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 ||= unison ||= D ||   ||
||= 1 ||= di ||= 22.64 ||= 81/80, 64/63, 50/49 ||= ^1 ||= up unison ||= D^ ||   ||
||= 2 ||= daw ||= 45.28 ||= 49/48, 36/35, 33/32, 128/125 ||= ^^1,
vvm2 ||= double-up unison,
double-down minor 2nd ||= D^^,
Ebvv || [[xenharmonic/Quartonic|Quartonic]] ||
||= 3 ||= ro ||= 67.92 ||= 27/26, 26/25, 25/24, 22/21 ||= vm2 ||= downminor 2nd ||= Ebv ||   ||
||= 4 ||= rih ||= 90.57 ||= 21/20, 256/243 ||= m2 ||= minor 2nd ||= Eb ||   ||
||= 5 ||= ra ||= 113.21 ||= 16/15, 15/14 ||= ^m2 ||= upminor 2nd ||= Eb^ ||   ||
||= 6 ||= ru ||= 135.85 ||= 14/13, 13/12, 27/25 ||= v~2 ||= downmid 2nd ||= Eb^^ ||   ||
||= 7 ||= ruh ||= 158.49 ||= 12/11, 11/10, 800/729 ||= ^~2 ||= upmid 2nd ||= Evv || [[xenharmonic/Hemikleismic|Hemikleismic]] ||
||= 8 ||= reh ||= 181.13 ||= 10/9 ||= vM2 ||= downmajor 2nd ||= Ev ||   ||
||= 9 ||= re ||= 203.77 ||= 9/8 ||= M2 ||= major 2nd ||= E ||   ||
||= 10 ||= ri ||= 226.42 ||= 8/7, 256/225 ||= ^M2 ||= upmajor 2nd ||= E^ ||   ||
||= 11 ||= raw ||= 249.06 ||= 15/13, 144/125 ||= ^^M2,
vvm3 ||= double-up major 2nd,
double-down minor 3rd ||= E^^,
Fvv || [[xenharmonic/Hemischis|Hemischis]] ||
||= 12 ||= ma ||= 271.70 ||= 7/6, 75/64 ||= vm3 ||= downminor 3rd ||= Fv || [[xenharmonic/Orwell|Orwell]] ||
||= 13 ||= meh ||= 294.34 ||= 13/11, 32/27 ||= m3 ||= minor 3rd ||= F ||   ||
||= 14 ||= me ||= 316.98 ||= 6/5 ||= ^m3 ||= upminor 3rd ||= F^ || [[xenharmonic/Hanson|Hanson]]/[[xenharmonic/Catakleismic|Catakleismic]] ||
||= 15 ||= mu ||= 339.62 ||= 11/9, 243/200 ||= v~3 ||= downmid 3rd ||= F^^ || [[xenharmonic/Amity|Amity]]/[[xenharmonic/Hitchcock|Hitchcock]] ||
||= 16 ||= muh ||= 362.26 ||= 16/13, 100/81 ||= ^~3 ||= upmid 3rd ||= F#vv ||   ||
||= 17 ||= mi ||= 384.91 ||= 5/4 ||= vM3 ||= downmajor 3rd ||= F#v ||   ||
||= 18 ||= maa ||= 407.55 ||= 81/64 ||= M3 ||= major 3rd ||= F# ||   ||
||= 19 ||= mo ||= 430.19 ||= 9/7, 14/11 ||= ^M3 ||= upmajor 3rd ||= F#^ || [[Hamity]] ||
||= 20 ||= maw ||= 452.83 ||= 13/10, 125/96 ||= ^^M3,
vv4 ||= double-up major 3rd,
double-down 4th ||= F#^^,
Gvv ||   ||
||= 21 ||= fe ||= 475.47 ||= 21/16, 675/512, 320/243 ||= v4 ||= down 4th ||= Gv || [[xenharmonic/Vulture|Vulture]]/[[xenharmonic/Buzzard|Buzzard]] ||
||= 22 ||= fa ||= 498.11 ||= 4/3 ||= P4 ||= perfect 4th ||= G ||   ||
||= 23 ||= fih ||= 520.75 ||= 27/20 ||= ^4 ||= up 4th ||= G^ ||   ||
||= 24 ||= fu ||= 543.40 ||= 11/8, 15/11 ||= ^^4 ||= double-up 4th ||= G^^ ||   ||
||= 25 ||= fuh ||= 566.04 ||= 18/13 ||= vvA4,
vd5 ||= double-down aug 4th,
downdim 5th ||= G#vv,
Abv || [[xenharmonic/Tricot|Tricot]] ||
||= 26 ||= fi ||= 588.68 ||= 7/5, 45/32 ||= vA4,
d5 ||= downaug 4th,
dim 5th ||= G#v,
Ab ||   ||
||= 27 ||= se ||= 611.32 ||= 10/7, 64/45 ||= A4,
^d5 ||= aug 4th,
updim 5th ||= G#,
Ab^ ||   ||
||= 28 ||= suh ||= 633.96 ||= 13/9 ||= ^A4,
^^d5 ||= upaug 4th,
double-up dim 5th ||= G#^,
Ab^^ ||   ||
||= 29 ||= su ||= 656.60 ||= 16/11, 22/15 ||= vv5 ||= double-down 5th ||= Avv ||   ||
||= 30 ||= sih ||= 679.25 ||= 40/27 ||= v5 ||= down 5th ||= Av ||   ||
||= 31 ||= sol ||= 701.89 ||= 3/2 ||= P5 ||= perfect 5th ||= A || [[xenharmonic/Helmholtz|Helmholtz]]/[[xenharmonic/Garibaldi|Garibaldi]] ||
||= 32 ||= si ||= 724.53 ||= 32/21, 243/160, 1024/675 ||= ^5 ||= up 5th ||= A^ ||   ||
||= 33 ||= saw ||= 747.17 ||= 20/13, 192/125 ||= ^^5,
vvm6 ||= double-up 5th,
double-down minor 6th ||= A^^,
Bbvv ||   ||
||= 34 ||= lo ||= 769.81 ||= 14/9, 25/16, 11/7 ||= vm6 ||= downminor 6th ||= Bbv ||   ||
||= 35 ||= leh ||= 792.45 ||= 128/81 ||= m6 ||= minor 6th ||= Bb ||   ||
||= 36 ||= le ||= 815.09 ||= 8/5 ||= ^m6 ||= upminor 6th ||= Bb^ ||   ||
||= 37 ||= lu ||= 837.74 ||= 13/8, 81/50 ||= v~6 ||= downmid 6th ||= Bb^^ ||   ||
||= 38 ||= luh ||= 860.38 ||= 18/11, 400/243 ||= ^~6 ||= upmid 6th ||= Bvv ||   ||
||= 39 ||= la ||= 883.02 ||= 5/3 ||= vM6 ||= downmajor 6th ||= Bv ||   ||
||= 40 ||= laa ||= 905.66 ||= 22/13, 27/16 ||= M6 ||= major 6th ||= B ||   ||
||= 41 ||= lo ||= 928.30 ||= 12/7 ||= ^M6 ||= upmajor 6th ||= B^ ||   ||
||= 42 ||= law ||= 950.94 ||= 26/15, 125/72 ||= ^^M6
vvm7 ||= double-up major 6th,
double-down minor 7th ||= B^^,
Cvv ||   ||
||= 43 ||= ta ||= 973.58 ||= 7/4 ||= vm7 ||= downminor 7th ||= Cv ||   ||
||= 44 ||= teh ||= 996.23 ||= 16/9 ||= m7 ||= minor 7th ||= C ||   ||
||= 45 ||= te ||= 1018.87 ||= 9/5 ||= ^m7 ||= upminor 7th ||= C^ ||   ||
||= 46 ||= tu ||= 1041.51 ||= 11/6, 20/11, 729/400 ||= v~7 ||= downmid 7th ||= C^^ ||   ||
||= 47 ||= tuh ||= 1064.15 ||= 13/7, 24/13, 50/27 ||= ^~7 ||= upmid 7th ||= C#vv ||   ||
||= 48 ||= ti ||= 1086.79 ||= 15/8 ||= vM7 ||= downmajor 7th ||= C#v ||   ||
||= 49 ||= tih ||= 1109.43 ||= 40/21, 243/128 ||= M7 ||= major 7th ||= C# ||   ||
||= 50 ||= to ||= 1132.08 ||= 48/25, 27/14 ||= ^M7 ||= upmajor 7th ||= C#^ ||   ||
||= 51 ||= taw ||= 1154.72 ||= 125/64 ||= ^^M7,
vv8 ||= double-up major 7th,
double-down 8ve ||= C#^^,
Dvv ||   ||
||= 52 ||= da ||= 1177.36 ||= 160/81 ||= v8 ||= down 8ve ||= Dv ||   ||
||= 53 ||= do ||= 1200 ||= 2/1 ||= P8 ||= perfect 8ve ||= D ||   ||
Combining ups and downs notation with [[Kite's color notation|color notation]], qualities can be loosely associated with colors:
||~ quality ||~ color ||~ monzo format ||~ examples ||
||= downminor ||= blue ||= {a, b, 0, 1} ||= 7/6, 7/4 ||
||= minor ||= fourthward white ||= {a, b}, b < -1 ||= 32/27, 16/9 ||
||= upminor ||= green ||= {a, b, -1} ||= 6/5, 9/5 ||
||= downmid ||= jade ||= {a, b, 0, 0, 1} ||= 11/9, 11/6 ||
||= upmid ||= amber ||= {a, b, 0, 0, -1} ||= 12/11, 18/11 ||
||= downmajor ||= yellow ||= {a, b, 1} ||= 5/4, 5/3 ||
||= major ||= fifthward white ||= {a, b}, b > 1 ||= 9/8, 27/16 ||
||= upmajor ||= red ||= {a, b, 0, -1} ||= 9/7, 12/7 ||
All 53edo chords can be named using ups and downs. Here are the blue, green, jade, yellow and red triads:
||~ color of the 3rd ||~ JI chord ||~ notes as edosteps ||~ notes of C chord ||~ written name ||~ spoken name ||
||= blue ||= 6:7:9 ||= 0-12-31 ||= C Ebv G ||= C.vm ||= C downminor ||
||= green ||= 10:12:15 ||= 0-14-31 ||= C Eb^ G ||= C.^m ||= C upminor ||
||= jade ||= 18:22:27 ||= 0-15-31 ||= C Eb^^ G ||= C.v~ ||= C downmid ||
||= yellow ||= 4:5:6 ||= 0-17-31 ||= C Ev G ||= C.v ||= C downmajor or C dot down ||
||= red ||= 14:18:27 ||= 0-19-31 ||= C E^ G ||= C.^ ||= C upmajor or C dot up ||
For a more complete list, see [[xenharmonic/Ups and Downs Notation#Chord%20names%20in%20other%20EDOs|Ups and Downs Notation - Chord names in other EDOs]].

=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]]
[[https://soundcloud.com/cam-taylor-2-1/mothers|mothers]] by Cam Taylor

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 --><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:&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 />
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:&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>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:&lt;h1&gt; --><h1 id="toc3"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:6 -->Intervals</h1>
 

<table class="wiki_table">
    <tr>
        <th>degree<br />
</th>
        <th>solfege<br />
</th>
        <th>cents<br />
</th>
        <th>approximate ratios<br />
</th>
        <th colspan="3"><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 />
</th>
        <th>generator for<br />
</th>
    </tr>
    <tr>
        <td style="text-align: center;">0<br />
</td>
        <td style="text-align: center;">do<br />
</td>
        <td style="text-align: center;">0.00<br />
</td>
        <td style="text-align: center;">1/1<br />
</td>
        <td style="text-align: center;">P1<br />
</td>
        <td style="text-align: center;">unison<br />
</td>
        <td style="text-align: center;">D<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">1<br />
</td>
        <td style="text-align: center;">di<br />
</td>
        <td style="text-align: center;">22.64<br />
</td>
        <td style="text-align: center;">81/80, 64/63, 50/49<br />
</td>
        <td style="text-align: center;">^1<br />
</td>
        <td style="text-align: center;">up unison<br />
</td>
        <td style="text-align: center;">D^<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">2<br />
</td>
        <td style="text-align: center;">daw<br />
</td>
        <td style="text-align: center;">45.28<br />
</td>
        <td style="text-align: center;">49/48, 36/35, 33/32, 128/125<br />
</td>
        <td style="text-align: center;">^^1,<br />
vvm2<br />
</td>
        <td style="text-align: center;">double-up unison,<br />
double-down minor 2nd<br />
</td>
        <td style="text-align: center;">D^^,<br />
Ebvv<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Quartonic">Quartonic</a><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">3<br />
</td>
        <td style="text-align: center;">ro<br />
</td>
        <td style="text-align: center;">67.92<br />
</td>
        <td style="text-align: center;">27/26, 26/25, 25/24, 22/21<br />
</td>
        <td style="text-align: center;">vm2<br />
</td>
        <td style="text-align: center;">downminor 2nd<br />
</td>
        <td style="text-align: center;">Ebv<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">4<br />
</td>
        <td style="text-align: center;">rih<br />
</td>
        <td style="text-align: center;">90.57<br />
</td>
        <td style="text-align: center;">21/20, 256/243<br />
</td>
        <td style="text-align: center;">m2<br />
</td>
        <td style="text-align: center;">minor 2nd<br />
</td>
        <td style="text-align: center;">Eb<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">5<br />
</td>
        <td style="text-align: center;">ra<br />
</td>
        <td style="text-align: center;">113.21<br />
</td>
        <td style="text-align: center;">16/15, 15/14<br />
</td>
        <td style="text-align: center;">^m2<br />
</td>
        <td style="text-align: center;">upminor 2nd<br />
</td>
        <td style="text-align: center;">Eb^<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">6<br />
</td>
        <td style="text-align: center;">ru<br />
</td>
        <td style="text-align: center;">135.85<br />
</td>
        <td style="text-align: center;">14/13, 13/12, 27/25<br />
</td>
        <td style="text-align: center;">v~2<br />
</td>
        <td style="text-align: center;">downmid 2nd<br />
</td>
        <td style="text-align: center;">Eb^^<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">7<br />
</td>
        <td style="text-align: center;">ruh<br />
</td>
        <td style="text-align: center;">158.49<br />
</td>
        <td style="text-align: center;">12/11, 11/10, 800/729<br />
</td>
        <td style="text-align: center;">^~2<br />
</td>
        <td style="text-align: center;">upmid 2nd<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 style="text-align: center;">8<br />
</td>
        <td style="text-align: center;">reh<br />
</td>
        <td style="text-align: center;">181.13<br />
</td>
        <td style="text-align: center;">10/9<br />
</td>
        <td style="text-align: center;">vM2<br />
</td>
        <td style="text-align: center;">downmajor 2nd<br />
</td>
        <td style="text-align: center;">Ev<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">9<br />
</td>
        <td style="text-align: center;">re<br />
</td>
        <td style="text-align: center;">203.77<br />
</td>
        <td style="text-align: center;">9/8<br />
</td>
        <td style="text-align: center;">M2<br />
</td>
        <td style="text-align: center;">major 2nd<br />
</td>
        <td style="text-align: center;">E<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">10<br />
</td>
        <td style="text-align: center;">ri<br />
</td>
        <td style="text-align: center;">226.42<br />
</td>
        <td style="text-align: center;">8/7, 256/225<br />
</td>
        <td style="text-align: center;">^M2<br />
</td>
        <td style="text-align: center;">upmajor 2nd<br />
</td>
        <td style="text-align: center;">E^<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">11<br />
</td>
        <td style="text-align: center;">raw<br />
</td>
        <td style="text-align: center;">249.06<br />
</td>
        <td style="text-align: center;">15/13, 144/125<br />
</td>
        <td style="text-align: center;">^^M2,<br />
vvm3<br />
</td>
        <td style="text-align: center;">double-up major 2nd,<br />
double-down minor 3rd<br />
</td>
        <td style="text-align: center;">E^^,<br />
Fvv<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Hemischis">Hemischis</a><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">12<br />
</td>
        <td style="text-align: center;">ma<br />
</td>
        <td style="text-align: center;">271.70<br />
</td>
        <td style="text-align: center;">7/6, 75/64<br />
</td>
        <td style="text-align: center;">vm3<br />
</td>
        <td style="text-align: center;">downminor 3rd<br />
</td>
        <td style="text-align: center;">Fv<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Orwell">Orwell</a><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">13<br />
</td>
        <td style="text-align: center;">meh<br />
</td>
        <td style="text-align: center;">294.34<br />
</td>
        <td style="text-align: center;">13/11, 32/27<br />
</td>
        <td style="text-align: center;">m3<br />
</td>
        <td style="text-align: center;">minor 3rd<br />
</td>
        <td style="text-align: center;">F<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">14<br />
</td>
        <td style="text-align: center;">me<br />
</td>
        <td style="text-align: center;">316.98<br />
</td>
        <td style="text-align: center;">6/5<br />
</td>
        <td style="text-align: center;">^m3<br />
</td>
        <td style="text-align: center;">upminor 3rd<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 style="text-align: center;">15<br />
</td>
        <td style="text-align: center;">mu<br />
</td>
        <td style="text-align: center;">339.62<br />
</td>
        <td style="text-align: center;">11/9, 243/200<br />
</td>
        <td style="text-align: center;">v~3<br />
</td>
        <td style="text-align: center;">downmid 3rd<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 style="text-align: center;">16<br />
</td>
        <td style="text-align: center;">muh<br />
</td>
        <td style="text-align: center;">362.26<br />
</td>
        <td style="text-align: center;">16/13, 100/81<br />
</td>
        <td style="text-align: center;">^~3<br />
</td>
        <td style="text-align: center;">upmid 3rd<br />
</td>
        <td style="text-align: center;">F#vv<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">17<br />
</td>
        <td style="text-align: center;">mi<br />
</td>
        <td style="text-align: center;">384.91<br />
</td>
        <td style="text-align: center;">5/4<br />
</td>
        <td style="text-align: center;">vM3<br />
</td>
        <td style="text-align: center;">downmajor 3rd<br />
</td>
        <td style="text-align: center;">F#v<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">18<br />
</td>
        <td style="text-align: center;">maa<br />
</td>
        <td style="text-align: center;">407.55<br />
</td>
        <td style="text-align: center;">81/64<br />
</td>
        <td style="text-align: center;">M3<br />
</td>
        <td style="text-align: center;">major 3rd<br />
</td>
        <td style="text-align: center;">F#<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">19<br />
</td>
        <td style="text-align: center;">mo<br />
</td>
        <td style="text-align: center;">430.19<br />
</td>
        <td style="text-align: center;">9/7, 14/11<br />
</td>
        <td style="text-align: center;">^M3<br />
</td>
        <td style="text-align: center;">upmajor 3rd<br />
</td>
        <td style="text-align: center;">F#^<br />
</td>
        <td><a class="wiki_link" href="/Hamity">Hamity</a><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">20<br />
</td>
        <td style="text-align: center;">maw<br />
</td>
        <td style="text-align: center;">452.83<br />
</td>
        <td style="text-align: center;">13/10, 125/96<br />
</td>
        <td style="text-align: center;">^^M3,<br />
vv4<br />
</td>
        <td style="text-align: center;">double-up major 3rd,<br />
double-down 4th<br />
</td>
        <td style="text-align: center;">F#^^,<br />
Gvv<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">21<br />
</td>
        <td style="text-align: center;">fe<br />
</td>
        <td style="text-align: center;">475.47<br />
</td>
        <td style="text-align: center;">21/16, 675/512, 320/243<br />
</td>
        <td style="text-align: center;">v4<br />
</td>
        <td style="text-align: center;">down 4th<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 style="text-align: center;">22<br />
</td>
        <td style="text-align: center;">fa<br />
</td>
        <td style="text-align: center;">498.11<br />
</td>
        <td style="text-align: center;">4/3<br />
</td>
        <td style="text-align: center;">P4<br />
</td>
        <td style="text-align: center;">perfect 4th<br />
</td>
        <td style="text-align: center;">G<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">23<br />
</td>
        <td style="text-align: center;">fih<br />
</td>
        <td style="text-align: center;">520.75<br />
</td>
        <td style="text-align: center;">27/20<br />
</td>
        <td style="text-align: center;">^4<br />
</td>
        <td style="text-align: center;">up 4th<br />
</td>
        <td style="text-align: center;">G^<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">24<br />
</td>
        <td style="text-align: center;">fu<br />
</td>
        <td style="text-align: center;">543.40<br />
</td>
        <td style="text-align: center;">11/8, 15/11<br />
</td>
        <td style="text-align: center;">^^4<br />
</td>
        <td style="text-align: center;">double-up 4th<br />
</td>
        <td style="text-align: center;">G^^<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">25<br />
</td>
        <td style="text-align: center;">fuh<br />
</td>
        <td style="text-align: center;">566.04<br />
</td>
        <td style="text-align: center;">18/13<br />
</td>
        <td style="text-align: center;">vvA4,<br />
vd5<br />
</td>
        <td style="text-align: center;">double-down aug 4th,<br />
downdim 5th<br />
</td>
        <td style="text-align: center;">G#vv,<br />
Abv<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Tricot">Tricot</a><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">26<br />
</td>
        <td style="text-align: center;">fi<br />
</td>
        <td style="text-align: center;">588.68<br />
</td>
        <td style="text-align: center;">7/5, 45/32<br />
</td>
        <td style="text-align: center;">vA4,<br />
d5<br />
</td>
        <td style="text-align: center;">downaug 4th,<br />
dim 5th<br />
</td>
        <td style="text-align: center;">G#v,<br />
Ab<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">27<br />
</td>
        <td style="text-align: center;">se<br />
</td>
        <td style="text-align: center;">611.32<br />
</td>
        <td style="text-align: center;">10/7, 64/45<br />
</td>
        <td style="text-align: center;">A4,<br />
^d5<br />
</td>
        <td style="text-align: center;">aug 4th,<br />
updim 5th<br />
</td>
        <td style="text-align: center;">G#,<br />
Ab^<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">28<br />
</td>
        <td style="text-align: center;">suh<br />
</td>
        <td style="text-align: center;">633.96<br />
</td>
        <td style="text-align: center;">13/9<br />
</td>
        <td style="text-align: center;">^A4,<br />
^^d5<br />
</td>
        <td style="text-align: center;">upaug 4th,<br />
double-up dim 5th<br />
</td>
        <td style="text-align: center;">G#^,<br />
Ab^^<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">29<br />
</td>
        <td style="text-align: center;">su<br />
</td>
        <td style="text-align: center;">656.60<br />
</td>
        <td style="text-align: center;">16/11, 22/15<br />
</td>
        <td style="text-align: center;">vv5<br />
</td>
        <td style="text-align: center;">double-down 5th<br />
</td>
        <td style="text-align: center;">Avv<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">30<br />
</td>
        <td style="text-align: center;">sih<br />
</td>
        <td style="text-align: center;">679.25<br />
</td>
        <td style="text-align: center;">40/27<br />
</td>
        <td style="text-align: center;">v5<br />
</td>
        <td style="text-align: center;">down 5th<br />
</td>
        <td style="text-align: center;">Av<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">31<br />
</td>
        <td style="text-align: center;">sol<br />
</td>
        <td style="text-align: center;">701.89<br />
</td>
        <td style="text-align: center;">3/2<br />
</td>
        <td style="text-align: center;">P5<br />
</td>
        <td style="text-align: center;">perfect 5th<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 style="text-align: center;">32<br />
</td>
        <td style="text-align: center;">si<br />
</td>
        <td style="text-align: center;">724.53<br />
</td>
        <td style="text-align: center;">32/21, 243/160, 1024/675<br />
</td>
        <td style="text-align: center;">^5<br />
</td>
        <td style="text-align: center;">up 5th<br />
</td>
        <td style="text-align: center;">A^<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">33<br />
</td>
        <td style="text-align: center;">saw<br />
</td>
        <td style="text-align: center;">747.17<br />
</td>
        <td style="text-align: center;">20/13, 192/125<br />
</td>
        <td style="text-align: center;">^^5,<br />
vvm6<br />
</td>
        <td style="text-align: center;">double-up 5th,<br />
double-down minor 6th<br />
</td>
        <td style="text-align: center;">A^^,<br />
Bbvv<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">34<br />
</td>
        <td style="text-align: center;">lo<br />
</td>
        <td style="text-align: center;">769.81<br />
</td>
        <td style="text-align: center;">14/9, 25/16, 11/7<br />
</td>
        <td style="text-align: center;">vm6<br />
</td>
        <td style="text-align: center;">downminor 6th<br />
</td>
        <td style="text-align: center;">Bbv<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">35<br />
</td>
        <td style="text-align: center;">leh<br />
</td>
        <td style="text-align: center;">792.45<br />
</td>
        <td style="text-align: center;">128/81<br />
</td>
        <td style="text-align: center;">m6<br />
</td>
        <td style="text-align: center;">minor 6th<br />
</td>
        <td style="text-align: center;">Bb<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">36<br />
</td>
        <td style="text-align: center;">le<br />
</td>
        <td style="text-align: center;">815.09<br />
</td>
        <td style="text-align: center;">8/5<br />
</td>
        <td style="text-align: center;">^m6<br />
</td>
        <td style="text-align: center;">upminor 6th<br />
</td>
        <td style="text-align: center;">Bb^<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">37<br />
</td>
        <td style="text-align: center;">lu<br />
</td>
        <td style="text-align: center;">837.74<br />
</td>
        <td style="text-align: center;">13/8, 81/50<br />
</td>
        <td style="text-align: center;">v~6<br />
</td>
        <td style="text-align: center;">downmid 6th<br />
</td>
        <td style="text-align: center;">Bb^^<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">38<br />
</td>
        <td style="text-align: center;">luh<br />
</td>
        <td style="text-align: center;">860.38<br />
</td>
        <td style="text-align: center;">18/11, 400/243<br />
</td>
        <td style="text-align: center;">^~6<br />
</td>
        <td style="text-align: center;">upmid 6th<br />
</td>
        <td style="text-align: center;">Bvv<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">39<br />
</td>
        <td style="text-align: center;">la<br />
</td>
        <td style="text-align: center;">883.02<br />
</td>
        <td style="text-align: center;">5/3<br />
</td>
        <td style="text-align: center;">vM6<br />
</td>
        <td style="text-align: center;">downmajor 6th<br />
</td>
        <td style="text-align: center;">Bv<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">40<br />
</td>
        <td style="text-align: center;">laa<br />
</td>
        <td style="text-align: center;">905.66<br />
</td>
        <td style="text-align: center;">22/13, 27/16<br />
</td>
        <td style="text-align: center;">M6<br />
</td>
        <td style="text-align: center;">major 6th<br />
</td>
        <td style="text-align: center;">B<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">41<br />
</td>
        <td style="text-align: center;">lo<br />
</td>
        <td style="text-align: center;">928.30<br />
</td>
        <td style="text-align: center;">12/7<br />
</td>
        <td style="text-align: center;">^M6<br />
</td>
        <td style="text-align: center;">upmajor 6th<br />
</td>
        <td style="text-align: center;">B^<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">42<br />
</td>
        <td style="text-align: center;">law<br />
</td>
        <td style="text-align: center;">950.94<br />
</td>
        <td style="text-align: center;">26/15, 125/72<br />
</td>
        <td style="text-align: center;">^^M6<br />
vvm7<br />
</td>
        <td style="text-align: center;">double-up major 6th,<br />
double-down minor 7th<br />
</td>
        <td style="text-align: center;">B^^,<br />
Cvv<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">43<br />
</td>
        <td style="text-align: center;">ta<br />
</td>
        <td style="text-align: center;">973.58<br />
</td>
        <td style="text-align: center;">7/4<br />
</td>
        <td style="text-align: center;">vm7<br />
</td>
        <td style="text-align: center;">downminor 7th<br />
</td>
        <td style="text-align: center;">Cv<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">44<br />
</td>
        <td style="text-align: center;">teh<br />
</td>
        <td style="text-align: center;">996.23<br />
</td>
        <td style="text-align: center;">16/9<br />
</td>
        <td style="text-align: center;">m7<br />
</td>
        <td style="text-align: center;">minor 7th<br />
</td>
        <td style="text-align: center;">C<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">45<br />
</td>
        <td style="text-align: center;">te<br />
</td>
        <td style="text-align: center;">1018.87<br />
</td>
        <td style="text-align: center;">9/5<br />
</td>
        <td style="text-align: center;">^m7<br />
</td>
        <td style="text-align: center;">upminor 7th<br />
</td>
        <td style="text-align: center;">C^<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">46<br />
</td>
        <td style="text-align: center;">tu<br />
</td>
        <td style="text-align: center;">1041.51<br />
</td>
        <td style="text-align: center;">11/6, 20/11, 729/400<br />
</td>
        <td style="text-align: center;">v~7<br />
</td>
        <td style="text-align: center;">downmid 7th<br />
</td>
        <td style="text-align: center;">C^^<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">47<br />
</td>
        <td style="text-align: center;">tuh<br />
</td>
        <td style="text-align: center;">1064.15<br />
</td>
        <td style="text-align: center;">13/7, 24/13, 50/27<br />
</td>
        <td style="text-align: center;">^~7<br />
</td>
        <td style="text-align: center;">upmid 7th<br />
</td>
        <td style="text-align: center;">C#vv<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">48<br />
</td>
        <td style="text-align: center;">ti<br />
</td>
        <td style="text-align: center;">1086.79<br />
</td>
        <td style="text-align: center;">15/8<br />
</td>
        <td style="text-align: center;">vM7<br />
</td>
        <td style="text-align: center;">downmajor 7th<br />
</td>
        <td style="text-align: center;">C#v<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">49<br />
</td>
        <td style="text-align: center;">tih<br />
</td>
        <td style="text-align: center;">1109.43<br />
</td>
        <td style="text-align: center;">40/21, 243/128<br />
</td>
        <td style="text-align: center;">M7<br />
</td>
        <td style="text-align: center;">major 7th<br />
</td>
        <td style="text-align: center;">C#<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">50<br />
</td>
        <td style="text-align: center;">to<br />
</td>
        <td style="text-align: center;">1132.08<br />
</td>
        <td style="text-align: center;">48/25, 27/14<br />
</td>
        <td style="text-align: center;">^M7<br />
</td>
        <td style="text-align: center;">upmajor 7th<br />
</td>
        <td style="text-align: center;">C#^<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">51<br />
</td>
        <td style="text-align: center;">taw<br />
</td>
        <td style="text-align: center;">1154.72<br />
</td>
        <td style="text-align: center;">125/64<br />
</td>
        <td style="text-align: center;">^^M7,<br />
vv8<br />
</td>
        <td style="text-align: center;">double-up major 7th,<br />
double-down 8ve<br />
</td>
        <td style="text-align: center;">C#^^,<br />
Dvv<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">52<br />
</td>
        <td style="text-align: center;">da<br />
</td>
        <td style="text-align: center;">1177.36<br />
</td>
        <td style="text-align: center;">160/81<br />
</td>
        <td style="text-align: center;">v8<br />
</td>
        <td style="text-align: center;">down 8ve<br />
</td>
        <td style="text-align: center;">Dv<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">53<br />
</td>
        <td style="text-align: center;">do<br />
</td>
        <td style="text-align: center;">1200<br />
</td>
        <td style="text-align: center;">2/1<br />
</td>
        <td style="text-align: center;">P8<br />
</td>
        <td style="text-align: center;">perfect 8ve<br />
</td>
        <td style="text-align: center;">D<br />
</td>
        <td><br />
</td>
    </tr>
</table>

Combining ups and downs notation with <a class="wiki_link" href="/Kite%27s%20color%20notation">color notation</a>, qualities can be loosely associated with colors:<br />


<table class="wiki_table">
    <tr>
        <th>quality<br />
</th>
        <th>color<br />
</th>
        <th>monzo format<br />
</th>
        <th>examples<br />
</th>
    </tr>
    <tr>
        <td style="text-align: center;">downminor<br />
</td>
        <td style="text-align: center;">blue<br />
</td>
        <td style="text-align: center;">{a, b, 0, 1}<br />
</td>
        <td style="text-align: center;">7/6, 7/4<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">minor<br />
</td>
        <td style="text-align: center;">fourthward white<br />
</td>
        <td style="text-align: center;">{a, b}, b &lt; -1<br />
</td>
        <td style="text-align: center;">32/27, 16/9<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">upminor<br />
</td>
        <td style="text-align: center;">green<br />
</td>
        <td style="text-align: center;">{a, b, -1}<br />
</td>
        <td style="text-align: center;">6/5, 9/5<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">downmid<br />
</td>
        <td style="text-align: center;">jade<br />
</td>
        <td style="text-align: center;">{a, b, 0, 0, 1}<br />
</td>
        <td style="text-align: center;">11/9, 11/6<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">upmid<br />
</td>
        <td style="text-align: center;">amber<br />
</td>
        <td style="text-align: center;">{a, b, 0, 0, -1}<br />
</td>
        <td style="text-align: center;">12/11, 18/11<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">downmajor<br />
</td>
        <td style="text-align: center;">yellow<br />
</td>
        <td style="text-align: center;">{a, b, 1}<br />
</td>
        <td style="text-align: center;">5/4, 5/3<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">major<br />
</td>
        <td style="text-align: center;">fifthward white<br />
</td>
        <td style="text-align: center;">{a, b}, b &gt; 1<br />
</td>
        <td style="text-align: center;">9/8, 27/16<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">upmajor<br />
</td>
        <td style="text-align: center;">red<br />
</td>
        <td style="text-align: center;">{a, b, 0, -1}<br />
</td>
        <td style="text-align: center;">9/7, 12/7<br />
</td>
    </tr>
</table>

All 53edo chords can be named using ups and downs. Here are the blue, green, jade, yellow and red triads:<br />


<table class="wiki_table">
    <tr>
        <th>color of the 3rd<br />
</th>
        <th>JI chord<br />
</th>
        <th>notes as edosteps<br />
</th>
        <th>notes of C chord<br />
</th>
        <th>written name<br />
</th>
        <th>spoken name<br />
</th>
    </tr>
    <tr>
        <td style="text-align: center;">blue<br />
</td>
        <td style="text-align: center;">6:7:9<br />
</td>
        <td style="text-align: center;">0-12-31<br />
</td>
        <td style="text-align: center;">C Ebv G<br />
</td>
        <td style="text-align: center;">C.vm<br />
</td>
        <td style="text-align: center;">C downminor<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">green<br />
</td>
        <td style="text-align: center;">10:12:15<br />
</td>
        <td style="text-align: center;">0-14-31<br />
</td>
        <td style="text-align: center;">C Eb^ G<br />
</td>
        <td style="text-align: center;">C.^m<br />
</td>
        <td style="text-align: center;">C upminor<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">jade<br />
</td>
        <td style="text-align: center;">18:22:27<br />
</td>
        <td style="text-align: center;">0-15-31<br />
</td>
        <td style="text-align: center;">C Eb^^ G<br />
</td>
        <td style="text-align: center;">C.v~<br />
</td>
        <td style="text-align: center;">C downmid<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">yellow<br />
</td>
        <td style="text-align: center;">4:5:6<br />
</td>
        <td style="text-align: center;">0-17-31<br />
</td>
        <td style="text-align: center;">C Ev G<br />
</td>
        <td style="text-align: center;">C.v<br />
</td>
        <td style="text-align: center;">C downmajor or C dot down<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">red<br />
</td>
        <td style="text-align: center;">14:18:27<br />
</td>
        <td style="text-align: center;">0-19-31<br />
</td>
        <td style="text-align: center;">C E^ G<br />
</td>
        <td style="text-align: center;">C.^<br />
</td>
        <td style="text-align: center;">C upmajor or C dot up<br />
</td>
    </tr>
</table>

For a more complete list, see <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Chord%20names%20in%20other%20EDOs">Ups and Downs Notation - Chord names in other EDOs</a>.<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><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><br />
<a class="wiki_link_ext" href="https://soundcloud.com/cam-taylor-2-1/mothers" rel="nofollow">mothers</a> by Cam Taylor</body></html>