25edo
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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:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- 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:<h1> --><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&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:<h1> --><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 />
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<br />
<!-- ws:start:WikiTextHeadingRule:7:<h1> --><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:<h1> --><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 "Superdiatonic" 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:<h1> --><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 < 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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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:<h1> --><h1 id="toc5"><a name="A 25edo keyboard"></a><!-- ws:end:WikiTextHeadingRule:13 -->A 25edo keyboard</h1>
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