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Wikispaces>phylingual **Imported revision 392037438 - Original comment: ** |
Wikispaces>Osmiorisbendi **Imported revision 437651882 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : This revision was by author [[User:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2013-06-11 17:46:26 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>437651882</tt>.<br> | ||
: The revision comment was: <tt></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> | 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> | <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">=<span style="color: #0061ff; font-size: | <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">=<span style="color: #0061ff; font-family: 'Times New Roman',Times,serif; font-size: 113%;">27 tone equal tempertament</span>= | ||
If octaves are kept pure, 27edo divides the [[octave]] in 27 equal parts each exactly 44.444... [[cent]]s in size. However, 27 is a prime candidate for [[octave shrinking]], and a step size of 44.3 to 44.35 cents would be reasonable. The reason for this is that 27edo tunes the [[5_4|third]], [[3_2|fifth]] and [[7_4|7/4]] sharply. | 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. | ||
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=Music= | =Music= | ||
[[http://www.archive.org/details/MusicForYourEars|Music For Your Ears]] <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://www.archive.org/download/MusicForYourEars/musicfor.mp3|play]]//</span> by [[Gene Ward Smith]] The central portion is in 27edo, the rest in [[46edo]]. | [[http://www.archive.org/details/MusicForYourEars|Music For Your Ears]] <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">////[[http://www.archive.org/download/MusicForYourEars/musicfor.mp3|play]]////</span> by [[Gene Ward Smith]] The central portion is in 27edo, the rest in [[46edo]]. | ||
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Sad%20Like%20Winter%20Leaves.mp3|Sad Like Winter Leaves]]//</span> by Igliashon Jones | <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">////[[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Sad%20Like%20Winter%20Leaves.mp3|Sad Like Winter Leaves]]////</span> by Igliashon Jones | ||
[[file:Superpythagorean Waltz.mp3|Superpythagorean Waltz]] by Igliashon Jones | //[[file:Superpythagorean Waltz.mp3|Superpythagorean Waltz]]// by Igliashon Jones | ||
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of27sonatina.mp3|Galticeran Sonatina]]//</span> by [[http://soundcloud.com/joelgranttaylor/galticeran_sonatina|Joel Taylor]] | <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">////[[http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of27sonatina.mp3|Galticeran Sonatina]]////</span> by [[http://soundcloud.com/joelgranttaylor/galticeran_sonatina|Joel Taylor]] | ||
<span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link">//[[http://www.youtube.com/watch?v=7QcwKlK6z4c|miniature prelude and fugue]]//</span> by Kosmorsky[[media type="custom" key="10942764"]] | <span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link">////[[http://www.youtube.com/watch?v=7QcwKlK6z4c|miniature prelude and fugue]]////</span> by Kosmorsky[[media type="custom" key="10942764"]] | ||
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://micro.soonlabel.com/27edo/daily20111202-deep-chasm-zeta-cp-1.mp3|Chicago Pile-1]]//</span> by [[Chris Vaisvil]] | <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">////[[http://micro.soonlabel.com/27edo/daily20111202-deep-chasm-zeta-cp-1.mp3|Chicago Pile-1]]////</span> by [[Chris Vaisvil]] | ||
//[[http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Perc-Sitar.mp3|Tetracot Perc-Sitar]]// by [[http://soundcloud.com/dustin-schallert/tetracot-perc-sitar|Dustin Schallert]] | ////[[http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Perc-Sitar.mp3|Tetracot Perc-Sitar]]//// by [[http://soundcloud.com/dustin-schallert/tetracot-perc-sitar|Dustin Schallert]] | ||
//[[http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Jam.mp3|Tetracot Jam]]// by [[http://soundcloud.com/dustin-schallert/tetracot-jam|Dustin Schallert]] | ////[[http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Jam.mp3|Tetracot Jam]]//// by [[http://soundcloud.com/dustin-schallert/tetracot-jam|Dustin Schallert]] | ||
//[[http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Pump.mp3|Tetracot Pump]]// by [[http://soundcloud.com/dustin-schallert/tetracot-pump|Dustin Schallert]] all in [[27edo]]</pre></div> | ////[[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]]</pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>27edo</title></head><body><!-- ws:start:WikiTextHeadingRule:1:&lt;h1&gt; --><h1 id="toc0"><a name="x27 tone equal tempertament"></a><!-- ws:end:WikiTextHeadingRule:1 --><span style="color: #0061ff; font-size: | <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"><html><head><title>27edo</title></head><body><!-- ws:start:WikiTextHeadingRule:1:&lt;h1&gt; --><h1 id="toc0"><a name="x27 tone equal tempertament"></a><!-- ws:end:WikiTextHeadingRule:1 --><span style="color: #0061ff; font-family: 'Times New Roman',Times,serif; font-size: 113%;">27 tone equal tempertament</span></h1> | ||
<br /> | <br /> | ||
If octaves are kept pure, 27edo divides the <a class="wiki_link" href="/octave">octave</a> in 27 equal parts each exactly 44.444... <a class="wiki_link" href="/cent">cent</a>s in size. However, 27 is a prime candidate for <a class="wiki_link" href="/octave%20shrinking">octave shrinking</a>, and a step size of 44.3 to 44.35 cents would be reasonable. The reason for this is that 27edo tunes the <a class="wiki_link" href="/5_4">third</a>, <a class="wiki_link" href="/3_2">fifth</a> and <a class="wiki_link" href="/7_4">7/4</a> sharply.<br /> | If octaves are kept pure, 27edo divides the <a class="wiki_link" href="/octave">octave</a> in 27 equal parts each exactly 44.444... <a class="wiki_link" href="/cent">cent</a>s in size. However, 27 is a prime candidate for <a class="wiki_link" href="/octave%20shrinking">octave shrinking</a>, and a step size of 44.3 to 44.35 cents would be reasonable. The reason for this is that 27edo tunes the <a class="wiki_link" href="/5_4">third</a>, <a class="wiki_link" href="/3_2">fifth</a> and <a class="wiki_link" href="/7_4">7/4</a> sharply.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:9:&lt;h1&gt; --><h1 id="toc4"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:9 -->Music</h1> | <!-- ws:start:WikiTextHeadingRule:9:&lt;h1&gt; --><h1 id="toc4"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:9 -->Music</h1> | ||
<br /> | <br /> | ||
<a class="wiki_link_ext" href="http://www.archive.org/details/MusicForYourEars" rel="nofollow">Music For Your Ears</a> <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link" | <a class="wiki_link_ext" href="http://www.archive.org/details/MusicForYourEars" rel="nofollow">Music For Your Ears</a> <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://www.archive.org/download/MusicForYourEars/musicfor.mp3" rel="nofollow">play</a></span> by <a class="wiki_link" href="/Gene%20Ward%20Smith">Gene Ward Smith</a> The central portion is in 27edo, the rest in <a class="wiki_link" href="/46edo">46edo</a>.<br /> | ||
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link" | <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Sad%20Like%20Winter%20Leaves.mp3" rel="nofollow">Sad Like Winter Leaves</a></span> by Igliashon Jones<br /> | ||
<a href="/file/view/Superpythagorean%20Waltz.mp3/392037262/Superpythagorean%20Waltz.mp3" onclick="ws.common.trackFileLink('/file/view/Superpythagorean%20Waltz.mp3/392037262/Superpythagorean%20Waltz.mp3');">Superpythagorean Waltz</a> by Igliashon Jones<br /> | <em><a href="/file/view/Superpythagorean%20Waltz.mp3/392037262/Superpythagorean%20Waltz.mp3" onclick="ws.common.trackFileLink('/file/view/Superpythagorean%20Waltz.mp3/392037262/Superpythagorean%20Waltz.mp3');">Superpythagorean Waltz</a></em> by Igliashon Jones<br /> | ||
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link" | <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of27sonatina.mp3" rel="nofollow">Galticeran Sonatina</a></span> by <a class="wiki_link_ext" href="http://soundcloud.com/joelgranttaylor/galticeran_sonatina" rel="nofollow">Joel Taylor</a><br /> | ||
<span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link" | <span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=7QcwKlK6z4c" rel="nofollow">miniature prelude and fugue</a></span> by Kosmorsky<!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/custom/10942764?h=0&amp;w=0&quot; class=&quot;WikiMedia WikiMediaCustom&quot; id=&quot;wikitext@@media@@type=&amp;quot;custom&amp;quot; key=&amp;quot;10942764&amp;quot;&quot; title=&quot;Custom Media&quot;/&gt; --><script type="text/javascript" src="http://mediaplayer.yahoo.com/js"> | ||
</script><!-- ws:end:WikiTextMediaRule:0 --><br /> | </script><!-- ws:end:WikiTextMediaRule:0 --><br /> | ||
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link" | <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/27edo/daily20111202-deep-chasm-zeta-cp-1.mp3" rel="nofollow">Chicago Pile-1</a></span> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br /> | ||
<a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Perc-Sitar.mp3" rel="nofollow">Tetracot Perc-Sitar</a> by <a class="wiki_link_ext" href="http://soundcloud.com/dustin-schallert/tetracot-perc-sitar" rel="nofollow">Dustin Schallert</a><br /> | |||
<a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Jam.mp3" rel="nofollow">Tetracot Jam</a> by <a class="wiki_link_ext" href="http://soundcloud.com/dustin-schallert/tetracot-jam" rel="nofollow">Dustin Schallert</a><br /> | |||
<a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Pump.mp3" rel="nofollow">Tetracot Pump</a> by <a class="wiki_link_ext" href="http://soundcloud.com/dustin-schallert/tetracot-pump" rel="nofollow">Dustin Schallert</a> all in <a class="wiki_link" href="/27edo">27edo</a></body></html></pre></div> |
Revision as of 17:46, 11 June 2013
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author Osmiorisbendi and made on 2013-06-11 17:46:26 UTC.
- The original revision id was 437651882.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
=<span style="color: #0061ff; font-family: 'Times New Roman',Times,serif; font-size: 113%;">27 tone equal tempertament</span>= If octaves are kept pure, 27edo divides the [[octave]] in 27 equal parts each exactly 44.444... [[cent]]s in size. However, 27 is a prime candidate for [[octave shrinking]], and a step size of 44.3 to 44.35 cents would be reasonable. The reason for this is that 27edo tunes the [[5_4|third]], [[3_2|fifth]] and [[7_4|7/4]] sharply. Assuming however pure octaves, 27 has a fifth sharp by slightly more than nine cents and a 7/4 sharp by slightly less, and the same 400 cent major third as [[12edo]], sharp 13 2/3 cents. The result is that [[6_5|6/5]], [[7_5|7/5]] and especially [[7_6|7/6]] are all tuned more accurately than this. 27edo, with its 400 cent major third, tempers out the [[diesis]] of 128/125, and also the [[septimal comma]], 64/63 (and hence 126/125 also.) These it shares with 12edo, making some relationships familiar, and as a consequence they both support augene temperament. It shares with [[22edo]] tempering out the allegedly Bohlen-Pierce comma 245/243 as well as 64/63, so that they both support superpyth temperament, with quite sharp "superpythagorean" fifths giving a sharp 9/7 in place of meantone's 5/4. Though the [[7-limit]] tuning of 27edo is not highly accurate, it nonetheless is the smallest equal division to represent the 7 odd limit both [[consistent]]ly and distinctly--that is, everything in the 7-limit [[Diamonds|diamond]] is uniquely represented by a certain number of steps of 27 equal. It also represents the 13th harmonic very well, and performs quite decently as a 2.3.5.7.13 temperament ==Intervals== || Degrees of 27-EDO || Cents value ||= Approximate Ratios* ||= Solfege || || 0 || 0 ||= 1/1 ||= do || || 1 || 44.44 ||= 36/35, 49/48, 50/49 ||= di || || 2 || 88.89 ||= 16/15, 21/20, 25/24 ||= ra || || 3 || 133.33 ||= 14/13, 13/12 ||= ru || || 4 || 177.78 ||= 10/9 ||= reh || || 5 || 222.22 ||= 8/7, 9/8 ||= re || || 6 || 266.67 ||= 7/6 ||= ma || || 7 || 311.11 ||= 6/5 ||= me || || 8 || 355.56 ||= 16/13 ||= mu || || 9 || 400 ||= 5/4 ||= mi || || 10 || 444.44 ||= 9/7, 13/10 ||= mo || || 11 || 488.89 ||= 4/3 ||= fa || || 12 || 533.33 ||= 49/36, 48/35 ||= fih || || 13 || 577.78 ||= 7/5, 18/13 ||= fi || || 14 || 622.22 ||= 10/7, 13/9 ||= se || || 15 || 666.67 ||= 72/49, 35/24 ||= sih || || 16 || 711.11 ||= 3/2 ||= so/sol || || 17 || 755.56 ||= 14/9, 20/13 ||= lo || || 18 || 800 ||= 8/5 ||= le || || 19 || 844.44 ||= 13/8 ||= lu || || 20 || 888.89 ||= 5/3 ||= la || || 21 || 933.33 ||= 12/7 ||= li || || 22 || 977.78 ||= 7/4, 16/9 ||= ta || || 23 || 1022.22 ||= 9/5 ||= te || || 24 || 1066,67 ||= 13/7, 24/13 ||= tu || || 25 || 1111.11 ||= 40/21 ||= ti || || 26 || 1155.56 ||= 35/18, 96/49, 49/25 ||= da || || 27 || 1200 ||= 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 < 27 43 63 76 93 100 |.) ||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 || ||= 128/125 ||< | 7 0 -3 > ||> 41.06 ||= Diesis ||= Augmented Comma ||= || ||= 20000/19683 ||< | 5 -9 4 > ||> 27.66 ||= Minimal Diesis ||= Tetracot Comma ||= || ||= 78732/78125 ||< | 2 9 -7 > ||> 13.40 ||= Medium Semicomma ||= Sensipent Comma ||= || ||= 4711802/4709457 ||< | 1 -27 18 > ||> 0.86 ||= Ennealimma ||= ||= || ||= 686/675 ||< | 1 -3 -2 3 > ||> 27.99 ||= Senga ||= ||= || ||= 64/63 ||< | 6 -2 0 -1 > ||> 27.26 ||= Septimal Comma ||= Archytas' Comma ||= Leipziger Komma || ||= 50421/50000 ||< | -4 1 -5 5 > ||> 14.52 ||= Trimyna ||= ||= || ||= 245/243 ||< | 0 -5 1 2 > ||> 14.19 ||= Sensamagic ||= ||= || ||= 126/125 ||< | 1 2 -3 1 > ||> 13.79 ||= Septimal Semicomma ||= Starling Comma ||= || ||= 4000/3969 ||< | 5 -4 3 -2 > ||> 13.47 ||= Octagar ||= ||= || ||= 1728/1715 ||< | 6 3 -1 -3 > ||> 13.07 ||= Orwellisma ||= Orwell Comma ||= || ||= 420175/419904 ||< | -6 -8 2 5 > ||> 1.12 ||= Wizma ||= ||= || ||= 2401/2400 ||< | -5 -1 -2 4 > ||> 0.72 ||= Breedsma ||= ||= || ||= 4375/4374 ||< | -1 -7 4 1 > ||> 0.40 ||= Ragisma ||= ||= || ||= 250047/250000 ||< | -4 6 -6 3 > ||> 0.33 ||= Landscape Comma ||= ||= || ||= 99/98 ||< | -1 2 0 -2 1 > ||> 17.58 ||= Mothwellsma ||= ||= || ||= 896/891 ||< | 7 -4 0 1 -1 > ||> 9.69 ||= Pentacircle ||= ||= || ||= 385/384 ||< | -7 -1 1 1 1 > ||> 4.50 ||= Keenanisma ||= ||= || ||= 91/90 ||< | -1 -2 -1 1 0 1 > ||> 19.13 ||= Superleap ||= ||= || =Music= [[http://www.archive.org/details/MusicForYourEars|Music For Your Ears]] <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">////[[http://www.archive.org/download/MusicForYourEars/musicfor.mp3|play]]////</span> by [[Gene Ward Smith]] The central portion is in 27edo, the rest in [[46edo]]. <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">////[[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Sad%20Like%20Winter%20Leaves.mp3|Sad Like Winter Leaves]]////</span> by Igliashon Jones //[[file:Superpythagorean Waltz.mp3|Superpythagorean Waltz]]// by Igliashon Jones <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">////[[http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of27sonatina.mp3|Galticeran Sonatina]]////</span> by [[http://soundcloud.com/joelgranttaylor/galticeran_sonatina|Joel Taylor]] <span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link">////[[http://www.youtube.com/watch?v=7QcwKlK6z4c|miniature prelude and fugue]]////</span> by Kosmorsky[[media type="custom" key="10942764"]] <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">////[[http://micro.soonlabel.com/27edo/daily20111202-deep-chasm-zeta-cp-1.mp3|Chicago Pile-1]]////</span> by [[Chris Vaisvil]] ////[[http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Perc-Sitar.mp3|Tetracot Perc-Sitar]]//// by [[http://soundcloud.com/dustin-schallert/tetracot-perc-sitar|Dustin Schallert]] ////[[http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Jam.mp3|Tetracot Jam]]//// by [[http://soundcloud.com/dustin-schallert/tetracot-jam|Dustin Schallert]] ////[[http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Pump.mp3|Tetracot Pump]]//// by [[http://soundcloud.com/dustin-schallert/tetracot-pump|Dustin Schallert]] all in [[27edo]]
Original HTML content:
<html><head><title>27edo</title></head><body><!-- ws:start:WikiTextHeadingRule:1:<h1> --><h1 id="toc0"><a name="x27 tone equal tempertament"></a><!-- ws:end:WikiTextHeadingRule:1 --><span style="color: #0061ff; font-family: 'Times New Roman',Times,serif; font-size: 113%;">27 tone equal tempertament</span></h1> <br /> If octaves are kept pure, 27edo divides the <a class="wiki_link" href="/octave">octave</a> in 27 equal parts each exactly 44.444... <a class="wiki_link" href="/cent">cent</a>s in size. However, 27 is a prime candidate for <a class="wiki_link" href="/octave%20shrinking">octave shrinking</a>, and a step size of 44.3 to 44.35 cents would be reasonable. The reason for this is that 27edo tunes the <a class="wiki_link" href="/5_4">third</a>, <a class="wiki_link" href="/3_2">fifth</a> and <a class="wiki_link" href="/7_4">7/4</a> sharply.<br /> <br /> Assuming however pure octaves, 27 has a fifth sharp by slightly more than nine cents and a 7/4 sharp by slightly less, and the same 400 cent major third as <a class="wiki_link" href="/12edo">12edo</a>, sharp 13 2/3 cents. The result is that <a class="wiki_link" href="/6_5">6/5</a>, <a class="wiki_link" href="/7_5">7/5</a> and especially <a class="wiki_link" href="/7_6">7/6</a> are all tuned more accurately than this.<br /> <br /> 27edo, with its 400 cent major third, tempers out the <a class="wiki_link" href="/diesis">diesis</a> of 128/125, and also the <a class="wiki_link" href="/septimal%20comma">septimal comma</a>, 64/63 (and hence 126/125 also.) These it shares with 12edo, making some relationships familiar, and as a consequence they both support augene temperament. It shares with <a class="wiki_link" href="/22edo">22edo</a> tempering out the allegedly Bohlen-Pierce comma 245/243 as well as 64/63, so that they both support superpyth temperament, with quite sharp "superpythagorean" fifths giving a sharp 9/7 in place of meantone's 5/4.<br /> <br /> Though the <a class="wiki_link" href="/7-limit">7-limit</a> tuning of 27edo is not highly accurate, it nonetheless is the smallest equal division to represent the 7 odd limit both <a class="wiki_link" href="/consistent">consistent</a>ly and distinctly--that is, everything in the 7-limit <a class="wiki_link" href="/Diamonds">diamond</a> is uniquely represented by a certain number of steps of 27 equal. It also represents the 13th harmonic very well, and performs quite decently as a 2.3.5.7.13 temperament<br /> <br /> <!-- ws:start:WikiTextHeadingRule:3:<h2> --><h2 id="toc1"><a name="x27 tone equal tempertament-Intervals"></a><!-- ws:end:WikiTextHeadingRule:3 -->Intervals</h2> <table class="wiki_table"> <tr> <td>Degrees of 27-EDO<br /> </td> <td>Cents value<br /> </td> <td style="text-align: center;">Approximate<br /> Ratios*<br /> </td> <td style="text-align: center;">Solfege<br /> </td> </tr> <tr> <td>0<br /> </td> <td>0<br /> </td> <td style="text-align: center;">1/1<br /> </td> <td style="text-align: center;">do<br /> </td> </tr> <tr> <td>1<br /> </td> <td>44.44<br /> </td> <td style="text-align: center;">36/35, 49/48, 50/49<br /> </td> <td style="text-align: center;">di<br /> </td> </tr> <tr> <td>2<br /> </td> <td>88.89<br /> </td> <td style="text-align: center;">16/15, 21/20, 25/24<br /> </td> <td style="text-align: center;">ra<br /> </td> </tr> <tr> <td>3<br /> </td> <td>133.33<br /> </td> <td style="text-align: center;">14/13, 13/12<br /> </td> <td style="text-align: center;">ru<br /> </td> </tr> <tr> <td>4<br /> </td> <td>177.78<br /> </td> <td style="text-align: center;">10/9<br /> </td> <td style="text-align: center;">reh<br /> </td> </tr> <tr> <td>5<br /> </td> <td>222.22<br /> </td> <td style="text-align: center;">8/7, 9/8<br /> </td> <td style="text-align: center;">re<br /> </td> </tr> <tr> <td>6<br /> </td> <td>266.67<br /> </td> <td style="text-align: center;">7/6<br /> </td> <td style="text-align: center;">ma<br /> </td> </tr> <tr> <td>7<br /> </td> <td>311.11<br /> </td> <td style="text-align: center;">6/5<br /> </td> <td style="text-align: center;">me<br /> </td> </tr> <tr> <td>8<br /> </td> <td>355.56<br /> </td> <td style="text-align: center;">16/13<br /> </td> <td style="text-align: center;">mu<br /> </td> </tr> <tr> <td>9<br /> </td> <td>400<br /> </td> <td style="text-align: center;">5/4<br /> </td> <td style="text-align: center;">mi<br /> </td> </tr> <tr> <td>10<br /> </td> <td>444.44<br /> </td> <td style="text-align: center;">9/7, 13/10<br /> </td> <td style="text-align: center;">mo<br /> </td> </tr> <tr> <td>11<br /> </td> <td>488.89<br /> </td> <td style="text-align: center;">4/3<br /> </td> <td style="text-align: center;">fa<br /> </td> </tr> <tr> <td>12<br /> </td> <td>533.33<br /> </td> <td style="text-align: center;">49/36, 48/35<br /> </td> <td style="text-align: center;">fih<br /> </td> </tr> <tr> <td>13<br /> </td> <td>577.78<br /> </td> <td style="text-align: center;">7/5, 18/13<br /> </td> <td style="text-align: center;">fi<br /> </td> </tr> <tr> <td>14<br /> </td> <td>622.22<br /> </td> <td style="text-align: center;">10/7, 13/9<br /> </td> <td style="text-align: center;">se<br /> </td> </tr> <tr> <td>15<br /> </td> <td>666.67<br /> </td> <td style="text-align: center;">72/49, 35/24<br /> </td> <td style="text-align: center;">sih<br /> </td> </tr> <tr> <td>16<br /> </td> <td>711.11<br /> </td> <td style="text-align: center;">3/2<br /> </td> <td style="text-align: center;">so/sol<br /> </td> </tr> <tr> <td>17<br /> </td> <td>755.56<br /> </td> <td style="text-align: center;">14/9, 20/13<br /> </td> <td style="text-align: center;">lo<br /> </td> </tr> <tr> <td>18<br /> </td> <td>800<br /> </td> <td style="text-align: center;">8/5<br /> </td> <td style="text-align: center;">le<br /> </td> </tr> <tr> <td>19<br /> </td> <td>844.44<br /> </td> <td style="text-align: center;">13/8<br /> </td> <td style="text-align: center;">lu<br /> </td> </tr> <tr> <td>20<br /> </td> <td>888.89<br /> </td> <td style="text-align: center;">5/3<br /> </td> <td style="text-align: center;">la<br /> </td> </tr> <tr> <td>21<br /> </td> <td>933.33<br /> </td> <td style="text-align: center;">12/7<br /> </td> <td style="text-align: center;">li<br /> </td> </tr> <tr> <td>22<br /> </td> <td>977.78<br /> </td> <td style="text-align: center;">7/4, 16/9<br /> </td> <td style="text-align: center;">ta<br /> </td> </tr> <tr> <td>23<br /> </td> <td>1022.22<br /> </td> <td style="text-align: center;">9/5<br /> </td> <td style="text-align: center;">te<br /> </td> </tr> <tr> <td>24<br /> </td> <td>1066,67<br /> </td> <td style="text-align: center;">13/7, 24/13<br /> </td> <td style="text-align: center;">tu<br /> </td> </tr> <tr> <td>25<br /> </td> <td>1111.11<br /> </td> <td style="text-align: center;">40/21<br /> </td> <td style="text-align: center;">ti<br /> </td> </tr> <tr> <td>26<br /> </td> <td>1155.56<br /> </td> <td style="text-align: center;">35/18, 96/49, 49/25<br /> </td> <td style="text-align: center;">da<br /> </td> </tr> <tr> <td>27<br /> </td> <td>1200<br /> </td> <td style="text-align: center;">2/1<br /> </td> <td style="text-align: center;">do<br /> </td> </tr> </table> *based on treating 27-EDO as a 2.3.5.7.13 subgroup temperament; other approaches are possible.<br /> <!-- ws:start:WikiTextHeadingRule:5:<h2> --><h2 id="toc2"><a name="x27 tone equal tempertament-Rank two temperaments"></a><!-- ws:end:WikiTextHeadingRule:5 -->Rank two temperaments</h2> <a class="wiki_link" href="/List%20of%2027edo%20rank%20two%20temperaments%20by%20badness">List of 27edo rank two temperaments by badness</a><br /> <a class="wiki_link" href="/List%20of%20edo-distinct%2027e%20rank%20two%20temperaments">List of edo-distinct 27e rank two temperaments</a><br /> <table class="wiki_table"> <tr> <th>Periods<br /> per octave<br /> </th> <th>Generator<br /> </th> <th>Temperaments<br /> </th> </tr> <tr> <td>1<br /> </td> <td>1\27<br /> </td> <td><a class="wiki_link" href="/Quartonic">Quartonic</a>/Quarto<br /> </td> </tr> <tr> <td>1<br /> </td> <td>2\27<br /> </td> <td><a class="wiki_link" href="/Octacot">Octacot</a>/Octocat<br /> </td> </tr> <tr> <td>1<br /> </td> <td>4\27<br /> </td> <td><a class="wiki_link" href="/Tetracot">Tetracot</a>/Modus/Wollemia<br /> </td> </tr> <tr> <td>1<br /> </td> <td>5\27<br /> </td> <td><a class="wiki_link" href="/Machine">Machine</a>/Kumonga<br /> </td> </tr> <tr> <td>1<br /> </td> <td>7\27<br /> </td> <td><a class="wiki_link" href="/Myna">Myna</a>/Coleto/Minah<br /> </td> </tr> <tr> <td>1<br /> </td> <td>8\27<br /> </td> <td><a class="wiki_link" href="/Beatles">Beatles</a>/Ringo<br /> </td> </tr> <tr> <td>1<br /> </td> <td>10\27<br /> </td> <td><a class="wiki_link" href="/Sensi">Sensi</a>/Sensis<br /> </td> </tr> <tr> <td>1<br /> </td> <td>11\27<br /> </td> <td><a class="wiki_link" href="/Superpyth">Superpyth</a><br /> </td> </tr> <tr> <td>1<br /> </td> <td>13\27<br /> </td> <td>Fervor<br /> </td> </tr> <tr> <td>3<br /> </td> <td>1\27<br /> </td> <td><a class="wiki_link" href="/Semiaug">Semiaug</a>/Hemiaug<br /> </td> </tr> <tr> <td>3<br /> </td> <td>2\27<br /> </td> <td><a class="wiki_link" href="/Augmented">Augmented</a>/<a class="wiki_link" href="/augene">Augene</a>/Ogene<br /> </td> </tr> <tr> <td>3<br /> </td> <td>4\27<br /> </td> <td>Oodako<br /> </td> </tr> <tr> <td>9<br /> </td> <td>1\27<br /> </td> <td>Terrible version of <a class="wiki_link" href="/Ennealimmal">Ennealimmal</a><br /> / Niner<br /> </td> </tr> </table> <!-- ws:start:WikiTextHeadingRule:7:<h2> --><h2 id="toc3"><a name="x27 tone equal tempertament-Commas"></a><!-- ws:end:WikiTextHeadingRule:7 -->Commas</h2> 27 EDO tempers out the following commas. (Note: This assumes the val < 27 43 63 76 93 100 |.)<br /> <table class="wiki_table"> <tr> <th>Comma<br /> </th> <th>Monzo<br /> </th> <th>Value (Cents)<br /> </th> <th>Name 1<br /> </th> <th>Name 2<br /> </th> <th>Name 3<br /> </th> </tr> <tr> <td style="text-align: center;">128/125<br /> </td> <td style="text-align: left;">| 7 0 -3 ><br /> </td> <td style="text-align: right;">41.06<br /> </td> <td style="text-align: center;">Diesis<br /> </td> <td style="text-align: center;">Augmented Comma<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">20000/19683<br /> </td> <td style="text-align: left;">| 5 -9 4 ><br /> </td> <td style="text-align: right;">27.66<br /> </td> <td style="text-align: center;">Minimal Diesis<br /> </td> <td style="text-align: center;">Tetracot Comma<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">78732/78125<br /> </td> <td style="text-align: left;">| 2 9 -7 ><br /> </td> <td style="text-align: right;">13.40<br /> </td> <td style="text-align: center;">Medium Semicomma<br /> </td> <td style="text-align: center;">Sensipent Comma<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">4711802/4709457<br /> </td> <td style="text-align: left;">| 1 -27 18 ><br /> </td> <td style="text-align: right;">0.86<br /> </td> <td style="text-align: center;">Ennealimma<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">686/675<br /> </td> <td style="text-align: left;">| 1 -3 -2 3 ><br /> </td> <td style="text-align: right;">27.99<br /> </td> <td style="text-align: center;">Senga<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">64/63<br /> </td> <td style="text-align: left;">| 6 -2 0 -1 ><br /> </td> <td style="text-align: right;">27.26<br /> </td> <td style="text-align: center;">Septimal Comma<br /> </td> <td style="text-align: center;">Archytas' Comma<br /> </td> <td style="text-align: center;">Leipziger Komma<br /> </td> </tr> <tr> <td style="text-align: center;">50421/50000<br /> </td> <td style="text-align: left;">| -4 1 -5 5 ><br /> </td> <td style="text-align: right;">14.52<br /> </td> <td style="text-align: center;">Trimyna<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">245/243<br /> </td> <td style="text-align: left;">| 0 -5 1 2 ><br /> </td> <td style="text-align: right;">14.19<br /> </td> <td style="text-align: center;">Sensamagic<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">126/125<br /> </td> <td style="text-align: left;">| 1 2 -3 1 ><br /> </td> <td style="text-align: right;">13.79<br /> </td> <td style="text-align: center;">Septimal Semicomma<br /> </td> <td style="text-align: center;">Starling Comma<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">4000/3969<br /> </td> <td style="text-align: left;">| 5 -4 3 -2 ><br /> </td> <td style="text-align: right;">13.47<br /> </td> <td style="text-align: center;">Octagar<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">1728/1715<br /> </td> <td style="text-align: left;">| 6 3 -1 -3 ><br /> </td> <td style="text-align: right;">13.07<br /> </td> <td style="text-align: center;">Orwellisma<br /> </td> <td style="text-align: center;">Orwell Comma<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">420175/419904<br /> </td> <td style="text-align: left;">| -6 -8 2 5 ><br /> </td> <td style="text-align: right;">1.12<br /> </td> <td style="text-align: center;">Wizma<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">2401/2400<br /> </td> <td style="text-align: left;">| -5 -1 -2 4 ><br /> </td> <td style="text-align: right;">0.72<br /> </td> <td style="text-align: center;">Breedsma<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">4375/4374<br /> </td> <td style="text-align: left;">| -1 -7 4 1 ><br /> </td> <td style="text-align: right;">0.40<br /> </td> <td style="text-align: center;">Ragisma<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">250047/250000<br /> </td> <td style="text-align: left;">| -4 6 -6 3 ><br /> </td> <td style="text-align: right;">0.33<br /> </td> <td style="text-align: center;">Landscape Comma<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">99/98<br /> </td> <td style="text-align: left;">| -1 2 0 -2 1 ><br /> </td> <td style="text-align: right;">17.58<br /> </td> <td style="text-align: center;">Mothwellsma<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">896/891<br /> </td> <td style="text-align: left;">| 7 -4 0 1 -1 ><br /> </td> <td style="text-align: right;">9.69<br /> </td> <td style="text-align: center;">Pentacircle<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">385/384<br /> </td> <td style="text-align: left;">| -7 -1 1 1 1 ><br /> </td> <td style="text-align: right;">4.50<br /> </td> <td style="text-align: center;">Keenanisma<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td style="text-align: center;">91/90<br /> </td> <td style="text-align: left;">| -1 -2 -1 1 0 1 ><br /> </td> <td style="text-align: right;">19.13<br /> </td> <td style="text-align: center;">Superleap<br /> </td> <td style="text-align: center;"><br /> </td> <td style="text-align: center;"><br /> </td> </tr> </table> <br /> <!-- ws:start:WikiTextHeadingRule:9:<h1> --><h1 id="toc4"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:9 -->Music</h1> <br /> <a class="wiki_link_ext" href="http://www.archive.org/details/MusicForYourEars" rel="nofollow">Music For Your Ears</a> <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://www.archive.org/download/MusicForYourEars/musicfor.mp3" rel="nofollow">play</a></span> by <a class="wiki_link" href="/Gene%20Ward%20Smith">Gene Ward Smith</a> The central portion is in 27edo, the rest in <a class="wiki_link" href="/46edo">46edo</a>.<br /> <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Sad%20Like%20Winter%20Leaves.mp3" rel="nofollow">Sad Like Winter Leaves</a></span> by Igliashon Jones<br /> <em><a href="/file/view/Superpythagorean%20Waltz.mp3/392037262/Superpythagorean%20Waltz.mp3" onclick="ws.common.trackFileLink('/file/view/Superpythagorean%20Waltz.mp3/392037262/Superpythagorean%20Waltz.mp3');">Superpythagorean Waltz</a></em> by Igliashon Jones<br /> <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of27sonatina.mp3" rel="nofollow">Galticeran Sonatina</a></span> by <a class="wiki_link_ext" href="http://soundcloud.com/joelgranttaylor/galticeran_sonatina" rel="nofollow">Joel Taylor</a><br /> <span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=7QcwKlK6z4c" rel="nofollow">miniature prelude and fugue</a></span> by Kosmorsky<!-- ws:start:WikiTextMediaRule:0:<img src="http://www.wikispaces.com/site/embedthumbnail/custom/10942764?h=0&w=0" class="WikiMedia WikiMediaCustom" id="wikitext@@media@@type=&quot;custom&quot; key=&quot;10942764&quot;" title="Custom Media"/> --><script type="text/javascript" src="http://mediaplayer.yahoo.com/js"> </script><!-- ws:end:WikiTextMediaRule:0 --><br /> <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/27edo/daily20111202-deep-chasm-zeta-cp-1.mp3" rel="nofollow">Chicago Pile-1</a></span> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br /> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Perc-Sitar.mp3" rel="nofollow">Tetracot Perc-Sitar</a> by <a class="wiki_link_ext" href="http://soundcloud.com/dustin-schallert/tetracot-perc-sitar" rel="nofollow">Dustin Schallert</a><br /> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Jam.mp3" rel="nofollow">Tetracot Jam</a> by <a class="wiki_link_ext" href="http://soundcloud.com/dustin-schallert/tetracot-jam" rel="nofollow">Dustin Schallert</a><br /> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Pump.mp3" rel="nofollow">Tetracot Pump</a> by <a class="wiki_link_ext" href="http://soundcloud.com/dustin-schallert/tetracot-pump" rel="nofollow">Dustin Schallert</a> all in <a class="wiki_link" href="/27edo">27edo</a></body></html>