5GIZOYMkkJ0|My Mother Said So]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Perry/My%20Mother%20Said%20So.mp3|play]]
[[http://www.macjams.com/song/62273|Black Salt - White Pepper]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Perry/Black%20Salt%20-%20White%20Pepper.mp3|play]]
[[http://www.macjams.com/song/64413|NGC 300]][[http://micro.soonlabel.com/gene_ward_smith/Others/Perry/NGC%20300.mp3|play]]
all by Robin Perry
[[http://x31eq.com/music/dingshi.mp3|Dingshi]] and
[[http://x31eq.com/music/jitter.ogg|Gene's Jitterbug (ogg)]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Breed/jitter.mp3|Gene's Jitterbug (mp3)]] [[http://x31eq.com/music/jitter60.pdf|Score]]
by Graham Breed

=Images= 
[[image:blue_60edo.png]]

[[image:60edoguitar.jpg]]
Robin Perry guitar

Original HTML content:

<html><head><title>60edo</title></head><body>The 60 equal division divides the octave into 60 parts of exactly 20 cents each. Since 60 = 5 * 12, it belongs to the family of edos which contain 12edo, and like the other small edos of this kind, it tempers out the <a class="wiki_link" href="/Pythagorean%20comma">Pythagorean comma</a>, 531441/524288 = |-19 12&gt;. In the 5-limit, it tempers out both the magic comma, 3125/3072, and the amity comma, 1600000/1594323, and supplies the optimal patent val for 5-limit magic, tempering out 3125/3072. In the 7-limit it tempers out 875/864, 245/243, 225/224 and 10976/10935, and supports magic, compton and tritonic temperaments. In the 11-limit, the 60e val scores lower in badness than the patent val, and makes for an excellent tritonic tuning. It tempers out 121/120 and 441/440, whereas the patent val tempers out 100/99, 385/384 and 540/539. The tuning of 13 is superb at half a cent flat, and the 60e val also works excellently for 13-limit tritonic. As a no-fives val, it is also excellent for the 2.3.7.11.13 <a class="wiki_link" href="/Chromatic%20pairs#Bleu">bleu temperament</a>.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:0 -->Intervals</h1>
 

<table class="wiki_table">
    <tr>
        <td>degrees of 60edo<br />
</td>
        <td>cents value<br />
</td>
        <td>approximate ratios in the 2.3.5.13 subgroup<br />
</td>
        <td>additional ratios of 7 and 11 (assuming flat values for primes)<br />
</td>
    </tr>
    <tr>
        <td>0<br />
</td>
        <td>0<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>20<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>40<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>60<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>80<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>100<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>120<br />
</td>
        <td>16/15<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>140<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>160<br />
</td>
        <td><br />
</td>
        <td>12/11, 11/10<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>180<br />
</td>
        <td>10/9<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>200<br />
</td>
        <td>9/8<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>220<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>240<br />
</td>
        <td>15/13<br />
</td>
        <td>8/7<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>260<br />
</td>
        <td><br />
</td>
        <td>7/6<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>280<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>300<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>320<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>340<br />
</td>
        <td><br />
</td>
        <td>11/9<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>360<br />
</td>
        <td>16/13<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>380<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>400<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>420<br />
</td>
        <td><br />
</td>
        <td>14/11<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>440<br />
</td>
        <td><br />
</td>
        <td>9/7<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>460<br />
</td>
        <td>13/10<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>480<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>500<br />
</td>
        <td>4/3<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>520<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>540<br />
</td>
        <td><br />
</td>
        <td>11/8, 15/11<br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>560<br />
</td>
        <td>18/13<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>580<br />
</td>
        <td><br />
</td>
        <td>7/5<br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td>600<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>620<br />
</td>
        <td><br />
</td>
        <td>10/7<br />
</td>
    </tr>
    <tr>
        <td>32<br />
</td>
        <td>640<br />
</td>
        <td>13/8<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>660<br />
</td>
        <td><br />
</td>
        <td>16/11, 22/15<br />
</td>
    </tr>
    <tr>
        <td>34<br />
</td>
        <td>680<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>35<br />
</td>
        <td>700<br />
</td>
        <td>3/2<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>36<br />
</td>
        <td>720<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>37<br />
</td>
        <td>740<br />
</td>
        <td>20/13<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>38<br />
</td>
        <td>760<br />
</td>
        <td><br />
</td>
        <td>14/9<br />
</td>
    </tr>
    <tr>
        <td>39<br />
</td>
        <td>780<br />
</td>
        <td><br />
</td>
        <td>11/7<br />
</td>
    </tr>
    <tr>
        <td>40<br />
</td>
        <td>800<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>41<br />
</td>
        <td>820<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>42<br />
</td>
        <td>840<br />
</td>
        <td>13/8<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>43<br />
</td>
        <td>860<br />
</td>
        <td><br />
</td>
        <td>18/11<br />
</td>
    </tr>
    <tr>
        <td>44<br />
</td>
        <td>880<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>45<br />
</td>
        <td>900<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>46<br />
</td>
        <td>920<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>47<br />
</td>
        <td>940<br />
</td>
        <td><br />
</td>
        <td>12/7<br />
</td>
    </tr>
    <tr>
        <td>48<br />
</td>
        <td>960<br />
</td>
        <td>26/15<br />
</td>
        <td>7/4<br />
</td>
    </tr>
    <tr>
        <td>49<br />
</td>
        <td>980<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>50<br />
</td>
        <td>1000<br />
</td>
        <td>16/9<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>51<br />
</td>
        <td>1020<br />
</td>
        <td>9/5<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>52<br />
</td>
        <td>1040<br />
</td>
        <td><br />
</td>
        <td>11/6, 20/11<br />
</td>
    </tr>
    <tr>
        <td>53<br />
</td>
        <td>1060<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>54<br />
</td>
        <td>1080<br />
</td>
        <td>15/8<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>55<br />
</td>
        <td>1100<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>56<br />
</td>
        <td>1120<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>57<br />
</td>
        <td>1140<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>58<br />
</td>
        <td>1160<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>59<br />
</td>
        <td>1180<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>60<br />
</td>
        <td>1200<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
</table>

<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:2 -->Compositions</h1>
 <a class="wiki_link_ext" href="http://eceserv0.ece.wisc.edu/%7Esethares/mp3s/rojqoq.html" rel="nofollow">Rojqoq (So-Called Peace)</a> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Sethares/Rojqoq.mp3" rel="nofollow">play</a> by William Sethares<br />
<a class="wiki_link_ext" href="http://youtu.be/1rrgmP9VYQU" rel="nofollow">Skating On Thin Ice</a> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Perry/Skating%20On%20Thin%20Ice.mp3" rel="nofollow">play</a><br />
<a class="wiki_link_ext" href="http://youtu.be/5GIZOYMkkJ0" rel="nofollow">My Mother Said So</a> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Perry/My%20Mother%20Said%20So.mp3" rel="nofollow">play</a><br />
<a class="wiki_link_ext" href="http://www.macjams.com/song/62273" rel="nofollow">Black Salt - White Pepper</a> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Perry/Black%20Salt%20-%20White%20Pepper.mp3" rel="nofollow">play</a><br />
<a class="wiki_link_ext" href="http://www.macjams.com/song/64413" rel="nofollow">NGC 300</a><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Perry/NGC%20300.mp3" rel="nofollow">play</a><br />
all by Robin Perry<br />
<a class="wiki_link_ext" href="http://x31eq.com/music/dingshi.mp3" rel="nofollow">Dingshi</a> and<br />
<a class="wiki_link_ext" href="http://x31eq.com/music/jitter.ogg" rel="nofollow">Gene's Jitterbug (ogg)</a> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Breed/jitter.mp3" rel="nofollow">Gene's Jitterbug (mp3)</a> <a class="wiki_link_ext" href="http://x31eq.com/music/jitter60.pdf" rel="nofollow">Score</a><br />
by Graham Breed<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Images"></a><!-- ws:end:WikiTextHeadingRule:4 -->Images</h1>
 <!-- ws:start:WikiTextLocalImageRule:628:&lt;img src=&quot;/file/view/blue_60edo.png/284591332/blue_60edo.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/blue_60edo.png/284591332/blue_60edo.png" alt="blue_60edo.png" title="blue_60edo.png" /><!-- ws:end:WikiTextLocalImageRule:628 --><br />
<br />
<!-- ws:start:WikiTextLocalImageRule:629:&lt;img src=&quot;/file/view/60edoguitar.jpg/312533826/60edoguitar.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/60edoguitar.jpg/312533826/60edoguitar.jpg" alt="60edoguitar.jpg" title="60edoguitar.jpg" /><!-- ws:end:WikiTextLocalImageRule:629 --><br />
Robin Perry guitar</body></html>

60edo: Difference between revisions

Revision as of 20:31, 22 March 2014

IMPORTED REVISION FROM WIKISPACES

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Original HTML content:

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