27edo: Difference between revisions

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=<span style="color: #0061ff; font-family: 'Times New Roman',Times,serif; font-size: 113%;">27 tone equal tempertament</span>= 

If octaves are kept pure, 27edo divides the [[octave]] in 27 equal parts each exactly 44.444... [[cent]]s in size. However, 27 is a prime candidate for [[octave shrinking]], and a step size of 44.3 to 44.35 cents would be reasonable. The reason for this is that 27edo tunes the [[5_4|third]], [[3_2|fifth]] and [[7_4|7/4]] sharply.

Assuming however pure octaves, 27 has a fifth sharp by slightly more than nine cents and a 7/4 sharp by slightly less, and the same 400 cent major third as [[12edo]], sharp 13 2/3 cents. The result is that [[6_5|6/5]], [[7_5|7/5]] and especially [[7_6|7/6]] are all tuned more accurately than this.

27edo, with its 400 cent major third, tempers out the [[diesis]] of 128/125, and also the [[septimal comma]], 64/63 (and hence 126/125 also.) These it shares with 12edo, making some relationships familiar, and as a consequence they both support augene temperament. It shares with [[22edo]] tempering out the allegedly Bohlen-Pierce comma 245/243 as well as 64/63, so that they both support superpyth temperament, with quite sharp "superpythagorean" fifths giving a sharp 9/7 in place of meantone's 5/4.

Though the [[7-limit]] tuning of 27edo is not highly accurate, it nonetheless is the smallest equal division to represent the 7 odd limit both [[consistent]]ly and distinctly--that is, everything in the 7-limit [[Diamonds|diamond]] is uniquely represented by a certain number of steps of 27 equal. It also represents the 13th harmonic very well, and performs quite decently as a 2.3.5.7.13 temperament

Its step, as well as the octave-inverted and octave-equivalent versions of it, holds the distinction for having around the highest [[harmonic entropy]] possible and thus is, in theory, most dissonant, assuming the relatively common values of a=2 and s=1%. This property is shared with all edos between around 24 and 30. Intervals smaller than this tend to be perceived as unison and are more consonant as a result; intervals larger than this have less "tension" and thus are also more consonant.

The 27 note system or one similar like a well temperament can be notated very easily, by a variation on the quartertone accidentals. In this case a sharp raises a note by 4 EDOsteps, just one EDOstep beneath the following nominal (for example C to C# describes the approximate 10/9 and 11/10 interval) and the flat conversely lowers: these are augmented unisons and diminished unisons. Just so, one finds that an accidental can be divided in half, and this fill the remaining places without need for double sharps and double flats. Enharmonically then, E double flat means C half sharp. In other words, the resemblance to quarter tone notation differs in enharmonic divergence. D flat, C half-sharp, D half flat, and C sharp are all different. The composer can decide for himself which tertiary accidental is necessary if he will need redundancy to keep the chromatic pitches within a compass on paper relative to the natural names (C, D, E etc.) otherwise is simple enough and the same tendency for A# to be higher than Bb is not only familiar, though here very exaggerated, to those working with pythagorean scale, but also to many classically trained violinists. et voila

==Intervals== 

==[[#x27 tone equal tempertament-Intervals]] Intervals== 
||= Degree ||= Cents value ||= Approximate
Ratios* ||= Solfege ||||||= [[xenharmonic/Ups and Downs Notation|ups and downs notation]] ||
||= 0 ||= 0 ||= 1/1 ||= do ||= P1 ||= perfect unison ||= D ||
||= 1 ||= 44.44 ||= 36/35, 49/48, 50/49 ||= di ||= ^1, m2 ||= minor 2nd ||= Eb ||
||= 2 ||= 88.89 ||= 16/15, 21/20, 25/24 ||= ra ||= ^^1, ^m2 ||= upminor 2nd ||= Eb^ ||
||= 3 ||= 133.33 ||= 14/13, 13/12 ||= ru ||= ~2 ||= mid 2nd ||= Evv ||
||= 4 ||= 177.78 ||= 10/9 ||= reh ||= vM2 ||= downmajor 2nd ||= Ev ||
||= 5 ||= 222.22 ||= 8/7, 9/8 ||= re ||= M2 ||= major 2nd ||= E ||
||= 6 ||= 266.67 ||= 7/6 ||= ma ||= m3 ||= minor 3rd ||= F ||
||= 7 ||= 311.11 ||= 6/5 ||= me ||= ^m3 ||= upminor 3rd ||= F^ ||
||= 8 ||= 355.56 ||= 16/13 ||= mu ||= ~3 ||= mid 3rd ||= F^^ ||
||= 9 ||= 400 ||= 5/4 ||= mi ||= vM3 ||= downmajor 3rd ||= F#v ||
||= 10 ||= 444.44 ||= 9/7, 13/10 ||= mo ||= M3 ||= major 3rd ||= F# ||
||= 11 ||= 488.89 ||= 4/3 ||= fa ||= P4 ||= perfect 4th ||= G ||
||= 12 ||= 533.33 ||= 49/36, 48/35 ||= fih ||= ^4 ||= up 4th ||= G^ ||
||= 13 ||= 577.78 ||= 7/5, 18/13 ||= fi ||= ^^4 ||= double-up 4th ||= G^^ ||
||= 14 ||= 622.22 ||= 10/7, 13/9 ||= se ||= vv5 ||= double-down 5th ||= Avv ||
||= 15 ||= 666.67 ||= 72/49, 35/24 ||= sih ||= v5 ||= down fifth ||= Av ||
||= 16 ||= 711.11 ||= 3/2 ||= so/sol ||= P5 ||= perfect 5th ||= A ||
||= 17 ||= 755.56 ||= 14/9, 20/13 ||= lo ||= m6 ||= minor 6th ||= Bb ||
||= 18 ||= 800 ||= 8/5 ||= le ||= ^m6 ||= upminor 6th ||= Bb^ ||
||= 19 ||= 844.44 ||= 13/8 ||= lu ||= ~6 ||= mid 6th ||= Bvv ||
||= 20 ||= 888.89 ||= 5/3 ||= la ||= vM6 ||= downmajor 6th ||= Bv ||
||= 21 ||= 933.33 ||= 12/7 ||= li ||= M6 ||= major 6th ||= B ||
||= 22 ||= 977.78 ||= 7/4, 16/9 ||= ta ||= m7 ||= minor 7th ||= C ||
||= 23 ||= 1022.22 ||= 9/5 ||= te ||= ^m7 ||= upminor 7th ||= C^ ||
||= 24 ||= 1066,67 ||= 13/7, 24/13 ||= tu ||= ~7 ||= mid 7th ||= C^^ ||
||= 25 ||= 1111.11 ||= 40/21 ||= ti ||= vM7 ||= downmajor 7th ||= C#v ||
||= 26 ||= 1155.56 ||= 35/18, 96/49, 49/25 ||= da ||= M7 ||= major 7th ||= C# ||
||= 27 ||= 1200 ||= 2/1 ||= do ||= P8 ||= 8ve ||= D ||
*based on treating 27-EDO as a 2.3.5.7.13 subgroup temperament; other approaches are possible.

Chords can be named with ups and downs as C upminor, E downmajor seventh, etc. See the [[22edo]] page for examples.

==Rank two temperaments== 
[[List of 27edo rank two temperaments by badness]]
[[List of edo-distinct 27e rank two temperaments]]
||~ Periods
per octave ||~ Generator ||~ Temperaments ||
|| 1 || 1\27 || [[Quartonic]]/Quarto ||
|| 1 || 2\27 || [[Octacot]]/Octocat ||
|| 1 || 4\27 || [[Tetracot]]/Modus/Wollemia ||
|| 1 || 5\27 || [[Machine]]/Kumonga ||
|| 1 || 7\27 || [[Myna]]/Coleto/Minah ||
|| 1 || 8\27 || [[Beatles]]/Ringo ||
|| 1 || 10\27 || [[Sensi]]/Sensis ||
|| 1 || 11\27 || [[Superpyth]] ||
|| 1 || 13\27 || Fervor ||
|| 3 || 1\27 || [[Semiaug]]/Hemiaug ||
|| 3 || 2\27 || [[Augmented]]/[[augene|Augene]]/Ogene ||
|| 3 || 4\27 || Oodako ||
|| 9 || 1\27 || Terrible version of [[Ennealimmal]]
/ Niner ||
==Commas== 
27 EDO tempers out the following commas. (Note: This assumes the val < 27 43 63 76 93 100 |.)
||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
||= 128/125 ||< | 7 0 -3 > ||> 41.06 ||= Diesis ||= Augmented Comma ||=   ||
||= 20000/19683 ||< | 5 -9 4 > ||> 27.66 ||= Minimal Diesis ||= Tetracot Comma ||=   ||
||= 78732/78125 ||< | 2 9 -7 > ||> 13.40 ||= Medium Semicomma ||= Sensipent Comma ||=   ||
||= 4711802/4709457 ||< | 1 -27 18 > ||> 0.86 ||= Ennealimma ||=   ||=   ||
||= 686/675 ||< | 1 -3 -2 3 > ||> 27.99 ||= Senga ||=   ||=   ||
||= 64/63 ||< | 6 -2 0 -1 > ||> 27.26 ||= Septimal Comma ||= Archytas' Comma ||= Leipziger Komma ||
||= 50421/50000 ||< | -4 1 -5 5 > ||> 14.52 ||= Trimyna ||=   ||=   ||
||= 245/243 ||< | 0 -5 1 2 > ||> 14.19 ||= Sensamagic ||=   ||=   ||
||= 126/125 ||< | 1 2 -3 1 > ||> 13.79 ||= Septimal Semicomma ||= Starling Comma ||=   ||
||= 4000/3969 ||< | 5 -4 3 -2 > ||> 13.47 ||= Octagar ||=   ||=   ||
||= 1728/1715 ||< | 6 3 -1 -3 > ||> 13.07 ||= Orwellisma ||= Orwell Comma ||=   ||
||= 420175/419904 ||< | -6 -8 2 5 > ||> 1.12 ||= Wizma ||=   ||=   ||
||= 2401/2400 ||< | -5 -1 -2 4 > ||> 0.72 ||= Breedsma ||=   ||=   ||
||= 4375/4374 ||< | -1 -7 4 1 > ||> 0.40 ||= Ragisma ||=   ||=   ||
||= 250047/250000 ||< | -4 6 -6 3 > ||> 0.33 ||= Landscape Comma ||=   ||=   ||
||= 99/98 ||< | -1 2 0 -2 1 > ||> 17.58 ||= Mothwellsma ||=   ||=   ||
||= 896/891 ||< | 7 -4 0 1 -1 > ||> 9.69 ||= Pentacircle ||=   ||=   ||
||= 385/384 ||< | -7 -1 1 1 1 > ||> 4.50 ||= Keenanisma ||=   ||=   ||
||= 91/90 ||< | -1 -2 -1 1 0 1 > ||> 19.13 ||= Superleap ||=   ||=   ||

=Music= 

[[http://www.archive.org/details/MusicForYourEars|Music For Your Ears]] <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://www.archive.org/download/MusicForYourEars/musicfor.mp3|play]]</span> by [[Gene Ward Smith]] The central portion is in 27edo, the rest in [[46edo]].
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Sad%20Like%20Winter%20Leaves.mp3|Sad Like Winter Leaves]]</span> by Igliashon Jones
//[[file:Superpythagorean Waltz.mp3|Superpythagorean Waltz]]// by Igliashon Jones
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of27sonatina.mp3|Galticeran Sonatina]]</span> by [[http://soundcloud.com/joelgranttaylor/galticeran_sonatina|Joel Taylor]]
<span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link">[[http://www.youtube.com/watch?v=7QcwKlK6z4c|miniature prelude and fugue]]</span> by Kosmorsky[[media type="custom" key="10942764"]]
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://micro.soonlabel.com/27edo/daily20111202-deep-chasm-zeta-cp-1.mp3|Chicago Pile-1]]</span> by [[Chris Vaisvil]]
[[http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Perc-Sitar.mp3|Tetracot Perc-Sitar]] by [[http://soundcloud.com/dustin-schallert/tetracot-perc-sitar|Dustin Schallert]]
[[http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Jam.mp3|Tetracot Jam]] by [[http://soundcloud.com/dustin-schallert/tetracot-jam|Dustin Schallert]]
[[http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Pump.mp3|Tetracot Pump]] by [[http://soundcloud.com/dustin-schallert/tetracot-pump|Dustin Schallert]] all in [[27edo]]
[[https://soundcloud.com/dustin-schallert/27-edo-guitar-1|27-EDO Guitar 1 by Dustin Schallert]]

Original HTML content:

<html><head><title>27edo</title></head><body><!-- ws:start:WikiTextHeadingRule:1:&lt;h1&gt; --><h1 id="toc0"><a name="x27 tone equal tempertament"></a><!-- ws:end:WikiTextHeadingRule:1 --><span style="color: #0061ff; font-family: 'Times New Roman',Times,serif; font-size: 113%;">27 tone equal tempertament</span></h1>
 <br />
If octaves are kept pure, 27edo divides the <a class="wiki_link" href="/octave">octave</a> in 27 equal parts each exactly 44.444... <a class="wiki_link" href="/cent">cent</a>s in size. However, 27 is a prime candidate for <a class="wiki_link" href="/octave%20shrinking">octave shrinking</a>, and a step size of 44.3 to 44.35 cents would be reasonable. The reason for this is that 27edo tunes the <a class="wiki_link" href="/5_4">third</a>, <a class="wiki_link" href="/3_2">fifth</a> and <a class="wiki_link" href="/7_4">7/4</a> sharply.<br />
<br />
Assuming however pure octaves, 27 has a fifth sharp by slightly more than nine cents and a 7/4 sharp by slightly less, and the same 400 cent major third as <a class="wiki_link" href="/12edo">12edo</a>, sharp 13 2/3 cents. The result is that <a class="wiki_link" href="/6_5">6/5</a>, <a class="wiki_link" href="/7_5">7/5</a> and especially <a class="wiki_link" href="/7_6">7/6</a> are all tuned more accurately than this.<br />
<br />
27edo, with its 400 cent major third, tempers out the <a class="wiki_link" href="/diesis">diesis</a> of 128/125, and also the <a class="wiki_link" href="/septimal%20comma">septimal comma</a>, 64/63 (and hence 126/125 also.) These it shares with 12edo, making some relationships familiar, and as a consequence they both support augene temperament. It shares with <a class="wiki_link" href="/22edo">22edo</a> tempering out the allegedly Bohlen-Pierce comma 245/243 as well as 64/63, so that they both support superpyth temperament, with quite sharp &quot;superpythagorean&quot; fifths giving a sharp 9/7 in place of meantone's 5/4.<br />
<br />
Though the <a class="wiki_link" href="/7-limit">7-limit</a> tuning of 27edo is not highly accurate, it nonetheless is the smallest equal division to represent the 7 odd limit both <a class="wiki_link" href="/consistent">consistent</a>ly and distinctly--that is, everything in the 7-limit <a class="wiki_link" href="/Diamonds">diamond</a> is uniquely represented by a certain number of steps of 27 equal. It also represents the 13th harmonic very well, and performs quite decently as a 2.3.5.7.13 temperament<br />
<br />
Its step, as well as the octave-inverted and octave-equivalent versions of it, holds the distinction for having around the highest <a class="wiki_link" href="/harmonic%20entropy">harmonic entropy</a> possible and thus is, in theory, most dissonant, assuming the relatively common values of a=2 and s=1%. This property is shared with all edos between around 24 and 30. Intervals smaller than this tend to be perceived as unison and are more consonant as a result; intervals larger than this have less &quot;tension&quot; and thus are also more consonant.<br />
<br />
The 27 note system or one similar like a well temperament can be notated very easily, by a variation on the quartertone accidentals. In this case a sharp raises a note by 4 EDOsteps, just one EDOstep beneath the following nominal (for example C to C# describes the approximate 10/9 and 11/10 interval) and the flat conversely lowers: these are augmented unisons and diminished unisons. Just so, one finds that an accidental can be divided in half, and this fill the remaining places without need for double sharps and double flats. Enharmonically then, E double flat means C half sharp. In other words, the resemblance to quarter tone notation differs in enharmonic divergence. D flat, C half-sharp, D half flat, and C sharp are all different. The composer can decide for himself which tertiary accidental is necessary if he will need redundancy to keep the chromatic pitches within a compass on paper relative to the natural names (C, D, E etc.) otherwise is simple enough and the same tendency for A# to be higher than Bb is not only familiar, though here very exaggerated, to those working with pythagorean scale, but also to many classically trained violinists. et voila<br />
<br />
<!-- ws:start:WikiTextHeadingRule:3:&lt;h2&gt; --><h2 id="toc1"><a name="x27 tone equal tempertament-Intervals"></a><!-- ws:end:WikiTextHeadingRule:3 -->Intervals</h2>
 <br />
<!-- ws:start:WikiTextHeadingRule:5:&lt;h2&gt; --><h2 id="toc2"><a name="x27 tone equal tempertament-Intervals"></a><!-- ws:end:WikiTextHeadingRule:5 --><!-- ws:start:WikiTextAnchorRule:13:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@x27 tone equal tempertament-Intervals&quot; title=&quot;Anchor: x27 tone equal tempertament-Intervals&quot;/&gt; --><a name="x27 tone equal tempertament-Intervals"></a><!-- ws:end:WikiTextAnchorRule:13 --> Intervals</h2>
 

<table class="wiki_table">
    <tr>
        <td style="text-align: center;">Degree<br />
</td>
        <td style="text-align: center;">Cents value<br />
</td>
        <td style="text-align: center;">Approximate<br />
Ratios*<br />
</td>
        <td style="text-align: center;">Solfege<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 notation</a><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">0<br />
</td>
        <td style="text-align: center;">0<br />
</td>
        <td style="text-align: center;">1/1<br />
</td>
        <td style="text-align: center;">do<br />
</td>
        <td style="text-align: center;">P1<br />
</td>
        <td style="text-align: center;">perfect unison<br />
</td>
        <td style="text-align: center;">D<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">1<br />
</td>
        <td style="text-align: center;">44.44<br />
</td>
        <td style="text-align: center;">36/35, 49/48, 50/49<br />
</td>
        <td style="text-align: center;">di<br />
</td>
        <td style="text-align: center;">^1, m2<br />
</td>
        <td style="text-align: center;">minor 2nd<br />
</td>
        <td style="text-align: center;">Eb<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">2<br />
</td>
        <td style="text-align: center;">88.89<br />
</td>
        <td style="text-align: center;">16/15, 21/20, 25/24<br />
</td>
        <td style="text-align: center;">ra<br />
</td>
        <td style="text-align: center;">^^1, ^m2<br />
</td>
        <td style="text-align: center;">upminor 2nd<br />
</td>
        <td style="text-align: center;">Eb^<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">3<br />
</td>
        <td style="text-align: center;">133.33<br />
</td>
        <td style="text-align: center;">14/13, 13/12<br />
</td>
        <td style="text-align: center;">ru<br />
</td>
        <td style="text-align: center;">~2<br />
</td>
        <td style="text-align: center;">mid 2nd<br />
</td>
        <td style="text-align: center;">Evv<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">4<br />
</td>
        <td style="text-align: center;">177.78<br />
</td>
        <td style="text-align: center;">10/9<br />
</td>
        <td style="text-align: center;">reh<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>
    </tr>
    <tr>
        <td style="text-align: center;">5<br />
</td>
        <td style="text-align: center;">222.22<br />
</td>
        <td style="text-align: center;">8/7, 9/8<br />
</td>
        <td style="text-align: center;">re<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>
    </tr>
    <tr>
        <td style="text-align: center;">6<br />
</td>
        <td style="text-align: center;">266.67<br />
</td>
        <td style="text-align: center;">7/6<br />
</td>
        <td style="text-align: center;">ma<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>
    </tr>
    <tr>
        <td style="text-align: center;">7<br />
</td>
        <td style="text-align: center;">311.11<br />
</td>
        <td style="text-align: center;">6/5<br />
</td>
        <td style="text-align: center;">me<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>
    </tr>
    <tr>
        <td style="text-align: center;">8<br />
</td>
        <td style="text-align: center;">355.56<br />
</td>
        <td style="text-align: center;">16/13<br />
</td>
        <td style="text-align: center;">mu<br />
</td>
        <td style="text-align: center;">~3<br />
</td>
        <td style="text-align: center;">mid 3rd<br />
</td>
        <td style="text-align: center;">F^^<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">9<br />
</td>
        <td style="text-align: center;">400<br />
</td>
        <td style="text-align: center;">5/4<br />
</td>
        <td style="text-align: center;">mi<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>
    </tr>
    <tr>
        <td style="text-align: center;">10<br />
</td>
        <td style="text-align: center;">444.44<br />
</td>
        <td style="text-align: center;">9/7, 13/10<br />
</td>
        <td style="text-align: center;">mo<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>
    </tr>
    <tr>
        <td style="text-align: center;">11<br />
</td>
        <td style="text-align: center;">488.89<br />
</td>
        <td style="text-align: center;">4/3<br />
</td>
        <td style="text-align: center;">fa<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>
    </tr>
    <tr>
        <td style="text-align: center;">12<br />
</td>
        <td style="text-align: center;">533.33<br />
</td>
        <td style="text-align: center;">49/36, 48/35<br />
</td>
        <td style="text-align: center;">fih<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>
    </tr>
    <tr>
        <td style="text-align: center;">13<br />
</td>
        <td style="text-align: center;">577.78<br />
</td>
        <td style="text-align: center;">7/5, 18/13<br />
</td>
        <td style="text-align: center;">fi<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>
    </tr>
    <tr>
        <td style="text-align: center;">14<br />
</td>
        <td style="text-align: center;">622.22<br />
</td>
        <td style="text-align: center;">10/7, 13/9<br />
</td>
        <td style="text-align: center;">se<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>
    </tr>
    <tr>
        <td style="text-align: center;">15<br />
</td>
        <td style="text-align: center;">666.67<br />
</td>
        <td style="text-align: center;">72/49, 35/24<br />
</td>
        <td style="text-align: center;">sih<br />
</td>
        <td style="text-align: center;">v5<br />
</td>
        <td style="text-align: center;">down fifth<br />
</td>
        <td style="text-align: center;">Av<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">16<br />
</td>
        <td style="text-align: center;">711.11<br />
</td>
        <td style="text-align: center;">3/2<br />
</td>
        <td style="text-align: center;">so/sol<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>
    </tr>
    <tr>
        <td style="text-align: center;">17<br />
</td>
        <td style="text-align: center;">755.56<br />
</td>
        <td style="text-align: center;">14/9, 20/13<br />
</td>
        <td style="text-align: center;">lo<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>
    </tr>
    <tr>
        <td style="text-align: center;">18<br />
</td>
        <td style="text-align: center;">800<br />
</td>
        <td style="text-align: center;">8/5<br />
</td>
        <td style="text-align: center;">le<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>
    </tr>
    <tr>
        <td style="text-align: center;">19<br />
</td>
        <td style="text-align: center;">844.44<br />
</td>
        <td style="text-align: center;">13/8<br />
</td>
        <td style="text-align: center;">lu<br />
</td>
        <td style="text-align: center;">~6<br />
</td>
        <td style="text-align: center;">mid 6th<br />
</td>
        <td style="text-align: center;">Bvv<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">20<br />
</td>
        <td style="text-align: center;">888.89<br />
</td>
        <td style="text-align: center;">5/3<br />
</td>
        <td style="text-align: center;">la<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>
    </tr>
    <tr>
        <td style="text-align: center;">21<br />
</td>
        <td style="text-align: center;">933.33<br />
</td>
        <td style="text-align: center;">12/7<br />
</td>
        <td style="text-align: center;">li<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>
    </tr>
    <tr>
        <td style="text-align: center;">22<br />
</td>
        <td style="text-align: center;">977.78<br />
</td>
        <td style="text-align: center;">7/4, 16/9<br />
</td>
        <td style="text-align: center;">ta<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>
    </tr>
    <tr>
        <td style="text-align: center;">23<br />
</td>
        <td style="text-align: center;">1022.22<br />
</td>
        <td style="text-align: center;">9/5<br />
</td>
        <td style="text-align: center;">te<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>
    </tr>
    <tr>
        <td style="text-align: center;">24<br />
</td>
        <td style="text-align: center;">1066,67<br />
</td>
        <td style="text-align: center;">13/7, 24/13<br />
</td>
        <td style="text-align: center;">tu<br />
</td>
        <td style="text-align: center;">~7<br />
</td>
        <td style="text-align: center;">mid 7th<br />
</td>
        <td style="text-align: center;">C^^<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">25<br />
</td>
        <td style="text-align: center;">1111.11<br />
</td>
        <td style="text-align: center;">40/21<br />
</td>
        <td style="text-align: center;">ti<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>
    </tr>
    <tr>
        <td style="text-align: center;">26<br />
</td>
        <td style="text-align: center;">1155.56<br />
</td>
        <td style="text-align: center;">35/18, 96/49, 49/25<br />
</td>
        <td style="text-align: center;">da<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>
    </tr>
    <tr>
        <td style="text-align: center;">27<br />
</td>
        <td style="text-align: center;">1200<br />
</td>
        <td style="text-align: center;">2/1<br />
</td>
        <td style="text-align: center;">do<br />
</td>
        <td style="text-align: center;">P8<br />
</td>
        <td style="text-align: center;">8ve<br />
</td>
        <td style="text-align: center;">D<br />
</td>
    </tr>
</table>

*based on treating 27-EDO as a 2.3.5.7.13 subgroup temperament; other approaches are possible.<br />
<br />
Chords can be named with ups and downs as C upminor, E downmajor seventh, etc. See the <a class="wiki_link" href="/22edo">22edo</a> page for examples.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:7:&lt;h2&gt; --><h2 id="toc3"><a name="x27 tone equal tempertament-Rank two temperaments"></a><!-- ws:end:WikiTextHeadingRule:7 -->Rank two temperaments</h2>
 <a class="wiki_link" href="/List%20of%2027edo%20rank%20two%20temperaments%20by%20badness">List of 27edo rank two temperaments by badness</a><br />
<a class="wiki_link" href="/List%20of%20edo-distinct%2027e%20rank%20two%20temperaments">List of edo-distinct 27e rank two temperaments</a><br />


<table class="wiki_table">
    <tr>
        <th>Periods<br />
per octave<br />
</th>
        <th>Generator<br />
</th>
        <th>Temperaments<br />
</th>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>1\27<br />
</td>
        <td><a class="wiki_link" href="/Quartonic">Quartonic</a>/Quarto<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>2\27<br />
</td>
        <td><a class="wiki_link" href="/Octacot">Octacot</a>/Octocat<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>4\27<br />
</td>
        <td><a class="wiki_link" href="/Tetracot">Tetracot</a>/Modus/Wollemia<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>5\27<br />
</td>
        <td><a class="wiki_link" href="/Machine">Machine</a>/Kumonga<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>7\27<br />
</td>
        <td><a class="wiki_link" href="/Myna">Myna</a>/Coleto/Minah<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>8\27<br />
</td>
        <td><a class="wiki_link" href="/Beatles">Beatles</a>/Ringo<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>10\27<br />
</td>
        <td><a class="wiki_link" href="/Sensi">Sensi</a>/Sensis<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>11\27<br />
</td>
        <td><a class="wiki_link" href="/Superpyth">Superpyth</a><br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>13\27<br />
</td>
        <td>Fervor<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>1\27<br />
</td>
        <td><a class="wiki_link" href="/Semiaug">Semiaug</a>/Hemiaug<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>2\27<br />
</td>
        <td><a class="wiki_link" href="/Augmented">Augmented</a>/<a class="wiki_link" href="/augene">Augene</a>/Ogene<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>4\27<br />
</td>
        <td>Oodako<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>1\27<br />
</td>
        <td>Terrible version of <a class="wiki_link" href="/Ennealimmal">Ennealimmal</a><br />
/ Niner<br />
</td>
    </tr>
</table>

<!-- ws:start:WikiTextHeadingRule:9:&lt;h2&gt; --><h2 id="toc4"><a name="x27 tone equal tempertament-Commas"></a><!-- ws:end:WikiTextHeadingRule:9 -->Commas</h2>
 27 EDO tempers out the following commas. (Note: This assumes the val &lt; 27 43 63 76 93 100 |.)<br />


<table class="wiki_table">
    <tr>
        <th>Comma<br />
</th>
        <th>Monzo<br />
</th>
        <th>Value (Cents)<br />
</th>
        <th>Name 1<br />
</th>
        <th>Name 2<br />
</th>
        <th>Name 3<br />
</th>
    </tr>
    <tr>
        <td style="text-align: center;">128/125<br />
</td>
        <td style="text-align: left;">| 7 0 -3 &gt;<br />
</td>
        <td style="text-align: right;">41.06<br />
</td>
        <td style="text-align: center;">Diesis<br />
</td>
        <td style="text-align: center;">Augmented Comma<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">20000/19683<br />
</td>
        <td style="text-align: left;">| 5 -9 4 &gt;<br />
</td>
        <td style="text-align: right;">27.66<br />
</td>
        <td style="text-align: center;">Minimal Diesis<br />
</td>
        <td style="text-align: center;">Tetracot Comma<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">78732/78125<br />
</td>
        <td style="text-align: left;">| 2 9 -7 &gt;<br />
</td>
        <td style="text-align: right;">13.40<br />
</td>
        <td style="text-align: center;">Medium Semicomma<br />
</td>
        <td style="text-align: center;">Sensipent Comma<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">4711802/4709457<br />
</td>
        <td style="text-align: left;">| 1 -27 18 &gt;<br />
</td>
        <td style="text-align: right;">0.86<br />
</td>
        <td style="text-align: center;">Ennealimma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">686/675<br />
</td>
        <td style="text-align: left;">| 1 -3 -2 3 &gt;<br />
</td>
        <td style="text-align: right;">27.99<br />
</td>
        <td style="text-align: center;">Senga<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">64/63<br />
</td>
        <td style="text-align: left;">| 6 -2 0 -1 &gt;<br />
</td>
        <td style="text-align: right;">27.26<br />
</td>
        <td style="text-align: center;">Septimal Comma<br />
</td>
        <td style="text-align: center;">Archytas' Comma<br />
</td>
        <td style="text-align: center;">Leipziger Komma<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">50421/50000<br />
</td>
        <td style="text-align: left;">| -4 1 -5 5 &gt;<br />
</td>
        <td style="text-align: right;">14.52<br />
</td>
        <td style="text-align: center;">Trimyna<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">245/243<br />
</td>
        <td style="text-align: left;">| 0 -5 1 2 &gt;<br />
</td>
        <td style="text-align: right;">14.19<br />
</td>
        <td style="text-align: center;">Sensamagic<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">126/125<br />
</td>
        <td style="text-align: left;">| 1 2 -3 1 &gt;<br />
</td>
        <td style="text-align: right;">13.79<br />
</td>
        <td style="text-align: center;">Septimal Semicomma<br />
</td>
        <td style="text-align: center;">Starling Comma<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">4000/3969<br />
</td>
        <td style="text-align: left;">| 5 -4 3 -2 &gt;<br />
</td>
        <td style="text-align: right;">13.47<br />
</td>
        <td style="text-align: center;">Octagar<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">1728/1715<br />
</td>
        <td style="text-align: left;">| 6 3 -1 -3 &gt;<br />
</td>
        <td style="text-align: right;">13.07<br />
</td>
        <td style="text-align: center;">Orwellisma<br />
</td>
        <td style="text-align: center;">Orwell Comma<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">420175/419904<br />
</td>
        <td style="text-align: left;">| -6 -8 2 5 &gt;<br />
</td>
        <td style="text-align: right;">1.12<br />
</td>
        <td style="text-align: center;">Wizma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">2401/2400<br />
</td>
        <td style="text-align: left;">| -5 -1 -2 4 &gt;<br />
</td>
        <td style="text-align: right;">0.72<br />
</td>
        <td style="text-align: center;">Breedsma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">4375/4374<br />
</td>
        <td style="text-align: left;">| -1 -7 4 1 &gt;<br />
</td>
        <td style="text-align: right;">0.40<br />
</td>
        <td style="text-align: center;">Ragisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">250047/250000<br />
</td>
        <td style="text-align: left;">| -4 6 -6 3 &gt;<br />
</td>
        <td style="text-align: right;">0.33<br />
</td>
        <td style="text-align: center;">Landscape Comma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">99/98<br />
</td>
        <td style="text-align: left;">| -1 2 0 -2 1 &gt;<br />
</td>
        <td style="text-align: right;">17.58<br />
</td>
        <td style="text-align: center;">Mothwellsma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">896/891<br />
</td>
        <td style="text-align: left;">| 7 -4 0 1 -1 &gt;<br />
</td>
        <td style="text-align: right;">9.69<br />
</td>
        <td style="text-align: center;">Pentacircle<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">385/384<br />
</td>
        <td style="text-align: left;">| -7 -1 1 1 1 &gt;<br />
</td>
        <td style="text-align: right;">4.50<br />
</td>
        <td style="text-align: center;">Keenanisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">91/90<br />
</td>
        <td style="text-align: left;">| -1 -2 -1 1 0 1 &gt;<br />
</td>
        <td style="text-align: right;">19.13<br />
</td>
        <td style="text-align: center;">Superleap<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:11:&lt;h1&gt; --><h1 id="toc5"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:11 -->Music</h1>
 <br />
<a class="wiki_link_ext" href="http://www.archive.org/details/MusicForYourEars" rel="nofollow">Music For Your Ears</a> <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://www.archive.org/download/MusicForYourEars/musicfor.mp3" rel="nofollow">play</a></span> by <a class="wiki_link" href="/Gene%20Ward%20Smith">Gene Ward Smith</a> The central portion is in 27edo, the rest in <a class="wiki_link" href="/46edo">46edo</a>.<br />
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Sad%20Like%20Winter%20Leaves.mp3" rel="nofollow">Sad Like Winter Leaves</a></span> by Igliashon Jones<br />
<em><a href="/file/view/Superpythagorean%20Waltz.mp3/392037262/Superpythagorean%20Waltz.mp3" onclick="ws.common.trackFileLink('/file/view/Superpythagorean%20Waltz.mp3/392037262/Superpythagorean%20Waltz.mp3');">Superpythagorean Waltz</a></em> by Igliashon Jones<br />
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of27sonatina.mp3" rel="nofollow">Galticeran Sonatina</a></span> by <a class="wiki_link_ext" href="http://soundcloud.com/joelgranttaylor/galticeran_sonatina" rel="nofollow">Joel Taylor</a><br />
<span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=7QcwKlK6z4c" rel="nofollow">miniature prelude and fugue</a></span> by Kosmorsky<!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/custom/10942764?h=0&amp;w=0&quot; class=&quot;WikiMedia WikiMediaCustom&quot; id=&quot;wikitext@@media@@type=&amp;quot;custom&amp;quot; key=&amp;quot;10942764&amp;quot;&quot; title=&quot;Custom Media&quot;/&gt; --><script type="text/javascript" src="http://mediaplayer.yahoo.com/js">
</script><!-- ws:end:WikiTextMediaRule:0 --><br />
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/27edo/daily20111202-deep-chasm-zeta-cp-1.mp3" rel="nofollow">Chicago Pile-1</a></span> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br />
<a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Perc-Sitar.mp3" rel="nofollow">Tetracot Perc-Sitar</a> by <a class="wiki_link_ext" href="http://soundcloud.com/dustin-schallert/tetracot-perc-sitar" rel="nofollow">Dustin Schallert</a><br />
<a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Jam.mp3" rel="nofollow">Tetracot Jam</a> by <a class="wiki_link_ext" href="http://soundcloud.com/dustin-schallert/tetracot-jam" rel="nofollow">Dustin Schallert</a><br />
<a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Pump.mp3" rel="nofollow">Tetracot Pump</a> by <a class="wiki_link_ext" href="http://soundcloud.com/dustin-schallert/tetracot-pump" rel="nofollow">Dustin Schallert</a> all in <a class="wiki_link" href="/27edo">27edo</a><br />
<a class="wiki_link_ext" href="https://soundcloud.com/dustin-schallert/27-edo-guitar-1" rel="nofollow">27-EDO Guitar 1 by Dustin Schallert</a></body></html>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:clumma|clumma]] and made on <tt>2016-12-18 14:27:38 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-28 02:37:50 UTC</tt>.<br>
-: The original revision id was <tt>602446804</tt>.<br>
+: The original revision id was <tt>602864584</tt>.<br>
-: The revision comment was: <tt>Reverted to Nov 1, 2016 3:24 pm</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>
 <h4>Original Wikitext content:</h4>
@@ Line 18: / Line 18: @@
 Its step, as well as the octave-inverted and octave-equivalent versions of it, holds the distinction for having around the highest [[harmonic entropy]] possible and thus is, in theory, most dissonant, assuming the relatively common values of a=2 and s=1%. This property is shared with all edos between around 24 and 30. Intervals smaller than this tend to be perceived as unison and are more consonant as a result; intervals larger than this have less "tension" and thus are also more consonant.
-The 27 note system or one similar like a well temperament can be notated very easily, by a variation on the quartertone accidentals. In this case a sharp raises a note just a hair beneath the following nominal (for example C to C# describes the approximate 10/9 and 11/10 interval) and the flat conversely lowers: these are augmented unisons and diminished unisons. Just so, one finds that an accidental can be divided in half, and this fill the remaining places without need for double sharps and double flats. Enharmonically then, E double flat means C half sharp. In other words, the resemblance to quarter tone notation differs in enharmonic divergence. D flat, C half-sharp, D half flat, and C sharp are all different. The composer can decide for himself which tertiary accidental is necessary if he will need redundancy to keep the chromatic pitches within a compass on paper relative to the natural names (C, D, E etc.) otherwise is simple enough and the same tendency for A# to be higher than Bb is not only familiar, though here very exaggerated, to those working with pythagorean scale, but also to many classically trained violinists. et voila
+The 27 note system or one similar like a well temperament can be notated very easily, by a variation on the quartertone accidentals. In this case a sharp raises a note by 4 EDOsteps, just one EDOstep beneath the following nominal (for example C to C# describes the approximate 10/9 and 11/10 interval) and the flat conversely lowers: these are augmented unisons and diminished unisons. Just so, one finds that an accidental can be divided in half, and this fill the remaining places without need for double sharps and double flats. Enharmonically then, E double flat means C half sharp. In other words, the resemblance to quarter tone notation differs in enharmonic divergence. D flat, C half-sharp, D half flat, and C sharp are all different. The composer can decide for himself which tertiary accidental is necessary if he will need redundancy to keep the chromatic pitches within a compass on paper relative to the natural names (C, D, E etc.) otherwise is simple enough and the same tendency for A# to be higher than Bb is not only familiar, though here very exaggerated, to those working with pythagorean scale, but also to many classically trained violinists. et voila
 ==Intervals==
-|| Degrees of 27-EDO || Cents value coarse/fine
-DMS value ||= Approximate
+==[[#x27 tone equal tempertament-Intervals]] Intervals==
-Ratios* ||= Solfege ||
+||= Degree ||= Cents value ||= Approximate
-|| 0 || 0 ||= 1/1 ||= do ||
+Ratios* ||= Solfege ||||||= [[xenharmonic/Ups and Downs Notation|ups and downs notation]] ||
-|| 1 || 44.44, 53.33
+||= 0 ||= 0 ||= 1/1 ||= do ||= P1 ||= perfect unison ||= D ||
-°20' ||= 36/35, 49/48, 50/49 ||= di ||
+||= 1 ||= 44.44 ||= 36/35, 49/48, 50/49 ||= di ||= ^1, m2 ||= minor 2nd ||= Eb ||
-|| 2 || 88.89, 106.67
+||= 2 ||= 88.89 ||= 16/15, 21/20, 25/24 ||= ra ||= ^^1, ^m2 ||= upminor 2nd ||= Eb^ ||
-°40' ||= 16/15, 21/20, 25/24 ||= ra ||
+||= 3 ||= 133.33 ||= 14/13, 13/12 ||= ru ||= ~2 ||= mid 2nd ||= Evv ||
-|| 3 || 133.33, 160
+||= 4 ||= 177.78 ||= 10/9 ||= reh ||= vM2 ||= downmajor 2nd ||= Ev ||
-° ||= 14/13, 13/12 ||= ru ||
+||= 5 ||= 222.22 ||= 8/7, 9/8 ||= re ||= M2 ||= major 2nd ||= E ||
-|| 4 || 177.78, 213.33
+||= 6 ||= 266.67 ||= 7/6 ||= ma ||= m3 ||= minor 3rd ||= F ||
-°20' ||= 10/9 ||= reh ||
+||= 7 ||= 311.11 ||= 6/5 ||= me ||= ^m3 ||= upminor 3rd ||= F^ ||
-|| 5 || 222.22, 266.67
+||= 8 ||= 355.56 ||= 16/13 ||= mu ||= ~3 ||= mid 3rd ||= F^^ ||
-°40' ||= 8/7, 9/8 ||= re ||
+||= 9 ||= 400 ||= 5/4 ||= mi ||= vM3 ||= downmajor 3rd ||= F#v ||
-|| 6 || 266.67, 320
+||= 10 ||= 444.44 ||= 9/7, 13/10 ||= mo ||= M3 ||= major 3rd ||= F# ||
-° ||= 7/6 ||= ma ||
+||= 11 ||= 488.89 ||= 4/3 ||= fa ||= P4 ||= perfect 4th ||= G ||
-|| 7 || 311.11, 373.33
+||= 12 ||= 533.33 ||= 49/36, 48/35 ||= fih ||= ^4 ||= up 4th ||= G^ ||
-°20' ||= 6/5 ||= me ||
+||= 13 ||= 577.78 ||= 7/5, 18/13 ||= fi ||= ^^4 ||= double-up 4th ||= G^^ ||
-|| 8 || 355.56, 426.67
+||= 14 ||= 622.22 ||= 10/7, 13/9 ||= se ||= vv5 ||= double-down 5th ||= Avv ||
-°40' ||= 16/13 ||= mu ||
+||= 15 ||= 666.67 ||= 72/49, 35/24 ||= sih ||= v5 ||= down fifth ||= Av ||
-|| 9 || 400, 480
+||= 16 ||= 711.11 ||= 3/2 ||= so/sol ||= P5 ||= perfect 5th ||= A ||
-° ||= 5/4 ||= mi ||
+||= 17 ||= 755.56 ||= 14/9, 20/13 ||= lo ||= m6 ||= minor 6th ||= Bb ||
-|| 10 || 444.44, 513.33
+||= 18 ||= 800 ||= 8/5 ||= le ||= ^m6 ||= upminor 6th ||= Bb^ ||
-°20' ||= 9/7, 13/10 ||= mo ||
+||= 19 ||= 844.44 ||= 13/8 ||= lu ||= ~6 ||= mid 6th ||= Bvv ||
-|| 11 || 488.89, 566.67
+||= 20 ||= 888.89 ||= 5/3 ||= la ||= vM6 ||= downmajor 6th ||= Bv ||
-°40' ||= 4/3 ||= fa ||
+||= 21 ||= 933.33 ||= 12/7 ||= li ||= M6 ||= major 6th ||= B ||
-|| 12 || 533.33, 640
+||= 22 ||= 977.78 ||= 7/4, 16/9 ||= ta ||= m7 ||= minor 7th ||= C ||
-° ||= 49/36, 48/35 ||= fih ||
+||= 23 ||= 1022.22 ||= 9/5 ||= te ||= ^m7 ||= upminor 7th ||= C^ ||
-|| 13 || 577.78, 693.33
+||= 24 ||= 1066,67 ||= 13/7, 24/13 ||= tu ||= ~7 ||= mid 7th ||= C^^ ||
-°20' ||= 7/5, 18/13 ||= fi ||
+||= 25 ||= 1111.11 ||= 40/21 ||= ti ||= vM7 ||= downmajor 7th ||= C#v ||
-|| 14 || 622.22, 746.67
+||= 26 ||= 1155.56 ||= 35/18, 96/49, 49/25 ||= da ||= M7 ||= major 7th ||= C# ||
-°40' ||= 10/7, 13/9 ||= se ||
+||= 27 ||= 1200 ||= 2/1 ||= do ||= P8 ||= 8ve ||= D ||
-|| 15 || 666.67, 800
-° ||= 72/49, 35/24 ||= sih ||
-|| 16 || 711.11, 853.33
-°20' ||= 3/2 ||= so/sol ||
-|| 17 || 755.56, 906.67
-°40' ||= 14/9, 20/13 ||= lo ||
-|| 18 || 800, 960
-° ||= 8/5 ||= le ||
-|| 19 || 844.44, 1013.33
-°20' ||= 13/8 ||= lu ||
-|| 20 || 888.89, 1066.67
-°40' ||= 5/3 ||= la ||
-|| 21 || 933.33, 1120
-° ||= 12/7 ||= li ||
-|| 22 || 977.78, 1173.33
-°20' ||= 7/4, 16/9 ||= ta ||
-|| 23 || 1022.22, 1226.67
-°40' ||= 9/5 ||= te ||
-|| 24 || 1066,67, 1280
-° ||= 13/7, 24/13 ||= tu ||
-|| 25 || 1111.11, 1333.33
-°20' ||= 40/21 ||= ti ||
-|| 26 || 1155.56, 1386.67
-°40' ||= 35/18, 96/49, 49/25 ||= da ||
-|| 27 || 1200, 1440
-° ||= 2/1 ||= do ||
 *based on treating 27-EDO as a 2.3.5.7.13 subgroup temperament; other approaches are possible.
+Chords can be named with ups and downs as C upminor, E downmajor seventh, etc. See the [[22edo]] page for examples.
 ==Rank two temperaments==
 [[List of 27edo rank two temperaments by badness]]
@@ Line 147: / Line 124: @@
 Its step, as well as the octave-inverted and octave-equivalent versions of it, holds the distinction for having around the highest &lt;a class="wiki_link" href="/harmonic%20entropy"&gt;harmonic entropy&lt;/a&gt; possible and thus is, in theory, most dissonant, assuming the relatively common values of a=2 and s=1%. This property is shared with all edos between around 24 and 30. Intervals smaller than this tend to be perceived as unison and are more consonant as a result; intervals larger than this have less &amp;quot;tension&amp;quot; and thus are also more consonant.&lt;br /&gt;
 &lt;br /&gt;
-The 27 note system or one similar like a well temperament can be notated very easily, by a variation on the quartertone accidentals. In this case a sharp raises a note just a hair beneath the following nominal (for example C to C# describes the approximate 10/9 and 11/10 interval) and the flat conversely lowers: these are augmented unisons and diminished unisons. Just so, one finds that an accidental can be divided in half, and this fill the remaining places without need for double sharps and double flats. Enharmonically then, E double flat means C half sharp. In other words, the resemblance to quarter tone notation differs in enharmonic divergence. D flat, C half-sharp, D half flat, and C sharp are all different. The composer can decide for himself which tertiary accidental is necessary if he will need redundancy to keep the chromatic pitches within a compass on paper relative to the natural names (C, D, E etc.) otherwise is simple enough and the same tendency for A# to be higher than Bb is not only familiar, though here very exaggerated, to those working with pythagorean scale, but also to many classically trained violinists. et voila&lt;br /&gt;
+The 27 note system or one similar like a well temperament can be notated very easily, by a variation on the quartertone accidentals. In this case a sharp raises a note by 4 EDOsteps, just one EDOstep beneath the following nominal (for example C to C# describes the approximate 10/9 and 11/10 interval) and the flat conversely lowers: these are augmented unisons and diminished unisons. Just so, one finds that an accidental can be divided in half, and this fill the remaining places without need for double sharps and double flats. Enharmonically then, E double flat means C half sharp. In other words, the resemblance to quarter tone notation differs in enharmonic divergence. D flat, C half-sharp, D half flat, and C sharp are all different. The composer can decide for himself which tertiary accidental is necessary if he will need redundancy to keep the chromatic pitches within a compass on paper relative to the natural names (C, D, E etc.) otherwise is simple enough and the same tendency for A# to be higher than Bb is not only familiar, though here very exaggerated, to those working with pythagorean scale, but also to many classically trained violinists. et voila&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:3:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x27 tone equal tempertament-Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:3 --&gt;Intervals&lt;/h2&gt;
+ &lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:5:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x27 tone equal tempertament-Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:5 --&gt;&lt;!-- ws:start:WikiTextAnchorRule:13:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@x27 tone equal tempertament-Intervals&amp;quot; title=&amp;quot;Anchor: x27 tone equal tempertament-Intervals&amp;quot;/&amp;gt; --&gt;&lt;a name="x27 tone equal tempertament-Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:13 --&gt; Intervals&lt;/h2&gt;
 &lt;table class="wiki_table"&gt;
      &lt;tr&gt;
-         &lt;td&gt;Degrees of 27-EDO&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Degree&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Cents value coarse/fine&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Cents value&lt;br /&gt;
-DMS value&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Approximate&lt;br /&gt;
@@ Line 163: / Line 141: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Solfege&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td colspan="3" style="text-align: center;"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation"&gt;ups and downs notation&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;0&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;0&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;0&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;0&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;1/1&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;do&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;P1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;perfect unison&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;D&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;44.44, 53.33&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;44.44&lt;br /&gt;
-°20'&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;36/35, 49/48, 50/49&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;di&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;^1, m2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;minor 2nd&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Eb&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;2&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;88.89, 106.67&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;88.89&lt;br /&gt;
-°40'&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;16/15, 21/20, 25/24&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;ra&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;^^1, ^m2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;upminor 2nd&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Eb^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;3&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;133.33, 160&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;133.33&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;14/13, 13/12&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;ru&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;~2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;mid 2nd&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Evv&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;4&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;4&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;177.78, 213.33&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;177.78&lt;br /&gt;
-°20'&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;10/9&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;reh&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;vM2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;downmajor 2nd&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Ev&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;5&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;222.22, 266.67&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;222.22&lt;br /&gt;
-°40'&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;8/7, 9/8&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;re&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;M2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;major 2nd&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;E&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;6&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;266.67, 320&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;266.67&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;7/6&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;ma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;m3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;minor 3rd&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;F&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;7&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;311.11, 373.33&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;311.11&lt;br /&gt;
-°20'&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;6/5&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;me&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;^m3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;upminor 3rd&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;F^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;8&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;8&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;355.56, 426.67&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;355.56&lt;br /&gt;
-°40'&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;16/13&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;mu&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;~3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;mid 3rd&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;F^^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;9&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;9&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;400, 480&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;400&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;5/4&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;mi&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;vM3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;downmajor 3rd&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;F#v&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;10&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;10&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;444.44, 513.33&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;444.44&lt;br /&gt;
-°20'&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;9/7, 13/10&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;mo&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;M3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;major 3rd&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;F#&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;11&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;11&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;488.89, 566.67&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;488.89&lt;br /&gt;
-°40'&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;4/3&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;fa&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;P4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;perfect 4th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;G&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;12&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;12&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;533.33, 640&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;533.33&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;49/36, 48/35&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;fih&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;^4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;up 4th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;G^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;13&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;13&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;577.78, 693.33&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;577.78&lt;br /&gt;
-°20'&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;7/5, 18/13&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;fi&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;^^4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;double-up 4th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;G^^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;14&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;14&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;622.22, 746.67&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;622.22&lt;br /&gt;
-°40'&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;10/7, 13/9&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;se&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;vv5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;double-down 5th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Avv&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;15&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;15&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;666.67, 800&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;666.67&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;72/49, 35/24&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;sih&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;v5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;down fifth&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Av&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;16&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;16&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;711.11, 853.33&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;711.11&lt;br /&gt;
-°20'&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;3/2&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;so/sol&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;P5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;perfect 5th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;A&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;17&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;17&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;755.56, 906.67&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;755.56&lt;br /&gt;
-°40'&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;14/9, 20/13&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;lo&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;m6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;minor 6th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Bb&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;18&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;18&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;800, 960&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;800&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;8/5&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;le&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;^m6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;upminor 6th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Bb^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;19&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;19&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;844.44, 1013.33&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;844.44&lt;br /&gt;
-°20'&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;13/8&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;lu&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;~6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;mid 6th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Bvv&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;20&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;20&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;888.89, 1066.67&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;888.89&lt;br /&gt;
-°40'&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;5/3&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;la&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;vM6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;downmajor 6th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Bv&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;21&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;21&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;933.33, 1120&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;933.33&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;12/7&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;li&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;M6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;major 6th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;B&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;22&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;22&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;977.78, 1173.33&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;977.78&lt;br /&gt;
-°20'&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;7/4, 16/9&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;ta&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;m7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;minor 7th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;C&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;23&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;23&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1022.22, 1226.67&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1022.22&lt;br /&gt;
-°40'&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;9/5&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;te&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;^m7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;upminor 7th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;C^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;24&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;24&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1066,67, 1280&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1066,67&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;13/7, 24/13&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;tu&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;~7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;mid 7th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;C^^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;25&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;25&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1111.11, 1333.33&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1111.11&lt;br /&gt;
-°20'&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;40/21&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;ti&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;vM7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;downmajor 7th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;C#v&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;26&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;26&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1155.56, 1386.67&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1155.56&lt;br /&gt;
-°40'&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;35/18, 96/49, 49/25&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;da&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;M7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;major 7th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;C#&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;27&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;27&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1200, 1440&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1200&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;2/1&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;do&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;P8&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;8ve&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;D&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 475: / Line 596: @@
 *based on treating 27-EDO as a 2.3.5.7.13 subgroup temperament; other approaches are possible.&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:5:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x27 tone equal tempertament-Rank two temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:5 --&gt;Rank two temperaments&lt;/h2&gt;
+&lt;br /&gt;
+Chords can be named with ups and downs as C upminor, E downmajor seventh, etc. See the &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt; page for examples.&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:7:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x27 tone equal tempertament-Rank two temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:7 --&gt;Rank two temperaments&lt;/h2&gt;
   &lt;a class="wiki_link" href="/List%20of%2027edo%20rank%20two%20temperaments%20by%20badness"&gt;List of 27edo rank two temperaments by badness&lt;/a&gt;&lt;br /&gt;
 &lt;a class="wiki_link" href="/List%20of%20edo-distinct%2027e%20rank%20two%20temperaments"&gt;List of edo-distinct 27e rank two temperaments&lt;/a&gt;&lt;br /&gt;
@@ Line 597: / Line 721: @@
 &lt;/table&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:7:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x27 tone equal tempertament-Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:7 --&gt;Commas&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:9:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="x27 tone equal tempertament-Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:9 --&gt;Commas&lt;/h2&gt;
 EDO tempers out the following commas. (Note: This assumes the val &amp;lt; 27 43 63 76 93 100 |.)&lt;br /&gt;
@@ Line 885: / Line 1,009: @@
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:9:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:9 --&gt;Music&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:11:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:11 --&gt;Music&lt;/h1&gt;
   &lt;br /&gt;
 &lt;a class="wiki_link_ext" href="http://www.archive.org/details/MusicForYourEars" rel="nofollow"&gt;Music For Your Ears&lt;/a&gt; &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;&lt;a class="wiki_link_ext" href="http://www.archive.org/download/MusicForYourEars/musicfor.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;/span&gt; by &lt;a class="wiki_link" href="/Gene%20Ward%20Smith"&gt;Gene Ward Smith&lt;/a&gt; The central portion is in 27edo, the rest in &lt;a class="wiki_link" href="/46edo"&gt;46edo&lt;/a&gt;.&lt;br /&gt;

27edo: Difference between revisions

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