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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox ET}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
{{ED intro}}
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-05 15:08:14 UTC</tt>.<br>
: The original revision id was <tt>601448948</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">=&lt;span style="color: #0061ff; font-family: 'Times New Roman',Times,serif; font-size: 113%;"&gt;27 tone equal tempertament&lt;/span&gt;=


If octaves are kept pure, 27edo divides the [[octave]] in 27 equal parts each exactly 44.444... [[cent]]s in size. However, 27 is a prime candidate for [[octave shrinking]], and a step size of 44.3 to 44.35 cents would be reasonable. The reason for this is that 27edo tunes the [[5_4|third]], [[3_2|fifth]] and [[7_4|7/4]] sharply.
== Theory ==
Assuming pure octaves, 27edo divides the [[octave]] in 27 equal parts each exactly 44{{frac|4|9}} [[cent]]s in size. Its fifth and harmonic seventh are both sharp by 9{{c}}, and the major third is the same 400-cent major third as [[12edo]], sharp by 13.7{{c}}. The result is that [[6/5]], [[7/5]], and especially [[7/6]] are all tuned more accurately than this. It can be considered the superpythagorean counterpart of [[19edo]], as its 5th is audibly indistinguishable from [[superpyth|1/3-septimal-comma superpyth]] in the same way that 19edo is audibly indistinguishable from [[1/3-comma meantone|1/3-syntonic-comma meantone]], where three fifths in 19edo reach a near-perfect [[6/5]] and [[5/3]] and three fifths in 27edo reaching a near-perfect [[7/6]] and [[12/7]].


Assuming however pure octaves, 27 has a fifth sharp by slightly more than nine cents and a 7/4 sharp by slightly less, and the same 400 cent major third as [[12edo]], sharp 13 2/3 cents. The result is that [[6_5|6/5]], [[7_5|7/5]] and especially [[7_6|7/6]] are all tuned more accurately than this.
Though 27edo's [[7-limit]] tuning is not highly accurate, it nonetheless is the smallest equal division to represent the [[7-odd-limit]] both [[consistent]]ly and distinctly—that is, everything in the [[7-odd-limit]] [[tonality diamond]] is uniquely represented by a certain number of steps of 27edo. It also represents the 13th harmonic very well, and performs quite decently as a 2.3.5.7.13.19 (no-11's, no-17's 19-limit) temperament. It also approximates [[19/10]], [[19/12]], and [[19/14]], so {{dash|0, 7, 13, 25|med}} does quite well as a 10:12:14:19 chord, with the major seventh 25\27 being less than one cent off from 19/10. Octave-inverted, these also form a quite convincing approximation of the main Bohlen–Pierce triads, 3:5:7 and 5:7:9, making 27 the smallest edo that can simulate tritave harmony, although it rapidly becomes rough if extended to the 11 and above, unlike a true tritave based system.


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


Though the [[7-limit]] tuning of 27edo is not highly accurate, it nonetheless is the smallest equal division to represent the 7 odd limit both [[consistent]]ly and distinctly--that is, everything in the 7-limit [[Diamonds|diamond]] is uniquely represented by a certain number of steps of 27 equal. It also represents the 13th harmonic very well, and performs quite decently as a 2.3.5.7.13 temperament
Its step of 44.4{{c}}, as well as the octave-inverted and octave-equivalent versions of it, holds the distinction for having very high [[harmonic entropy]]. In other words, there is a general perception of quartertones as being the most dissonant intervals. This property is shared with all edos between around 20 and 30. Intervals smaller than this tend to be perceived as unison and are more consonant as a result; intervals larger than this have less "tension" and thus are also more consonant.


Its step, as well as the octave-inverted and octave-equivalent versions of it, holds the distinction for having around the highest [[harmonic entropy]] possible and thus is, in theory, most dissonant, assuming the relatively common values of a=2 and s=1%. This property is shared with all edos between around 24 and 30. Intervals smaller than this tend to be perceived as unison and are more consonant as a result; intervals larger than this have less "tension" and thus are also more consonant.
The [[chromatic semitone]] of 27edo, at 178{{c}}, is equal to a submajor second in size, meaning 27edo is a candidate for [[extraclassical tonality]] due to its sharp major third of 444 cents.


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


==Intervals==  
=== Octave stretch ===
|| Degrees of 27-EDO || Cents value coarse/fine
Since the harmonics whose intervals it approximates well (3, 5, 7, 13, and 19) are all tuned sharp of just, 27edo is a prime candidate for [[stretched and compressed tuning|octave compression]]. The local zeta peak around 27 is at 27.086614, which corresponds to a step size of 44.3023{{c}}. More generally, narrowing the steps to between 44.2 and 44.35{{c}} would be better in theory; [[43edt]], [[70ed6]], [[90ed10]], and [[97ed12]] are good options if octave compression is acceptable, and these narrow the octaves by 5.75, 3.53, 4.11, and 2.55{{c}}, respectively.
DMS value ||= Approximate
Ratios* ||= Solfege ||
|| 0 || 0 ||= 1/1 ||= do ||
|| 1 || 44.44, 53.33
13°20' ||= 36/35, 49/48, 50/49 ||= di ||
|| 2 || 88.89, 106.67
26°40' ||= 16/15, 21/20, 25/24 ||= ra ||
|| 3 || 133.33, 160
40° ||= 14/13, 13/12 ||= ru ||
|| 4 || 177.78, 213.33
53°20' ||= 10/9 ||= reh ||
|| 5 || 222.22, 266.67
66°40' ||= 8/7, 9/8 ||= re ||
|| 6 || 266.67, 320
80° ||= 7/6 ||= ma ||
|| 7 || 311.11, 373.33
93°20' ||= 6/5 ||= me ||
|| 8 || 355.56, 426.67
106°40' ||= 16/13 ||= mu ||
|| 9 || 400, 480
120° ||= 5/4 ||= mi ||
|| 10 || 444.44, 513.33
133°20' ||= 9/7, 13/10 ||= mo ||
|| 11 || 488.89, 566.67
146°40' ||= 4/3 ||= fa ||
|| 12 || 533.33, 640
160° ||= 49/36, 48/35 ||= fih ||
|| 13 || 577.78, 693.33
173°20' ||= 7/5, 18/13 ||= fi ||
|| 14 || 622.22, 746.67
186°40' ||= 10/7, 13/9 ||= se ||
|| 15 || 666.67, 800
200° ||= 72/49, 35/24 ||= sih ||
|| 16 || 711.11, 853.33
213°20' ||= 3/2 ||= so/sol ||
|| 17 || 755.56, 906.67
226°40' ||= 14/9, 20/13 ||= lo ||
|| 18 || 800, 960
240° ||= 8/5 ||= le ||
|| 19 || 844.44, 1013.33
253°20' ||= 13/8 ||= lu ||
|| 20 || 888.89, 1066.67
266°40' ||= 5/3 ||= la ||
|| 21 || 933.33, 1120
280° ||= 12/7 ||= li ||
|| 22 || 977.78, 1173.33
293°20' ||= 7/4, 16/9 ||= ta ||
|| 23 || 1022.22, 1226.67
306°40' ||= 9/5 ||= te ||
|| 24 || 1066,67, 1280
320° ||= 13/7, 24/13 ||= tu ||
|| 25 || 1111.11, 1333.33
333°20' ||= 40/21 ||= ti ||
|| 26 || 1155.56, 1386.67
346°40' ||= 35/18, 96/49, 49/25 ||= da ||
|| 27 || 1200, 1440
360° ||= 2/1 ||= do ||
*based on treating 27-EDO as a 2.3.5.7.13 subgroup temperament; other approaches are possible.
==Rank two temperaments==
[[List of 27edo rank two temperaments by badness]]
[[List of edo-distinct 27e rank two temperaments]]
||~ Periods
per octave ||~ Generator ||~ Temperaments ||
|| 1 || 1\27 || [[Quartonic]]/Quarto ||
|| 1 || 2\27 || [[Octacot]]/Octocat ||
|| 1 || 4\27 || [[Tetracot]]/Modus/Wollemia ||
|| 1 || 5\27 || [[Machine]]/Kumonga ||
|| 1 || 7\27 || [[Myna]]/Coleto/Minah ||
|| 1 || 8\27 || [[Beatles]]/Ringo ||
|| 1 || 10\27 || [[Sensi]]/Sensis ||
|| 1 || 11\27 || [[Superpyth]] ||
|| 1 || 13\27 || Fervor ||
|| 3 || 1\27 || [[Semiaug]]/Hemiaug ||
|| 3 || 2\27 || [[Augmented]]/[[augene|Augene]]/Ogene ||
|| 3 || 4\27 || Oodako ||
|| 9 || 1\27 || Terrible version of [[Ennealimmal]]
/ Niner ||
==Commas==
27 EDO tempers out the following commas. (Note: This assumes the val &lt; 27 43 63 76 93 100/1 |.)
||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
||= 128/125 ||&lt; | 7 0 -3 &gt; ||&gt; 41.06 ||= Diesis ||= Augmented Comma ||=  ||
||= 20000/19683 ||&lt; | 5 -9 4 &gt; ||&gt; 27.66 ||= Minimal Diesis ||= Tetracot Comma ||=  ||
||= 78732/78125 ||&lt; | 2 9 -7 &gt; ||&gt; 13.40 ||= Medium Semicomma ||= Sensipent Comma ||=  ||
||=  ||&lt; | 1 -27 18 &gt; ||&gt; 0.86 ||= Ennealimma ||=  ||=  ||
||= 686/675 ||&lt; | 1 -3 -2 3 &gt; ||&gt; 27.99 ||= Senga ||=  ||=  ||
||= 64/63 ||&lt; | 6 -2 0 -1 &gt; ||&gt; 27.26 ||= Septimal Comma ||= Archytas' Comma ||= Leipziger Komma ||
||= 50421/50000 ||&lt; | -4 1 -5 5 &gt; ||&gt; 14.52 ||= Trimyna ||=  ||=  ||
||= 245/243 ||&lt; | 0 -5 1 2 &gt; ||&gt; 14.19 ||= Sensamagic ||=  ||=  ||
||= 126/125 ||&lt; | 1 2 -3 1 &gt; ||&gt; 13.79 ||= Septimal Semicomma ||= Starling Comma ||=  ||
||= 4000/3969 ||&lt; | 5 -4 3 -2 &gt; ||&gt; 13.47 ||= Octagar ||=  ||=  ||
||= 1728/1715 ||&lt; | 6 3 -1 -3 &gt; ||&gt; 13.07 ||= Orwellisma ||= Orwell Comma ||=  ||
||=  ||&lt; | -6 -8 2 5 &gt; ||&gt; 1.12 ||= Wizma ||=  ||=  ||
||= 2401/2400 ||&lt; | -5 -1 -2 4 &gt; ||&gt; 0.72 ||= Breedsma ||=  ||=  ||
||= 4375/4374 ||&lt; | -1 -7 4 1 &gt; ||&gt; 0.40 ||= Ragisma ||=  ||=  ||
||=  ||&lt; | -4 6 -6 3 &gt; ||&gt; 0.33 ||= Landscape Comma ||=  ||=  ||
||= 99/98 ||&lt; | -1 2 0 -2 1 &gt; ||&gt; 17.58 ||= Mothwellsma ||=  ||=  ||
||= 896/891 ||&lt; | 7 -4 0 1 -1 &gt; ||&gt; 9.69 ||= Pentacircle ||=  ||=  ||
||= 385/384 ||&lt; | -7 -1 1 1 1 &gt; ||&gt; 4.50 ||= Keenanisma ||=  ||=  ||
||= 91/90 ||&lt; | -1 -2 -1 1 0 1 &gt; ||&gt; 19.13 ||= Superleap ||=  ||=  ||


=Music=  
=== Subsets and supersets ===
Since 27 factors into primes as 3<sup>3</sup>, 27edo contains [[3edo]] and [[9edo]] as subsets.  Multiplying it by 3 gives [[81edo]], which is a good [[meantone]] tuning.


[[http://www.archive.org/details/MusicForYourEars|Music For Your Ears]] &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;[[http://www.archive.org/download/MusicForYourEars/musicfor.mp3|play]]&lt;/span&gt; by [[Gene Ward Smith]] The central portion is in 27edo, the rest in [[46edo]].
== Intervals ==
&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;[[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Sad%20Like%20Winter%20Leaves.mp3|Sad Like Winter Leaves]]&lt;/span&gt; by Igliashon Jones
{| class="wikitable center-all right-2 left-3"
//[[file:Superpythagorean Waltz.mp3|Superpythagorean Waltz]]// by Igliashon Jones
|-
&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;[[http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of27sonatina.mp3|Galticeran Sonatina]]&lt;/span&gt; by [[http://soundcloud.com/joelgranttaylor/galticeran_sonatina|Joel Taylor]]
! #
&lt;span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link"&gt;[[http://www.youtube.com/watch?v=7QcwKlK6z4c|miniature prelude and fugue]]&lt;/span&gt; by Kosmorsky[[media type="custom" key="10942764"]]
! Cents
&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;[[http://micro.soonlabel.com/27edo/daily20111202-deep-chasm-zeta-cp-1.mp3|Chicago Pile-1]]&lt;/span&gt; by [[Chris Vaisvil]]
! Approximate ratios<ref group="note">{{sg|27et|limit=2.3.5.7.13.19-[[subgroup]]}}</ref>
[[http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Perc-Sitar.mp3|Tetracot Perc-Sitar]] by [[http://soundcloud.com/dustin-schallert/tetracot-perc-sitar|Dustin Schallert]]
! colspan="3" | [[Ups and downs notation]] ([[Enharmonic unisons in ups and downs notation|EUs]]: v<sup>4</sup>A1 and vm2)
[[http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Jam.mp3|Tetracot Jam]] by [[http://soundcloud.com/dustin-schallert/tetracot-jam|Dustin Schallert]]
! [[Interval region]]s
[[http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Pump.mp3|Tetracot Pump]] by [[http://soundcloud.com/dustin-schallert/tetracot-pump|Dustin Schallert]] all in [[27edo]]
! colspan="2" | [[Solfege]]s
[[https://soundcloud.com/dustin-schallert/27-edo-guitar-1|27-EDO Guitar 1 by Dustin Schallert]]</pre></div>
|-
<h4>Original HTML content:</h4>
| 0
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;27edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:1:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x27 tone equal tempertament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:1 --&gt;&lt;span style="color: #0061ff; font-family: 'Times New Roman',Times,serif; font-size: 113%;"&gt;27 tone equal tempertament&lt;/span&gt;&lt;/h1&gt;
| 0.0
&lt;br /&gt;
| [[1/1]]
If octaves are kept pure, 27edo divides the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; in 27 equal parts each exactly 44.444... &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s in size. However, 27 is a prime candidate for &lt;a class="wiki_link" href="/octave%20shrinking"&gt;octave shrinking&lt;/a&gt;, and a step size of 44.3 to 44.35 cents would be reasonable. The reason for this is that 27edo tunes the &lt;a class="wiki_link" href="/5_4"&gt;third&lt;/a&gt;, &lt;a class="wiki_link" href="/3_2"&gt;fifth&lt;/a&gt; and &lt;a class="wiki_link" href="/7_4"&gt;7/4&lt;/a&gt; sharply.&lt;br /&gt;
| P1
&lt;br /&gt;
| perfect unison
Assuming however pure octaves, 27 has a fifth sharp by slightly more than nine cents and a 7/4 sharp by slightly less, and the same 400 cent major third as &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;, sharp 13 2/3 cents. The result is that &lt;a class="wiki_link" href="/6_5"&gt;6/5&lt;/a&gt;, &lt;a class="wiki_link" href="/7_5"&gt;7/5&lt;/a&gt; and especially &lt;a class="wiki_link" href="/7_6"&gt;7/6&lt;/a&gt; are all tuned more accurately than this.&lt;br /&gt;
| D
&lt;br /&gt;
| unison
27edo, with its 400 cent major third, tempers out the &lt;a class="wiki_link" href="/diesis"&gt;diesis&lt;/a&gt; of 128/125, and also the &lt;a class="wiki_link" href="/septimal%20comma"&gt;septimal comma&lt;/a&gt;, 64/63 (and hence 126/125 also.) These it shares with 12edo, making some relationships familiar, and as a consequence they both support augene temperament. It shares with &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt; tempering out the allegedly Bohlen-Pierce comma 245/243 as well as 64/63, so that they both support superpyth temperament, with quite sharp &amp;quot;superpythagorean&amp;quot; fifths giving a sharp 9/7 in place of meantone's 5/4.&lt;br /&gt;
| da
&lt;br /&gt;
| do
Though the &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt; tuning of 27edo is not highly accurate, it nonetheless is the smallest equal division to represent the 7 odd limit both &lt;a class="wiki_link" href="/consistent"&gt;consistent&lt;/a&gt;ly and distinctly--that is, everything in the 7-limit &lt;a class="wiki_link" href="/Diamonds"&gt;diamond&lt;/a&gt; is uniquely represented by a certain number of steps of 27 equal. It also represents the 13th harmonic very well, and performs quite decently as a 2.3.5.7.13 temperament&lt;br /&gt;
|-
&lt;br /&gt;
| 1
Its step, as well as the octave-inverted and octave-equivalent versions of it, holds the distinction for having around the highest &lt;a class="wiki_link" href="/harmonic%20entropy"&gt;harmonic entropy&lt;/a&gt; possible and thus is, in theory, most dissonant, assuming the relatively common values of a=2 and s=1%. This property is shared with all edos between around 24 and 30. Intervals smaller than this tend to be perceived as unison and are more consonant as a result; intervals larger than this have less &amp;quot;tension&amp;quot; and thus are also more consonant.&lt;br /&gt;
| 44.4
&lt;br /&gt;
| [[28/27]], [[36/35]], [[39/38]], [[49/48]], [[50/49]], ''[[81/80]]''
The 27 note system or one similar like a well temperament can be notated very easily, by a variation on the quartertone accidentals. In this case a sharp raises a note just a hair beneath the following nominal (for example C to C# describes the approximate 10/9 and 11/10 interval) and the flat conversely lowers: these are augmented unisons and diminished unisons. Just so, one finds that an accidental can be divided in half, and this fill the remaining places without need for double sharps and double flats. Enharmonically then, E double flat means C half sharp. In other words, the resemblance to quarter tone notation differs in enharmonic divergence. D flat, C half-sharp, D half flat, and C sharp are all different. The composer can decide for himself which tertiary accidental is necessary if he will need redundancy to keep the chromatic pitches within a compass on paper relative to the natural names (C, D, E etc.) otherwise is simple enough and the same tendency for A# to be higher than Bb is not only familiar, though here very exaggerated, to those working with pythagorean scale, but also to many classically trained violinists. et voila&lt;br /&gt;
| ^1, m2
&lt;br /&gt;
| up unison, minor 2nd
&lt;!-- ws:start:WikiTextHeadingRule:3:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x27 tone equal tempertament-Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:3 --&gt;Intervals&lt;/h2&gt;
| ^D, Eb
| diesis
| fra
| di
|-
| 2
| 88.9
| ''[[16/15]]'', [[21/20]], [[25/24]], [[19/18]], [[20/19]]
| ^^1, ^m2
| dup unison, upminor 2nd
| ^^D, ^Eb
| minor second
| fru
| ra
|-
| 3
| 133.3
| [[15/14]], [[14/13]], [[13/12]]
| vA1, ~2
| downaug 1sn, mid 2nd
| vD#, vvE
| neutral second
| ri
| ru
|-
| 4
| 177.8
| [[10/9]]
| A1, vM2
| aug 1sn, downmajor 2nd
| D#, vE
| small major second
| ro
| reh
|-
| 5
| 222.2
| [[8/7]], [[9/8]]
| M2
| major 2nd
| E
| large major second
| ra
| re
|-
| 6
| 266.7
| [[7/6]]
| m3
| minor 3rd
| F
| subminor third
| na
| ma
|-
| 7
| 311.1
| [[6/5]], [[19/16]]
| ^m3
| upminor 3rd
| Gb
| minor third
| nu
| me
|-
| 8
| 355.6
| [[16/13]]
| ~3
| mid 3rd
| ^Gb
| neutral third
| mi
| mu
|-
| 9
| 400.0
| [[5/4]], [[24/19]]
| vM3
| downmajor 3rd
| vF#
| major third
| mo
| mi
|-
| 10
| 444.4
| [[9/7]], [[13/10]]
| M3
| major 3rd
| F#
| supermajor third
| ma
| mo
|-
| 11
| 488.9
| [[4/3]]
| P4
| perfect 4th
| G
| fourth
| fa
| fa
|-
| 12
| 533.3
| [[19/14]], [[26/19]], [[27/20]], [[48/35]]
| ^4
| up 4th
| Ab
| superfourth
| fu/sha
| fih
|-
| 13
| 577.8
| [[7/5]], [[18/13]]
| ~4, ^d5
| mid 4th, updim 5th
| ^^G, ^Ab
| small tritone
| fi/shu
| fi
|-
| 14
| 622.2
| [[10/7]], [[13/9]]
| vA4, ~5
| downaug 4th, mid 5th
| vG#, vvA
| large tritone
| po/si
| se
|-
| 15
| 666.7
| [[19/13]], [[28/19]], [[35/24]], [[40/27]]
| v5
| down fifth
| G#
| subfifth
| pa/so
| sih
|-
| 16
| 711.1
| [[3/2]]
| P5
| perfect 5th
| A
| fifth
| sa
| so/sol
|-
| 17
| 755.6
| [[14/9]], [[20/13]]
| m6
| minor 6th
| Bb
| subminor sixth
| fla
| lo
|-
| 18
| 800.0
| [[8/5]], [[19/12]]
| ^m6
| upminor 6th
| ^Bb
| minor sixth
| flu
| le
|-
| 19
| 844.4
| [[13/8]]
| ~6
| mid 6th
| vA#
| neutral sixth
| li
| lu
|-
| 20
| 888.9
| [[5/3]], [[32/19]]
| vM6
| downmajor 6th
| A#
| major sixth
| lo
| la
|-
| 21
| 933.3
| [[12/7]]
| M6
| major 6th
| B
| supermajor sixth
| la
| li
|-
| 22
| 977.8
| [[7/4]], [[16/9]]
| m7
| minor 7th
| C
| harmonic seventh
| tha
| ta
|-
| 23
| 1022.2
| [[9/5]]
| ^m7
| upminor 7th
| Db
| large minor seventh
| thu
| te
|-
| 24
| 1066.7
| [[13/7]], [[24/13]], [[28/15]]
| ~7
| mid 7th
| ^Db
| neutral seventh
| ti
| tu
|-
| 25
| 1111.1
| ''[[15/8]]'', [[19/10]], [[36/19]], [[40/21]], [[48/25]]
| vM7
| downmajor 7th
| vC#
| major seventh
| to
| ti
|-
| 26
| 1155.6
| [[27/14]], [[35/18]], [[49/25]], [[96/49]], ''[[160/81]]''
| M7
| major 7th
| C#
| supermajor seventh
| ta
| da
|-
| 27
| 1200.0
| [[2/1]]
| P8
| 8ve
| D
| octave
| da
| do
|}
<references group="note" />


&lt;table class="wiki_table"&gt;
=== Interval quality and chord names in color notation ===
    &lt;tr&gt;
Combining ups and downs notation with [[color notation]], qualities can be loosely associated with colors:
        &lt;td&gt;Degrees of 27-EDO&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Cents value coarse/fine&lt;br /&gt;
DMS value&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Approximate&lt;br /&gt;
Ratios*&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Solfege&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;do&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;44.44, 53.33&lt;br /&gt;
13°20'&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;36/35, 49/48, 50/49&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;di&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;88.89, 106.67&lt;br /&gt;
26°40'&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;16/15, 21/20, 25/24&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;ra&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;133.33, 160&lt;br /&gt;
40°&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;14/13, 13/12&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;ru&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;177.78, 213.33&lt;br /&gt;
53°20'&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;10/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;reh&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;222.22, 266.67&lt;br /&gt;
66°40'&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;8/7, 9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;re&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;266.67, 320&lt;br /&gt;
80°&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7/6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;ma&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;311.11, 373.33&lt;br /&gt;
93°20'&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;me&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;355.56, 426.67&lt;br /&gt;
106°40'&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;16/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;mu&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;400, 480&lt;br /&gt;
120°&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;mi&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;444.44, 513.33&lt;br /&gt;
133°20'&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;9/7, 13/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;mo&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;488.89, 566.67&lt;br /&gt;
146°40'&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;fa&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;533.33, 640&lt;br /&gt;
160°&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;49/36, 48/35&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;fih&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;577.78, 693.33&lt;br /&gt;
173°20'&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7/5, 18/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;fi&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;622.22, 746.67&lt;br /&gt;
186°40'&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;10/7, 13/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;se&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;666.67, 800&lt;br /&gt;
200°&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;72/49, 35/24&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;sih&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;711.11, 853.33&lt;br /&gt;
213°20'&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;so/sol&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;755.56, 906.67&lt;br /&gt;
226°40'&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;14/9, 20/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;lo&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;18&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;800, 960&lt;br /&gt;
240°&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;8/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;le&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;844.44, 1013.33&lt;br /&gt;
253°20'&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;13/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;lu&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;20&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;888.89, 1066.67&lt;br /&gt;
266°40'&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;la&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;933.33, 1120&lt;br /&gt;
280°&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;12/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;li&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;22&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;977.78, 1173.33&lt;br /&gt;
293°20'&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7/4, 16/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;ta&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1022.22, 1226.67&lt;br /&gt;
306°40'&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;te&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;24&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1066,67, 1280&lt;br /&gt;
320°&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;13/7, 24/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;tu&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1111.11, 1333.33&lt;br /&gt;
333°20'&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;40/21&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;ti&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;26&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1155.56, 1386.67&lt;br /&gt;
346°40'&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;35/18, 96/49, 49/25&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;da&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1200, 1440&lt;br /&gt;
360°&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;do&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


*based on treating 27-EDO as a 2.3.5.7.13 subgroup temperament; other approaches are possible.&lt;br /&gt;
{| class="wikitable center-all"
&lt;!-- ws:start:WikiTextHeadingRule:5:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x27 tone equal tempertament-Rank two temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:5 --&gt;Rank two temperaments&lt;/h2&gt;
|-
&lt;a class="wiki_link" href="/List%20of%2027edo%20rank%20two%20temperaments%20by%20badness"&gt;List of 27edo rank two temperaments by badness&lt;/a&gt;&lt;br /&gt;
! Quality
&lt;a class="wiki_link" href="/List%20of%20edo-distinct%2027e%20rank%20two%20temperaments"&gt;List of edo-distinct 27e rank two temperaments&lt;/a&gt;&lt;br /&gt;
! [[Color name]]
! Monzo format
! Examples
|-
| rowspan="2" | minor
| zo
| {{monzo| a, b, 0, 1 }}
| 7/6, 7/4
|-
| fourthward wa
| {{monzo| a, b }}, {{nowrap|b &lt; −1}}
| 32/27, 16/9
|-
| upminor
| gu
| {{monzo| a, b, −1 }}
| 6/5, 9/5
|-
| rowspan="2" | mid
| tho
| {{monzo| a, b, 0, 0, 0, 1 }}
| 13/12, 13/8
|-
| thu
| {{monzo| a, b, 0, 0, 0, −1 }}
| 16/13, 24/13
|-
| downmajor
| yo
| {{monzo| a, b, 1 }}
| 5/4, 5/3
|-
| rowspan="2" | major
| fifthward wa
| {{monzo| a, b }}, {{nowrap|b &gt; 1}}
| 9/8, 27/16
|-
| ru
| {{monzo| a, b, 0, −1 }}
| 9/7, 12/7
|}


All 27edo chords can be named using ups and downs. Alterations are always enclosed in parentheses, additions never are. An up or down after the chord root affects the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13). Here are the zo, gu, ilo, yo and ru triads:


&lt;table class="wiki_table"&gt;
{| class="wikitable center-all"
    &lt;tr&gt;
|-
        &lt;th&gt;Periods&lt;br /&gt;
! [[Color notation|Color of the 3rd]]
per octave&lt;br /&gt;
! JI chord
&lt;/th&gt;
! Notes as edosteps
        &lt;th&gt;Generator&lt;br /&gt;
! Notes of C chord
&lt;/th&gt;
! Written name
        &lt;th&gt;Temperaments&lt;br /&gt;
! Spoken name
&lt;/th&gt;
|-
    &lt;/tr&gt;
| zo
    &lt;tr&gt;
| 6:7:9
        &lt;td&gt;1&lt;br /&gt;
| 0–6–16
&lt;/td&gt;
| C–E♭–G
        &lt;td&gt;1\27&lt;br /&gt;
| Cm
&lt;/td&gt;
| C minor
        &lt;td&gt;&lt;a class="wiki_link" href="/Quartonic"&gt;Quartonic&lt;/a&gt;/Quarto&lt;br /&gt;
|-
&lt;/td&gt;
| gu
    &lt;/tr&gt;
| 10:12:15
    &lt;tr&gt;
| 0–7–16
        &lt;td&gt;1&lt;br /&gt;
| C–F♭–G, C–E{{flatup}}–G
&lt;/td&gt;
| C^m
        &lt;td&gt;2\27&lt;br /&gt;
| C upminor
&lt;/td&gt;
|-
        &lt;td&gt;&lt;a class="wiki_link" href="/Octacot"&gt;Octacot&lt;/a&gt;/Octocat&lt;br /&gt;
| ilo
&lt;/td&gt;
| 18:22:27
    &lt;/tr&gt;
| 0–8–16
    &lt;tr&gt;
| C–E{{demiflat2}}–G
        &lt;td&gt;1&lt;br /&gt;
| C~
&lt;/td&gt;
| C mid
        &lt;td&gt;4\27&lt;br /&gt;
|-
&lt;/td&gt;
| yo
        &lt;td&gt;&lt;a class="wiki_link" href="/Tetracot"&gt;Tetracot&lt;/a&gt;/Modus/Wollemia&lt;br /&gt;
| 4:5:6
&lt;/td&gt;
| 0–9–16
    &lt;/tr&gt;
| C–D♯–G, C–E{{naturaldown}}–G
    &lt;tr&gt;
| Cv
        &lt;td&gt;1&lt;br /&gt;
| C downmajor or C down
&lt;/td&gt;
|-
        &lt;td&gt;5\27&lt;br /&gt;
| ru
&lt;/td&gt;
| 14:18:21
        &lt;td&gt;&lt;a class="wiki_link" href="/Machine"&gt;Machine&lt;/a&gt;/Kumonga&lt;br /&gt;
| 0–10–16
&lt;/td&gt;
| C–E–G
    &lt;/tr&gt;
| C
    &lt;tr&gt;
| C major or C
        &lt;td&gt;1&lt;br /&gt;
|}
&lt;/td&gt;
For a more complete list, see [[Ups and downs notation #Chords and chord progressions]]. See also the [[22edo]] page.
        &lt;td&gt;7\27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Myna"&gt;Myna&lt;/a&gt;/Coleto/Minah&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8\27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Beatles"&gt;Beatles&lt;/a&gt;/Ringo&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10\27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Sensi"&gt;Sensi&lt;/a&gt;/Sensis&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11\27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Superpyth"&gt;Superpyth&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13\27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Fervor&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1\27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Semiaug"&gt;Semiaug&lt;/a&gt;/Hemiaug&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2\27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Augmented"&gt;Augmented&lt;/a&gt;/&lt;a class="wiki_link" href="/augene"&gt;Augene&lt;/a&gt;/Ogene&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4\27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Oodako&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1\27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Terrible version of &lt;a class="wiki_link" href="/Ennealimmal"&gt;Ennealimmal&lt;/a&gt;&lt;br /&gt;
/ Niner&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;!-- ws:start:WikiTextHeadingRule:7:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x27 tone equal tempertament-Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:7 --&gt;Commas&lt;/h2&gt;
== Notation ==
27 EDO tempers out the following commas. (Note: This assumes the val &amp;lt; 27 43 63 76 93 100/1 |.)&lt;br /&gt;
{| class="wikitable center-all floatright"
|+ style="font-size: 105%;" | Circle of fifths in 27edo
|- style="white-space: nowrap;"
!Cents
! colspan="2" | Extended<br />Pythagorean<br />notation
! colspan="2" | Quartertone<br />notation
|-
| 0.0
| colspan="2" | C
| colspan="2" | A{{sesquisharp2}}
|-
| 711.1
| colspan="2" | G
| colspan="2" | E{{sesquisharp2}}
|-
| 222.2
| colspan="2" | D
| B{{sesquisharp2}}
| F{{sesquiflat2}}
|-
| 933.3
| colspan="2" | A
| colspan="2" | C{{sesquiflat2}}
|-
| 444.4
| colspan="2" | E
| colspan="2" | G{{sesquiflat2}}
|-
| 1155.6
| colspan="2" | B
| colspan="2" | D{{sesquiflat2}}
|-
| 666.7
| colspan="2" | F♯
| colspan="2" | A{{sesquiflat2}}
|-
| 177.8
| colspan="2" | C♯
| colspan="2" | E{{sesquiflat2}}
|-
| 888.9
| colspan="2" | G♯
| colspan="2" | B{{sesquiflat2}}
|-
| 400.0
| colspan="2" | D♯
| colspan="2" | F{{demiflat2}}
|-
| 1111.1
| colspan="2" | A♯
| colspan="2" | C{{demiflat2}}
|-
| 622.2
| colspan="2" | E♯
| colspan="2" | G{{demiflat2}}
|-
| 133.3
| B♯
| F𝄫
| colspan="2" | D{{demiflat2}}
|-
| 844.4
| F𝄪
| C𝄫
| colspan="2" | A{{demiflat2}}
|-
| 355.6
| C𝄪
| G𝄫
| colspan="2" | E{{demiflat2}}
|-
| 1066.7
| G𝄪
| D𝄫
| colspan="2" | B{{demiflat2}}
|-
| 577.8
| D𝄪
| A𝄫
| colspan="2" | F{{demisharp2}}
|-
| 88.9
| A𝄪
| E𝄫
| colspan="2" | C{{demisharp2}}
|-
| 800.0
| E𝄪
| B𝄫
| colspan="2" | G{{demisharp2}}
|-
| 311.1
| B𝄪
| F♭
| colspan="2" | D{{demisharp2}}
|-
| 1022.2
| colspan="2" | C♭
| colspan="2" | A{{demisharp2}}
|-
| 533.3
| colspan="2" | G♭
| colspan="2" | E{{demisharp2}}
|-
| 44.4
| colspan="2" | D♭
| colspan="2" | B{{demisharp2}}
|-
| 755.6
| colspan="2" | A♭
| colspan="2" | F{{sesquisharp2}}
|-
| 266.7
| colspan="2" | E♭
| colspan="2" | C{{sesquisharp2}}
|-
| 977.8
| colspan="2" | B♭
| colspan="2" | G{{sesquisharp2}}
|-
| 488.9
| colspan="2" | F
| colspan="2" | D{{sesquisharp2}}
|-
| 0.0
| colspan="2" | C
| colspan="2" | A{{sesquisharp2}}
|}


=== Extended Pythagorean notation ===
27edo being a superpythagorean system, the 5/4 major third present in the 4:5:6 chord is technically an augmented second, since (for example) C–E is a 9/7 supermajor third and so the note located 5/4 above C must be notated as D♯. Conversely, the 6/5 minor third of a 10:12:15 chord is actually reached by a diminished fourth, since (for example) D–F is a 7/6 subminor third and so the note located 6/5 above D must be notated as G♭. The diminished 2nd is a descending interval, thus A♯ is higher than B♭. Though here very exaggerated, this should be familiar to those working with the Pythagorean scale (see [[53edo]]), and also to many classically trained violinists.


&lt;table class="wiki_table"&gt;
=== Quartertone notation ===
    &lt;tr&gt;
Using standard [[chain-of-fifths notation]], a sharp (an augmented unison) raises a note by 4 edosteps, just one edostep beneath the following nominal, and the flat conversely lowers. The sharp is quite wide at about 178¢, sounding like a narrow major 2nd. C to C♯ describes the approximate 10/9 and 11/10 interval. An accidental can be divided in half, and the remaining places can then be filled in with half-sharps, half-flats, sesquisharps, and sesquiflats, reducing the need for double sharps and double flats. The half-sharp is notated as a quartertone, but at about 89¢ it sounds more like a narrow semitone. The gamut from C to D is C, D♭, C{{demisharp2}}, D{{demiflat2}}, C♯, and D, with many ascending intervals appearing to be descending on the staff.
        &lt;th&gt;Comma&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Monzo&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Value (Cents)&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Name 1&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Name 2&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Name 3&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;128/125&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;| 7 0 -3 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;41.06&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Diesis&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Augmented Comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;20000/19683&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;| 5 -9 4 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;27.66&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Minimal Diesis&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Tetracot Comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;78732/78125&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;| 2 9 -7 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;13.40&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Medium Semicomma&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Sensipent Comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;| 1 -27 18 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;0.86&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Ennealimma&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;686/675&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;| 1 -3 -2 3 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;27.99&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Senga&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;64/63&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;| 6 -2 0 -1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;27.26&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Septimal Comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Archytas' Comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Leipziger Komma&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;50421/50000&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;| -4 1 -5 5 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;14.52&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Trimyna&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;245/243&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;| 0 -5 1 2 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;14.19&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Sensamagic&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;126/125&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;| 1 2 -3 1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;13.79&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Septimal Semicomma&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Starling Comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;4000/3969&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;| 5 -4 3 -2 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;13.47&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Octagar&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;1728/1715&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;| 6 3 -1 -3 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;13.07&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Orwellisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Orwell Comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;| -6 -8 2 5 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;1.12&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Wizma&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;2401/2400&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;| -5 -1 -2 4 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;0.72&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Breedsma&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;4375/4374&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;| -1 -7 4 1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;0.40&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Ragisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;| -4 6 -6 3 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;0.33&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Landscape Comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;99/98&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;| -1 2 0 -2 1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;17.58&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Mothwellsma&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;896/891&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;| 7 -4 0 1 -1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;9.69&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Pentacircle&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;385/384&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;| -7 -1 1 1 1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;4.50&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Keenanisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;91/90&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: left;"&gt;| -1 -2 -1 1 0 1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;19.13&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Superleap&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
===Ups and downs notation===
&lt;!-- ws:start:WikiTextHeadingRule:9:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:9 --&gt;Music&lt;/h1&gt;
27edo can be notated with [[ups and downs]], spoken as up, dup, downsharp, sharp, upsharp etc. and down, dud, upflat etc. Note that dup is equivalent to dudsharp and dud is equivalent to dupflat.
&lt;br /&gt;
{{Sharpness-sharp4a}}
&lt;a class="wiki_link_ext" href="http://www.archive.org/details/MusicForYourEars" rel="nofollow"&gt;Music For Your Ears&lt;/a&gt; &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;&lt;a class="wiki_link_ext" href="http://www.archive.org/download/MusicForYourEars/musicfor.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;/span&gt; by &lt;a class="wiki_link" href="/Gene%20Ward%20Smith"&gt;Gene Ward Smith&lt;/a&gt; The central portion is in 27edo, the rest in &lt;a class="wiki_link" href="/46edo"&gt;46edo&lt;/a&gt;.&lt;br /&gt;
[[Alternative symbols for ups and downs notation|Alternatively,]] sharps and flats with arrows can be used, borrowed from extended [[Helmholtz–Ellis notation]]:
&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Sad%20Like%20Winter%20Leaves.mp3" rel="nofollow"&gt;Sad Like Winter Leaves&lt;/a&gt;&lt;/span&gt; by Igliashon Jones&lt;br /&gt;
{{Sharpness-sharp4}}
&lt;em&gt;&lt;a href="/file/view/Superpythagorean%20Waltz.mp3/392037262/Superpythagorean%20Waltz.mp3" onclick="ws.common.trackFileLink('/file/view/Superpythagorean%20Waltz.mp3/392037262/Superpythagorean%20Waltz.mp3');"&gt;Superpythagorean Waltz&lt;/a&gt;&lt;/em&gt; by Igliashon Jones&lt;br /&gt;
 
&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of27sonatina.mp3" rel="nofollow"&gt;Galticeran Sonatina&lt;/a&gt;&lt;/span&gt; by &lt;a class="wiki_link_ext" href="http://soundcloud.com/joelgranttaylor/galticeran_sonatina" rel="nofollow"&gt;Joel Taylor&lt;/a&gt;&lt;br /&gt;
=== Sagittal notation ===
&lt;span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link"&gt;&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=7QcwKlK6z4c" rel="nofollow"&gt;miniature prelude and fugue&lt;/a&gt;&lt;/span&gt; by Kosmorsky&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/custom/10942764?h=0&amp;amp;w=0&amp;quot; class=&amp;quot;WikiMedia WikiMediaCustom&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;custom&amp;amp;quot; key=&amp;amp;quot;10942764&amp;amp;quot;&amp;quot; title=&amp;quot;Custom Media&amp;quot;/&amp;gt; --&gt;&lt;script type="text/javascript" src="http://mediaplayer.yahoo.com/js"&gt;
This notation is a subset of the notation for [[54edo #Sagittal notation|54edo]].
&lt;/script&gt;&lt;!-- ws:end:WikiTextMediaRule:0 --&gt;&lt;br /&gt;
 
&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/27edo/daily20111202-deep-chasm-zeta-cp-1.mp3" rel="nofollow"&gt;Chicago Pile-1&lt;/a&gt;&lt;/span&gt; by &lt;a class="wiki_link" href="/Chris%20Vaisvil"&gt;Chris Vaisvil&lt;/a&gt;&lt;br /&gt;
==== Evo and Revo flavors ====
&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Perc-Sitar.mp3" rel="nofollow"&gt;Tetracot Perc-Sitar&lt;/a&gt; by &lt;a class="wiki_link_ext" href="http://soundcloud.com/dustin-schallert/tetracot-perc-sitar" rel="nofollow"&gt;Dustin Schallert&lt;/a&gt;&lt;br /&gt;
<imagemap>
&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Jam.mp3" rel="nofollow"&gt;Tetracot Jam&lt;/a&gt; by &lt;a class="wiki_link_ext" href="http://soundcloud.com/dustin-schallert/tetracot-jam" rel="nofollow"&gt;Dustin Schallert&lt;/a&gt;&lt;br /&gt;
File:27-EDO_Sagittal.svg
&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Pump.mp3" rel="nofollow"&gt;Tetracot Pump&lt;/a&gt; by &lt;a class="wiki_link_ext" href="http://soundcloud.com/dustin-schallert/tetracot-pump" rel="nofollow"&gt;Dustin Schallert&lt;/a&gt; all in &lt;a class="wiki_link" href="/27edo"&gt;27edo&lt;/a&gt;&lt;br /&gt;
desc none
&lt;a class="wiki_link_ext" href="https://soundcloud.com/dustin-schallert/27-edo-guitar-1" rel="nofollow"&gt;27-EDO Guitar 1 by Dustin Schallert&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
rect 80 0 300 50 [[Sagittal_notation]]
rect 487 0 647 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 120 106 [[81/80]]
rect 120 80 270 106 [[8505/8192]]
rect 270 80 380 106 [[27/26]]
default [[File:27-EDO_Sagittal.svg]]
</imagemap>
 
==== Alternative Evo flavor ====
<imagemap>
File:27-EDO_Alternative_Evo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 511 0 671 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 120 106 [[81/80]]
rect 120 80 270 106 [[8505/8192]]
rect 270 80 380 106 [[27/26]]
default [[File:27-EDO_Alternative_Evo_Sagittal.svg]]
</imagemap>
 
==== Evo-SZ flavor ====
<imagemap>
File:27-EDO_Evo-SZ_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 487 0 647 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 120 106 [[81/80]]
rect 120 80 270 106 [[8505/8192]]
rect 270 80 380 106 [[27/26]]
default [[File:27-EDO_Evo-SZ_Sagittal.svg]]
</imagemap>
 
In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation #Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this edo.
 
=== 6L 1s (archeotonic) notation ===
The notation of Tetracot[7]. The generator is the perfect 2nd. Notes are denoted as {{nowrap|LLLLLLs {{=}} CDEFGABC}}, and raising and lowering by a chroma ({{nowrap|L − s}}), 1 edostep in this instance, is denoted by ♯ and ♭.
 
{| class="wikitable center-1 right-2 center-3 mw-collapsible mw-collapsed"
|-
! &#35;
! Cents
! Note
! Name
! Associated ratio
|-
| 0
| 0.0
| C
| perfect unison
| [[1/1]]
|-
| 1
| 44.4
| C#, Dbbb
| aug 1sn, triple-dim 2nd
| [[40/39]], [[45/44]], [[55/54]], [[81/80]]
|-
| 2
| 88.9
| Cx, Dbb
| double-aug 1sn, double-dim 2nd
| [[16/15]], [[25/24]]
|-
| 3
| 133.3
| Db
| dim 2nd
| [[12/11]], [[13/12]]
|-
| 4
| 177.8
| D
| perfect 2nd
| [[10/9]], [[11/10]]
|-
| 5
| 222.2
| D#, Ebbb
| aug 2nd, double-dim 3rd
| [[9/8]]
|-
| 6
| 266.7
| Dx, Ebb
| double-aug 2nd, dim 3rd
| [[15/13]]
|-
| 7
| 311.1
| Eb
| minor 3rd
| [[6/5]]
|-
| 8
| 355.6
| E
| major 3rd
| [[11/9]], [[16/13]]
|-
| 9
| 400.0
| E#, Fbbb
| aug 3rd, double-dim 4th
| [[5/4]]
|-
| 10
| 444.4
| Ex, Fbb
| double-aug 3rd, dim 4th
| [[13/10]]
|-
| 11
| 488.9
| Ex#, Fb
| minor 4th
| [[4/3]]
|-
| 12
| 533.3
| F
| major 4th
| [[15/11]], [[27/20]]
|-
| 13
| 577.8
| F#, Gbbb
| aug 4th, double-dim 5th
| [[11/8]], [[18/13]]
|-
| 14
| 622.2
| Fx, Gbb
| double-aug 4th, dim 5th
| [[13/9]], [[16/11]]
|-
| 15
| 666.7
| Fx#, Gb
| minor 5th
| [[22/15]], [[40/27]]
|-
| 16
| 711.1
| G
| major 5th
| [[3/2]]
|-
| 17
| 755.6
| G#, Abbb
| aug 5th, double-dim 6th
| [[20/13]]
|-
| 18
| 800.0
| Gx, Abb
| double-aug 5th, dim 6th
| [[8/5]]
|-
| 19
| 844.4
| Ab
| minor 6th
| [[13/8]], [[18/11]]
|-
| 20
| 888.9
| A
| major 6th
| [[5/3]]
|-
| 21
| 933.3
| A#, Bbbb
| aug 6th, double-dim 7th
| [[26/15]]
|-
| 22
| 977.8
| Ax, Bbb
| double-aug 6th, dim 7th
| [[16/9]]
|-
| 23
| 1022.2
| Bb
| perfect 7th
| [[9/5]], [[20/11]]
|-
| 24
| 1066.7
| B
| aug 7th
| [[11/6]], [[24/13]]
|-
| 25
| 1111.1
| B#, Cbb
| double-aug 7th, double-dim 8ve
| [[15/8]], [[48/25]]
|-
| 26
| 1155.6
| Bx, Cb
| triple-aug 7th, dim 8ve
| [[39/20]], [[88/45]], [[108/55]], [[160/81]]
|-
| 27
| 1200.0
| C
| 8ve
| 2/1
|}
{{clear}}
 
== Approximation to JI ==
[[File:27ed2.svg|250px|thumb|right|alt=alt : Your browser has no SVG support.|Selected 19-limit intervals approximated in 27edo]]
 
=== Interval mappings ===
{{Q-odd-limit intervals|27}}
{{Q-odd-limit intervals|27.1|apx=val|header=none|tag=none|title=15-odd-limit intervals by 27e val mapping}}
 
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
|-
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{monzo| 43 -27 }}
| {{mapping| 27 43 }}
| −2.89
| 2.88
| 6.50
|-
| 2.3.5
| 128/125, 20000/19683
| {{mapping| 27 43 63 }}
| −3.88
| 2.74
| 6.19
|-
| 2.3.5.7
| 64/63, 126/125, 245/243
| {{mapping| 27 43 63 76 }}
| −3.71
| 2.39
| 5.40
|-
| 2.3.5.7.13
| 64/63, 91/90, 126/125, 169/168
| {{mapping| 27 43 63 76 100 }}
| −3.18
| 2.39
| 5.39
|-
| 2.3.5.7.13.19
| 64/63, 76/75, 91/90, 126/125, 169/168
| {{mapping| 27 43 63 76 100 115 }}
| −3.18
| 2.18
| 4.92
|}
* 27et (27eg val) is lower in relative error than any previous equal temperaments in the 13-, 17-, and 19-limit. The next equal temperaments doing better in those subgroups are [[31edo|31]], 31, and [[46edo|46]], respectively.  
* 27et is particularly strong in the 2.3.5.7.13.19 subgroup. The next equal temperament that does better in this subgroup is [[53edo|53]].
 
=== Uniform maps ===
{{Uniform map|edo=27}}
 
=== Rank-2 temperaments ===
* [[List of 27edo rank two temperaments by badness]]
* [[List of edo-distinct 27e rank two temperaments]]
 
{| class="wikitable center-all left-3 left-4"
|-
! Periods<br>per 8ve
! Generator
! Temperaments
! Mos scales
|-
| 1
| 1\27
| [[Quartonic]] / quarto (27e) / quartz (27)
|
|-
| 1
| 2\27
| [[Octacot]] / octocat (27e)
| [[1L 12s]], [[13L 1s]]
|-
| 1
| 4\27
| [[Tetracot]] (27e) / modus (27e) / wollemia (27e)
| [[1L 5s]], [[6L 1s]], [[7L 6s]], [[7L 13s]]
|-
| 1
| 5\27
| [[Machine]] (27)<br>[[Kumonga]] (27e)
| [[1L 4s]], [[5L 1s]], [[5L 6s]], [[11L 5s]]
|-
| 1
| 7\27
| [[Myna]] (27e) / coleto (27e) / myno (27)<br>[[Oolong]] (27e)
| [[4L 3s]], [[4L 7s]], [[4L 11s]], [[4L 15s]], [[4L 19s]]
|-
| 1
| 8\27
| [[Beatles]] (27e) / ringo (27e) / beetle (27)
| [[3L 4s]], [[7L 3s]], [[10L 7s]]
|-
| 1
| 10\27
| [[Sensi]]
| [[3L 2s]], [[3L 5s]], [[8L 3s]], [[8L 11s]]
|-
| 1
| 11\27
| [[Superpyth]] (27e)
| [[5L 2s]], [[5L 7s]], [[5L 12s]], [[5L 17s]]
|-
| 1
| 13\27
| [[Fervor]] (27e)
| [[2L 3s]], [[2L 5s]], [[2L 7s]], [[2L 9s]], [[2L 11s]], etc. … [[2L 23s]]
|-
| 3
| 1\27
| [[Hemiaug]] (27e)
|
|-
| 3
| 2\27
| [[Augene]] (27e) / Eugene (27)
| [[3L 3s]], [[3L 6s]], [[3L 9s]], [[12L 3s]]
|-
| 3
| 4\27
| [[Oodako]] (27e)<br>[[Terrain]]
| [[3L 3s]], [[6L 3s]], [[6L 9s]], [[6L 15s]]
|-
| 9
| 1\27
| [[Niner]] (27e)<br>[[Ennealimmal]] (out of tune)
| [[9L 9s]]
|}
 
=== Commas ===
27et [[tempering out|tempers out]] the following [[commas]]. (Note: This assumes the patent [[val]], {{val| 27 43 63 76 93 100 }}.)
 
{| class="commatable wikitable center-all left-3 right-4 left-6"
|-
! [[Harmonic limit|Prime<br>limit]]
! [[Ratio]]<ref group="note">{{rd}}</ref>
! [[Monzo]]
! [[Cent]]s
! [[Color name]]
! Name
|-
| 5
| [[128/125]]
| {{monzo| 7 0 -3 }}
| 41.06
| Trigu
| Augmented comma, lesser diesis
|-
| 5
| [[20000/19683]]
| {{monzo| 5 -9 4 }}
| 27.66
| Saquadyo
| Tetracot comma, minimal diesis
|-
| 5
| [[78732/78125]]
| {{monzo| 2 9 -7 }}
| 13.40
| Sepgu
| Sensipent comma
|-
| 5
| <abbr title="7629394531250/7625597484987">(26 digits)</abbr>
| {{monzo| 1 -27 18 }}
| 0.86
| Satritribiyo
| [[Ennealimma]]
|-
| 7
| [[686/675]]
| {{monzo| 1 -3 -2 3 }}
| 27.99
| Trizo-agugu
| Senga
|-
| 7
| [[64/63]]
| {{monzo| 6 -2 0 -1 }}
| 27.26
| Ru
| Septimal comma
|-
| 7
| [[50421/50000]]
| {{monzo| -4 1 -5 5 }}
| 14.52
| Quinzogu
| Trimyna comma
|-
| 7
| [[245/243]]
| {{monzo| 0 -5 1 2 }}
| 14.19
| Zozoyo
| Sensamagic comma
|-
| 7
| [[126/125]]
| {{monzo| 1 2 -3 1 }}
| 13.79
| Zotrigu
| Starling comma
|-
| 7
| [[4000/3969]]
| {{monzo| 5 -4 3 -2 }}
| 13.47
| Rurutriyo
| Octagar comma
|-
| 7
| [[1728/1715]]
| {{monzo| 6 3 -1 -3 }}
| 13.07
| Triru-agu
| Orwellisma
|-
| 7
| <abbr title="40353607/40310784">(16 digits)</abbr>
| {{monzo| -11 -9 0 9 }}
| 1.84
| Tritrizo
| [[Septimal ennealimma]]
|-
| 7
| <abbr title="420175/419904">(12 digits)</abbr>
| {{monzo| -6 -8 2 5 }}
| 1.12
| Quinzo-ayoyo
| [[Wizma]]
|-
| 7
| [[2401/2400]]
| {{monzo| -5 -1 -2 4 }}
| 0.72
| Bizozogu
| Breedsma
|-
| 7
| [[4375/4374]]
| {{monzo| -1 -7 4 1 }}
| 0.40
| Zoquadyo
| Ragisma
|-
| 7
| <abbr title="250047/250000">(12 digits)</abbr>
| {{monzo| -4 6 -6 3 }}
| 0.33
| Trizogugu
| [[Landscape comma]]
|-
| 11
| [[55/54]]
| {{monzo| -1 -3 1 0 1 }}
| 31.77
| Loyo
| Telepathma
|-
| 11
| [[99/98]]
| {{monzo| -1 2 0 -2 1 }}
| 17.58
| Loruru
| Mothwellsma
|-
| 11
| [[896/891]]
| {{monzo| 7 -4 0 1 -1 }}
| 9.69
| Saluzo
| Pentacircle comma
|-
| 11
| [[385/384]]
| {{monzo| -7 -1 1 1 1 }}
| 4.50
| Lozoyo
| Keenanisma
|-
| 13
| [[66/65]]
| {{monzo| 1 1 -1 0 1 -1 }}
| 26.43
| Thulogu
| Winmeanma
|-
| 13
| [[91/90]]
| {{monzo| -1 -2 -1 1 0 1 }}
| 19.13
| Thozogu
| Superleap comma, biome comma
|-
| 13
| [[512/507]]
| {{monzo| 9 -1 0 0 0 -2 }}
| 16.99
| Thuthu
| Tridecimal neutral thirds comma
|-
| 13
| [[325/324]]
| {{monzo| -2 -4 2 0 0 1 }}
| 5.34
| Thoyoyo
| Marveltwin comma
|-
| 13
| [[351/350]]
| {{monzo| -1 3 -2 -1 0 1 }}
| 4.94
| Thorugugu
| Ratwolfsma
|-
| 13
| [[31213/31104]]
| {{monzo| -7 -5 0 4 0 1 }}
| 6.06
| Thoquadzo
| Praveensma
|-
| 17
| [[85/84]]
| {{monzo| -2 -1 1 -1 0 0 1 }}
| 20.49
| Soruyo
| Monk comma
|-
| 17
| [[154/153]]
| {{monzo| 1 -2 0 1 1 0 -1 }}
| 11.28
| Sulozo
| Augustma
|-
| 19
| [[77/76]]
| {{monzo| 2 -1 -2 0 0 0 0 1 }}
| 22.63
| Nulozo
| Small undevicesimal ninth tone
|-
| 19
| [[96/95]]
| {{monzo| 5 1 -1 0 0 0 0 -1 }}
| 18.13
| Nugu
| 19th-partial chroma
|}
<references group="note" />
 
== Scales ==
=== MOS scales ===
{{Main|List of MOS scales in 27edo}}
* Superpyth pentic – Superpyth[5] [[2L 3s]] (gen = 11\27): 5 5 6 5 6
* Superpyth diatonic – Superpyth[7] [[5L 2s]] (gen = 11\27): 5 5 1 5 5 5 1
* Superpyth chromatic – Superpyth[12] [[5L 7s]] (gen = 11\27): 4 1 1 4 1 4 1 4 1 1 4 1
* Superpyth enharmonic – Superpyth[17] [[5L 12s]] (gen = 11\27): 1 3 1 1 3 1 1 1 3 1 1 3 1 1 3 1 1
* Augene[6] [[3L 3s]] (period = 9\27, gen = 2\27): 7 2 7 2 7 2
* Augene[9] [[3L 6s]] (period = 9\27, gen = 2\27): 5 2 2 5 2 2 5 2 2
* Augene[12] [[3L 9s]] (period = 9\27, gen = 2\27): 3 2 2 2 3 2 2 2 3 2 2 2
* Augene[15] [[12L 3s]] (period = 9\27, gen = 2\27): 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2
* Beatles[7] [[3L 4s]] (gen = 8\27): 3 5 3 5 3 5 3
* Beatles[10] [[7L 3s]] (gen = 8\27): 3 3 2 3 3 2 3 3 2 3
* Beatles[17] [[10L 7s]] (gen = 8\27): 2 1 2 1 2 2 1 2 1 2 2 1 2 1 2 2 1
* Sensi[5] [[3L 2s]] (gen = 10\27): 7 3 7 3 7
* Sensi[8] [[3L 5s]] (gen = 10\27): 3 4 3 3 4 3 3 4
* Sensi[11] [[8L 3s]] (gen = 10\27): 3 3 1 3 3 3 1 3 3 3 1
* Machine[5] [[1L 4s]] (gen = 5\27): 5 5 5 5 7
* Machine[6] [[5L 1s]] (gen = 5\27): 5 5 5 5 5 2
* Machine[11] [[5L 6s]] (gen = 5\27): 2 3 2 3 2 3 2 3 2 3 2
* Machine[16] [[11L 5s]] (gen = 5\27): 2 2 1 2 2 1 2 2 1 2 2 1 2 2 1 2
* Tetracot[6] [[1L 5s]] (gen = 4\27): 4 4 4 4 4 7
* Tetracot[7] [[6L 1s]] (gen = 4\27): 4 4 4 4 4 4 3
* Tetracot[13] [[7L 6s]] (gen = 4\27): 3 1 3 1 3 1 3 1 3 1 3 1 3
* Tetracot[20] [[7L 13s]] (gen = 4\27): 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1
* Octacot[13] [[1L 12s]] (gen = 2\27): 2 2 2 2 2 2 2 2 2 2 2 2 3
* Octacot[14] [[13L 1s]] (gen = 2\27): 2 2 2 2 2 2 2 2 2 2 2 2 2 1
* Myna[7] [[4L 3s]] (gen = 7\27): 6 1 6 1 6 1 6
* Myna[11] [[4L 7s]] (gen = 7\27): 5 1 1 5 1 1 5 1 1 5 1
* Myna[15] [[4L 11s]] (gen = 7\27): 4 1 1 1 4 1 1 1 4 1 1 1 4 1 1
* Myna[19] [[4L 15s]] (gen = 7\27): 3 1 1 1 1 3 1 1 1 1 3 1 1 1 1 3 1 1 1
 
=== Other scales ===
* 5-limit / pental / [[The Pinetone System#Pinetone pentatonic|Pinetone major pentatonic]]: 5 4 7 4 7
* 5-limit / pental / [[The Pinetone System#Pinetone pentatonic|Pinetone minor pentatonic]]: 7 4 5 7 4
* enharmonic trichord octave species: 9 2 5 9 2, 2 9 5 2 9
* 5-limit / pental double harmonic  hexatonic (Augmented[6] [[4M]]): 2 7 2 7 7 2, 7 7 2 2 7 2
* Superpyth melodic minor – Superpyth 2|4 #6 #7 or 5|1 b3: 5 1 5 5 5 5 1
* Superpyth harmonic minor – Superpyth 2|4 #7: 5 1 5 5 1 9 1
* Superpyth harmonic major – Superpyth 5|1 b6: 5 5 1 5 1 9 1
* Superpyth double harmonic major – Superpyth 5|1 b2 b6: 1 9 1 5 1 9 1
* [[Zarlino]] / Ptolemy diatonic, "just" major: 5 4 2 5 4 5 2
* "Just" minor (inverse of "just" major): 5 2 4 5 2 5 4
* 5-limit / pental tetrachordal major: 5 4 2 5 5 4 2
* 5-limit / pental tetrachordal minor: 5 2 4 5 5 2 4
* 5-limit / pental melodic minor: 5 2 4 5 4 5 2
* 5-limit / pental harmonic minor: 5 2 4 5 2 7 2
* 5-limit / pental harmonic major: 5 4 2 5 2 7 2
* 5-odd limit tonality diamond: 7 2 2 5 2 2 7
* 7-odd limit tonality diamond: 5 1 1 2 2 2 1 2 2 2 1 1 5
* 9-odd limit tonality diamond: 4 1 1 1 2 1 1 2 1 2 1 1 2 1 1 1 4
* [[SNS (2/1, 3/2, 5/4)-7|5-limit / pental double harmonic major]]: 2 7 2 5 2 7 2
* enharmonic tetrachord octave species: 9 1 1 5 9 1 1, 1 9 1 5 1 9 1 (also Superpyth double harmonic major), 1 1 9 5 1 1 9
* [[The Pinetone System #The Pinetone diatonic|Pinetone diatonic]]: 4 3 4 5 4 3 4
* [[The Pinetone System #Pinetone octatonic scales|Pinetone major-harmonic octatonic]]: 4 3 4 2 3 4 3 4
* [[The Pinetone System #Pinetone octatonic scales|Pinetone minor-harmonic octatonic]]: 4 3 2 4 3 4 4 3
* [[The Pinetone System #Pinetone diminished octatonic|Pinetone diminished octatonic]] / [[Porcusmine]]: 3 4 2 4 3 4 3 4
* [[The Pinetone System #Pinetone harmonic diminished octatonic|Pinetone harmonic diminished]]: 3 4 2 5 2 4 3 4
* [[The Pinetone System #Pinetone chromatic|Pinetone chromatic]] / pinechrome: 1 3 3 1 3 2 3 1 3 3 1 3
* 5-limit / pental double harmonic nonatonic (subset of Augene[12]): 2 5 2 2 5 2 5 2 2, 2 2 5 2 5 2 2 5 2 (Augene[9] [[4M]])
* 5-limit / pental double harmonic decatonic (subset of Augene[12]): 2 5 2 2 3 2 2 5 2 2
* 5-limit / pental double harmonic chromatic: 2 2 3 2 2 3 2 2 2 3 2 2, 2 2 3 2 2 2 3 2 2 3 2 2 (Augene[12] [[4M]])
* [[Blackdye]] / [[syntonic dipentatonic]] (superset of [[Zarlino]]): 1 4 2 4 1 4 2 4 1 4
* [[Blackville]] / [[SNS ((2/1, 3/2)-5, 16/15)-10|5-limit dipentatonic]] (superset of [[Zarlino]]): 3 2 4 2 3 2 4 2 3 2
* Direct sunlight (original/default tuning; subset of [[Sensi]][19]): 1 2 8 5 1 9 1 ((1, 3, 11, 16, 17, 26, 27)\27)
* Hypersakura (original/default tuning; subset of Sensi[19]): 1 10 5 1 10 ((1 11 16 17 27)\27)
 
== Instruments ==
[[File:27edo_Guitar.jpg|200px|thumb|right|Brendan Byrnes, guitarist]]
While playing 27edo instruments requires significantly more frets or keys than 12edo, it is still possible to create physical instruments that can play all its notes. Probably the most notable of these is owned by Brendan Byrnes and played on some of his tracks listed in the music section.
 
However, the frets are very close together and playing high up the neck requires careful use of fingernails for fretting. A skip-fretted guitar would have notes only slightly closer together than 12edo and be easier to play, particularly when tuned in the configuration detailed below.
 
* [[Skip fretting system 27 2 9]]
 
27edo can also be played on the Lumatone, with various layouts discussed here.
 
* [[Lumatone mapping for 27edo]]
 
== Music ==
{{Catrel| 27edo tracks }}
 
; [[Abnormality]]
* [https://www.youtube.com/watch?v=gfGNKd8SWWc ''Boiling''] (2024)
 
; [[Nae Ayy]]
* [https://www.youtube.com/watch?v=Pr5E5brBGuw ''What Happens Next''] (2021)
 
; [[Beheld]]
* [https://www.youtube.com/watch?v=JH4zrwGqv6A ''Thick vibe''] (2023)
 
; [[Gregoire Blanc]]
* [https://youtu.be/a4-JhcaZSUs?feature=shared ''A microtonal teatime jam''] (2023)
 
; [[Brendan Byrnes]]
* [https://youtu.be/sWaqlAgSWcc ''Sunspots''] (2022)
 
; [[Bryan Deister]]
* [https://www.youtube.com/watch?v=hDP8cfJqWOI ''microtonal improvisation in 27edo''] (2023)
 
; [[Francium]]
* [https://www.youtube.com/watch?v=3Ty3FpmAdGA ''Happy Birthday in 27edo''] (2025)
 
; [[Igliashon Jones]]
* [https://web.archive.org/web/20201127012539/http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Sad%20Like%20Winter%20Leaves.mp3 ''Sad Like Winter Leaves''] – in Augene[12] tuned to 27edo
* [[:File:Superpythagorean_Waltz.mp3|''Superpythagorean Waltz'']] (2012)
* [https://pixelarchipelago.bandcamp.com/track/stuttering-anticipation-27edo ''Stuttering Anticipation''] (2021)
 
; [[Peter Kosmorsky]]
* [https://www.youtube.com/watch?v=7QcwKlK6z4c ''miniature prelude and fugue''] (2011)
 
; [[Claudi Meneghin]]
* [https://www.youtube.com/watch?v=nR8orkai8tQ ''Chorale in 27edo for Organ''] (2019)
 
; [[Herman Miller]]
* ''[https://soundcloud.com/morphosyntax-1/nusu-laj-stille-nacht Stille Nacht (cover)]'' (2019)
 
; [[NullPointerException Music]]
* [https://www.youtube.com/watch?v=II817QeOHoQ ''Edolian - Adventure''] (2020)
 
; [[Dustin Schallert]]
* [http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Perc-Sitar.mp3 ''Tetracot Perc-Sitar'']{{dead link}} (on [https://soundcloud.com/dustin-schallert/tetracot-perc-sitar SoundCloud]){{dead link}}
* [http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Jam.mp3 ''Tetracot Jam'']{{dead link}} (on [https://soundcloud.com/dustin-schallert/tetracot-jam SoundCloud]){{dead link}}
* [http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Pump.mp3 ''Tetracot Pump'']{{dead link}} (on [https://soundcloud.com/dustin-schallert/tetracot-pump SoundCloud]){{dead link}}
* [https://soundcloud.com/dustin-schallert/27-edo-guitar-1 ''27-EDO Guitar 1'']{{dead link}}
 
; [[Gene Ward Smith]]
* [https://www.archive.org/details/MusicForYourEars ''Music For Your Ears''] [https://www.archive.org/download/MusicForYourEars/musicfor.mp3 play] – the central portion is in 27edo, the rest in [[46edo]].
 
; [[Joel Taylor]]
* [https://web.archive.org/web/20201127012922/http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of27sonatina.mp3 ''Galticeran Sonatina''] – in Augene[12] tuned to 27edo
 
; [[Tristan Bay]]
* [https://youtu.be/R30aRbNtoIY ''Pitchblende''] (2023)
 
; [[Uncreative Name]]
* [https://www.youtube.com/watch?v=dcQe6ebpGFU ''Autumn''] (2024) – in Blackdye, 27edo tuning
 
; [[Chris Vaisvil]]
* [http://micro.soonlabel.com/27edo/daily20111202-deep-chasm-zeta-cp-1.mp3 ''Chicago Pile-1''] (2011)
 
; [[Xotla]]
* "Funkrotonal" from ''Microtonal Allsorts'' (2023) – [https://open.spotify.com/track/1zjNkbm8kIkuCxtodyFCL0 Spotify] | [https://xotla.bandcamp.com/track/funkrotonal-27edo Bandcamp] | [https://www.youtube.com/watch?v=7gt1BBJuJsE YouTube]
 
[[Category:Augene]]
[[Category:Listen]]
[[Category:Sensi]]
[[Category:Superpyth]]
[[Category:Tetracot]]
[[Category:Twentuning]]
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