25edo: Difference between revisions

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[[toc|flat]]
=<span style="color: #006b2e; font-family: 'Times New Roman',Times,serif; font-size: 113%;">25 tone equal temperament</span>= 

25EDO divides the [[octave]] in 25 equal steps of exact size 48 [[cent]]s each. It is a good way to tune the [[Blackwood temperament]], which takes the very sharp fifths of [[5EDO]] as a given, tempers out 28/27 and 49/48, and attempts to optimize the tunings for 5 ([[5_4|5/4]]) and 7 ([[7_4|7/4]]). It also tunes sixix temperament with a sharp fifth. It supplies the optimal patent val for the 11-limit 6&25 temperament tempering out 49/48, 77/75 and 605/576, and the 13-limit extension also tempering out 66/65.

25EDO has fifths 18 cents sharp, but its major thirds are excellent and its 7/4 is acceptable. Moreover, in full 7-limit including the 3, it is not [[consistent]]. It therefore makes sense to use it as a 2.5.7 [[Just intonation subgroups|subgroup]] tuning. Looking just at 2, 5, and 7, it equates five [[8_7|8/7]]s with the octave, and so tempers out (8/7)^5 / 2 = 16807/16384. It also equates a [[128_125|128/125]] [[diesis]] and two [[septimal tritones]] of [[7_5|7/5]] with the octave, and hence tempers out 3136/3125. If we want to temper out both of these and also have decent fifths, the obvious solution is [[50EDO]]. An alternative fifth, 14\25, which is 672 cents, provides an alternative very flat fifth which can be used for [[mavila]] temperament.

If 5/4 and 7/4 aren't good enough, it also does 17/16 and 19/16, just like 12EDO. In fact, on the [[k*N subgroups|2*25 subgroup]] 2.9.5.7.33.39.17.19 it provides the same tuning and tempers out the same commas as 50et, which makes for a wide range of harmony.

=Music= 
//[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Rapoport/StudyInFives.mp3|Study in Fives]]// by [[http://en.wikipedia.org/wiki/Paul_Rapoport_%28music_critic%29|Paul Rapoport]]
[[http://chrisvaisvil.com/?p=2377|Fantasy for Piano in 25 Note per Octave Tuning]] //[[http://micro.soonlabel.com/25edo/fantasy_for_piano_in_25_edo.mp3|play]]// by Chris Vaisvil
//[[http://micro.soonlabel.com/gene_ward_smith/Others/Fiale/flat%20fourth%20blues.mp3|Flat fourth blues]]// by Fabrizio Fulvio Fausto Fiale

[[media type="file" key="25edochorale.mid" width="300" height="50"]] [[file:25edochorale.mid]] Peter Kosmorsky (10/14/10, 2.5.7 subgroup, a friend responded "The <span class="il">25edo</span> canon has a nice theme, but all the harmonizations from there are laughably dissonant. I showed them to my roomie and he found it disturbing, hahaha. He had an unintentional physical reaction to it with his mouth in which his muscles did a smirk sort of thing, without him even trying to, hahaha. So, my point; this I think this 25 edo idea was an example of where tonal thinking doesn't suit the sound of the scale.")
[[media type="file" key="25 edo prelude largo.mid" width="300" height="50"]] [[file:25 edo prelude largo.mid]] Peter Kosmorsky (2011, Blackwood)

=Intervals= 

||= Degrees ||= Cents ||= Approximate
Ratios* ||= Armodue
Notation ||||||= [[xenharmonic/Ups and Downs Notation|ups and downs notation]] ||
||= 0 ||= 0 ||= 1/1 ||= 1 ||= P1 ||= perfect 1sn ||= D, Eb ||
||= 1 ||= 48 ||= 33/32, 39/38, 34/33 ||= 1# ||= ^1, ^m2 ||= up 1sn, upminor 2nd ||= D^, Eb^ ||
||= 2 ||= 96 ||= 17/16, 20/19, 18/17 ||= 2b ||= ^^m2 ||= double-upminor 2nd ||= Eb^^ ||
||= 3 ||= 144 ||= 12/11, 38/35 ||= 2 ||= vvM2 ||= double-downmajor 2nd ||= Evv ||
||= 4 ||= 192 ||= 9/8, 10/9, 19/17 ||= 2# ||= vM2 ||= downmajor 2nd ||= Ev ||
||= 5· ||= 240 ||= 8/7 ||= 3b ||= M2, m3 ||= major 2nd, minor 3rd ||= E, F ||
||= 6 ||= 288 ||= 19/16, 20/17 ||= 3 ||= ^m3 ||= upminor 3rd ||= F^ ||
||= 7 ||= 336 ||= 39/32, 17/14, 40/33 ||= 3# ||= ^^m3 ||= double-upminor 3rd ||= F^^ ||
||= 8· ||= 384 ||= 5/4 ||= 4b ||= vvM3 ||= double-downmajor 3rd ||= F#vv ||
||= 9 ||= 432 ||= 9/7, 32/25, 50/39 ||= 4 ||= vM3 ||= downmajor ||= F#v ||
||= 10 ||= 480 ||= 33/25, 25/19 ||= 4#/5b ||= M3, P4 ||= major 3rd, perfect 4th ||= F#, G ||
||= 11· ||= 528 ||= 31/21, 34/25 ||= 5 ||= ^4 ||= up 4th ||= G^ ||
||= 12 ||= 576 ||= 7/5, 39/28 ||= 5# ||= ^^4,^^d5 ||= double-up 4th,
double-up dim 5th ||= G^^, Ab^^ ||
||= 13 ||= 624 ||= 10/7, 56/39 ||= 6b ||= vvA4,vv5 ||= double-down aug 4th,
double-down 5th ||= G#vv, Avv ||
||= 14· ||= 672 ||= 42/31, 25/17 ||= 6 ||= v5 ||= down 5th ||= Av ||
||= 15 ||= 720 ||= 50/33, 38/25 ||= 6# ||= P5, m6 ||= perfect 5th, minor 6th ||= A, Bb ||
||= 16 ||= 768 ||= 14/9, 25/16, 39/25 ||= 7b ||= ^m6 ||= upminor 6th ||= Bb^ ||
||= 17· ||= 816 ||= 8/5 ||= 7 ||= ^^m6 ||= double-upminor 6th ||= Bb^^ ||
||= 18 ||= 864 ||= 64/39, 28/17, 33/20 ||= 7# ||= vvM6 ||= double-downmajor 6th ||= Bvv ||
||= 19 ||= 912 ||= 32/19, 17/10 ||= 8b ||= vM6 ||= downmajor 6th ||= Bv ||
||= 20· ||= 960 ||= 7/4 ||= 8 ||= M6, m7 ||= major 6th, minor 7th ||= B, C ||
||= 21 ||= 1008 ||= 16/9, 9/5, 34/19 ||= 8# ||= ^m7 ||= upminor 7th ||= C^ ||
||= 22 ||= 1056 ||= 11/6, 35/19 ||= 9b ||= ^^m7 ||= double-upminor 7th ||= C^^ ||
||= 23 ||= 1104 ||= 32/17, 17/9, 19/10 ||= 9 ||= vvM7 ||= double-downmajor 7th ||= C#vv ||
||= 24 ||= 1152 ||= 33/17, 64/33, 76/39 ||= 9#/1b ||= vM7 ||= downmajor 7th ||= C#v ||
||= 25 ||= 1200 ||= 2/1 ||= 1 ||= P8 ||= perfect 8ve ||= C#, D ||
*based on treating 25-EDO as a 2.9.5.7.33.39.17.19 subgroup; other approaches are possible.

[[media type="custom" key="25100128"]]

[[file:25ed2-001.svg]]


=Relationship to Armodue= 

Like [[16edo|16-EDO]] and [[23edo|23-EDO]], 25-EDO contains the 9-note "Superdiatonic" scale of [[7L 2s|7L2s]] (LLLsLLLLs) that is generated by a circle of heavily-flattened 3/2s (ranging in size from 5\9-EDO or 666.67 cents, to 4\7-EDO or 685.71 cents). The 25-EDO generator for this scale is the 672-cent interval. This allows 25-EDO to be used with the [[Armodue theory|Armodue]] notation system in much the same way that [[19edo|19-EDO]] is used with the standard diatonic notation; see the above interval chart for the Armodue names. Because the 25-EDO Armodue 6th is flatter than that of 16-EDO (the middle of the Armodue spectrum), sharps are lower in pitch than enharmonic flats.

=Commas= 
25 EDO tempers out the following commas. (Note: This assumes the val < 25 40 58 70 86 93 |.)
||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
||= 256/243 ||< | 8 -5 > ||> 90.22 ||= Limma ||= Pythagorean Minor 2nd ||=   ||
||= 3125/3072 ||< | -10 -1 5 > ||> 29.61 ||= Small Diesis ||= Magic Comma ||=   ||
||=   ||< | 38 -2 -15 > ||> 1.38 ||= Hemithirds Comma ||=   ||=   ||
||= 16807/16384 || | -14 0 0 5 > ||> 44.13 ||   ||   ||   ||
||= 49/48 ||< | -4 -1 0 2 > ||> 35.70 ||= Slendro Diesis ||=   ||=   ||
||= 64/63 ||< | 6 -2 0 -1 > ||> 27.26 ||= Septimal Comma ||= Archytas' Comma ||= Leipziger Komma ||
||= 3125/3087 ||< | 0 -2 5 -3 > ||> 21.18 ||= Gariboh ||=   ||=   ||
||= 50421/50000 ||< | -4 1 -5 5 > ||> 14.52 ||= Trimyna ||=   ||=   ||
||= 1029/1024 ||< | -10 1 0 3 > ||> 8.43 ||= Gamelisma ||=   ||=   ||
||= 3136/3125 ||< | 6 0 -5 2 > ||> 6.08 ||= Hemimean ||=   ||=   ||
||= 65625/65536 ||< | -16 1 5 1 > ||> 2.35 ||= Horwell ||=   ||=   ||
||= 100/99 ||< | 2 -2 2 0 -1 > ||> 17.40 ||= Ptolemisma ||=   ||=   ||
||= 176/175 ||< | 4 0 -2 -1 1 > ||> 9.86 ||= Valinorsma ||=   ||=   ||
||= 91/90 ||< | -1 -2 -1 1 0 1 > ||> 19.13 ||= Superleap ||=   ||=   ||
||= 676/675 ||< | 2 -3 -2 0 0 2 > ||> 2.56 ||= Parizeksma ||=   ||=   ||

=A 25edo keyboard= 

[[image:mm25.PNG]]

Original HTML content:

<html><head><title>25edo</title></head><body><!-- ws:start:WikiTextTocRule:15:&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:15 --><!-- ws:start:WikiTextTocRule:16: --><a href="#x25 tone equal temperament">25 tone equal temperament</a><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --> | <a href="#Music">Music</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --> | <a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> | <a href="#Relationship to Armodue">Relationship to Armodue</a><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --> | <a href="#A 25edo keyboard">A 25edo keyboard</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: -->
<!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextHeadingRule:3:&lt;h1&gt; --><h1 id="toc0"><a name="x25 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:3 --><span style="color: #006b2e; font-family: 'Times New Roman',Times,serif; font-size: 113%;">25 tone equal temperament</span></h1>
 <br />
25EDO divides the <a class="wiki_link" href="/octave">octave</a> in 25 equal steps of exact size 48 <a class="wiki_link" href="/cent">cent</a>s each. It is a good way to tune the <a class="wiki_link" href="/Blackwood%20temperament">Blackwood temperament</a>, which takes the very sharp fifths of <a class="wiki_link" href="/5EDO">5EDO</a> as a given, tempers out 28/27 and 49/48, and attempts to optimize the tunings for 5 (<a class="wiki_link" href="/5_4">5/4</a>) and 7 (<a class="wiki_link" href="/7_4">7/4</a>). It also tunes sixix temperament with a sharp fifth. It supplies the optimal patent val for the 11-limit 6&amp;25 temperament tempering out 49/48, 77/75 and 605/576, and the 13-limit extension also tempering out 66/65.<br />
<br />
25EDO has fifths 18 cents sharp, but its major thirds are excellent and its 7/4 is acceptable. Moreover, in full 7-limit including the 3, it is not <a class="wiki_link" href="/consistent">consistent</a>. It therefore makes sense to use it as a 2.5.7 <a class="wiki_link" href="/Just%20intonation%20subgroups">subgroup</a> tuning. Looking just at 2, 5, and 7, it equates five <a class="wiki_link" href="/8_7">8/7</a>s with the octave, and so tempers out (8/7)^5 / 2 = 16807/16384. It also equates a <a class="wiki_link" href="/128_125">128/125</a> <a class="wiki_link" href="/diesis">diesis</a> and two <a class="wiki_link" href="/septimal%20tritones">septimal tritones</a> of <a class="wiki_link" href="/7_5">7/5</a> with the octave, and hence tempers out 3136/3125. If we want to temper out both of these and also have decent fifths, the obvious solution is <a class="wiki_link" href="/50EDO">50EDO</a>. An alternative fifth, 14\25, which is 672 cents, provides an alternative very flat fifth which can be used for <a class="wiki_link" href="/mavila">mavila</a> temperament.<br />
<br />
If 5/4 and 7/4 aren't good enough, it also does 17/16 and 19/16, just like 12EDO. In fact, on the <a class="wiki_link" href="/k%2AN%20subgroups">2*25 subgroup</a> 2.9.5.7.33.39.17.19 it provides the same tuning and tempers out the same commas as 50et, which makes for a wide range of harmony.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:5:&lt;h1&gt; --><h1 id="toc1"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:5 -->Music</h1>
 <em><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Rapoport/StudyInFives.mp3" rel="nofollow">Study in Fives</a></em> by <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Paul_Rapoport_%28music_critic%29" rel="nofollow">Paul Rapoport</a><br />
<a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=2377" rel="nofollow">Fantasy for Piano in 25 Note per Octave Tuning</a> <em><a class="wiki_link_ext" href="http://micro.soonlabel.com/25edo/fantasy_for_piano_in_25_edo.mp3" rel="nofollow">play</a></em> by Chris Vaisvil<br />
<em><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Fiale/flat%20fourth%20blues.mp3" rel="nofollow">Flat fourth blues</a></em> by Fabrizio Fulvio Fausto Fiale<br />
<br />
<!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/25edochorale.mid?h=50&amp;w=300&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;25edochorale.mid&amp;quot; width=&amp;quot;300&amp;quot; height=&amp;quot;50&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;50&quot; width=&quot;300&quot;/&gt; --><embed type="audio/midi" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/25edochorale.mid" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"></embed><!-- ws:end:WikiTextMediaRule:0 --> <!-- ws:start:WikiTextFileRule:680:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file/25edochorale.mid?h=52&amp;w=320&quot; class=&quot;WikiFile&quot; id=&quot;wikitext@@file@@25edochorale.mid&quot; title=&quot;File: 25edochorale.mid&quot; width=&quot;320&quot; height=&quot;52&quot; /&gt; --><div class="objectEmbed"><a href="/file/view/25edochorale.mid/314425794/25edochorale.mid" onclick="ws.common.trackFileLink('/file/view/25edochorale.mid/314425794/25edochorale.mid');"><img src="http://c1.wikicdn.com/i/mime/32/empty.png" height="32" width="32" alt="25edochorale.mid" /></a><div><a href="/file/view/25edochorale.mid/314425794/25edochorale.mid" onclick="ws.common.trackFileLink('/file/view/25edochorale.mid/314425794/25edochorale.mid');" class="filename" title="25edochorale.mid">25edochorale.mid</a><br /><ul><li><a href="/file/detail/25edochorale.mid">Details</a></li><li><a href="/file/view/25edochorale.mid/314425794/25edochorale.mid">Download</a></li><li style="color: #666">4 KB</li></ul></div></div><!-- ws:end:WikiTextFileRule:680 --> Peter Kosmorsky (10/14/10, 2.5.7 subgroup, a friend responded &quot;The <span class="il">25edo</span> canon has a nice theme, but all the harmonizations from there are laughably dissonant. I showed them to my roomie and he found it disturbing, hahaha. He had an unintentional physical reaction to it with his mouth in which his muscles did a smirk sort of thing, without him even trying to, hahaha. So, my point; this I think this 25 edo idea was an example of where tonal thinking doesn't suit the sound of the scale.&quot;)<br />
<!-- ws:start:WikiTextMediaRule:1:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/25%20edo%20prelude%20largo.mid?h=50&amp;w=300&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;25 edo prelude largo.mid&amp;quot; width=&amp;quot;300&amp;quot; height=&amp;quot;50&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;50&quot; width=&quot;300&quot;/&gt; --><embed type="audio/midi" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/25+edo+prelude+largo.mid" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"></embed><!-- ws:end:WikiTextMediaRule:1 --> <!-- ws:start:WikiTextFileRule:681:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file/25%20edo%20prelude%20largo.mid?h=52&amp;w=320&quot; class=&quot;WikiFile&quot; id=&quot;wikitext@@file@@25 edo prelude largo.mid&quot; title=&quot;File: 25 edo prelude largo.mid&quot; width=&quot;320&quot; height=&quot;52&quot; /&gt; --><div class="objectEmbed"><a href="/file/view/25%20edo%20prelude%20largo.mid/314425914/25%20edo%20prelude%20largo.mid" onclick="ws.common.trackFileLink('/file/view/25%20edo%20prelude%20largo.mid/314425914/25%20edo%20prelude%20largo.mid');"><img src="http://c1.wikicdn.com/i/mime/32/empty.png" height="32" width="32" alt="25 edo prelude largo.mid" /></a><div><a href="/file/view/25%20edo%20prelude%20largo.mid/314425914/25%20edo%20prelude%20largo.mid" onclick="ws.common.trackFileLink('/file/view/25%20edo%20prelude%20largo.mid/314425914/25%20edo%20prelude%20largo.mid');" class="filename" title="25 edo prelude largo.mid">25 edo prelude largo.mid</a><br /><ul><li><a href="/file/detail/25%20edo%20prelude%20largo.mid">Details</a></li><li><a href="/file/view/25%20edo%20prelude%20largo.mid/314425914/25%20edo%20prelude%20largo.mid">Download</a></li><li style="color: #666">6 KB</li></ul></div></div><!-- ws:end:WikiTextFileRule:681 --> Peter Kosmorsky (2011, Blackwood)<br />
<br />
<!-- ws:start:WikiTextHeadingRule:7:&lt;h1&gt; --><h1 id="toc2"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:7 -->Intervals</h1>
 <br />


<table class="wiki_table">
    <tr>
        <td style="text-align: center;">Degrees<br />
</td>
        <td style="text-align: center;">Cents<br />
</td>
        <td style="text-align: center;">Approximate<br />
Ratios*<br />
</td>
        <td style="text-align: center;">Armodue<br />
Notation<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;">1<br />
</td>
        <td style="text-align: center;">P1<br />
</td>
        <td style="text-align: center;">perfect 1sn<br />
</td>
        <td style="text-align: center;">D, Eb<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">1<br />
</td>
        <td style="text-align: center;">48<br />
</td>
        <td style="text-align: center;">33/32, 39/38, 34/33<br />
</td>
        <td style="text-align: center;">1#<br />
</td>
        <td style="text-align: center;">^1, ^m2<br />
</td>
        <td style="text-align: center;">up 1sn, upminor 2nd<br />
</td>
        <td style="text-align: center;">D^, Eb^<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">2<br />
</td>
        <td style="text-align: center;">96<br />
</td>
        <td style="text-align: center;">17/16, 20/19, 18/17<br />
</td>
        <td style="text-align: center;">2b<br />
</td>
        <td style="text-align: center;">^^m2<br />
</td>
        <td style="text-align: center;">double-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;">144<br />
</td>
        <td style="text-align: center;">12/11, 38/35<br />
</td>
        <td style="text-align: center;">2<br />
</td>
        <td style="text-align: center;">vvM2<br />
</td>
        <td style="text-align: center;">double-downmajor 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;">192<br />
</td>
        <td style="text-align: center;">9/8, 10/9, 19/17<br />
</td>
        <td style="text-align: center;">2#<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;">240<br />
</td>
        <td style="text-align: center;">8/7<br />
</td>
        <td style="text-align: center;">3b<br />
</td>
        <td style="text-align: center;">M2, m3<br />
</td>
        <td style="text-align: center;">major 2nd, minor 3rd<br />
</td>
        <td style="text-align: center;">E, F<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">6<br />
</td>
        <td style="text-align: center;">288<br />
</td>
        <td style="text-align: center;">19/16, 20/17<br />
</td>
        <td style="text-align: center;">3<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;">7<br />
</td>
        <td style="text-align: center;">336<br />
</td>
        <td style="text-align: center;">39/32, 17/14, 40/33<br />
</td>
        <td style="text-align: center;">3#<br />
</td>
        <td style="text-align: center;">^^m3<br />
</td>
        <td style="text-align: center;">double-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;">384<br />
</td>
        <td style="text-align: center;">5/4<br />
</td>
        <td style="text-align: center;">4b<br />
</td>
        <td style="text-align: center;">vvM3<br />
</td>
        <td style="text-align: center;">double-downmajor 3rd<br />
</td>
        <td style="text-align: center;">F#vv<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">9<br />
</td>
        <td style="text-align: center;">432<br />
</td>
        <td style="text-align: center;">9/7, 32/25, 50/39<br />
</td>
        <td style="text-align: center;">4<br />
</td>
        <td style="text-align: center;">vM3<br />
</td>
        <td style="text-align: center;">downmajor<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;">480<br />
</td>
        <td style="text-align: center;">33/25, 25/19<br />
</td>
        <td style="text-align: center;">4#/5b<br />
</td>
        <td style="text-align: center;">M3, P4<br />
</td>
        <td style="text-align: center;">major 3rd, perfect 4th<br />
</td>
        <td style="text-align: center;">F#, G<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">11·<br />
</td>
        <td style="text-align: center;">528<br />
</td>
        <td style="text-align: center;">31/21, 34/25<br />
</td>
        <td style="text-align: center;">5<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;">12<br />
</td>
        <td style="text-align: center;">576<br />
</td>
        <td style="text-align: center;">7/5, 39/28<br />
</td>
        <td style="text-align: center;">5#<br />
</td>
        <td style="text-align: center;">^^4,^^d5<br />
</td>
        <td style="text-align: center;">double-up 4th,<br />
double-up dim 5th<br />
</td>
        <td style="text-align: center;">G^^, Ab^^<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">13<br />
</td>
        <td style="text-align: center;">624<br />
</td>
        <td style="text-align: center;">10/7, 56/39<br />
</td>
        <td style="text-align: center;">6b<br />
</td>
        <td style="text-align: center;">vvA4,vv5<br />
</td>
        <td style="text-align: center;">double-down aug 4th,<br />
double-down 5th<br />
</td>
        <td style="text-align: center;">G#vv, Avv<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">14·<br />
</td>
        <td style="text-align: center;">672<br />
</td>
        <td style="text-align: center;">42/31, 25/17<br />
</td>
        <td style="text-align: center;">6<br />
</td>
        <td style="text-align: center;">v5<br />
</td>
        <td style="text-align: center;">down 5th<br />
</td>
        <td style="text-align: center;">Av<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">15<br />
</td>
        <td style="text-align: center;">720<br />
</td>
        <td style="text-align: center;">50/33, 38/25<br />
</td>
        <td style="text-align: center;">6#<br />
</td>
        <td style="text-align: center;">P5, m6<br />
</td>
        <td style="text-align: center;">perfect 5th, minor 6th<br />
</td>
        <td style="text-align: center;">A, Bb<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">16<br />
</td>
        <td style="text-align: center;">768<br />
</td>
        <td style="text-align: center;">14/9, 25/16, 39/25<br />
</td>
        <td style="text-align: center;">7b<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;">17·<br />
</td>
        <td style="text-align: center;">816<br />
</td>
        <td style="text-align: center;">8/5<br />
</td>
        <td style="text-align: center;">7<br />
</td>
        <td style="text-align: center;">^^m6<br />
</td>
        <td style="text-align: center;">double-upminor 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;">864<br />
</td>
        <td style="text-align: center;">64/39, 28/17, 33/20<br />
</td>
        <td style="text-align: center;">7#<br />
</td>
        <td style="text-align: center;">vvM6<br />
</td>
        <td style="text-align: center;">double-downmajor 6th<br />
</td>
        <td style="text-align: center;">Bvv<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">19<br />
</td>
        <td style="text-align: center;">912<br />
</td>
        <td style="text-align: center;">32/19, 17/10<br />
</td>
        <td style="text-align: center;">8b<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;">20·<br />
</td>
        <td style="text-align: center;">960<br />
</td>
        <td style="text-align: center;">7/4<br />
</td>
        <td style="text-align: center;">8<br />
</td>
        <td style="text-align: center;">M6, m7<br />
</td>
        <td style="text-align: center;">major 6th, minor 7th<br />
</td>
        <td style="text-align: center;">B, C<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">21<br />
</td>
        <td style="text-align: center;">1008<br />
</td>
        <td style="text-align: center;">16/9, 9/5, 34/19<br />
</td>
        <td style="text-align: center;">8#<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;">22<br />
</td>
        <td style="text-align: center;">1056<br />
</td>
        <td style="text-align: center;">11/6, 35/19<br />
</td>
        <td style="text-align: center;">9b<br />
</td>
        <td style="text-align: center;">^^m7<br />
</td>
        <td style="text-align: center;">double-upminor 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;">1104<br />
</td>
        <td style="text-align: center;">32/17, 17/9, 19/10<br />
</td>
        <td style="text-align: center;">9<br />
</td>
        <td style="text-align: center;">vvM7<br />
</td>
        <td style="text-align: center;">double-downmajor 7th<br />
</td>
        <td style="text-align: center;">C#vv<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">24<br />
</td>
        <td style="text-align: center;">1152<br />
</td>
        <td style="text-align: center;">33/17, 64/33, 76/39<br />
</td>
        <td style="text-align: center;">9#/1b<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;">25<br />
</td>
        <td style="text-align: center;">1200<br />
</td>
        <td style="text-align: center;">2/1<br />
</td>
        <td style="text-align: center;">1<br />
</td>
        <td style="text-align: center;">P8<br />
</td>
        <td style="text-align: center;">perfect 8ve<br />
</td>
        <td style="text-align: center;">C#, D<br />
</td>
    </tr>
</table>

*based on treating 25-EDO as a 2.9.5.7.33.39.17.19 subgroup; other approaches are possible.<br />
<br />
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<!-- ws:start:WikiTextHeadingRule:9:&lt;h1&gt; --><h1 id="toc3"><a name="Relationship to Armodue"></a><!-- ws:end:WikiTextHeadingRule:9 -->Relationship to Armodue</h1>
 <br />
Like <a class="wiki_link" href="/16edo">16-EDO</a> and <a class="wiki_link" href="/23edo">23-EDO</a>, 25-EDO contains the 9-note &quot;Superdiatonic&quot; scale of <a class="wiki_link" href="/7L%202s">7L2s</a> (LLLsLLLLs) that is generated by a circle of heavily-flattened 3/2s (ranging in size from 5\9-EDO or 666.67 cents, to 4\7-EDO or 685.71 cents). The 25-EDO generator for this scale is the 672-cent interval. This allows 25-EDO to be used with the <a class="wiki_link" href="/Armodue%20theory">Armodue</a> notation system in much the same way that <a class="wiki_link" href="/19edo">19-EDO</a> is used with the standard diatonic notation; see the above interval chart for the Armodue names. Because the 25-EDO Armodue 6th is flatter than that of 16-EDO (the middle of the Armodue spectrum), sharps are lower in pitch than enharmonic flats.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:11:&lt;h1&gt; --><h1 id="toc4"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:11 -->Commas</h1>
 25 EDO tempers out the following commas. (Note: This assumes the val &lt; 25 40 58 70 86 93 |.)<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;">256/243<br />
</td>
        <td style="text-align: left;">| 8 -5 &gt;<br />
</td>
        <td style="text-align: right;">90.22<br />
</td>
        <td style="text-align: center;">Limma<br />
</td>
        <td style="text-align: center;">Pythagorean Minor 2nd<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">3125/3072<br />
</td>
        <td style="text-align: left;">| -10 -1 5 &gt;<br />
</td>
        <td style="text-align: right;">29.61<br />
</td>
        <td style="text-align: center;">Small Diesis<br />
</td>
        <td style="text-align: center;">Magic Comma<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: left;">| 38 -2 -15 &gt;<br />
</td>
        <td style="text-align: right;">1.38<br />
</td>
        <td style="text-align: center;">Hemithirds Comma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">16807/16384<br />
</td>
        <td>| -14 0 0 5 &gt;<br />
</td>
        <td style="text-align: right;">44.13<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">49/48<br />
</td>
        <td style="text-align: left;">| -4 -1 0 2 &gt;<br />
</td>
        <td style="text-align: right;">35.70<br />
</td>
        <td style="text-align: center;">Slendro Diesis<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;">3125/3087<br />
</td>
        <td style="text-align: left;">| 0 -2 5 -3 &gt;<br />
</td>
        <td style="text-align: right;">21.18<br />
</td>
        <td style="text-align: center;">Gariboh<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><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;">1029/1024<br />
</td>
        <td style="text-align: left;">| -10 1 0 3 &gt;<br />
</td>
        <td style="text-align: right;">8.43<br />
</td>
        <td style="text-align: center;">Gamelisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">3136/3125<br />
</td>
        <td style="text-align: left;">| 6 0 -5 2 &gt;<br />
</td>
        <td style="text-align: right;">6.08<br />
</td>
        <td style="text-align: center;">Hemimean<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">65625/65536<br />
</td>
        <td style="text-align: left;">| -16 1 5 1 &gt;<br />
</td>
        <td style="text-align: right;">2.35<br />
</td>
        <td style="text-align: center;">Horwell<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">100/99<br />
</td>
        <td style="text-align: left;">| 2 -2 2 0 -1 &gt;<br />
</td>
        <td style="text-align: right;">17.40<br />
</td>
        <td style="text-align: center;">Ptolemisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">176/175<br />
</td>
        <td style="text-align: left;">| 4 0 -2 -1 1 &gt;<br />
</td>
        <td style="text-align: right;">9.86<br />
</td>
        <td style="text-align: center;">Valinorsma<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>
    <tr>
        <td style="text-align: center;">676/675<br />
</td>
        <td style="text-align: left;">| 2 -3 -2 0 0 2 &gt;<br />
</td>
        <td style="text-align: right;">2.56<br />
</td>
        <td style="text-align: center;">Parizeksma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:13:&lt;h1&gt; --><h1 id="toc5"><a name="A 25edo keyboard"></a><!-- ws:end:WikiTextHeadingRule:13 -->A 25edo keyboard</h1>
 <br />
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@@ 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:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-05 14:56:01 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-25 18:52:38 UTC</tt>.<br>
-: The original revision id was <tt>601447782</tt>.<br>
+: The original revision id was <tt>602808482</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>
@@ Line 25: / Line 25: @@
 =Intervals=
-|| Degrees || Cents value ||= Approximate
+||= Degrees ||= Cents ||= Approximate
 Ratios* ||= Armodue
-Notation ||
+Notation ||||||= [[xenharmonic/Ups and Downs Notation|ups and downs notation]] ||
-|| 0 || 0
+||= 0 ||= 0 ||= 1/1 ||= 1 ||= P1 ||= perfect 1sn ||= D, Eb ||
-° ||= 1/1 ||= 1 ||
+||= 1 ||= 48 ||= 33/32, 39/38, 34/33 ||= 1# ||= ^1, ^m2 ||= up 1sn, upminor 2nd ||= D^, Eb^ ||
-|| 1 || 48, //57.6//
+||= 2 ||= 96 ||= 17/16, 20/19, 18/17 ||= 2b ||= ^^m2 ||= double-upminor 2nd ||= Eb^^ ||
-°24' ||= 33/32, 39/38, 34/33 ||= 1# ||
+||= 3 ||= 144 ||= 12/11, 38/35 ||= 2 ||= vvM2 ||= double-downmajor 2nd ||= Evv ||
-|| 2 || 96, //115.2//
+||= 4 ||= 192 ||= 9/8, 10/9, 19/17 ||= 2# ||= vM2 ||= downmajor 2nd ||= Ev ||
-°48' ||= 17/16, 20/19, 18/17 ||= 2b ||
+||= 5· ||= 240 ||= 8/7 ||= 3b ||= M2, m3 ||= major 2nd, minor 3rd ||= E, F ||
-|| 3 || 144, //172.8//
+||= 6 ||= 288 ||= 19/16, 20/17 ||= 3 ||= ^m3 ||= upminor 3rd ||= F^ ||
-°12' ||= 12/11, 38/35 ||= 2 ||
+||= 7 ||= 336 ||= 39/32, 17/14, 40/33 ||= 3# ||= ^^m3 ||= double-upminor 3rd ||= F^^ ||
-|| 4 || 192, //230.4//
+||= 8· ||= 384 ||= 5/4 ||= 4b ||= vvM3 ||= double-downmajor 3rd ||= F#vv ||
-°36' ||= 9/8, 10/9, 19/17 ||= 2# ||
+||= 9 ||= 432 ||= 9/7, 32/25, 50/39 ||= 4 ||= vM3 ||= downmajor ||= F#v ||
-|| 5· || 240, 288
+||= 10 ||= 480 ||= 33/25, 25/19 ||= 4#/5b ||= M3, P4 ||= major 3rd, perfect 4th ||= F#, G ||
-° ||= 8/7 ||= 3b ||
+||= 11· ||= 528 ||= 31/21, 34/25 ||= 5 ||= ^4 ||= up 4th ||= G^ ||
-|| 6 || 288, //345.6//
+||= 12 ||= 576 ||= 7/5, 39/28 ||= 5# ||= ^^4,^^d5 ||= double-up 4th,
-°24' ||= 19/16, 20/17 ||= 3 ||
+double-up dim 5th ||= G^^, Ab^^ ||
-|| 7 || 336, //403.2//
+||= 13 ||= 624 ||= 10/7, 56/39 ||= 6b ||= vvA4,vv5 ||= double-down aug 4th,
-°48' ||= 39/32, 17/14, 40/33 ||= 3# ||
+double-down 5th ||= G#vv, Avv ||
-|| 8· || 384, //460.8//
+||= 14· ||= 672 ||= 42/31, 25/17 ||= 6 ||= v5 ||= down 5th ||= Av ||
-°12' ||= 5/4 ||= 4b ||
+||= 15 ||= 720 ||= 50/33, 38/25 ||= 6# ||= P5, m6 ||= perfect 5th, minor 6th ||= A, Bb ||
-|| 9 || 432, //518.4//
+||= 16 ||= 768 ||= 14/9, 25/16, 39/25 ||= 7b ||= ^m6 ||= upminor 6th ||= Bb^ ||
-°36' ||= 9/7, 32/25, 50/39 ||= 4 ||
+||= 17· ||= 816 ||= 8/5 ||= 7 ||= ^^m6 ||= double-upminor 6th ||= Bb^^ ||
-|| 10 || 480, 576
+||= 18 ||= 864 ||= 64/39, 28/17, 33/20 ||= 7# ||= vvM6 ||= double-downmajor 6th ||= Bvv ||
-° ||= 33/25, 25/19 ||= 4#/5b ||
+||= 19 ||= 912 ||= 32/19, 17/10 ||= 8b ||= vM6 ||= downmajor 6th ||= Bv ||
-|| 11· || 528, //633.6//
+||= 20· ||= 960 ||= 7/4 ||= 8 ||= M6, m7 ||= major 6th, minor 7th ||= B, C ||
-°24' ||= 31/21, 34/25 ||= 5 ||
+||= 21 ||= 1008 ||= 16/9, 9/5, 34/19 ||= 8# ||= ^m7 ||= upminor 7th ||= C^ ||
-|| 12 || 576, //691.2//
+||= 22 ||= 1056 ||= 11/6, 35/19 ||= 9b ||= ^^m7 ||= double-upminor 7th ||= C^^ ||
-°48' ||= 7/5, 39/28 ||= 5# ||
+||= 23 ||= 1104 ||= 32/17, 17/9, 19/10 ||= 9 ||= vvM7 ||= double-downmajor 7th ||= C#vv ||
-|| 13 || 624, //748.8//
+||= 24 ||= 1152 ||= 33/17, 64/33, 76/39 ||= 9#/1b ||= vM7 ||= downmajor 7th ||= C#v ||
-°12' ||= 10/7, 56/39 ||= 6b ||
+||= 25 ||= 1200 ||= 2/1 ||= 1 ||= P8 ||= perfect 8ve ||= C#, D ||
-|| 14· || 672, //806.4//
-°36' ||= 42/31, 25/17 ||= 6 ||
-|| 15 || 720, 864
-° ||= 50/33, 38/25 ||= 6# ||
-|| 16 || 768, //921.6//
-°24' ||= 14/9, 25/16, 39/25 ||= 7b ||
-|| 17· || 816, //979.2//
-°48' ||= 8/5 ||= 7 ||
-|| 18 || 864, //1036.8//
-°12' ||= 64/39, 28/17, 33/20 ||= 7# ||
-|| 19 || 912, //1094.4//
-°36' ||= 32/19, 17/10 ||= 8b ||
-|| 20· || 960, 1152
-° ||= 7/4 ||= 8 ||
-|| 21 || 1008, //1209.6//
-°14' ||= 16/9, 9/5, 34/19 ||= 8# ||
-|| 22 || 1056, //1267.2//
-°48' ||= 11/6, 35/19 ||= 9b ||
-|| 23 || 1104, //1324.8//
-°12' ||= 32/17, 17/9, 19/10 ||= 9 ||
-|| 24 || 1152, //1382.4//
-°36' ||= 33/17, 64/33, 76/39 ||= 9#/1b ||
-|| 25 || 1200, 1440
-° ||= 2/1 ||= 1 ||
 *based on treating 25-EDO as a 2.9.5.7.33.39.17.19 subgroup; other approaches are possible.
@@ Line 92: / Line 68: @@
 =Commas=
-EDO tempers out the following commas. (Note: This assumes the val &lt; 25 40 58 70 86 93/1 |.)
+EDO tempers out the following commas. (Note: This assumes the val &lt; 25 40 58 70 86 93 |.)
 ||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
 ||= 256/243 ||&lt; | 8 -5 &gt; ||&gt; 90.22 ||= Limma ||= Pythagorean Minor 2nd ||=   ||
@@ Line 128: / Line 104: @@
 &lt;em&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Fiale/flat%20fourth%20blues.mp3" rel="nofollow"&gt;Flat fourth blues&lt;/a&gt;&lt;/em&gt; by Fabrizio Fulvio Fausto Fiale&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/25edochorale.mid?h=50&amp;amp;w=300&amp;quot; class=&amp;quot;WikiMedia WikiMediaFile&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;file&amp;amp;quot; key=&amp;amp;quot;25edochorale.mid&amp;amp;quot; width=&amp;amp;quot;300&amp;amp;quot; height=&amp;amp;quot;50&amp;amp;quot;&amp;quot; title=&amp;quot;Local Media File&amp;quot;height=&amp;quot;50&amp;quot; width=&amp;quot;300&amp;quot;/&amp;gt; --&gt;&lt;embed type="audio/midi" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/25edochorale.mid" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"&gt;&lt;/embed&gt;&lt;!-- ws:end:WikiTextMediaRule:0 --&gt; &lt;!-- ws:start:WikiTextFileRule:522:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file/25edochorale.mid?h=52&amp;amp;w=320&amp;quot; class=&amp;quot;WikiFile&amp;quot; id=&amp;quot;wikitext@@file@@25edochorale.mid&amp;quot; title=&amp;quot;File: 25edochorale.mid&amp;quot; width=&amp;quot;320&amp;quot; height=&amp;quot;52&amp;quot; /&amp;gt; --&gt;&lt;div class="objectEmbed"&gt;&lt;a href="/file/view/25edochorale.mid/314425794/25edochorale.mid" onclick="ws.common.trackFileLink('/file/view/25edochorale.mid/314425794/25edochorale.mid');"&gt;&lt;img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="25edochorale.mid" /&gt;&lt;/a&gt;&lt;div&gt;&lt;a href="/file/view/25edochorale.mid/314425794/25edochorale.mid" onclick="ws.common.trackFileLink('/file/view/25edochorale.mid/314425794/25edochorale.mid');" class="filename" title="25edochorale.mid"&gt;25edochorale.mid&lt;/a&gt;&lt;br /&gt;&lt;ul&gt;&lt;li&gt;&lt;a href="/file/detail/25edochorale.mid"&gt;Details&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a href="/file/view/25edochorale.mid/314425794/25edochorale.mid"&gt;Download&lt;/a&gt;&lt;/li&gt;&lt;li style="color: #666"&gt;4 KB&lt;/li&gt;&lt;/ul&gt;&lt;/div&gt;&lt;/div&gt;&lt;!-- ws:end:WikiTextFileRule:522 --&gt; Peter Kosmorsky (10/14/10, 2.5.7 subgroup, a friend responded &amp;quot;The &lt;span class="il"&gt;25edo&lt;/span&gt; canon has a nice theme, but all the harmonizations from there are laughably dissonant. I showed them to my roomie and he found it disturbing, hahaha. He had an unintentional physical reaction to it with his mouth in which his muscles did a smirk sort of thing, without him even trying to, hahaha. So, my point; this I think this 25 edo idea was an example of where tonal thinking doesn't suit the sound of the scale.&amp;quot;)&lt;br /&gt;
+&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/25edochorale.mid?h=50&amp;amp;w=300&amp;quot; class=&amp;quot;WikiMedia WikiMediaFile&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;file&amp;amp;quot; key=&amp;amp;quot;25edochorale.mid&amp;amp;quot; width=&amp;amp;quot;300&amp;amp;quot; height=&amp;amp;quot;50&amp;amp;quot;&amp;quot; title=&amp;quot;Local Media File&amp;quot;height=&amp;quot;50&amp;quot; width=&amp;quot;300&amp;quot;/&amp;gt; --&gt;&lt;embed type="audio/midi" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/25edochorale.mid" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"&gt;&lt;/embed&gt;&lt;!-- ws:end:WikiTextMediaRule:0 --&gt; &lt;!-- ws:start:WikiTextFileRule:680:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file/25edochorale.mid?h=52&amp;amp;w=320&amp;quot; class=&amp;quot;WikiFile&amp;quot; id=&amp;quot;wikitext@@file@@25edochorale.mid&amp;quot; title=&amp;quot;File: 25edochorale.mid&amp;quot; width=&amp;quot;320&amp;quot; height=&amp;quot;52&amp;quot; /&amp;gt; --&gt;&lt;div class="objectEmbed"&gt;&lt;a href="/file/view/25edochorale.mid/314425794/25edochorale.mid" onclick="ws.common.trackFileLink('/file/view/25edochorale.mid/314425794/25edochorale.mid');"&gt;&lt;img src="http://c1.wikicdn.com/i/mime/32/empty.png" height="32" width="32" alt="25edochorale.mid" /&gt;&lt;/a&gt;&lt;div&gt;&lt;a href="/file/view/25edochorale.mid/314425794/25edochorale.mid" onclick="ws.common.trackFileLink('/file/view/25edochorale.mid/314425794/25edochorale.mid');" class="filename" title="25edochorale.mid"&gt;25edochorale.mid&lt;/a&gt;&lt;br /&gt;&lt;ul&gt;&lt;li&gt;&lt;a href="/file/detail/25edochorale.mid"&gt;Details&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a href="/file/view/25edochorale.mid/314425794/25edochorale.mid"&gt;Download&lt;/a&gt;&lt;/li&gt;&lt;li style="color: #666"&gt;4 KB&lt;/li&gt;&lt;/ul&gt;&lt;/div&gt;&lt;/div&gt;&lt;!-- ws:end:WikiTextFileRule:680 --&gt; Peter Kosmorsky (10/14/10, 2.5.7 subgroup, a friend responded &amp;quot;The &lt;span class="il"&gt;25edo&lt;/span&gt; canon has a nice theme, but all the harmonizations from there are laughably dissonant. I showed them to my roomie and he found it disturbing, hahaha. He had an unintentional physical reaction to it with his mouth in which his muscles did a smirk sort of thing, without him even trying to, hahaha. So, my point; this I think this 25 edo idea was an example of where tonal thinking doesn't suit the sound of the scale.&amp;quot;)&lt;br /&gt;
-&lt;!-- ws:start:WikiTextMediaRule:1:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/25%20edo%20prelude%20largo.mid?h=50&amp;amp;w=300&amp;quot; class=&amp;quot;WikiMedia WikiMediaFile&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;file&amp;amp;quot; key=&amp;amp;quot;25 edo prelude largo.mid&amp;amp;quot; width=&amp;amp;quot;300&amp;amp;quot; height=&amp;amp;quot;50&amp;amp;quot;&amp;quot; title=&amp;quot;Local Media File&amp;quot;height=&amp;quot;50&amp;quot; width=&amp;quot;300&amp;quot;/&amp;gt; --&gt;&lt;embed type="audio/midi" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/25+edo+prelude+largo.mid" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"&gt;&lt;/embed&gt;&lt;!-- ws:end:WikiTextMediaRule:1 --&gt; &lt;!-- ws:start:WikiTextFileRule:523:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file/25%20edo%20prelude%20largo.mid?h=52&amp;amp;w=320&amp;quot; class=&amp;quot;WikiFile&amp;quot; id=&amp;quot;wikitext@@file@@25 edo prelude largo.mid&amp;quot; title=&amp;quot;File: 25 edo prelude largo.mid&amp;quot; width=&amp;quot;320&amp;quot; height=&amp;quot;52&amp;quot; /&amp;gt; --&gt;&lt;div class="objectEmbed"&gt;&lt;a href="/file/view/25%20edo%20prelude%20largo.mid/314425914/25%20edo%20prelude%20largo.mid" onclick="ws.common.trackFileLink('/file/view/25%20edo%20prelude%20largo.mid/314425914/25%20edo%20prelude%20largo.mid');"&gt;&lt;img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="25 edo prelude largo.mid" /&gt;&lt;/a&gt;&lt;div&gt;&lt;a href="/file/view/25%20edo%20prelude%20largo.mid/314425914/25%20edo%20prelude%20largo.mid" onclick="ws.common.trackFileLink('/file/view/25%20edo%20prelude%20largo.mid/314425914/25%20edo%20prelude%20largo.mid');" class="filename" title="25 edo prelude largo.mid"&gt;25 edo prelude largo.mid&lt;/a&gt;&lt;br /&gt;&lt;ul&gt;&lt;li&gt;&lt;a href="/file/detail/25%20edo%20prelude%20largo.mid"&gt;Details&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a href="/file/view/25%20edo%20prelude%20largo.mid/314425914/25%20edo%20prelude%20largo.mid"&gt;Download&lt;/a&gt;&lt;/li&gt;&lt;li style="color: #666"&gt;6 KB&lt;/li&gt;&lt;/ul&gt;&lt;/div&gt;&lt;/div&gt;&lt;!-- ws:end:WikiTextFileRule:523 --&gt; Peter Kosmorsky (2011, Blackwood)&lt;br /&gt;
+&lt;!-- ws:start:WikiTextMediaRule:1:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/25%20edo%20prelude%20largo.mid?h=50&amp;amp;w=300&amp;quot; class=&amp;quot;WikiMedia WikiMediaFile&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;file&amp;amp;quot; key=&amp;amp;quot;25 edo prelude largo.mid&amp;amp;quot; width=&amp;amp;quot;300&amp;amp;quot; height=&amp;amp;quot;50&amp;amp;quot;&amp;quot; title=&amp;quot;Local Media File&amp;quot;height=&amp;quot;50&amp;quot; width=&amp;quot;300&amp;quot;/&amp;gt; --&gt;&lt;embed type="audio/midi" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/25+edo+prelude+largo.mid" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"&gt;&lt;/embed&gt;&lt;!-- ws:end:WikiTextMediaRule:1 --&gt; &lt;!-- ws:start:WikiTextFileRule:681:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file/25%20edo%20prelude%20largo.mid?h=52&amp;amp;w=320&amp;quot; class=&amp;quot;WikiFile&amp;quot; id=&amp;quot;wikitext@@file@@25 edo prelude largo.mid&amp;quot; title=&amp;quot;File: 25 edo prelude largo.mid&amp;quot; width=&amp;quot;320&amp;quot; height=&amp;quot;52&amp;quot; /&amp;gt; --&gt;&lt;div class="objectEmbed"&gt;&lt;a href="/file/view/25%20edo%20prelude%20largo.mid/314425914/25%20edo%20prelude%20largo.mid" onclick="ws.common.trackFileLink('/file/view/25%20edo%20prelude%20largo.mid/314425914/25%20edo%20prelude%20largo.mid');"&gt;&lt;img src="http://c1.wikicdn.com/i/mime/32/empty.png" height="32" width="32" alt="25 edo prelude largo.mid" /&gt;&lt;/a&gt;&lt;div&gt;&lt;a href="/file/view/25%20edo%20prelude%20largo.mid/314425914/25%20edo%20prelude%20largo.mid" onclick="ws.common.trackFileLink('/file/view/25%20edo%20prelude%20largo.mid/314425914/25%20edo%20prelude%20largo.mid');" class="filename" title="25 edo prelude largo.mid"&gt;25 edo prelude largo.mid&lt;/a&gt;&lt;br /&gt;&lt;ul&gt;&lt;li&gt;&lt;a href="/file/detail/25%20edo%20prelude%20largo.mid"&gt;Details&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a href="/file/view/25%20edo%20prelude%20largo.mid/314425914/25%20edo%20prelude%20largo.mid"&gt;Download&lt;/a&gt;&lt;/li&gt;&lt;li style="color: #666"&gt;6 KB&lt;/li&gt;&lt;/ul&gt;&lt;/div&gt;&lt;/div&gt;&lt;!-- ws:end:WikiTextFileRule:681 --&gt; Peter Kosmorsky (2011, Blackwood)&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:7:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:7 --&gt;Intervals&lt;/h1&gt;
@@ Line 137: / Line 113: @@
 &lt;table class="wiki_table"&gt;
      &lt;tr&gt;
-         &lt;td&gt;Degrees&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Degrees&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Cents value&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Cents&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Approximate&lt;br /&gt;
@@ Line 146: / Line 122: @@
          &lt;td style="text-align: center;"&gt;Armodue&lt;br /&gt;
 Notation&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;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;1&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 1sn&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;D, Eb&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;48, &lt;em&gt;57.6&lt;/em&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;48&lt;br /&gt;
-°24'&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;33/32, 39/38, 34/33&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;1#&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;up 1sn, upminor 2nd&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;D^, 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;96, &lt;em&gt;115.2&lt;/em&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;96&lt;br /&gt;
-°48'&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;17/16, 20/19, 18/17&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;2b&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;double-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;144, &lt;em&gt;172.8&lt;/em&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;144&lt;br /&gt;
-°12'&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;12/11, 38/35&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;vvM2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;double-downmajor 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;192, &lt;em&gt;230.4&lt;/em&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;192&lt;br /&gt;
-°36'&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;9/8, 10/9, 19/17&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;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;240, 288&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;240&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;8/7&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;3b&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;M2, m3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;major 2nd, minor 3rd&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;E, F&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;288, &lt;em&gt;345.6&lt;/em&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;288&lt;br /&gt;
-°24'&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;19/16, 20/17&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;^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;7&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;336, &lt;em&gt;403.2&lt;/em&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;336&lt;br /&gt;
-°48'&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;39/32, 17/14, 40/33&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;^^m3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;double-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;384, &lt;em&gt;460.8&lt;/em&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;384&lt;br /&gt;
-°12'&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;4b&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;vvM3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;double-downmajor 3rd&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;F#vv&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;432, &lt;em&gt;518.4&lt;/em&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;432&lt;br /&gt;
-°36'&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;9/7, 32/25, 50/39&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;vM3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;downmajor&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;480, 576&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;480&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;33/25, 25/19&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;4#/5b&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;M3, P4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;major 3rd, perfect 4th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;F#, G&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;528, &lt;em&gt;633.6&lt;/em&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;528&lt;br /&gt;
-°24'&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;31/21, 34/25&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;5&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;12&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;12&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;576, &lt;em&gt;691.2&lt;/em&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;576&lt;br /&gt;
-°48'&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;7/5, 39/28&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;5#&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;^^4,^^d5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;double-up 4th,&lt;br /&gt;
+double-up dim 5th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;G^^, Ab^^&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;624, &lt;em&gt;748.8&lt;/em&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;624&lt;br /&gt;
-°12'&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;10/7, 56/39&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;6b&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;vvA4,vv5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;double-down aug 4th,&lt;br /&gt;
+double-down 5th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;G#vv, Avv&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;672, &lt;em&gt;806.4&lt;/em&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;672&lt;br /&gt;
-°36'&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;42/31, 25/17&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;v5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;down 5th&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;15&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;15&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;720, 864&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;720&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;50/33, 38/25&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;P5, m6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;perfect 5th, minor 6th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;A, Bb&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;768, &lt;em&gt;921.6&lt;/em&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;768&lt;br /&gt;
-°24'&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;14/9, 25/16, 39/25&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;7b&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;17·&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;17·&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;816, &lt;em&gt;979.2&lt;/em&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;816&lt;br /&gt;
-°48'&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;7&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;double-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;18&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;18&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;864, &lt;em&gt;1036.8&lt;/em&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;864&lt;br /&gt;
-°12'&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;64/39, 28/17, 33/20&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;vvM6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;double-downmajor 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;19&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;19&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;912, &lt;em&gt;1094.4&lt;/em&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;912&lt;br /&gt;
-°36'&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;32/19, 17/10&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;8b&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;20·&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;20·&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;960, 1152&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;960&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;7/4&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;8&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;M6, m7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;major 6th, minor 7th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;B, C&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;1008, &lt;em&gt;1209.6&lt;/em&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1008&lt;br /&gt;
-°14'&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;16/9, 9/5, 34/19&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;8#&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;22&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;22&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1056, &lt;em&gt;1267.2&lt;/em&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1056&lt;br /&gt;
-°48'&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;11/6, 35/19&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;9b&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;double-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;23&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;23&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1104, &lt;em&gt;1324.8&lt;/em&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1104&lt;br /&gt;
-°12'&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;32/17, 17/9, 19/10&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;vvM7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;double-downmajor 7th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;C#vv&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;1152, &lt;em&gt;1382.4&lt;/em&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1152&lt;br /&gt;
-°36'&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;33/17, 64/33, 76/39&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;9#/1b&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;25&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;25&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;1&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;perfect 8ve&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;C#, D&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
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-EDO tempers out the following commas. (Note: This assumes the val &amp;lt; 25 40 58 70 86 93/1 |.)&lt;br /&gt;
+EDO tempers out the following commas. (Note: This assumes the val &amp;lt; 25 40 58 70 86 93 |.)&lt;br /&gt;
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25edo: Difference between revisions

Revision as of 18:52, 25 December 2016

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