53edo
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[[toc|flat]] <span style="display: block; text-align: right;">Other languages: [[xenharmonie/53edo|Deutsch]] </span> =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]]. It can also be treated as a no-elevens, no-seventeens tuning, on which it is consistent all the way up to the 21-limit. [[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 ||~ ratio ||~ size ||~ difference || || perfect fifth || 3/2 ||= 31 || −0.07 cents || || major third || 5/4 ||= 17 || −1.40 cents || || minor third || 6/5 ||= 14 || +1.34 cents || || major tone || 9/8 ||= 9 || −0.14 cents || || minor tone || 10/9 ||= 8 || −1.27 cents || || diat. semitone || 16/15 ||= 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= || degree || solfege || cents || approximate ratios ||||= [[xenharmonic/Ups and Downs Notation|ups and downs ]][[xenharmonic/Ups and Downs Notation|notation]] || generator for || || 0 || do || 0.00 || 1/1 ||= P1 ||= D || || || 1 || di || 22.64 || 81/80, 64/63, 50/49 ||= ^1 ||= D^ || || || 2 || daw || 45.28 || 49/48, 36/35, 33/32, 128/125 ||= ^^1, vvm2 ||= D^^, Ebvv || [[xenharmonic/Quartonic|Quartonic]] || || 3 || ro || 67.92 || 27/26, 26/25, 25/24, 22/21 ||= vm2 ||= Ebv || || || 4 || rih || 90.57 || 21/20, 256/243 ||= m2 ||= Eb || || || 5 || ra || 113.21 || 16/15, 15/14 ||= ^m2 ||= Eb^ || || || 6 || ru || 135.85 || 14/13, 13/12, 27/25 ||= ^^m2 ||= Eb^^ || || || 7 || ruh || 158.49 || 12/11, 11/10, 800/729 ||= vvM2 ||= Evv || [[xenharmonic/Hemikleismic|Hemikleismic]] || || 8 || reh || 181.13 || 10/9 ||= vM2 ||= Ev || || || 9 || re || 203.77 || 9/8 ||= M2 ||= E || || || 10 || ri || 226.42 || 8/7, 256/225 ||= ^M2 ||= E^ || || || 11 || raw || 249.06 || 15/13, 144/125 ||= vvM2, vvm3 ||= E^^, vvF || [[xenharmonic/Hemischis|Hemischis]] || || 12 || ma || 271.70 || 7/6, 75/64 ||= vm3 ||= vF || [[xenharmonic/Orwell|Orwell]] || || 13 || meh || 294.34 || 13/11, 32/27 ||= m3 ||= F || || || 14 || me || 316.98 || 6/5 ||= ^m3 ||= F^ || [[xenharmonic/Hanson|Hanson]]/[[xenharmonic/Catakleismic|Catakleismic]] || || 15 || mu || 339.62 || 11/9, 243/200 ||= ^^m3 ||= F^^ || [[xenharmonic/Amity|Amity]]/[[xenharmonic/Hitchcock|Hitchcock]] || || 16 || muh || 362.26 || 16/13, 100/81 ||= vvM3 ||= F#vv || || || 17 || mi || 384.91 || 5/4 ||= vM3 ||= F#v || || || 18 || maa || 407.55 || 81/64 ||= M3 ||= F# || || || 19 || mo || 430.19 || 9/7, 14/11 ||= ^M3 ||= F#^ || [[Hamity]] || || 20 || maw || 452.83 || 13/10, 125/96 ||= ^^M3, vv4 ||= F#^^, Gvv || || || 21 || fe || 475.47 || 21/16, 675/512, 320/243 ||= v4 ||= Gv || [[xenharmonic/Vulture|Vulture]]/[[xenharmonic/Buzzard|Buzzard]] || || 22 || fa || 498.11 || 4/3 ||= P4 ||= G || || || 23 || fih || 520.75 || 27/20 ||= ^4 ||= G^ || || || 24 || fu || 543.40 || 11/8, 15/11 ||= ^^4 ||= G^^ || || || 25 || fuh || 566.04 || 18/13 ||= vvA4, vd5 ||= G#vv, Abv || [[xenharmonic/Tricot|Tricot]] || || 26 || fi || 588.68 || 7/5, 45/32 ||= vA4, d5 ||= G#v, Ab || || || 27 || se || 611.32 || 10/7, 64/45 ||= A4, ^d5 ||= G#, Ab^ || || || 28 || suh || 633.96 || 13/9 ||= ^A4, ^^d5 ||= G#^, Ab^^ || || || 29 || su || 656.60 || 16/11, 22/15 ||= vv5 ||= Avv || || || 30 || sih || 679.25 || 40/27 ||= v5 ||= Av || || || 31 || sol || 701.89 || 3/2 ||= P5 ||= A || [[xenharmonic/Helmholtz|Helmholtz]]/[[xenharmonic/Garibaldi|Garibaldi]] || || 32 || si || 724.53 || 32/21, 243/160, 1024/675 ||= ^5 ||= A^ || || || 33 || saw || 747.17 || 20/13, 192/125 ||= ^^5, vvm6 ||= A^^, Bbvv || || || 34 || lo || 769.81 || 14/9, 25/16, 11/7 ||= vm6 ||= Bbv || || || 35 || leh || 792.45 || 128/81 ||= m6 ||= Bb || || || 36 || le || 815.09 || 8/5 ||= ^m6 ||= Bb^ || || || 37 || lu || 837.74 || 13/8, 81/50 ||= ^^m6 ||= Bb^^ || || || 38 || luh || 860.38 || 18/11, 400/243 ||= vvM6 ||= Bvv || || || 39 || la || 883.02 || 5/3 ||= vM6 ||= Bv || || || 40 || laa || 905.66 || 22/13, 27/16 ||= M6 ||= B || || || 41 || lo || 928.30 || 12/7 ||= ^M6 ||= B^ || || || 42 || law || 950.94 || 26/15, 125/72 ||= ^^M6, vvm7 ||= B^^, Cvv || || || 43 || ta || 973.58 || 7/4 ||= vm7 ||= Cv || || || 44 || teh || 996.23 || 16/9 ||= m7 ||= C || || || 45 || te || 1018.87 || 9/5 ||= ^m7 ||= C^ || || || 46 || tu || 1041.51 || 11/6, 20/11, 729/400 ||= ^^m7 ||= C^^ || || || 47 || tuh || 1064.15 || 13/7, 24/13, 50/27 ||= vvM7 ||= C#vv || || || 48 || ti || 1086.79 || 15/8 ||= vM7 ||= C#v || || || 49 || tih || 1109.43 || 40/21, 243/128 ||= M7 ||= C# || || || 50 || to || 1132.08 || 48/25, 27/14 ||= ^M7 ||= C#^ || || || 51 || taw || 1154.72 || 125/64 ||= ^^M7, vv8 ||= C#^^, Dvv || || || 52 || da || 1177.36 || 160/81 ||= v8 ||= Dv || || || 53 || do || 1200 || 2/1 ||= P8 ||= D || || =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]] [[http://chrisvaisvil.com/the-fallen-of-kleismic15/|The Fallen of Kleismic15]][[http://micro.soonlabel.com/53edo/20130903_Kleismic%5b15%5d.mp3|play]] by [[Chris Vaisvil]]
Original HTML content:
<html><head><title>53edo</title></head><body><!-- ws:start:WikiTextTocRule:10:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- 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 --><span style="display: block; text-align: right;">Other languages: <a class="wiki_link" href="http://xenharmonie.wikispaces.com/53edo">Deutsch</a><br />
</span><br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:<h1> --><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 />
It can also be treated as a no-elevens, no-seventeens tuning, on which it is consistent all the way up to the 21-limit.<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:<h1> --><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:<h1> --><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 "just major" scale.<br />
<table class="wiki_table">
<tr>
<th>interval<br />
</th>
<th>ratio<br />
</th>
<th>size<br />
</th>
<th>difference<br />
</th>
</tr>
<tr>
<td>perfect fifth<br />
</td>
<td>3/2<br />
</td>
<td style="text-align: center;">31<br />
</td>
<td>−0.07 cents<br />
</td>
</tr>
<tr>
<td>major third<br />
</td>
<td>5/4<br />
</td>
<td style="text-align: center;">17<br />
</td>
<td>−1.40 cents<br />
</td>
</tr>
<tr>
<td>minor third<br />
</td>
<td>6/5<br />
</td>
<td style="text-align: center;">14<br />
</td>
<td>+1.34 cents<br />
</td>
</tr>
<tr>
<td>major tone<br />
</td>
<td>9/8<br />
</td>
<td style="text-align: center;">9<br />
</td>
<td>−0.14 cents<br />
</td>
</tr>
<tr>
<td>minor tone<br />
</td>
<td>10/9<br />
</td>
<td style="text-align: center;">8<br />
</td>
<td>−1.27 cents<br />
</td>
</tr>
<tr>
<td>diat. semitone<br />
</td>
<td>16/15<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:<h1> --><h1 id="toc3"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:6 -->Intervals</h1>
<table class="wiki_table">
<tr>
<td>degree<br />
</td>
<td>solfege<br />
</td>
<td>cents<br />
</td>
<td>approximate ratios<br />
</td>
<td colspan="2" style="text-align: center;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation">ups and downs </a><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation">notation</a><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 style="text-align: center;">P1<br />
</td>
<td style="text-align: center;">D<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 style="text-align: center;">^1<br />
</td>
<td style="text-align: center;">D^<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, 128/125<br />
</td>
<td style="text-align: center;">^^1, vvm2<br />
</td>
<td style="text-align: center;">D^^, Ebvv<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 style="text-align: center;">vm2<br />
</td>
<td style="text-align: center;">Ebv<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>rih<br />
</td>
<td>90.57<br />
</td>
<td>21/20, 256/243<br />
</td>
<td style="text-align: center;">m2<br />
</td>
<td style="text-align: center;">Eb<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 style="text-align: center;">^m2<br />
</td>
<td style="text-align: center;">Eb^<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, 27/25<br />
</td>
<td style="text-align: center;">^^m2<br />
</td>
<td style="text-align: center;">Eb^^<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, 800/729<br />
</td>
<td style="text-align: center;">vvM2<br />
</td>
<td style="text-align: center;">Evv<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 style="text-align: center;">vM2<br />
</td>
<td style="text-align: center;">Ev<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 style="text-align: center;">M2<br />
</td>
<td style="text-align: center;">E<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>ri<br />
</td>
<td>226.42<br />
</td>
<td>8/7, 256/225<br />
</td>
<td style="text-align: center;">^M2<br />
</td>
<td style="text-align: center;">E^<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>raw<br />
</td>
<td>249.06<br />
</td>
<td>15/13, 144/125<br />
</td>
<td style="text-align: center;">vvM2, vvm3<br />
</td>
<td style="text-align: center;">E^^, vvF<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, 75/64<br />
</td>
<td style="text-align: center;">vm3<br />
</td>
<td style="text-align: center;">vF<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, 32/27<br />
</td>
<td style="text-align: center;">m3<br />
</td>
<td style="text-align: center;">F<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 style="text-align: center;">^m3<br />
</td>
<td style="text-align: center;">F^<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, 243/200<br />
</td>
<td style="text-align: center;">^^m3<br />
</td>
<td style="text-align: center;">F^^<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, 100/81<br />
</td>
<td style="text-align: center;">vvM3<br />
</td>
<td style="text-align: center;">F#vv<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 style="text-align: center;">vM3<br />
</td>
<td style="text-align: center;">F#v<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>maa<br />
</td>
<td>407.55<br />
</td>
<td>81/64<br />
</td>
<td style="text-align: center;">M3<br />
</td>
<td style="text-align: center;">F#<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 style="text-align: center;">^M3<br />
</td>
<td style="text-align: center;">F#^<br />
</td>
<td><a class="wiki_link" href="/Hamity">Hamity</a><br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>maw<br />
</td>
<td>452.83<br />
</td>
<td>13/10, 125/96<br />
</td>
<td style="text-align: center;">^^M3, vv4<br />
</td>
<td style="text-align: center;">F#^^, Gvv<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>fe<br />
</td>
<td>475.47<br />
</td>
<td>21/16, 675/512, 320/243<br />
</td>
<td style="text-align: center;">v4<br />
</td>
<td style="text-align: center;">Gv<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 style="text-align: center;">P4<br />
</td>
<td style="text-align: center;">G<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 style="text-align: center;">^4<br />
</td>
<td style="text-align: center;">G^<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 style="text-align: center;">^^4<br />
</td>
<td style="text-align: center;">G^^<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 style="text-align: center;">vvA4, vd5<br />
</td>
<td style="text-align: center;">G#vv, Abv<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, 45/32<br />
</td>
<td style="text-align: center;">vA4, d5<br />
</td>
<td style="text-align: center;">G#v, Ab<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>se<br />
</td>
<td>611.32<br />
</td>
<td>10/7, 64/45<br />
</td>
<td style="text-align: center;">A4, ^d5<br />
</td>
<td style="text-align: center;">G#, Ab^<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 style="text-align: center;">^A4, ^^d5<br />
</td>
<td style="text-align: center;">G#^, Ab^^<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 style="text-align: center;">vv5<br />
</td>
<td style="text-align: center;">Avv<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 style="text-align: center;">v5<br />
</td>
<td style="text-align: center;">Av<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 style="text-align: center;">P5<br />
</td>
<td style="text-align: center;">A<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, 243/160, 1024/675<br />
</td>
<td style="text-align: center;">^5<br />
</td>
<td style="text-align: center;">A^<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>saw<br />
</td>
<td>747.17<br />
</td>
<td>20/13, 192/125<br />
</td>
<td style="text-align: center;">^^5, vvm6<br />
</td>
<td style="text-align: center;">A^^, Bbvv<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 style="text-align: center;">vm6<br />
</td>
<td style="text-align: center;">Bbv<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td>leh<br />
</td>
<td>792.45<br />
</td>
<td>128/81<br />
</td>
<td style="text-align: center;">m6<br />
</td>
<td style="text-align: center;">Bb<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 style="text-align: center;">^m6<br />
</td>
<td style="text-align: center;">Bb^<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td>lu<br />
</td>
<td>837.74<br />
</td>
<td>13/8, 81/50<br />
</td>
<td style="text-align: center;">^^m6<br />
</td>
<td style="text-align: center;">Bb^^<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td>luh<br />
</td>
<td>860.38<br />
</td>
<td>18/11, 400/243<br />
</td>
<td style="text-align: center;">vvM6<br />
</td>
<td style="text-align: center;">Bvv<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 style="text-align: center;">vM6<br />
</td>
<td style="text-align: center;">Bv<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 style="text-align: center;">M6<br />
</td>
<td style="text-align: center;">B<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 style="text-align: center;">^M6<br />
</td>
<td style="text-align: center;">B^<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>42<br />
</td>
<td>law<br />
</td>
<td>950.94<br />
</td>
<td>26/15, 125/72<br />
</td>
<td style="text-align: center;">^^M6, vvm7<br />
</td>
<td style="text-align: center;">B^^, Cvv<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 style="text-align: center;">vm7<br />
</td>
<td style="text-align: center;">Cv<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 style="text-align: center;">m7<br />
</td>
<td style="text-align: center;">C<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 style="text-align: center;">^m7<br />
</td>
<td style="text-align: center;">C^<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, 729/400<br />
</td>
<td style="text-align: center;">^^m7<br />
</td>
<td style="text-align: center;">C^^<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, 50/27<br />
</td>
<td style="text-align: center;">vvM7<br />
</td>
<td style="text-align: center;">C#vv<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 style="text-align: center;">vM7<br />
</td>
<td style="text-align: center;">C#v<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>49<br />
</td>
<td>tih<br />
</td>
<td>1109.43<br />
</td>
<td>40/21, 243/128<br />
</td>
<td style="text-align: center;">M7<br />
</td>
<td style="text-align: center;">C#<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>50<br />
</td>
<td>to<br />
</td>
<td>1132.08<br />
</td>
<td>48/25, 27/14<br />
</td>
<td style="text-align: center;">^M7<br />
</td>
<td style="text-align: center;">C#^<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>51<br />
</td>
<td>taw<br />
</td>
<td>1154.72<br />
</td>
<td>125/64<br />
</td>
<td style="text-align: center;">^^M7, vv8<br />
</td>
<td style="text-align: center;">C#^^, Dvv<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>52<br />
</td>
<td>da<br />
</td>
<td>1177.36<br />
</td>
<td>160/81<br />
</td>
<td style="text-align: center;">v8<br />
</td>
<td style="text-align: center;">Dv<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>53<br />
</td>
<td>do<br />
</td>
<td>1200<br />
</td>
<td>2/1<br />
</td>
<td style="text-align: center;">P8<br />
</td>
<td style="text-align: center;">D<br />
</td>
<td><br />
</td>
</tr>
</table>
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:<h1> --><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><br />
<a class="wiki_link_ext" href="http://chrisvaisvil.com/the-fallen-of-kleismic15/" rel="nofollow">The Fallen of Kleismic15</a><a class="wiki_link_ext" href="http://micro.soonlabel.com/53edo/20130903_Kleismic%5b15%5d.mp3" rel="nofollow">play</a> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a></body></html>