5edo

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[[toc|flat]]
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=5 Equal Divisions of the Octave: Theory= 
==="equal pentatonic"=== 

5-edo divides the 1200-[[cent]] octave into 5 equal parts, making its smallest interval exactly 240 [[cent]], or the fifth root of 2.

5-edo is the smallest [[edo]] containing xenharmonic intervals! (1edo 2edo 3edo 4edo are all subsets of 12edo)

==Intervals in 5-edo== 
|| **Interval,**
**in fifths of**
**an octave** || **Interval**
**in ¢** || **Closest**
**diatonic**
**interval name** || **The "neighborhood" of just intervals** ||
|| 0 || 0.0 || unison / prime || exactly 1/1 ||
|| 1 || 240.0 || second / third || +8.826 c from septimal second 8/7
-4.969 c from diminished third 144/125
-13.076 c from augmented second 125/108
-26.871 c from septimal minor third 7/6 ||
|| 2 || 480.0 || fourth || +9.219 c from narrow fourth 21/16
-0.686 c from smaller fourth 33/25
-18.045 c from just fourth 4/3 ||
|| 3 || 720.0 || fifth || +18.045 c from just fifth 3/2
+0.686 c from bigger fifth 50/33
-9.219 c from wide fifth 32/21 ||
|| 4 || 960.0 || sixth, seventh || 26.871 c from septimal major sixth 12/7
13.076 c from diminished seventh 216/125
4.969 c from augmented sixth 125/72
-8.826 c from septimal seventh 7/4 ||
|| 5 || 1200.0 || eighth || exactly 2/1 ||

==Related scales== 
* By its cardinality, 5-edo is related to other [[pentatonic]] scales, and it is especially close in sound to many Indonesian [[slendro|slendros]].
* Due to the interest around the "fifth" interval size, there are many [[nonoctave]] "stretch sisters" to 5-edo: square root of 4/3, cube root of 3/2, 8th root of 3, etc.
* For the same reason there are many "circle sisters":
** Make a chain of five "bigger fifths" (50/33), which makes three octaves 3.227¢ flat. (50/33)^5=7.985099.

==As a temperament== 
If 5-edo is regarded as a temperament, which is to say as 5-et, then the most salient fact is that 16/15 is tempered out. This means in 5-et the major third and the fourth, and the minor sixth and the fifth, are not distinguished; this is 5-limit [[Trienstonic clan|father temperament]]. This is at the very edge what can sensibly be called temperament, but it does make sense and can be used.

Also tempered out is 27/25, if we temper this out in preference to 16/15 we obtain [[Bug family|bug temperament]], which equates 10/9 with 6/5: it is a little more perverse even than father. Because these intervals are so large, this sort of analysis is less significant with 5 than it becomes with larger and more accurate divisions, but it still plays a role. For example, I-IV-V-I is the same as 1-III-V-I and involves triads with common intervals because of fourth-thirds equivalence.

Despite its lack of accuracy, 5EDO is the second Zeta function integral tuning, after 2EDO. See http://www.research.att.com/~njas/sequences/A117538. It also is the smallest equal division representing the 9-limit consistently, giving a distinct value modulo five to 2, 3, 5, 7 and 9. Hence in a way similar to how [[4edo]] can be used, and which is discussed in that article, it can be used to represent 7-limit intervals in terms of their position in a pentad, by giving a triple of integers representing a pentad in the [[The Seven Limit Symmetrical Lattices|lattice]] of tetrads/pentads together with the number of scale steps in 5EDO. However, while [[2edo]] represents the 3-limit consistently, [[3edo]] the 5-limit, [[4edo]] the 7-limit and [[5edo]] the 9-limit, to represent the 11-limit consistently with a [[patent val]] requires going all the way to [[22edo]].

==Cycles, Divisions== 
5 is a prime number so 5-edo contains no sub-edos. Only simple cycles:
Cycle of seconds: 0-1-2-3-4-0
Cycle of fourths: 0-2-4-1-3-0
Cycle of fifths: 0-3-1-4-2-0
Cycle of sevenths: 0-4-3-2-1-0

=5-edo in Musicmaking= 
==**Compositions**, improvisations== 
** [[http://www.io.com/%7Ehmiller/|Herman Miller]]: //[[http://micro.soonlabel.com/herman_miller/Daybreak.mp3|Daybreak on Slendro Mountain]]// (2000)
** Aaron K. Johnson: //[[http://www.akjmusic.com/audio/5tet_funk.mp3|5tet funk]]// (2004)
** [[http://www.soundclick.com/bands/page_songInfo.cfm?bandID=122613&songID=1519939|Andrew Heathwaite: //Pinta Penta// (2004)]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+pintapentain5tet.mp3|play]] (rendered in 6 alternative pentatonics as well)
** [[Hans Straub]]: [[http://home.datacomm.ch/straub/mamuth/5tet_e.html#asimchomsaia|Asîmchômsaia]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Straub/asimchomsaia.mp3|play]]
** [[Brian Wong]]: [[http://bwong.ca/template1.php?sub=3|Slendronica#1b]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Wong/Slendronica1b.ogg|play]]
** Brian McLaren: various and sundry
** Paul Rubenstein: various, with electric guitars in 10- and 15-edo
** X.J.Scott: //Sleeping Through It All// (2004)
** Bill Sethares: //5-tet funk// (2004), //Pentacle// (2004)
** "Cenobyte" Ukulele [[http://www.youtube.com/watch?v=UKUCRnEJKKU| http://www.youtube.com/watch?v=UKUCRnEJKKU]]

==Notation== 
** via Reinhard's cents notation
** Sagittal: naturals on a five-line staff, with enharmonics (used interchangably) E=F and B=C
** a four-line hybrid treble/bass staff.

==Harmony== 
5edo does not have any strong consonance nor dissonance. The 240 cent interval can serve as either a major second or minor third, and the 960 cent interval as either a major sixth or minor seventh. The fourth is about 18 cents flat of a just fourth, making it rather "dirty" but recognizable. The fifth is likewise about 18 cents sharp of a just fifth, dissonant but still easily recognizable.

Important chords:
* 0+1+3
* 0+2+3
* 0+1+3+4
* 0+2+3+4

==Melody== 
First from edos which can be use for melodies in "standard" way. Relatively large step of 240.00 c can be used as major second for the melody construction. The scale has whole-tone as well as pentatonic character.

==Chord or scale?== 
Either way, it is hard to wander very far from where you start. However, it has the scale-like feature that there are (barely) enough notes to create melody, in the form of an equal version of pentatonic.

==Commas Tempered== 
5-EDO tempers out the following commas. (Note: This assumes the val < 5 8 12 14 17 19 |.)

||~ Comma ||~ Value (cents) ||~ Name ||~ Second Name ||~ Third Name ||~ Val ||
||= 256/243 ||> 90.225 || Limma || Pythagorean Minor 2nd || || | 8 -5 > ||
||= 81/80 ||> 21.506 || Syntonic Comma || Didymos Comma || Meantone Comma || | -4 4 -1 > ||
||= 2889416/2882415 ||> 4.200 || Vulture || || || | 24 -21 4 > ||
||= 36/35 ||> 48.770 || Septimal Quarter Tone || || || | 2 2 -1 -1 > ||
||= 49/48 ||> 35.697 || Slendro Diesis || || || | -4 -1 0 2 > ||
||= 64/63 ||> 27.264 || Septimal Comma || Archytas' Comma || Leipziger Komma || | 6 -2 0 -1 > ||
||= 245/243 ||> 14.191 || Sensamagic || || || | 0 -5 1 2 > ||
||= 1728/1715 ||> 13.074 || Orwellisma || Orwell Comma || || | 6 3 -1 -3 > ||
||= 1029/1024 ||> 8.433 || Gamelisma || || || | -10 1 0 3 > ||
||= 19683/19600 ||> 7.316 || Cataharry || || || | -4 9 -2 -2 > ||
||= 5120/5103 ||> 5.758 || Hemifamity || || || | 10 -6 1 -1 > ||
||= 1065875/1063543 ||> 3.792 || Wadisma || || || | -26 -1 1 9 > ||
||= 420175/419904 ||> 1.117 || Wizma || || || | -6 -8 2 5 > ||
||= 99/98 ||> 17.576 || Mothwellsma || || || | -1 2 0 -2 1 > ||
||= 896/891 ||> 9.688 || Pentacircle || || || | 7 -4 0 1 -1 > ||
||= 385/384 ||> 4.503 || Keenanisma || || || | -7 -1 1 1 1 > ||
||= 441/440 ||> 3.930 || Werckisma || || || | -3 2 -1 2 -1 > ||
||= 3025/3024 ||> 0.572 || Lehmerisma || || || | -4 -3 2 -1 2 > ||
||= 91/90 ||> 19.130 || Superleap || || || | -1 -2 -1 1 0 1 > ||
||= 676/675 ||> 2.563 || Parizeksma || || || | 2 -3 -2 0 0 2 > || ||

Original HTML content:

<html><head><title>5edo</title></head><body><!-- ws:start:WikiTextTocRule:26:&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:26 --><!-- ws:start:WikiTextTocRule:27: --><a href="#x5 Equal Divisions of the Octave: Theory">5 Equal Divisions of the Octave: Theory</a><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --> | <a href="#x5-edo in Musicmaking">5-edo in Musicmaking</a><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: -->
<!-- ws:end:WikiTextTocRule:40 --><hr />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x5 Equal Divisions of the Octave: Theory"></a><!-- ws:end:WikiTextHeadingRule:0 -->5 Equal Divisions of the Octave: Theory</h1>
 <!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x5 Equal Divisions of the Octave: Theory--&quot;equal pentatonic&quot;"></a><!-- ws:end:WikiTextHeadingRule:2 -->&quot;equal pentatonic&quot;</h3>
 <br />
5-edo divides the 1200-<a class="wiki_link" href="/cent">cent</a> octave into 5 equal parts, making its smallest interval exactly 240 <a class="wiki_link" href="/cent">cent</a>, or the fifth root of 2.<br />
<br />
5-edo is the smallest <a class="wiki_link" href="/edo">edo</a> containing xenharmonic intervals! (1edo 2edo 3edo 4edo are all subsets of 12edo)<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x5 Equal Divisions of the Octave: Theory-Intervals in 5-edo"></a><!-- ws:end:WikiTextHeadingRule:4 -->Intervals in 5-edo</h2>
 

<table class="wiki_table">
    <tr>
        <td><strong>Interval,</strong><br />
<strong>in fifths of</strong><br />
<strong>an octave</strong><br />
</td>
        <td><strong>Interval</strong><br />
<strong>in ¢</strong><br />
</td>
        <td><strong>Closest</strong><br />
<strong>diatonic</strong><br />
<strong>interval name</strong><br />
</td>
        <td><strong>The &quot;neighborhood&quot; of just intervals</strong><br />
</td>
    </tr>
    <tr>
        <td>0<br />
</td>
        <td>0.0<br />
</td>
        <td>unison / prime<br />
</td>
        <td>exactly 1/1<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>240.0<br />
</td>
        <td>second / third<br />
</td>
        <td>+8.826 c from septimal second 8/7<br />
-4.969 c from diminished third 144/125<br />
-13.076 c from augmented second 125/108<br />
-26.871 c from septimal minor third 7/6<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>480.0<br />
</td>
        <td>fourth<br />
</td>
        <td>+9.219 c from narrow fourth 21/16<br />
-0.686 c from smaller fourth 33/25<br />
-18.045 c from just fourth 4/3<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>720.0<br />
</td>
        <td>fifth<br />
</td>
        <td>+18.045 c from just fifth 3/2<br />
+0.686 c from bigger fifth 50/33<br />
-9.219 c from wide fifth 32/21<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>960.0<br />
</td>
        <td>sixth, seventh<br />
</td>
        <td>26.871 c from septimal major sixth 12/7<br />
13.076 c from diminished seventh 216/125<br />
4.969 c from augmented sixth 125/72<br />
-8.826 c from septimal seventh 7/4<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>1200.0<br />
</td>
        <td>eighth<br />
</td>
        <td>exactly 2/1<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x5 Equal Divisions of the Octave: Theory-Related scales"></a><!-- ws:end:WikiTextHeadingRule:6 -->Related scales</h2>
 <ul><li>By its cardinality, 5-edo is related to other <a class="wiki_link" href="/pentatonic">pentatonic</a> scales, and it is especially close in sound to many Indonesian <a class="wiki_link" href="/slendro">slendros</a>.</li><li>Due to the interest around the &quot;fifth&quot; interval size, there are many <a class="wiki_link" href="/nonoctave">nonoctave</a> &quot;stretch sisters&quot; to 5-edo: square root of 4/3, cube root of 3/2, 8th root of 3, etc.</li><li>For the same reason there are many &quot;circle sisters&quot;:<ul><li>Make a chain of five &quot;bigger fifths&quot; (50/33), which makes three octaves 3.227¢ flat. (50/33)^5=7.985099.</li></ul></li></ul><br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="x5 Equal Divisions of the Octave: Theory-As a temperament"></a><!-- ws:end:WikiTextHeadingRule:8 -->As a temperament</h2>
 If 5-edo is regarded as a temperament, which is to say as 5-et, then the most salient fact is that 16/15 is tempered out. This means in 5-et the major third and the fourth, and the minor sixth and the fifth, are not distinguished; this is 5-limit <a class="wiki_link" href="/Trienstonic%20clan">father temperament</a>. This is at the very edge what can sensibly be called temperament, but it does make sense and can be used.<br />
<br />
Also tempered out is 27/25, if we temper this out in preference to 16/15 we obtain <a class="wiki_link" href="/Bug%20family">bug temperament</a>, which equates 10/9 with 6/5: it is a little more perverse even than father. Because these intervals are so large, this sort of analysis is less significant with 5 than it becomes with larger and more accurate divisions, but it still plays a role. For example, I-IV-V-I is the same as 1-III-V-I and involves triads with common intervals because of fourth-thirds equivalence.<br />
<br />
Despite its lack of accuracy, 5EDO is the second Zeta function integral tuning, after 2EDO. See <!-- ws:start:WikiTextUrlRule:698:http://www.research.att.com/~njas/sequences/A117538 --><a class="wiki_link_ext" href="http://www.research.att.com/~njas/sequences/A117538" rel="nofollow">http://www.research.att.com/~njas/sequences/A117538</a><!-- ws:end:WikiTextUrlRule:698 -->. It also is the smallest equal division representing the 9-limit consistently, giving a distinct value modulo five to 2, 3, 5, 7 and 9. Hence in a way similar to how <a class="wiki_link" href="/4edo">4edo</a> can be used, and which is discussed in that article, it can be used to represent 7-limit intervals in terms of their position in a pentad, by giving a triple of integers representing a pentad in the <a class="wiki_link" href="/The%20Seven%20Limit%20Symmetrical%20Lattices">lattice</a> of tetrads/pentads together with the number of scale steps in 5EDO. However, while <a class="wiki_link" href="/2edo">2edo</a> represents the 3-limit consistently, <a class="wiki_link" href="/3edo">3edo</a> the 5-limit, <a class="wiki_link" href="/4edo">4edo</a> the 7-limit and <a class="wiki_link" href="/5edo">5edo</a> the 9-limit, to represent the 11-limit consistently with a <a class="wiki_link" href="/patent%20val">patent val</a> requires going all the way to <a class="wiki_link" href="/22edo">22edo</a>.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="x5 Equal Divisions of the Octave: Theory-Cycles, Divisions"></a><!-- ws:end:WikiTextHeadingRule:10 -->Cycles, Divisions</h2>
 5 is a prime number so 5-edo contains no sub-edos. Only simple cycles:<br />
Cycle of seconds: 0-1-2-3-4-0<br />
Cycle of fourths: 0-2-4-1-3-0<br />
Cycle of fifths: 0-3-1-4-2-0<br />
Cycle of sevenths: 0-4-3-2-1-0<br />
<br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="x5-edo in Musicmaking"></a><!-- ws:end:WikiTextHeadingRule:12 -->5-edo in Musicmaking</h1>
 <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="x5-edo in Musicmaking-Compositions, improvisations"></a><!-- ws:end:WikiTextHeadingRule:14 --><strong>Compositions</strong>, improvisations</h2>
 <ul><ul><li><a class="wiki_link_ext" href="http://www.io.com/%7Ehmiller/" rel="nofollow">Herman Miller</a>: <em><a class="wiki_link_ext" href="http://micro.soonlabel.com/herman_miller/Daybreak.mp3" rel="nofollow">Daybreak on Slendro Mountain</a></em> (2000)</li><li>Aaron K. Johnson: <em><a class="wiki_link_ext" href="http://www.akjmusic.com/audio/5tet_funk.mp3" rel="nofollow">5tet funk</a></em> (2004)</li><li><a class="wiki_link_ext" href="http://www.soundclick.com/bands/page_songInfo.cfm?bandID=122613&amp;songID=1519939" rel="nofollow">Andrew Heathwaite: //Pinta Penta// (2004)</a> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+pintapentain5tet.mp3" rel="nofollow">play</a> (rendered in 6 alternative pentatonics as well)</li><li><a class="wiki_link" href="/Hans%20Straub">Hans Straub</a>: <a class="wiki_link_ext" href="http://home.datacomm.ch/straub/mamuth/5tet_e.html#asimchomsaia" rel="nofollow">Asîmchômsaia</a> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Straub/asimchomsaia.mp3" rel="nofollow">play</a></li><li><a class="wiki_link" href="/Brian%20Wong">Brian Wong</a>: <a class="wiki_link_ext" href="http://bwong.ca/template1.php?sub=3" rel="nofollow">Slendronica#1b</a> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Wong/Slendronica1b.ogg" rel="nofollow">play</a></li><li>Brian McLaren: various and sundry</li><li>Paul Rubenstein: various, with electric guitars in 10- and 15-edo</li><li>X.J.Scott: <em>Sleeping Through It All</em> (2004)</li><li>Bill Sethares: <em>5-tet funk</em> (2004), <em>Pentacle</em> (2004)</li><li>&quot;Cenobyte&quot; Ukulele <a class="wiki_link_ext" href="http://www.youtube.com/watch?v=UKUCRnEJKKU" rel="nofollow"> http://www.youtube.com/watch?v=UKUCRnEJKKU</a></li></ul></ul><br />
<!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="x5-edo in Musicmaking-Notation"></a><!-- ws:end:WikiTextHeadingRule:16 -->Notation</h2>
 <ul><ul><li>via Reinhard's cents notation</li><li>Sagittal: naturals on a five-line staff, with enharmonics (used interchangably) E=F and B=C</li><li>a four-line hybrid treble/bass staff.</li></ul></ul><br />
<!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="x5-edo in Musicmaking-Harmony"></a><!-- ws:end:WikiTextHeadingRule:18 -->Harmony</h2>
 5edo does not have any strong consonance nor dissonance. The 240 cent interval can serve as either a major second or minor third, and the 960 cent interval as either a major sixth or minor seventh. The fourth is about 18 cents flat of a just fourth, making it rather &quot;dirty&quot; but recognizable. The fifth is likewise about 18 cents sharp of a just fifth, dissonant but still easily recognizable.<br />
<br />
Important chords:<br />
<ul><li>0+1+3</li><li>0+2+3</li><li>0+1+3+4</li><li>0+2+3+4</li></ul><br />
<!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="x5-edo in Musicmaking-Melody"></a><!-- ws:end:WikiTextHeadingRule:20 -->Melody</h2>
 First from edos which can be use for melodies in &quot;standard&quot; way. Relatively large step of 240.00 c can be used as major second for the melody construction. The scale has whole-tone as well as pentatonic character.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="x5-edo in Musicmaking-Chord or scale?"></a><!-- ws:end:WikiTextHeadingRule:22 -->Chord or scale?</h2>
 Either way, it is hard to wander very far from where you start. However, it has the scale-like feature that there are (barely) enough notes to create melody, in the form of an equal version of pentatonic.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="x5-edo in Musicmaking-Commas Tempered"></a><!-- ws:end:WikiTextHeadingRule:24 -->Commas Tempered</h2>
 5-EDO tempers out the following commas. (Note: This assumes the val &lt; 5 8 12 14 17 19 |.)<br />
<br />


<table class="wiki_table">
    <tr>
        <th>Comma<br />
</th>
        <th>Value (cents)<br />
</th>
        <th>Name<br />
</th>
        <th>Second Name<br />
</th>
        <th>Third Name<br />
</th>
        <th>Val<br />
</th>
    </tr>
    <tr>
        <td style="text-align: center;">256/243<br />
</td>
        <td style="text-align: right;">90.225<br />
</td>
        <td>Limma<br />
</td>
        <td>Pythagorean Minor 2nd<br />
</td>
        <td><br />
</td>
        <td>| 8 -5 &gt;<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">81/80<br />
</td>
        <td style="text-align: right;">21.506<br />
</td>
        <td>Syntonic Comma<br />
</td>
        <td>Didymos Comma<br />
</td>
        <td>Meantone Comma<br />
</td>
        <td>| -4 4 -1 &gt;<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">2889416/2882415<br />
</td>
        <td style="text-align: right;">4.200<br />
</td>
        <td>Vulture<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>| 24 -21 4 &gt;<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">36/35<br />
</td>
        <td style="text-align: right;">48.770<br />
</td>
        <td>Septimal Quarter Tone<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>| 2 2 -1 -1 &gt;<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">49/48<br />
</td>
        <td style="text-align: right;">35.697<br />
</td>
        <td>Slendro Diesis<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>| -4 -1 0 2 &gt;<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">64/63<br />
</td>
        <td style="text-align: right;">27.264<br />
</td>
        <td>Septimal Comma<br />
</td>
        <td>Archytas' Comma<br />
</td>
        <td>Leipziger Komma<br />
</td>
        <td>| 6 -2 0 -1 &gt;<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">245/243<br />
</td>
        <td style="text-align: right;">14.191<br />
</td>
        <td>Sensamagic<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>| 0 -5 1 2 &gt;<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">1728/1715<br />
</td>
        <td style="text-align: right;">13.074<br />
</td>
        <td>Orwellisma<br />
</td>
        <td>Orwell Comma<br />
</td>
        <td><br />
</td>
        <td>| 6 3 -1 -3 &gt;<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">1029/1024<br />
</td>
        <td style="text-align: right;">8.433<br />
</td>
        <td>Gamelisma<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>| -10 1 0 3 &gt;<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">19683/19600<br />
</td>
        <td style="text-align: right;">7.316<br />
</td>
        <td>Cataharry<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>| -4 9 -2 -2 &gt;<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">5120/5103<br />
</td>
        <td style="text-align: right;">5.758<br />
</td>
        <td>Hemifamity<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>| 10 -6 1 -1 &gt;<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">1065875/1063543<br />
</td>
        <td style="text-align: right;">3.792<br />
</td>
        <td>Wadisma<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>| -26 -1 1 9 &gt;<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">420175/419904<br />
</td>
        <td style="text-align: right;">1.117<br />
</td>
        <td>Wizma<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>| -6 -8 2 5 &gt;<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">99/98<br />
</td>
        <td style="text-align: right;">17.576<br />
</td>
        <td>Mothwellsma<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>| -1 2 0 -2 1 &gt;<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">896/891<br />
</td>
        <td style="text-align: right;">9.688<br />
</td>
        <td>Pentacircle<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>| 7 -4 0 1 -1 &gt;<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">385/384<br />
</td>
        <td style="text-align: right;">4.503<br />
</td>
        <td>Keenanisma<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>| -7 -1 1 1 1 &gt;<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">441/440<br />
</td>
        <td style="text-align: right;">3.930<br />
</td>
        <td>Werckisma<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>| -3 2 -1 2 -1 &gt;<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">3025/3024<br />
</td>
        <td style="text-align: right;">0.572<br />
</td>
        <td>Lehmerisma<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>| -4 -3 2 -1 2 &gt;<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">91/90<br />
</td>
        <td style="text-align: right;">19.130<br />
</td>
        <td>Superleap<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>| -1 -2 -1 1 0 1 &gt;<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">676/675<br />
</td>
        <td style="text-align: right;">2.563<br />
</td>
        <td>Parizeksma<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>| 2 -3 -2 0 0 2 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
</table>

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