53edo: Difference between revisions

Revision as of 22:21, 4 July 2012

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[[toc|flat]]
=Theory= 
The famous //53 equal division// divides the octave into 53 equal comma-sized parts of 22.642 cents each. It is notable as a [[xenharmonic/5-limit|5-limit]] system, a fact apparently first noted by Isaac Newton, tempering out the schisma, 32805/32768, the kleisma, 15625/15552, the amity comma, 1600000/1594323 and the semicomma, 2109375/2097152. In the 7-limit it tempers out 225/224, 1728/1715 and 3125/3087, the marvel comma, the gariboh, and the orwell comma. In the 11-limit, it tempers out 99/98 and 121/120, and is the [[xenharmonic/optimal patent val|optimal patent val]] for [[xenharmonic/Nuwell family|Big Brother]] temperament, which tempers out both, as well as 11-limit [[xenharmonic/Semicomma family|orwell temperament]], which also tempers out the 11-limit comma 176/175. In the 13-limit, it tempers out 169/168 and 245/243, and gives the optimal patent val for [[xenharmonic/Marvel family|athene temperament]]. It is the eighth [[xenharmonic/The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta integral edo]] and the 16th [[xenharmonic/prime numbers|prime]] edo, following [[xenharmonic/47edo|47edo]] and coming before [[xenharmonic/59edo|59edo]].

53EDO has also found a certain dissemination as an EDO tuning for [[Arabic, Turkish, Persian|Arabic/Turkish/Persian music]] .

[[http://en.wikipedia.org/wiki/53_equal_temperament|Wikipeda article about 53edo]]

=Linear temperaments= 
[[List of edo-distinct 53et rank two temperaments]]

=Just Approximation= 
53edo provides excellent approximations for the classic 5-limit [[xenharmonic/just|just]] chords and scales, such as the Ptolemy-Zarlino "just major" scale.
||~ interval ||~ size ||~ diff ||
|| perfect fifth ||= 31 || −0.07 cents ||
|| major third ||= 17 || −1.40 cents ||
|| minor third ||= 14 || +1.34 cents ||
|| major tone ||= 9 || −0.14 cents ||
|| minor tone ||= 8 || −1.27 cents ||
|| diat. semitone ||= 5 || +1.48 cents ||

One notable property of 53EDO is that it offers good approximations for both pure and pythagorean major thirds.

The perfect fifth is almost perfectly equal to the just interval 3/2, with only a 0.07 cent difference! 53EDO is practically equal to an extended Pythagorean. The 14- and 17- degree intervals are also very close to 6/5 and 5/4 respectively, and so 5-limit tuning can also be closely approximated. In addition, the 43-degree interval is only 4.8 cents away from the just ratio 7/4, so 53EDO can also be used for 7-limit harmony, tempering out the [[xenharmonic/septimal kleisma|septimal kleisma]], 225/224.

=Intervals= 
|| degrees of 53edo || solfege || cents value || approximate 13-limit ratios || generator for ||
|| 0 || do || 0.00 || 1/1 ||   ||
|| 1 || di || 22.64 || 81/80, 64/63, 50/49 ||   ||
|| 2 || daw || 45.28 || 49/48, 36/35, 33/32 || [[xenharmonic/Quartonic|Quartonic]] ||
|| 3 || ro || 67.92 || 27/26, 26/25, 25/24, 22/21 ||   ||
|| 4 || rih || 90.57 || 21/20 ||   ||
|| 5 || ra || 113.21 || 16/15, 15/14 ||   ||
|| 6 || ru || 135.85 || 14/13, 13/12 ||   ||
|| 7 || ruh || 158.49 || 12/11, 11/10 || [[xenharmonic/Hemikleismic|Hemikleismic]] ||
|| 8 || reh || 181.13 || 10/9 ||   ||
|| 9 || re || 203.77 || 9/8 ||   ||
|| 10 || ri || 226.42 || 8/7 ||   ||
|| 11 || raw || 249.06 || 15/13 || [[xenharmonic/Hemischis|Hemischis]] ||
|| 12 || ma || 271.70 || 7/6 || [[xenharmonic/Orwell|Orwell]] ||
|| 13 || meh || 294.34 || 13/11 ||   ||
|| 14 || me || 316.98 || 6/5 || [[xenharmonic/Hanson|Hanson]]/[[xenharmonic/Catakleismic|Catakleismic]] ||
|| 15 || mu || 339.62 || 11/9 || [[xenharmonic/Amity|Amity]]/[[xenharmonic/Hitchcock|Hitchcock]] ||
|| 16 || muh || 362.26 || 16/13 ||   ||
|| 17 || mi || 384.91 || 5/4 ||   ||
|| 18 || maa || 407.55 ||   ||   ||
|| 19 || mo || 430.19 || 9/7, 14/11 ||   ||
|| 20 || maw || 452.83 || 13/10 ||   ||
|| 21 || fe || 475.47 || 21/16 || [[xenharmonic/Vulture|Vulture]]/[[xenharmonic/Buzzard|Buzzard]] ||
|| 22 || fa || 498.11 || 4/3 ||   ||
|| 23 || fih || 520.75 || 27/20 ||   ||
|| 24 || fu || 543.40 || 11/8, 15/11 ||   ||
|| 25 || fuh || 566.04 || 18/13 || [[xenharmonic/Tricot|Tricot]] ||
|| 26 || fi || 588.68 || 7/5 ||   ||
|| 27 || se || 611.32 || 10/7 ||   ||
|| 28 || suh || 633.96 || 13/9 ||   ||
|| 29 || su || 656.60 || 16/11, 22/15 ||   ||
|| 30 || sih || 679.25 || 40/27 ||   ||
|| 31 || sol || 701.89 || 3/2 || [[xenharmonic/Helmholtz|Helmholtz]]/[[xenharmonic/Garibaldi|Garibaldi]] ||
|| 32 || si || 724.53 || 32/21 ||   ||
|| 33 || saw || 747.17 || 20/13 ||   ||
|| 34 || lo || 769.81 || 14/9, 25/16, 11/7 ||   ||
|| 35 || leh || 792.45 ||   ||   ||
|| 36 || le || 815.09 || 8/5 ||   ||
|| 37 || lu || 837.74 || 13/8 ||   ||
|| 38 || luh || 860.38 || 18/11 ||   ||
|| 39 || la || 883.02 || 5/3 ||   ||
|| 40 || laa || 905.66 || 22/13, 27/16 ||   ||
|| 41 || lo || 928.30 || 12/7 ||   ||
|| 42 || law || 950.94 || 26/15 ||   ||
|| 43 || ta || 973.58 || 7/4 ||   ||
|| 44 || teh || 996.23 || 16/9 ||   ||
|| 45 || te || 1018.87 || 9/5 ||   ||
|| 46 || tu || 1041.51 || 11/6, 20/11 ||   ||
|| 47 || tuh || 1064.15 || 13/7, 24/13 ||   ||
|| 48 || ti || 1086.79 || 15/8 ||   ||
|| 49 || tih || 1109.43 || 40/21 ||   ||
|| 50 || to || 1132.08 || 48/25 ||   ||
|| 51 || taw || 1154.72 ||   ||   ||
|| 52 || da || 1177.36 ||   ||   ||


=Compositions= 
[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Khramov/prelude1-53.mp3|Bach WTC1 Prelude 1 in 53]] by Bach and [[xenharmonic/Mykhaylo Khramov|Mykhaylo Khramov]]
[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Khramov/fugue1-53.mp3|Bach WTC1 Fugue 1 in 53]] by Bach and Mykhaylo Khramov
[[http://bumpermusic.blogspot.com/2007/05/whisper-song-in-53-edo-now-526-slower.html|Whisper Song in 53EDO]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Prent/sing53-c5-slow.mp3|play]] by [[xenharmonic/Prent Rodgers|Prent Rodgers]]
[[http://www.archive.org/details/TrioInOrwell|Trio in Orwell]] [[http://www.archive.org/download/TrioInOrwell/TrioInOrwell.mp3|play]] by [[xenharmonic/Gene Ward Smith|Gene Ward Smith]]
[[http://www.akjmusic.com/audio/desert_prayer.mp3|Desert Prayer]] by [[http://www.akjmusic.com/|Aaron Krister Johnson]]
[[http://micro.soonlabel.com/gene_ward_smith/Others/Rodgers/sing53-c5-slow.mp3|Whisper Song in 53 EDO]] by [[Prent Rodgers]]
[[@http://andrewheathwaite.bandcamp.com/track/elf-dine-on-ho-ho|Elf Dine on Ho Ho]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2005%20Elf%20Dine%20on%20Ho%20Ho.mp3|play]] and [[@http://andrewheathwaite.bandcamp.com/track/spun|Spun]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2008%20Spun.mp3|play]] by [[xenharmonic/Andrew Heathwaite|Andrew Heathwaite]]

Original HTML content:

<html><head><title>53edo</title></head><body><!-- ws:start:WikiTextTocRule:10:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:10 --><!-- ws:start:WikiTextTocRule:11: --><a href="#Theory">Theory</a><!-- ws:end:WikiTextTocRule:11 --><!-- ws:start:WikiTextTocRule:12: --> | <a href="#Linear temperaments">Linear temperaments</a><!-- ws:end:WikiTextTocRule:12 --><!-- ws:start:WikiTextTocRule:13: --> | <a href="#Just Approximation">Just Approximation</a><!-- ws:end:WikiTextTocRule:13 --><!-- ws:start:WikiTextTocRule:14: --> | <a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --> | <a href="#Compositions">Compositions</a><!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: -->
<!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Theory"></a><!-- ws:end:WikiTextHeadingRule:0 -->Theory</h1>
 The famous <em>53 equal division</em> divides the octave into 53 equal comma-sized parts of 22.642 cents each. It is notable as a <a class="wiki_link" href="http://xenharmonic.wikispaces.com/5-limit">5-limit</a> system, a fact apparently first noted by Isaac Newton, tempering out the schisma, 32805/32768, the kleisma, 15625/15552, the amity comma, 1600000/1594323 and the semicomma, 2109375/2097152. In the 7-limit it tempers out 225/224, 1728/1715 and 3125/3087, the marvel comma, the gariboh, and the orwell comma. In the 11-limit, it tempers out 99/98 and 121/120, and is the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/optimal%20patent%20val">optimal patent val</a> for <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Nuwell%20family">Big Brother</a> temperament, which tempers out both, as well as 11-limit <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Semicomma%20family">orwell temperament</a>, which also tempers out the 11-limit comma 176/175. In the 13-limit, it tempers out 169/168 and 245/243, and gives the optimal patent val for <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Marvel%20family">athene temperament</a>. It is the eighth <a class="wiki_link" href="http://xenharmonic.wikispaces.com/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">zeta integral edo</a> and the 16th <a class="wiki_link" href="http://xenharmonic.wikispaces.com/prime%20numbers">prime</a> edo, following <a class="wiki_link" href="http://xenharmonic.wikispaces.com/47edo">47edo</a> and coming before <a class="wiki_link" href="http://xenharmonic.wikispaces.com/59edo">59edo</a>.<br />
<br />
53EDO has also found a certain dissemination as an EDO tuning for <a class="wiki_link" href="/Arabic%2C%20Turkish%2C%20Persian">Arabic/Turkish/Persian music</a> .<br />
<br />
<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/53_equal_temperament" rel="nofollow">Wikipeda article about 53edo</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Linear temperaments"></a><!-- ws:end:WikiTextHeadingRule:2 -->Linear temperaments</h1>
 <a class="wiki_link" href="/List%20of%20edo-distinct%2053et%20rank%20two%20temperaments">List of edo-distinct 53et rank two temperaments</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Just Approximation"></a><!-- ws:end:WikiTextHeadingRule:4 -->Just Approximation</h1>
 53edo provides excellent approximations for the classic 5-limit <a class="wiki_link" href="http://xenharmonic.wikispaces.com/just">just</a> chords and scales, such as the Ptolemy-Zarlino &quot;just major&quot; scale.<br />


<table class="wiki_table">
    <tr>
        <th>interval<br />
</th>
        <th>size<br />
</th>
        <th>diff<br />
</th>
    </tr>
    <tr>
        <td>perfect fifth<br />
</td>
        <td style="text-align: center;">31<br />
</td>
        <td>−0.07 cents<br />
</td>
    </tr>
    <tr>
        <td>major third<br />
</td>
        <td style="text-align: center;">17<br />
</td>
        <td>−1.40 cents<br />
</td>
    </tr>
    <tr>
        <td>minor third<br />
</td>
        <td style="text-align: center;">14<br />
</td>
        <td>+1.34 cents<br />
</td>
    </tr>
    <tr>
        <td>major tone<br />
</td>
        <td style="text-align: center;">9<br />
</td>
        <td>−0.14 cents<br />
</td>
    </tr>
    <tr>
        <td>minor tone<br />
</td>
        <td style="text-align: center;">8<br />
</td>
        <td>−1.27 cents<br />
</td>
    </tr>
    <tr>
        <td>diat. semitone<br />
</td>
        <td style="text-align: center;">5<br />
</td>
        <td>+1.48 cents<br />
</td>
    </tr>
</table>

<br />
One notable property of 53EDO is that it offers good approximations for both pure and pythagorean major thirds.<br />
<br />
The perfect fifth is almost perfectly equal to the just interval 3/2, with only a 0.07 cent difference! 53EDO is practically equal to an extended Pythagorean. The 14- and 17- degree intervals are also very close to 6/5 and 5/4 respectively, and so 5-limit tuning can also be closely approximated. In addition, the 43-degree interval is only 4.8 cents away from the just ratio 7/4, so 53EDO can also be used for 7-limit harmony, tempering out the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/septimal%20kleisma">septimal kleisma</a>, 225/224.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:6 -->Intervals</h1>
 

<table class="wiki_table">
    <tr>
        <td>degrees of 53edo<br />
</td>
        <td>solfege<br />
</td>
        <td>cents value<br />
</td>
        <td>approximate 13-limit ratios<br />
</td>
        <td>generator for<br />
</td>
    </tr>
    <tr>
        <td>0<br />
</td>
        <td>do<br />
</td>
        <td>0.00<br />
</td>
        <td>1/1<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>di<br />
</td>
        <td>22.64<br />
</td>
        <td>81/80, 64/63, 50/49<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>daw<br />
</td>
        <td>45.28<br />
</td>
        <td>49/48, 36/35, 33/32<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Quartonic">Quartonic</a><br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>ro<br />
</td>
        <td>67.92<br />
</td>
        <td>27/26, 26/25, 25/24, 22/21<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>rih<br />
</td>
        <td>90.57<br />
</td>
        <td>21/20<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>ra<br />
</td>
        <td>113.21<br />
</td>
        <td>16/15, 15/14<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>ru<br />
</td>
        <td>135.85<br />
</td>
        <td>14/13, 13/12<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>ruh<br />
</td>
        <td>158.49<br />
</td>
        <td>12/11, 11/10<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Hemikleismic">Hemikleismic</a><br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>reh<br />
</td>
        <td>181.13<br />
</td>
        <td>10/9<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>re<br />
</td>
        <td>203.77<br />
</td>
        <td>9/8<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>ri<br />
</td>
        <td>226.42<br />
</td>
        <td>8/7<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>raw<br />
</td>
        <td>249.06<br />
</td>
        <td>15/13<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Hemischis">Hemischis</a><br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>ma<br />
</td>
        <td>271.70<br />
</td>
        <td>7/6<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Orwell">Orwell</a><br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>meh<br />
</td>
        <td>294.34<br />
</td>
        <td>13/11<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>me<br />
</td>
        <td>316.98<br />
</td>
        <td>6/5<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Hanson">Hanson</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Catakleismic">Catakleismic</a><br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>mu<br />
</td>
        <td>339.62<br />
</td>
        <td>11/9<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Amity">Amity</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Hitchcock">Hitchcock</a><br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>muh<br />
</td>
        <td>362.26<br />
</td>
        <td>16/13<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>mi<br />
</td>
        <td>384.91<br />
</td>
        <td>5/4<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>maa<br />
</td>
        <td>407.55<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>mo<br />
</td>
        <td>430.19<br />
</td>
        <td>9/7, 14/11<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>maw<br />
</td>
        <td>452.83<br />
</td>
        <td>13/10<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>fe<br />
</td>
        <td>475.47<br />
</td>
        <td>21/16<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Vulture">Vulture</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Buzzard">Buzzard</a><br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>fa<br />
</td>
        <td>498.11<br />
</td>
        <td>4/3<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>fih<br />
</td>
        <td>520.75<br />
</td>
        <td>27/20<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>fu<br />
</td>
        <td>543.40<br />
</td>
        <td>11/8, 15/11<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>fuh<br />
</td>
        <td>566.04<br />
</td>
        <td>18/13<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Tricot">Tricot</a><br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>fi<br />
</td>
        <td>588.68<br />
</td>
        <td>7/5<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>se<br />
</td>
        <td>611.32<br />
</td>
        <td>10/7<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>suh<br />
</td>
        <td>633.96<br />
</td>
        <td>13/9<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>su<br />
</td>
        <td>656.60<br />
</td>
        <td>16/11, 22/15<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td>sih<br />
</td>
        <td>679.25<br />
</td>
        <td>40/27<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>sol<br />
</td>
        <td>701.89<br />
</td>
        <td>3/2<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Helmholtz">Helmholtz</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Garibaldi">Garibaldi</a><br />
</td>
    </tr>
    <tr>
        <td>32<br />
</td>
        <td>si<br />
</td>
        <td>724.53<br />
</td>
        <td>32/21<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>saw<br />
</td>
        <td>747.17<br />
</td>
        <td>20/13<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>34<br />
</td>
        <td>lo<br />
</td>
        <td>769.81<br />
</td>
        <td>14/9, 25/16, 11/7<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>35<br />
</td>
        <td>leh<br />
</td>
        <td>792.45<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>36<br />
</td>
        <td>le<br />
</td>
        <td>815.09<br />
</td>
        <td>8/5<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>37<br />
</td>
        <td>lu<br />
</td>
        <td>837.74<br />
</td>
        <td>13/8<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>38<br />
</td>
        <td>luh<br />
</td>
        <td>860.38<br />
</td>
        <td>18/11<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>39<br />
</td>
        <td>la<br />
</td>
        <td>883.02<br />
</td>
        <td>5/3<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>40<br />
</td>
        <td>laa<br />
</td>
        <td>905.66<br />
</td>
        <td>22/13, 27/16<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>41<br />
</td>
        <td>lo<br />
</td>
        <td>928.30<br />
</td>
        <td>12/7<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>42<br />
</td>
        <td>law<br />
</td>
        <td>950.94<br />
</td>
        <td>26/15<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>43<br />
</td>
        <td>ta<br />
</td>
        <td>973.58<br />
</td>
        <td>7/4<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>44<br />
</td>
        <td>teh<br />
</td>
        <td>996.23<br />
</td>
        <td>16/9<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>45<br />
</td>
        <td>te<br />
</td>
        <td>1018.87<br />
</td>
        <td>9/5<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>46<br />
</td>
        <td>tu<br />
</td>
        <td>1041.51<br />
</td>
        <td>11/6, 20/11<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>47<br />
</td>
        <td>tuh<br />
</td>
        <td>1064.15<br />
</td>
        <td>13/7, 24/13<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>48<br />
</td>
        <td>ti<br />
</td>
        <td>1086.79<br />
</td>
        <td>15/8<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>49<br />
</td>
        <td>tih<br />
</td>
        <td>1109.43<br />
</td>
        <td>40/21<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>50<br />
</td>
        <td>to<br />
</td>
        <td>1132.08<br />
</td>
        <td>48/25<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>51<br />
</td>
        <td>taw<br />
</td>
        <td>1154.72<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>52<br />
</td>
        <td>da<br />
</td>
        <td>1177.36<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
</table>

<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:8 -->Compositions</h1>
 <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Khramov/prelude1-53.mp3" rel="nofollow">Bach WTC1 Prelude 1 in 53</a> by Bach and <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Mykhaylo%20Khramov">Mykhaylo Khramov</a><br />
<a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Khramov/fugue1-53.mp3" rel="nofollow">Bach WTC1 Fugue 1 in 53</a> by Bach and Mykhaylo Khramov<br />
<a class="wiki_link_ext" href="http://bumpermusic.blogspot.com/2007/05/whisper-song-in-53-edo-now-526-slower.html" rel="nofollow">Whisper Song in 53EDO</a> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Prent/sing53-c5-slow.mp3" rel="nofollow">play</a> by <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Prent%20Rodgers">Prent Rodgers</a><br />
<a class="wiki_link_ext" href="http://www.archive.org/details/TrioInOrwell" rel="nofollow">Trio in Orwell</a> <a class="wiki_link_ext" href="http://www.archive.org/download/TrioInOrwell/TrioInOrwell.mp3" rel="nofollow">play</a> by <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Gene%20Ward%20Smith">Gene Ward Smith</a><br />
<a class="wiki_link_ext" href="http://www.akjmusic.com/audio/desert_prayer.mp3" rel="nofollow">Desert Prayer</a> by <a class="wiki_link_ext" href="http://www.akjmusic.com/" rel="nofollow">Aaron Krister Johnson</a><br />
<a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Rodgers/sing53-c5-slow.mp3" rel="nofollow">Whisper Song in 53 EDO</a> by <a class="wiki_link" href="/Prent%20Rodgers">Prent Rodgers</a><br />
<a class="wiki_link_ext" href="http://andrewheathwaite.bandcamp.com/track/elf-dine-on-ho-ho" rel="nofollow" target="_blank">Elf Dine on Ho Ho</a> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2005%20Elf%20Dine%20on%20Ho%20Ho.mp3" rel="nofollow">play</a> and <a class="wiki_link_ext" href="http://andrewheathwaite.bandcamp.com/track/spun" rel="nofollow" target="_blank">Spun</a> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2008%20Spun.mp3" rel="nofollow">play</a> by <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Andrew%20Heathwaite">Andrew Heathwaite</a></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:genewardsmith|genewardsmith]] and made on <tt>2012-07-01 15:18:20 UTC</tt>.<br>
+: This revision was by author [[User:phylingual|phylingual]] and made on <tt>2012-07-04 22:21:50 UTC</tt>.<br>
-: The original revision id was <tt>349377598</tt>.<br>
+: The original revision id was <tt>350344726</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 32: / Line 32: @@
 =Intervals=
-|| degrees of 53edo || cents value || approximate 13-limit ratios || generator for ||
+|| degrees of 53edo || solfege || cents value || approximate 13-limit ratios || generator for ||
-|| 0 || 0.00 || 1/1 ||   ||
+|| 0 || do || 0.00 || 1/1 ||   ||
-|| 1 || 22.64 || 81/80, 64/63, 50/49 ||   ||
+|| 1 || di || 22.64 || 81/80, 64/63, 50/49 ||   ||
-|| 2 || 45.28 || 49/48, 36/35, 33/32 || [[xenharmonic/Quartonic|Quartonic]] ||
+|| 2 || daw || 45.28 || 49/48, 36/35, 33/32 || [[xenharmonic/Quartonic|Quartonic]] ||
-|| 3 || 67.92 || 27/26, 26/25, 25/24, 22/21 ||   ||
+|| 3 || ro || 67.92 || 27/26, 26/25, 25/24, 22/21 ||   ||
-|| 4 || 90.57 || 21/20 ||   ||
+|| 4 || rih || 90.57 || 21/20 ||   ||
-|| 5 || 113.21 || 16/15, 15/14 ||   ||
+|| 5 || ra || 113.21 || 16/15, 15/14 ||   ||
-|| 6 || 135.85 || 14/13, 13/12 ||   ||
+|| 6 || ru || 135.85 || 14/13, 13/12 ||   ||
-|| 7 || 158.49 || 12/11, 11/10 || [[xenharmonic/Hemikleismic|Hemikleismic]] ||
+|| 7 || ruh || 158.49 || 12/11, 11/10 || [[xenharmonic/Hemikleismic|Hemikleismic]] ||
-|| 8 || 181.13 || 10/9 ||   ||
+|| 8 || reh || 181.13 || 10/9 ||   ||
-|| 9 || 203.77 || 9/8 ||   ||
+|| 9 || re || 203.77 || 9/8 ||   ||
-|| 10 || 226.42 || 8/7 ||   ||
+|| 10 || ri || 226.42 || 8/7 ||   ||
-|| 11 || 249.06 || 15/13 || [[xenharmonic/Hemischis|Hemischis]] ||
+|| 11 || raw || 249.06 || 15/13 || [[xenharmonic/Hemischis|Hemischis]] ||
-|| 12 || 271.70 || 7/6 || [[xenharmonic/Orwell|Orwell]] ||
+|| 12 || ma || 271.70 || 7/6 || [[xenharmonic/Orwell|Orwell]] ||
-|| 13 || 294.34 || 13/11 ||   ||
+|| 13 || meh || 294.34 || 13/11 ||   ||
-|| 14 || 316.98 || 6/5 || [[xenharmonic/Hanson|Hanson]]/[[xenharmonic/Catakleismic|Catakleismic]] ||
+|| 14 || me || 316.98 || 6/5 || [[xenharmonic/Hanson|Hanson]]/[[xenharmonic/Catakleismic|Catakleismic]] ||
-|| 15 || 339.62 || 11/9 || [[xenharmonic/Amity|Amity]]/[[xenharmonic/Hitchcock|Hitchcock]] ||
+|| 15 || mu || 339.62 || 11/9 || [[xenharmonic/Amity|Amity]]/[[xenharmonic/Hitchcock|Hitchcock]] ||
-|| 16 || 362.26 || 16/13 ||   ||
+|| 16 || muh || 362.26 || 16/13 ||   ||
-|| 17 || 384.91 || 5/4 ||   ||
+|| 17 || mi || 384.91 || 5/4 ||   ||
-|| 18 || 407.55 ||   ||   ||
+|| 18 || maa || 407.55 ||   ||   ||
-|| 19 || 430.19 || 9/7, 14/11 ||   ||
+|| 19 || mo || 430.19 || 9/7, 14/11 ||   ||
-|| 20 || 452.83 || 13/10 ||   ||
+|| 20 || maw || 452.83 || 13/10 ||   ||
-|| 21 || 475.47 || 21/16 || [[xenharmonic/Vulture|Vulture]]/[[xenharmonic/Buzzard|Buzzard]] ||
+|| 21 || fe || 475.47 || 21/16 || [[xenharmonic/Vulture|Vulture]]/[[xenharmonic/Buzzard|Buzzard]] ||
-|| 22 || 498.11 || 4/3 ||   ||
+|| 22 || fa || 498.11 || 4/3 ||   ||
-|| 23 || 520.75 || 27/20 ||   ||
+|| 23 || fih || 520.75 || 27/20 ||   ||
-|| 24 || 543.40 || 11/8, 15/11 ||   ||
+|| 24 || fu || 543.40 || 11/8, 15/11 ||   ||
-|| 25 || 566.04 || 18/13 || [[xenharmonic/Tricot|Tricot]] ||
+|| 25 || fuh || 566.04 || 18/13 || [[xenharmonic/Tricot|Tricot]] ||
-|| 26 || 588.68 || 7/5 ||   ||
+|| 26 || fi || 588.68 || 7/5 ||   ||
-|| 27 || 611.32 || 10/7 ||   ||
+|| 27 || se || 611.32 || 10/7 ||   ||
-|| 28 || 633.96 || 13/9 ||   ||
+|| 28 || suh || 633.96 || 13/9 ||   ||
-|| 29 || 656.60 || 16/11, 22/15 ||   ||
+|| 29 || su || 656.60 || 16/11, 22/15 ||   ||
-|| 30 || 679.25 || 40/27 ||   ||
+|| 30 || sih || 679.25 || 40/27 ||   ||
-|| 31 || 701.89 || 3/2 || [[xenharmonic/Helmholtz|Helmholtz]]/[[xenharmonic/Garibaldi|Garibaldi]] ||
+|| 31 || sol || 701.89 || 3/2 || [[xenharmonic/Helmholtz|Helmholtz]]/[[xenharmonic/Garibaldi|Garibaldi]] ||
-|| 32 || 724.53 || 32/21 ||   ||
+|| 32 || si || 724.53 || 32/21 ||   ||
-|| 33 || 747.17 || 20/13 ||   ||
+|| 33 || saw || 747.17 || 20/13 ||   ||
-|| 34 || 769.81 || 14/9, 25/16, 11/7 ||   ||
+|| 34 || lo || 769.81 || 14/9, 25/16, 11/7 ||   ||
-|| 35 || 792.45 ||   ||   ||
+|| 35 || leh || 792.45 ||   ||   ||
-|| 36 || 815.09 || 8/5 ||   ||
+|| 36 || le || 815.09 || 8/5 ||   ||
-|| 37 || 837.74 || 13/8 ||   ||
+|| 37 || lu || 837.74 || 13/8 ||   ||
-|| 38 || 860.38 || 18/11 ||   ||
+|| 38 || luh || 860.38 || 18/11 ||   ||
-|| 39 || 883.02 || 5/3 ||   ||
+|| 39 || la || 883.02 || 5/3 ||   ||
-|| 40 || 905.66 || 22/13, 27/16 ||   ||
+|| 40 || laa || 905.66 || 22/13, 27/16 ||   ||
-|| 41 || 928.30 || 12/7 ||   ||
+|| 41 || lo || 928.30 || 12/7 ||   ||
-|| 42 || 950.94 || 26/15 ||   ||
+|| 42 || law || 950.94 || 26/15 ||   ||
-|| 43 || 973.58 || 7/4 ||   ||
+|| 43 || ta || 973.58 || 7/4 ||   ||
-|| 44 || 996.23 || 16/9 ||   ||
+|| 44 || teh || 996.23 || 16/9 ||   ||
-|| 45 || 1018.87 || 9/5 ||   ||
+|| 45 || te || 1018.87 || 9/5 ||   ||
-|| 46 || 1041.51 || 11/6, 20/11 ||   ||
+|| 46 || tu || 1041.51 || 11/6, 20/11 ||   ||
-|| 47 || 1064.15 || 13/7, 24/13 ||   ||
+|| 47 || tuh || 1064.15 || 13/7, 24/13 ||   ||
-|| 48 || 1086.79 || 15/8 ||   ||
+|| 48 || ti || 1086.79 || 15/8 ||   ||
-|| 49 || 1109.43 || 40/21 ||   ||
+|| 49 || tih || 1109.43 || 40/21 ||   ||
-|| 50 || 1132.08 || 48/25 ||   ||
+|| 50 || to || 1132.08 || 48/25 ||   ||
-|| 51 || 1154.72 ||   ||   ||
+|| 51 || taw || 1154.72 ||   ||   ||
-|| 52 || 1177.36 ||   ||   ||
+|| 52 || da || 1177.36 ||   ||   ||
@@ Line 182: / Line 182: @@
      &lt;tr&gt;
          &lt;td&gt;degrees of 53edo&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;solfege&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;cents value&lt;br /&gt;
@@ Line 192: / Line 194: @@
      &lt;tr&gt;
          &lt;td&gt;0&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;do&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;0.00&lt;br /&gt;
@@ Line 202: / Line 206: @@
      &lt;tr&gt;
          &lt;td&gt;1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;di&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;22.64&lt;br /&gt;
@@ Line 212: / Line 218: @@
      &lt;tr&gt;
          &lt;td&gt;2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;daw&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;45.28&lt;br /&gt;
@@ Line 222: / Line 230: @@
      &lt;tr&gt;
          &lt;td&gt;3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;ro&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;67.92&lt;br /&gt;
@@ Line 232: / Line 242: @@
      &lt;tr&gt;
          &lt;td&gt;4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;rih&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;90.57&lt;br /&gt;
@@ Line 242: / Line 254: @@
      &lt;tr&gt;
          &lt;td&gt;5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;ra&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;113.21&lt;br /&gt;
@@ Line 252: / Line 266: @@
      &lt;tr&gt;
          &lt;td&gt;6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;ru&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;135.85&lt;br /&gt;
@@ Line 262: / Line 278: @@
      &lt;tr&gt;
          &lt;td&gt;7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;ruh&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;158.49&lt;br /&gt;
@@ Line 272: / Line 290: @@
      &lt;tr&gt;
          &lt;td&gt;8&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;reh&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;181.13&lt;br /&gt;
@@ Line 282: / Line 302: @@
      &lt;tr&gt;
          &lt;td&gt;9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;re&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;203.77&lt;br /&gt;
@@ Line 292: / Line 314: @@
      &lt;tr&gt;
          &lt;td&gt;10&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;ri&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;226.42&lt;br /&gt;
@@ Line 302: / Line 326: @@
      &lt;tr&gt;
          &lt;td&gt;11&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;raw&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;249.06&lt;br /&gt;
@@ Line 312: / Line 338: @@
      &lt;tr&gt;
          &lt;td&gt;12&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;ma&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;271.70&lt;br /&gt;
@@ Line 322: / Line 350: @@
      &lt;tr&gt;
          &lt;td&gt;13&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;meh&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;294.34&lt;br /&gt;
@@ Line 332: / Line 362: @@
      &lt;tr&gt;
          &lt;td&gt;14&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;me&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;316.98&lt;br /&gt;
@@ Line 342: / Line 374: @@
      &lt;tr&gt;
          &lt;td&gt;15&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;mu&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;339.62&lt;br /&gt;
@@ Line 352: / Line 386: @@
      &lt;tr&gt;
          &lt;td&gt;16&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;muh&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;362.26&lt;br /&gt;
@@ Line 362: / Line 398: @@
      &lt;tr&gt;
          &lt;td&gt;17&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;mi&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;384.91&lt;br /&gt;
@@ Line 372: / Line 410: @@
      &lt;tr&gt;
          &lt;td&gt;18&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;maa&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;407.55&lt;br /&gt;
@@ Line 382: / Line 422: @@
      &lt;tr&gt;
          &lt;td&gt;19&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;mo&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;430.19&lt;br /&gt;
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@@ Line 712: / Line 818: @@
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+&lt;/td&gt;
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          &lt;td&gt;1177.36&lt;br /&gt;

53edo: Difference between revisions

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