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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-01-02 06:39:27 UTC</tt>.<br>
: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-01-02 06:40:55 UTC</tt>.<br>
: The original revision id was <tt>602956382</tt>.<br>
: The original revision id was <tt>602956402</tt>.<br>
: The revision comment was: <tt></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>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
Line 40: Line 40:
|| 0 || do || 0.00 || 1/1 ||= P1 ||= unison ||= D ||  ||
|| 0 || do || 0.00 || 1/1 ||= P1 ||= unison ||= D ||  ||
|| 1 || di || 22.64 || 81/80, 64/63, 50/49 ||= ^1 ||= up 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,  
|| 2 || daw || 45.28 || 49/48, 36/35, 33/32, 128/125 ||= ^^1,
vvm2 ||= double-up unison,
vvm2 ||= double-up unison,
double-down min 2nd ||= D^^,
double-down min 2nd ||= D^^,
Line 65: Line 65:
|| 19 || mo || 430.19 || 9/7, 14/11 ||= ^M3 ||= upmajor 3rd ||= F#^ || [[Hamity]] ||
|| 19 || mo || 430.19 || 9/7, 14/11 ||= ^M3 ||= upmajor 3rd ||= F#^ || [[Hamity]] ||
|| 20 || maw || 452.83 || 13/10, 125/96 ||= ^^M3,
|| 20 || maw || 452.83 || 13/10, 125/96 ||= ^^M3,
vv4 ||= double-up major 3rd,
vv4 ||= double-up major 3rd,
double-down 4th ||= F#^^,
double-down 4th ||= F#^^,
Line 74: Line 73:
|| 24 || fu || 543.40 || 11/8, 15/11 ||= ^^4 ||= double-up 4th ||= G^^ ||  ||
|| 24 || fu || 543.40 || 11/8, 15/11 ||= ^^4 ||= double-up 4th ||= G^^ ||  ||
|| 25 || fuh || 566.04 || 18/13 ||= vvA4,
|| 25 || fuh || 566.04 || 18/13 ||= vvA4,
vd5 ||= double-down aug 4th,  
vd5 ||= double-down aug 4th,
downdim 5th ||= G#vv,
downdim 5th ||= G#vv,
Abv || [[xenharmonic/Tricot|Tricot]] ||
Abv || [[xenharmonic/Tricot|Tricot]] ||
Line 86: Line 85:
Ab^ ||  ||
Ab^ ||  ||
|| 28 || suh || 633.96 || 13/9 ||= ^A4,
|| 28 || suh || 633.96 || 13/9 ||= ^A4,
^^d5 ||= upaug 4th,
^^d5 ||= upaug 4th,
double-up dim 5th ||= G#^,
double-up dim 5th ||= G#^,
Line 95: Line 93:
|| 32 || si || 724.53 || 32/21, 243/160, 1024/675 ||= ^5 ||= up 5th ||= A^ ||  ||
|| 32 || si || 724.53 || 32/21, 243/160, 1024/675 ||= ^5 ||= up 5th ||= A^ ||  ||
|| 33 || saw || 747.17 || 20/13, 192/125 ||= ^^5,
|| 33 || saw || 747.17 || 20/13, 192/125 ||= ^^5,
vvm6 ||= double-up 5th,
vvm6 ||= double-up 5th,
double-down minor 6th ||= A^^,
double-down minor 6th ||= A^^,
Line 107: Line 104:
|| 40 || laa || 905.66 || 22/13, 27/16 ||= M6 ||= major 6th ||= B ||  ||
|| 40 || laa || 905.66 || 22/13, 27/16 ||= M6 ||= major 6th ||= B ||  ||
|| 41 || lo || 928.30 || 12/7 ||= ^M6 ||= upmajor 6th ||= B^ ||  ||
|| 41 || lo || 928.30 || 12/7 ||= ^M6 ||= upmajor 6th ||= B^ ||  ||
|| 42 || law || 950.94 || 26/15, 125/72 ||= ^^M6  
|| 42 || law || 950.94 || 26/15, 125/72 ||= ^^M6
vvm7 ||= double-up major 6th,
vvm7 ||= double-up major 6th,
double-down minor 7th ||= B^^,
double-down minor 7th ||= B^^,
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|| 50 || to || 1132.08 || 48/25, 27/14 ||= ^M7 ||= upmajor 7th ||= C#^ ||  ||
|| 50 || to || 1132.08 || 48/25, 27/14 ||= ^M7 ||= upmajor 7th ||= C#^ ||  ||
|| 51 || taw || 1154.72 || 125/64 ||= ^^M7,
|| 51 || taw || 1154.72 || 125/64 ||= ^^M7,
vv8 ||= double-up major 7th,
vv8 ||= double-up major 7th,
double-down 8ve ||= C#^^,
double-down 8ve ||= C#^^,
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         &lt;td&gt;49/48, 36/35, 33/32, 128/125&lt;br /&gt;
         &lt;td&gt;49/48, 36/35, 33/32, 128/125&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;^^1, &lt;br /&gt;
         &lt;td style="text-align: center;"&gt;^^1,&lt;br /&gt;
vvm2&lt;br /&gt;
vvm2&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 630: Line 626:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;^^M3,&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;^^M3,&lt;br /&gt;
&lt;br /&gt;
vv4&lt;br /&gt;
vv4&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
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vd5&lt;br /&gt;
vd5&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;double-down aug 4th, &lt;br /&gt;
         &lt;td style="text-align: center;"&gt;double-down aug 4th,&lt;br /&gt;
downdim 5th&lt;br /&gt;
downdim 5th&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;^A4,&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;^A4,&lt;br /&gt;
&lt;br /&gt;
^^d5&lt;br /&gt;
^^d5&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;^^5,&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;^^5,&lt;br /&gt;
&lt;br /&gt;
vvm6&lt;br /&gt;
vvm6&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 1,046: Line 1,039:
         &lt;td&gt;26/15, 125/72&lt;br /&gt;
         &lt;td&gt;26/15, 125/72&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;^^M6 &lt;br /&gt;
         &lt;td style="text-align: center;"&gt;^^M6&lt;br /&gt;
vvm7&lt;br /&gt;
vvm7&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 1,212: Line 1,205:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;^^M7,&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;^^M7,&lt;br /&gt;
&lt;br /&gt;
vv8&lt;br /&gt;
vv8&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;

Revision as of 06:40, 2 January 2017

IMPORTED REVISION FROM WIKISPACES

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

This revision was by author TallKite and made on 2017-01-02 06:40:55 UTC.
The original revision id was 602956402.
The revision comment was:

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Original Wikitext content:

[[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 min 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 ||= down-mid 2nd ||= Eb^^ ||   ||
|| 7 || ruh || 158.49 || 12/11, 11/10, 800/729 ||= ^~2 ||= up-mid 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 min 3rd ||= E^^,
vvF || [[xenharmonic/Hemischis|Hemischis]] ||
|| 12 || ma || 271.70 || 7/6, 75/64 ||= vm3 ||= downminor 3rd ||= vF || [[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 ||   ||
The distance from C to C# is 5 keys or frets or EDOsteps, and one up equals one fifth of a sharp. Chords can be named using ups and downs as C upminor, D downmajor seven, etc. 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]]

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>
        <td>degree<br />
</td>
        <td>solfege<br />
</td>
        <td>cents<br />
</td>
        <td>approximate ratios<br />
</td>
        <td colspan="3" 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;">unison<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;">up unison<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,<br />
vvm2<br />
</td>
        <td style="text-align: center;">double-up unison,<br />
double-down min 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>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;">downminor 2nd<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;">minor 2nd<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;">upminor 2nd<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;">v~2<br />
</td>
        <td style="text-align: center;">down-mid 2nd<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;">^~2<br />
</td>
        <td style="text-align: center;">up-mid 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>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;">downmajor 2nd<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;">major 2nd<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;">upmajor 2nd<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;">^^M2,<br />
vvm3<br />
</td>
        <td style="text-align: center;">double-up major 2nd,<br />
double-down min 3rd<br />
</td>
        <td style="text-align: center;">E^^,<br />
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;">downminor 3rd<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;">minor 3rd<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;">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>15<br />
</td>
        <td>mu<br />
</td>
        <td>339.62<br />
</td>
        <td>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>16<br />
</td>
        <td>muh<br />
</td>
        <td>362.26<br />
</td>
        <td>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>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;">downmajor 3rd<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;">major 3rd<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;">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>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,<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>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;">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>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;">perfect 4th<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;">up 4th<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;">double-up 4th<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,<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>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,<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>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,<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>28<br />
</td>
        <td>suh<br />
</td>
        <td>633.96<br />
</td>
        <td>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>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;">double-down 5th<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;">down 5th<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;">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>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;">up 5th<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,<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>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;">downminor 6th<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;">minor 6th<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;">upminor 6th<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;">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>38<br />
</td>
        <td>luh<br />
</td>
        <td>860.38<br />
</td>
        <td>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>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;">downmajor 6th<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;">major 6th<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;">upmajor 6th<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<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>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;">downminor 7th<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;">minor 7th<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;">upminor 7th<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;">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>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;">^~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>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;">downmajor 7th<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;">major 7th<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;">upmajor 7th<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,<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>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;">down 8ve<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;">perfect 8ve<br />
</td>
        <td style="text-align: center;">D<br />
</td>
        <td><br />
</td>
    </tr>
</table>

The distance from C to C# is 5 keys or frets or EDOsteps, and one up equals one fifth of a sharp. Chords can be named using ups and downs as C upminor, D downmajor seven, etc. 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></body></html>
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