14edo: Difference between revisions

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=<span style="color: #790025; font-family: 'Times New Roman',Times,serif; font-size: 109%;">[[media type="custom" key="10021329"]]14 tone equal temperament</span>= 

==**14-EDO intervals:**== 
|| **DEGREE** || **NOTE** || **CENTS** ||= **Approximate**
**Ratios*** ||= **Nearest**
**Harmonic** || **Interval Type** ||
|| 0 || C || 0 ||= 1/1 ||= 1 || Unison ||
|| 1 || C* || 85.714 ||= 81/77, 126/121 ||= 67 || Narrow Minor 2nd ||
|| 2 || D || 171.429 ||= 11/10, 10/9 ||= 71 || Neutral 2nd, or 
Narrow Major 2nd ||
|| 3· || D* || 257.143 ||= 81/70, 90/77 ||= 37 || Subminor 3rd ||
|| 4 || E || 342.857 ||= 11/9 ||= 39 || Neutral 3rd ||
|| 5· || E* || 428.571 ||= 9/7, 14/11 ||= 41 || Supermajor 3rd ||
|| 6 || F || 514.286 ||= 110/81, 121/90 ||= 43 || Wide 4th ||
|| 7· || F* || 600 ||= 7/5, 10/7 ||= 91 || Tritone ||
|| 8 || G || 685.714 ||= 81/55, 180/121 ||= 95 || Narrow 5th ||
|| 9· || G* || 771.429 ||= 14/9, 11/7 ||= 25 || Subminor 6th ||
|| 10 || A || 857.143 ||= 18/11 ||= 105 || Neutral 6th ||
|| 11· || A* || 942.857 ||= 140/81, 77/45 ||= 55 || Supermajor 6th ||
|| 12 || B || 1028.571 ||= 20/11, 9/5 ||= 29 || Neutral 7th, or
Wide Minor 7th ||
|| 13 || B* || 1114.286 ||= 154/81, 121/63 ||= 61 || Wide Major 7th ||
|| 14··(or 0) || C || 1200 ||= 2/1 ||= 2 || Octave ||
*based on treating 14-EDO as a 2.11/5.11/7.11/9 subgroup; other approaches are possible.
==Harmony== 

The character of 14-EDO does not well serve those seeking low-limit JI approaches, with the exception of 5:7:9:11 (which is quite well approximated, relative to other JI approximations of the low-numbered EDOs).

14-EDO has quite a bit of xenharmonic appeal, in a similar way to 17-EDO, on account of having three types of 3rd and three types of 6th, rather than the usual two of 12-TET. Since 14-EDO also has a recognizable 4th and 5th, this makes it good for those wishing to explore alternative triadic harmonies without adding significantly more notes. It possesses a triad-rich 9-note MOS scale of 5L4s, wherein 7 of 9 notes are tonic to a subminor, supermajor, and/or neutral triad.


[[image:Ciclo_Tetradecafonía.png width="456" height="468" caption="Intervallic Cycle of 14 steps Equal per Octave"]]

==<span style="font-size: 1.3em;">Commas:</span>== 
14 EDO [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes the val < 14 22 33 39 48 52 |.)
||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||
||= 2187/2048 ||< | -11 7 > ||> 113.69 ||= Apotome ||=   ||
||= 2048/2025 ||< | 11 -4 -2 > ||> 19.55 ||= Diaschisma ||=   ||
||= 36/35 ||< | 2 2 -1 -1 > ||> 48.77 ||= Septimal Quarter Tone ||=   ||
||= 49/48 ||< | -4 -1 0 2 > ||> 35.70 ||= Slendro Diesis ||=   ||
||= 1728/1715 ||< | 6 3 -1 -3 > ||> 13.07 ||= Orwellisma ||= Orwell Comma ||
||= 10976/10935 ||< | 5 -7 -1 3 > ||> 6.48 ||= Hemimage ||=   ||
||=   ||< | 47 -7 -7 -7 > ||> 0.34 ||= Akjaysma ||= 5\7 Octave Comma ||
||= 99/98 ||< | -1 2 0 -2 1 > ||> 17.58 ||= Mothwellsma ||=   ||
||= 243/242 ||< | -1 5 0 0 -2 > ||> 7.14 ||= Rastma ||=   ||
||= 385/384 ||< | -7 -1 1 1 1 > ||> 4.50 ||= Keenanisma ||=   ||
||= 91/90 ||< | -1 -2 -1 1 0 1 > ||> 19.13 ||= Superleap ||=   ||
||= 676/675 ||< | 2 -3 -2 0 0 2 > ||> 2.56 ||= Parizeksma ||=   ||

==**14 tone equal [[modes]]:**== 
6 6 2 - [[MOSScales|MOS]] of [[2L1s]]
5 5 4 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of <span style="cursor: pointer;">[[2L1s]]</span>
5 4 5 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of <span style="cursor: pointer;">[[2L1s]]</span>
4 4 4 2 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of [[3L1s]]
4 2 4 4 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of <span style="cursor: pointer;">[[3L1s]]</span>
4 1 4 4 1 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of [[3L2s]]
4 1 4 1 4 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of <span style="cursor: pointer;">[[3L2s]]</span>
3 3 3 3 2 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of [[4L1s]]
3 2 3 3 3 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of <span style="cursor: pointer;">[[4L1s]]</span>
3 2 2 2 2 3 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of [[2L4s]]
2 2 3 2 2 3 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of <span style="cursor: pointer;">[[2L4s]]</span>
**3 3 1 3 3 1 -** <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of [[4L2s]]
3 1 3 3 1 3 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of <span style="cursor: pointer;">[[4L2s]]</span>
3 1 3 1 3 3 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of <span style="cursor: pointer;">[[4L2s]]</span>
2 2 2 2 2 2 2 = [[7edo]]
2 2 1 2 2 2 2 1 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of [[6L2s]]
2 2 2 1 2 2 2 1 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of <span style="cursor: pointer;">[[6L2s]]</span>
**2 2 2 2 1 2 2 1 -** <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of <span style="cursor: pointer;">[[6L2s]]</span>
2 1 2 2 1 2 2 2 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of <span style="cursor: pointer;">[[6L2s]]</span>
2 1 2 1 2 1 2 1 2 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of [[5L4s]]
2 1 2 1 2 1 2 2 1 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of <span style="cursor: pointer;">[[5L4s]]</span>
2 1 2 1 2 2 1 2 1 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of <span style="cursor: pointer;">[[5L4s]]</span>
2 1 1 2 1 2 1 1 2 1 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of [[4L6s]]
2 1 1 1 2 1 1 2 1 1 1 - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of [[3L8s]]
**1 1 2 1 1 1 2 1 1 1 2** - <span style="cursor: pointer;">[[MOSScales|MOS]]</span> of <span style="cursor: pointer;">[[3L8s]]</span>

==Instruments:== 
[[image:http://4.bp.blogspot.com/_7rDA1Q80rL8/S9M8H2YTpaI/AAAAAAAAAHM/Qkxp5gioOF0/s1600/14edo+guitar+%282%29.jpg width="750" height="256"]]
//A Tetradecaphonic Guitar. 14-EDO Guitar by Ron Sword.//

==**Books:**== 
[[image:Libro_Tetradecafónico.PNG width="360" height="431"]]
//Sword, Ron. "Tetradecaphonic Scales for Guitar" IAAA Press. First Ed: June 2009.//

==**Compositions:**== 
[[media type="custom" key="9748118"]]

<span class="ymp-btn-page-play ymp-media-4c2dab90062954a92dc59831018d92d9">[[http://micro.soonlabel.com/14-et/daily20110610-sax-Riding_The_L.mp3|Riding the L]]</span> by [[@http://chrisvaisvil.com/?p=943|Chris Vaisvil]]
<span class="ymp-btn-page-play ymp-media-579db51554bd270599a9397e8446cdb9">[[http://clones.soonlabel.com/public/micro/jon-lyle-smith/Thorium%20Road.mp3|Thorium Road]]</span> by [[Jon Lyle Smith]]
[[https://sites.google.com/site/teamouse/home|This Way to the Egress]] <span class="ymp-btn-page-play ymp-media-0135aaddbe40aa681d77552715064991">[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/egress-gpo.mp3|play]]</span> by [[http://www.io.com/%7Ehmiller/music/index.html|Herman Miller]]
[[http://www.soundclick.com/bands/page_songInfo.cfm?bandID=145852&songID=3680443|Hyperimprovisation 'Tasty']] <span class="ymp-btn-page-play ymp-media-882819e185058b65278d03572ba40da1">[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Barton/Hyperimprovisation%20Tasty.mp3|play]]</span> by [[Jacob Barton]]
<span class="ymp-btn-page-play ymp-media-285313eab060867d8d5d941dea1d4152">[[http://www.h-pi.com/mp3/14ETPrelude.mp3|14ETPrelude]]</span> by [[Aaron Andrew Hunt]]
[[http://ralphjarzombek.webs.com/|14-tone Equal Temperament]] by Ralph Jarzombek
[[http://home.snafu.de/djwolf/IvorDarregInEagleRock.pdf|Ivor Darreg in Eagle Rock]] by [[Daniel Wolf]]

Original HTML content:

<html><head><title>14edo</title></head><body><!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc0"><a name="x14 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:2 --><span style="color: #790025; font-family: 'Times New Roman',Times,serif; font-size: 109%;"><!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/custom/10021329?h=0&amp;w=0&quot; class=&quot;WikiMedia WikiMediaCustom&quot; id=&quot;wikitext@@media@@type=&amp;quot;custom&amp;quot; key=&amp;quot;10021329&amp;quot;&quot; title=&quot;Custom Media&quot;/&gt; --><script type="text/javascript" src="http://webplayer.yahooapis.com/player.js">
</script><!-- ws:end:WikiTextMediaRule:0 -->14 tone equal temperament</span></h1>
 <br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc1"><a name="x14 tone equal temperament-14-EDO intervals:"></a><!-- ws:end:WikiTextHeadingRule:4 --><strong>14-EDO intervals:</strong></h2>
 

<table class="wiki_table">
    <tr>
        <td><strong>DEGREE</strong><br />
</td>
        <td><strong>NOTE</strong><br />
</td>
        <td><strong>CENTS</strong><br />
</td>
        <td style="text-align: center;"><strong>Approximate</strong><br />
<strong>Ratios</strong>*<br />
</td>
        <td style="text-align: center;"><strong>Nearest</strong><br />
<strong>Harmonic</strong><br />
</td>
        <td><strong>Interval Type</strong><br />
</td>
    </tr>
    <tr>
        <td>0<br />
</td>
        <td>C<br />
</td>
        <td>0<br />
</td>
        <td style="text-align: center;">1/1<br />
</td>
        <td style="text-align: center;">1<br />
</td>
        <td>Unison<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>C*<br />
</td>
        <td>85.714<br />
</td>
        <td style="text-align: center;">81/77, 126/121<br />
</td>
        <td style="text-align: center;">67<br />
</td>
        <td>Narrow Minor 2nd<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>D<br />
</td>
        <td>171.429<br />
</td>
        <td style="text-align: center;">11/10, 10/9<br />
</td>
        <td style="text-align: center;">71<br />
</td>
        <td>Neutral 2nd, or <br />
Narrow Major 2nd<br />
</td>
    </tr>
    <tr>
        <td>3·<br />
</td>
        <td>D*<br />
</td>
        <td>257.143<br />
</td>
        <td style="text-align: center;">81/70, 90/77<br />
</td>
        <td style="text-align: center;">37<br />
</td>
        <td>Subminor 3rd<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>E<br />
</td>
        <td>342.857<br />
</td>
        <td style="text-align: center;">11/9<br />
</td>
        <td style="text-align: center;">39<br />
</td>
        <td>Neutral 3rd<br />
</td>
    </tr>
    <tr>
        <td>5·<br />
</td>
        <td>E*<br />
</td>
        <td>428.571<br />
</td>
        <td style="text-align: center;">9/7, 14/11<br />
</td>
        <td style="text-align: center;">41<br />
</td>
        <td>Supermajor 3rd<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>F<br />
</td>
        <td>514.286<br />
</td>
        <td style="text-align: center;">110/81, 121/90<br />
</td>
        <td style="text-align: center;">43<br />
</td>
        <td>Wide 4th<br />
</td>
    </tr>
    <tr>
        <td>7·<br />
</td>
        <td>F*<br />
</td>
        <td>600<br />
</td>
        <td style="text-align: center;">7/5, 10/7<br />
</td>
        <td style="text-align: center;">91<br />
</td>
        <td>Tritone<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>G<br />
</td>
        <td>685.714<br />
</td>
        <td style="text-align: center;">81/55, 180/121<br />
</td>
        <td style="text-align: center;">95<br />
</td>
        <td>Narrow 5th<br />
</td>
    </tr>
    <tr>
        <td>9·<br />
</td>
        <td>G*<br />
</td>
        <td>771.429<br />
</td>
        <td style="text-align: center;">14/9, 11/7<br />
</td>
        <td style="text-align: center;">25<br />
</td>
        <td>Subminor 6th<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>A<br />
</td>
        <td>857.143<br />
</td>
        <td style="text-align: center;">18/11<br />
</td>
        <td style="text-align: center;">105<br />
</td>
        <td>Neutral 6th<br />
</td>
    </tr>
    <tr>
        <td>11·<br />
</td>
        <td>A*<br />
</td>
        <td>942.857<br />
</td>
        <td style="text-align: center;">140/81, 77/45<br />
</td>
        <td style="text-align: center;">55<br />
</td>
        <td>Supermajor 6th<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>B<br />
</td>
        <td>1028.571<br />
</td>
        <td style="text-align: center;">20/11, 9/5<br />
</td>
        <td style="text-align: center;">29<br />
</td>
        <td>Neutral 7th, or<br />
Wide Minor 7th<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>B*<br />
</td>
        <td>1114.286<br />
</td>
        <td style="text-align: center;">154/81, 121/63<br />
</td>
        <td style="text-align: center;">61<br />
</td>
        <td>Wide Major 7th<br />
</td>
    </tr>
    <tr>
        <td>14··(or 0)<br />
</td>
        <td>C<br />
</td>
        <td>1200<br />
</td>
        <td style="text-align: center;">2/1<br />
</td>
        <td style="text-align: center;">2<br />
</td>
        <td>Octave<br />
</td>
    </tr>
</table>

*based on treating 14-EDO as a 2.11/5.11/7.11/9 subgroup; other approaches are possible.<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc2"><a name="x14 tone equal temperament-Harmony"></a><!-- ws:end:WikiTextHeadingRule:6 -->Harmony</h2>
 <br />
The character of 14-EDO does not well serve those seeking low-limit JI approaches, with the exception of 5:7:9:11 (which is quite well approximated, relative to other JI approximations of the low-numbered EDOs).<br />
<br />
14-EDO has quite a bit of xenharmonic appeal, in a similar way to 17-EDO, on account of having three types of 3rd and three types of 6th, rather than the usual two of 12-TET. Since 14-EDO also has a recognizable 4th and 5th, this makes it good for those wishing to explore alternative triadic harmonies without adding significantly more notes. It possesses a triad-rich 9-note MOS scale of 5L4s, wherein 7 of 9 notes are tonic to a subminor, supermajor, and/or neutral triad.<br />
<br />
<br />
<!-- ws:start:WikiTextLocalImageRule:402:&lt;img src=&quot;/file/view/Ciclo_Tetradecafon%C3%ADa.png/233692646/456x468/Ciclo_Tetradecafon%C3%ADa.png&quot; alt=&quot;Intervallic Cycle of 14 steps Equal per Octave&quot; title=&quot;Intervallic Cycle of 14 steps Equal per Octave&quot; style=&quot;height: 468px; width: 456px;&quot; /&gt; --><table class="captionBox"><tr><td class="captionedImage"><img src="/file/view/Ciclo_Tetradecafon%C3%ADa.png/233692646/456x468/Ciclo_Tetradecafon%C3%ADa.png" alt="Ciclo_Tetradecafonía.png" title="Ciclo_Tetradecafonía.png" style="height: 468px; width: 456px;" /></td></tr><tr><td class="imageCaption">Intervallic Cycle of 14 steps Equal per Octave</td></tr></table><!-- ws:end:WikiTextLocalImageRule:402 --><br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc3"><a name="x14 tone equal temperament-Commas:"></a><!-- ws:end:WikiTextHeadingRule:8 --><span style="font-size: 1.3em;">Commas:</span></h2>
 14 EDO <a class="wiki_link" href="/tempering%20out">tempers out</a> the following <a class="wiki_link" href="/comma">comma</a>s. (Note: This assumes the val &lt; 14 22 33 39 48 52 |.)<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>
    </tr>
    <tr>
        <td style="text-align: center;">2187/2048<br />
</td>
        <td style="text-align: left;">| -11 7 &gt;<br />
</td>
        <td style="text-align: right;">113.69<br />
</td>
        <td style="text-align: center;">Apotome<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">2048/2025<br />
</td>
        <td style="text-align: left;">| 11 -4 -2 &gt;<br />
</td>
        <td style="text-align: right;">19.55<br />
</td>
        <td style="text-align: center;">Diaschisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">36/35<br />
</td>
        <td style="text-align: left;">| 2 2 -1 -1 &gt;<br />
</td>
        <td style="text-align: right;">48.77<br />
</td>
        <td style="text-align: center;">Septimal Quarter Tone<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">49/48<br />
</td>
        <td style="text-align: left;">| -4 -1 0 2 &gt;<br />
</td>
        <td style="text-align: right;">35.70<br />
</td>
        <td style="text-align: center;">Slendro Diesis<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">1728/1715<br />
</td>
        <td style="text-align: left;">| 6 3 -1 -3 &gt;<br />
</td>
        <td style="text-align: right;">13.07<br />
</td>
        <td style="text-align: center;">Orwellisma<br />
</td>
        <td style="text-align: center;">Orwell Comma<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">10976/10935<br />
</td>
        <td style="text-align: left;">| 5 -7 -1 3 &gt;<br />
</td>
        <td style="text-align: right;">6.48<br />
</td>
        <td style="text-align: center;">Hemimage<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: left;">| 47 -7 -7 -7 &gt;<br />
</td>
        <td style="text-align: right;">0.34<br />
</td>
        <td style="text-align: center;">Akjaysma<br />
</td>
        <td style="text-align: center;">5\7 Octave Comma<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">99/98<br />
</td>
        <td style="text-align: left;">| -1 2 0 -2 1 &gt;<br />
</td>
        <td style="text-align: right;">17.58<br />
</td>
        <td style="text-align: center;">Mothwellsma<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">243/242<br />
</td>
        <td style="text-align: left;">| -1 5 0 0 -2 &gt;<br />
</td>
        <td style="text-align: right;">7.14<br />
</td>
        <td style="text-align: center;">Rastma<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">385/384<br />
</td>
        <td style="text-align: left;">| -7 -1 1 1 1 &gt;<br />
</td>
        <td style="text-align: right;">4.50<br />
</td>
        <td style="text-align: center;">Keenanisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">91/90<br />
</td>
        <td style="text-align: left;">| -1 -2 -1 1 0 1 &gt;<br />
</td>
        <td style="text-align: right;">19.13<br />
</td>
        <td style="text-align: center;">Superleap<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">676/675<br />
</td>
        <td style="text-align: left;">| 2 -3 -2 0 0 2 &gt;<br />
</td>
        <td style="text-align: right;">2.56<br />
</td>
        <td style="text-align: center;">Parizeksma<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc4"><a name="x14 tone equal temperament-14 tone equal modes:"></a><!-- ws:end:WikiTextHeadingRule:10 --><strong>14 tone equal <a class="wiki_link" href="/modes">modes</a>:</strong></h2>
 6 6 2 - <a class="wiki_link" href="/MOSScales">MOS</a> of <a class="wiki_link" href="/2L1s">2L1s</a><br />
5 5 4 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <span style="cursor: pointer;"><a class="wiki_link" href="/2L1s">2L1s</a></span><br />
5 4 5 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <span style="cursor: pointer;"><a class="wiki_link" href="/2L1s">2L1s</a></span><br />
4 4 4 2 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <a class="wiki_link" href="/3L1s">3L1s</a><br />
4 2 4 4 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <span style="cursor: pointer;"><a class="wiki_link" href="/3L1s">3L1s</a></span><br />
4 1 4 4 1 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <a class="wiki_link" href="/3L2s">3L2s</a><br />
4 1 4 1 4 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <span style="cursor: pointer;"><a class="wiki_link" href="/3L2s">3L2s</a></span><br />
3 3 3 3 2 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <a class="wiki_link" href="/4L1s">4L1s</a><br />
3 2 3 3 3 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <span style="cursor: pointer;"><a class="wiki_link" href="/4L1s">4L1s</a></span><br />
3 2 2 2 2 3 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <a class="wiki_link" href="/2L4s">2L4s</a><br />
2 2 3 2 2 3 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <span style="cursor: pointer;"><a class="wiki_link" href="/2L4s">2L4s</a></span><br />
<strong>3 3 1 3 3 1 -</strong> <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <a class="wiki_link" href="/4L2s">4L2s</a><br />
3 1 3 3 1 3 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <span style="cursor: pointer;"><a class="wiki_link" href="/4L2s">4L2s</a></span><br />
3 1 3 1 3 3 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <span style="cursor: pointer;"><a class="wiki_link" href="/4L2s">4L2s</a></span><br />
2 2 2 2 2 2 2 = <a class="wiki_link" href="/7edo">7edo</a><br />
2 2 1 2 2 2 2 1 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <a class="wiki_link" href="/6L2s">6L2s</a><br />
2 2 2 1 2 2 2 1 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <span style="cursor: pointer;"><a class="wiki_link" href="/6L2s">6L2s</a></span><br />
<strong>2 2 2 2 1 2 2 1 -</strong> <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <span style="cursor: pointer;"><a class="wiki_link" href="/6L2s">6L2s</a></span><br />
2 1 2 2 1 2 2 2 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <span style="cursor: pointer;"><a class="wiki_link" href="/6L2s">6L2s</a></span><br />
2 1 2 1 2 1 2 1 2 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <a class="wiki_link" href="/5L4s">5L4s</a><br />
2 1 2 1 2 1 2 2 1 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <span style="cursor: pointer;"><a class="wiki_link" href="/5L4s">5L4s</a></span><br />
2 1 2 1 2 2 1 2 1 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <span style="cursor: pointer;"><a class="wiki_link" href="/5L4s">5L4s</a></span><br />
2 1 1 2 1 2 1 1 2 1 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <a class="wiki_link" href="/4L6s">4L6s</a><br />
2 1 1 1 2 1 1 2 1 1 1 - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <a class="wiki_link" href="/3L8s">3L8s</a><br />
<strong>1 1 2 1 1 1 2 1 1 1 2</strong> - <span style="cursor: pointer;"><a class="wiki_link" href="/MOSScales">MOS</a></span> of <span style="cursor: pointer;"><a class="wiki_link" href="/3L8s">3L8s</a></span><br />
<br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc5"><a name="x14 tone equal temperament-Instruments:"></a><!-- ws:end:WikiTextHeadingRule:12 -->Instruments:</h2>
 <!-- ws:start:WikiTextRemoteImageRule:404:&lt;img src=&quot;http://4.bp.blogspot.com/_7rDA1Q80rL8/S9M8H2YTpaI/AAAAAAAAAHM/Qkxp5gioOF0/s1600/14edo+guitar+%282%29.jpg&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 256px; width: 750px;&quot; /&gt; --><img src="http://4.bp.blogspot.com/_7rDA1Q80rL8/S9M8H2YTpaI/AAAAAAAAAHM/Qkxp5gioOF0/s1600/14edo+guitar+%282%29.jpg" alt="external image 14edo+guitar+%282%29.jpg" title="external image 14edo+guitar+%282%29.jpg" style="height: 256px; width: 750px;" /><!-- ws:end:WikiTextRemoteImageRule:404 --><br />
<em>A Tetradecaphonic Guitar. 14-EDO Guitar by Ron Sword.</em><br />
<br />
<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc6"><a name="x14 tone equal temperament-Books:"></a><!-- ws:end:WikiTextHeadingRule:14 --><strong>Books:</strong></h2>
 <!-- ws:start:WikiTextLocalImageRule:403:&lt;img src=&quot;/file/view/Libro_Tetradecaf%C3%B3nico.PNG/163539671/360x431/Libro_Tetradecaf%C3%B3nico.PNG&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 431px; width: 360px;&quot; /&gt; --><img src="/file/view/Libro_Tetradecaf%C3%B3nico.PNG/163539671/360x431/Libro_Tetradecaf%C3%B3nico.PNG" alt="Libro_Tetradecafónico.PNG" title="Libro_Tetradecafónico.PNG" style="height: 431px; width: 360px;" /><!-- ws:end:WikiTextLocalImageRule:403 --><br />
<em>Sword, Ron. &quot;Tetradecaphonic Scales for Guitar&quot; IAAA Press. First Ed: June 2009.</em><br />
<br />
<!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc7"><a name="x14 tone equal temperament-Compositions:"></a><!-- ws:end:WikiTextHeadingRule:16 --><strong>Compositions:</strong></h2>
 <!-- ws:start:WikiTextMediaRule:1:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/custom/9748118?h=0&amp;w=0&quot; class=&quot;WikiMedia WikiMediaCustom&quot; id=&quot;wikitext@@media@@type=&amp;quot;custom&amp;quot; key=&amp;quot;9748118&amp;quot;&quot; title=&quot;Custom Media&quot;/&gt; --><script type="text/javascript" src="http://webplayer.yahooapis.com/player.js">
</script><!-- ws:end:WikiTextMediaRule:1 --><br />
<br />
<span class="ymp-btn-page-play ymp-media-4c2dab90062954a92dc59831018d92d9"><a class="wiki_link_ext" href="http://micro.soonlabel.com/14-et/daily20110610-sax-Riding_The_L.mp3" rel="nofollow">Riding the L</a></span> by <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=943" rel="nofollow" target="_blank">Chris Vaisvil</a><br />
<span class="ymp-btn-page-play ymp-media-579db51554bd270599a9397e8446cdb9"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/jon-lyle-smith/Thorium%20Road.mp3" rel="nofollow">Thorium Road</a></span> by <a class="wiki_link" href="/Jon%20Lyle%20Smith">Jon Lyle Smith</a><br />
<a class="wiki_link_ext" href="https://sites.google.com/site/teamouse/home" rel="nofollow">This Way to the Egress</a> <span class="ymp-btn-page-play ymp-media-0135aaddbe40aa681d77552715064991"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/egress-gpo.mp3" rel="nofollow">play</a></span> by <a class="wiki_link_ext" href="http://www.io.com/%7Ehmiller/music/index.html" rel="nofollow">Herman Miller</a><br />
<a class="wiki_link_ext" href="http://www.soundclick.com/bands/page_songInfo.cfm?bandID=145852&amp;songID=3680443" rel="nofollow">Hyperimprovisation 'Tasty'</a> <span class="ymp-btn-page-play ymp-media-882819e185058b65278d03572ba40da1"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Barton/Hyperimprovisation%20Tasty.mp3" rel="nofollow">play</a></span> by <a class="wiki_link" href="/Jacob%20Barton">Jacob Barton</a><br />
<span class="ymp-btn-page-play ymp-media-285313eab060867d8d5d941dea1d4152"><a class="wiki_link_ext" href="http://www.h-pi.com/mp3/14ETPrelude.mp3" rel="nofollow">14ETPrelude</a></span> by <a class="wiki_link" href="/Aaron%20Andrew%20Hunt">Aaron Andrew Hunt</a><br />
<a class="wiki_link_ext" href="http://ralphjarzombek.webs.com/" rel="nofollow">14-tone Equal Temperament</a> by Ralph Jarzombek<br />
<a class="wiki_link_ext" href="http://home.snafu.de/djwolf/IvorDarregInEagleRock.pdf" rel="nofollow">Ivor Darreg in Eagle Rock</a> by <a class="wiki_link" href="/Daniel%20Wolf">Daniel Wolf</a></body></html>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:igliashon|igliashon]] and made on <tt>2011-07-18 22:49:47 UTC</tt>.<br>
+: This revision was by author [[User:guest|guest]] and made on <tt>2011-07-21 00:03:10 UTC</tt>.<br>
-: The original revision id was <tt>241875649</tt>.<br>
+: The original revision id was <tt>242215355</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
@@ Line 9: / Line 9: @@
 ==**14-EDO intervals:**==
-|| **DEGREE** || **NOTE** || **CENTS** || **Nearest**
+|| **DEGREE** || **NOTE** || **CENTS** ||= **Approximate**
-**Ratio** || **Cents** || **Error** ||= **Approximate**
+**Ratios*** ||= **Nearest**
-**Just Interval** ||= **Nearest**
+**Harmonic** || **Interval Type** ||
-**Harmonic** ||
+|| 0 || C || 0 ||= 1/1 ||= 1 || Unison ||
-|| 0 || **C** || 0 || **1/1** || 0 || **None** ||= 1/1 ||= 1 ||
+|| 1 || C* || 85.714 ||= 81/77, 126/121 ||= 67 || Narrow Minor 2nd ||
-|| 1 || C* || 85.714 || 21/20 || 84.467 || +1.247 ||=   ||= 67 ||
+|| 2 || D || 171.429 ||= 11/10, 10/9 ||= 71 || Neutral 2nd, or
-|| 2 || D || 171.429 || 32/29 || 170.423 || +1.006 ||= 11/10, 10/9 ||= 71 ||
+Narrow Major 2nd ||
-|| **3·** || **D*** || **257.143** || **36/31** || **258.874** || **-1.731** ||= 7/6, 8/7 ||= 37 ||
+|| 3· || D* || 257.143 ||= 81/70, 90/77 ||= 37 || Subminor 3rd ||
-|| 4 || E || 342.857 || 39/32 || 342.483 || +0.374 ||= 11/9 ||= 39 ||
+|| 4 || E || 342.857 ||= 11/9 ||= 39 || Neutral 3rd ||
-|| **5·** || **E*** || **428.571** || **32/25** || **427.373** || **+1.198** ||= 9/7 ||= 41 ||
+|| 5· || E* || 428.571 ||= 9/7, 14/11 ||= 41 || Supermajor 3rd ||
-|| 6 || F || 514.286 || 39/29 || 512.905 || +1.381 ||= 4/3 ||= 43 ||
+|| 6 || F || 514.286 ||= 110/81, 121/90 ||= 43 || Wide 4th ||
-|| **7·** || **F*** || **600** || **99/70** || **600.088** || **-0.088** ||= 7/5, 10/7 ||= 91 ||
+|| 7· || F* || 600 ||= 7/5, 10/7 ||= 91 || Tritone ||
-|| 8 || G || 685.714 || 58/39 || 687.095 || -1.381 ||= 3/2 ||= 95 ||
+|| 8 || G || 685.714 ||= 81/55, 180/121 ||= 95 || Narrow 5th ||
-|| **9·** || **G*** || **771.429** || **25/16** || **772.627** || **-1.198** ||= 14/9 ||= 25 ||
+|| 9· || G* || 771.429 ||= 14/9, 11/7 ||= 25 || Subminor 6th ||
-|| 10 || A || 857.143 || 64/39 || 857.517 || -0.374 ||= 18/11 ||= 105 ||
+|| 10 || A || 857.143 ||= 18/11 ||= 105 || Neutral 6th ||
-|| **11·** || **A*** || **942.857** || **31/18** || **941.126** || **+1.731** ||= 12/7, 7/4 ||= 55 ||
+|| 11· || A* || 942.857 ||= 140/81, 77/45 ||= 55 || Supermajor 6th ||
-|| 12 || B || 1028.571 || 29/16 || 1029.577 || -1.006 ||= 20/11, 9/5 ||= 29 ||
+|| 12 || B || 1028.571 ||= 20/11, 9/5 ||= 29 || Neutral 7th, or
-|| 13 || B* || 1114.286 || 40/21 || 1115.533 || -1.247 ||=   ||= 61 ||
+Wide Minor 7th ||
-|| **14··(or 0)** || **C** || **1200** || **2/1** || **1200** || **None** ||= 2/1 ||= 2 ||
+|| 13 || B* || 1114.286 ||= 154/81, 121/63 ||= 61 || Wide Major 7th ||
+|| 14··(or 0) || C || 1200 ||= 2/1 ||= 2 || Octave ||
+*based on treating 14-EDO as a 2.11/5.11/7.11/9 subgroup; other approaches are possible.
 ==Harmony==
-The character of 14-EDO does not well serve those seeking low-limit JI approaches, with the exception of 5:7:9:11 (which is quite well approximated, relative to other JI approximations of the low-numbered EDOs, and in 28-EDO we can bump that up to 4:5:7:9:11, perhaps even 4:5:6:7:9:11 if we are feeling charitable). 6:7:9 appears to be better-approximated than it actually sounds, though it is still reasonably consonant.
+The character of 14-EDO does not well serve those seeking low-limit JI approaches, with the exception of 5:7:9:11 (which is quite well approximated, relative to other JI approximations of the low-numbered EDOs).
 -EDO has quite a bit of xenharmonic appeal, in a similar way to 17-EDO, on account of having three types of 3rd and three types of 6th, rather than the usual two of 12-TET. Since 14-EDO also has a recognizable 4th and 5th, this makes it good for those wishing to explore alternative triadic harmonies without adding significantly more notes. It possesses a triad-rich 9-note MOS scale of 5L4s, wherein 7 of 9 notes are tonic to a subminor, supermajor, and/or neutral triad.
@@ Line 112: / Line 114: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;strong&gt;CENTS&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;Nearest&lt;/strong&gt;&lt;br /&gt;
-&lt;strong&gt;Ratio&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;Cents&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;Error&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;strong&gt;Approximate&lt;/strong&gt;&lt;br /&gt;
-&lt;strong&gt;Just Interval&lt;/strong&gt;&lt;br /&gt;
+&lt;strong&gt;Ratios&lt;/strong&gt;*&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;strong&gt;Nearest&lt;/strong&gt;&lt;br /&gt;
 &lt;strong&gt;Harmonic&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;Interval Type&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 130: / Line 127: @@
          &lt;td&gt;0&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;C&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;C&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;0&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;1/1&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;0&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;None&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;1/1&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Unison&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 152: / Line 145: @@
          &lt;td&gt;85.714&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;21/20&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;81/77, 126/121&lt;br /&gt;
 &lt;/td&gt;
-        &lt;td&gt;84.467&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;67&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;+1.247&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;67&lt;br /&gt;
+         &lt;td&gt;Narrow Minor 2nd&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 169: / Line 158: @@
 &lt;/td&gt;
          &lt;td&gt;171.429&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;32/29&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;170.423&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;+1.006&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;11/10, 10/9&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;71&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Neutral 2nd, or &lt;br /&gt;
+Narrow Major 2nd&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;&lt;strong&gt;3·&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;3·&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;D&lt;/strong&gt;*&lt;br /&gt;
+         &lt;td&gt;D*&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;257.143&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;257.143&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;36/31&lt;/strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;81/70, 90/77&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;258.874&lt;/strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;37&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;-1.731&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;Subminor 3rd&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;7/6, 8/7&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;37&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 205: / Line 187: @@
 &lt;/td&gt;
          &lt;td&gt;342.857&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;39/32&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;342.483&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;+0.374&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;11/9&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;39&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Neutral 3rd&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;&lt;strong&gt;5·&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;5·&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;E&lt;/strong&gt;*&lt;br /&gt;
+         &lt;td&gt;E*&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;428.571&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;428.571&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;32/25&lt;/strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;9/7, 14/11&lt;br /&gt;
 &lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;427.373&lt;/strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;41&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;+1.198&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;9/7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;41&lt;br /&gt;
+         &lt;td&gt;Supermajor 3rd&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 242: / Line 216: @@
          &lt;td&gt;514.286&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;39/29&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;110/81, 121/90&lt;br /&gt;
 &lt;/td&gt;
-        &lt;td&gt;512.905&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;43&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;+1.381&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;43&lt;br /&gt;
+         &lt;td&gt;Wide 4th&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;&lt;strong&gt;7·&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;7·&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;F&lt;/strong&gt;*&lt;br /&gt;
+         &lt;td&gt;F*&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;600&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;600&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;99/70&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;600.088&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;-0.088&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;7/5, 10/7&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;91&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Tritone&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 278: / Line 244: @@
          &lt;td&gt;685.714&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;58/39&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;81/55, 180/121&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;687.095&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;95&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;-1.381&lt;br /&gt;
+         &lt;td&gt;Narrow 5th&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;95&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;&lt;strong&gt;9·&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;9·&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;G&lt;/strong&gt;*&lt;br /&gt;
+         &lt;td&gt;G*&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;771.429&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;771.429&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;25/16&lt;/strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;14/9, 11/7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;772.627&lt;/strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;25&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;-1.198&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;Subminor 6th&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;14/9&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;25&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 313: / Line 271: @@
 &lt;/td&gt;
          &lt;td&gt;857.143&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;64/39&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;857.517&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;-0.374&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;18/11&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;105&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Neutral 6th&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;&lt;strong&gt;11·&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;11·&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;*&lt;br /&gt;
+         &lt;td&gt;A*&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;942.857&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;942.857&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;31/18&lt;/strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;140/81, 77/45&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;941.126&lt;/strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;55&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;+1.731&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;Supermajor 6th&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;12/7, 7/4&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;55&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 349: / Line 299: @@
 &lt;/td&gt;
          &lt;td&gt;1028.571&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;29/16&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;1029.577&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;-1.006&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;20/11, 9/5&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;29&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Neutral 7th, or&lt;br /&gt;
+Wide Minor 7th&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 368: / Line 315: @@
          &lt;td&gt;1114.286&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;40/21&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;154/81, 121/63&lt;br /&gt;
 &lt;/td&gt;
-        &lt;td&gt;1115.533&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;61&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;-1.247&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;61&lt;br /&gt;
+         &lt;td&gt;Wide Major 7th&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;&lt;strong&gt;14··(or 0)&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;14··(or 0)&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;C&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;1200&lt;/strong&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;strong&gt;2/1&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;1200&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;C&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;None&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;1200&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;2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Octave&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
 &lt;/table&gt;
+*based on treating 14-EDO as a 2.11/5.11/7.11/9 subgroup; other approaches are possible.&lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x14 tone equal temperament-Harmony"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Harmony&lt;/h2&gt;
   &lt;br /&gt;
-The character of 14-EDO does not well serve those seeking low-limit JI approaches, with the exception of 5:7:9:11 (which is quite well approximated, relative to other JI approximations of the low-numbered EDOs, and in 28-EDO we can bump that up to 4:5:7:9:11, perhaps even 4:5:6:7:9:11 if we are feeling charitable). 6:7:9 appears to be better-approximated than it actually sounds, though it is still reasonably consonant.&lt;br /&gt;
+The character of 14-EDO does not well serve those seeking low-limit JI approaches, with the exception of 5:7:9:11 (which is quite well approximated, relative to other JI approximations of the low-numbered EDOs).&lt;br /&gt;
 &lt;br /&gt;
 -EDO has quite a bit of xenharmonic appeal, in a similar way to 17-EDO, on account of having three types of 3rd and three types of 6th, rather than the usual two of 12-TET. Since 14-EDO also has a recognizable 4th and 5th, this makes it good for those wishing to explore alternative triadic harmonies without adding significantly more notes. It possesses a triad-rich 9-note MOS scale of 5L4s, wherein 7 of 9 notes are tonic to a subminor, supermajor, and/or neutral triad.&lt;br /&gt;
 &lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:466:&amp;lt;img src=&amp;quot;/file/view/Ciclo_Tetradecafon%C3%ADa.png/233692646/456x468/Ciclo_Tetradecafon%C3%ADa.png&amp;quot; alt=&amp;quot;Intervallic Cycle of 14 steps Equal per Octave&amp;quot; title=&amp;quot;Intervallic Cycle of 14 steps Equal per Octave&amp;quot; style=&amp;quot;height: 468px; width: 456px;&amp;quot; /&amp;gt; --&gt;&lt;table class="captionBox"&gt;&lt;tr&gt;&lt;td class="captionedImage"&gt;&lt;img src="/file/view/Ciclo_Tetradecafon%C3%ADa.png/233692646/456x468/Ciclo_Tetradecafon%C3%ADa.png" alt="Ciclo_Tetradecafonía.png" title="Ciclo_Tetradecafonía.png" style="height: 468px; width: 456px;" /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td class="imageCaption"&gt;Intervallic Cycle of 14 steps Equal per Octave&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;!-- ws:end:WikiTextLocalImageRule:466 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:402:&amp;lt;img src=&amp;quot;/file/view/Ciclo_Tetradecafon%C3%ADa.png/233692646/456x468/Ciclo_Tetradecafon%C3%ADa.png&amp;quot; alt=&amp;quot;Intervallic Cycle of 14 steps Equal per Octave&amp;quot; title=&amp;quot;Intervallic Cycle of 14 steps Equal per Octave&amp;quot; style=&amp;quot;height: 468px; width: 456px;&amp;quot; /&amp;gt; --&gt;&lt;table class="captionBox"&gt;&lt;tr&gt;&lt;td class="captionedImage"&gt;&lt;img src="/file/view/Ciclo_Tetradecafon%C3%ADa.png/233692646/456x468/Ciclo_Tetradecafon%C3%ADa.png" alt="Ciclo_Tetradecafonía.png" title="Ciclo_Tetradecafonía.png" style="height: 468px; width: 456px;" /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td class="imageCaption"&gt;Intervallic Cycle of 14 steps Equal per Octave&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;!-- ws:end:WikiTextLocalImageRule:402 --&gt;&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x14 tone equal temperament-Commas:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;&lt;span style="font-size: 1.3em;"&gt;Commas:&lt;/span&gt;&lt;/h2&gt;
@@ Line 600: / Line 540: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="x14 tone equal temperament-Instruments:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Instruments:&lt;/h2&gt;
-  &lt;!-- ws:start:WikiTextRemoteImageRule:468:&amp;lt;img src=&amp;quot;http://4.bp.blogspot.com/_7rDA1Q80rL8/S9M8H2YTpaI/AAAAAAAAAHM/Qkxp5gioOF0/s1600/14edo+guitar+%282%29.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 256px; width: 750px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://4.bp.blogspot.com/_7rDA1Q80rL8/S9M8H2YTpaI/AAAAAAAAAHM/Qkxp5gioOF0/s1600/14edo+guitar+%282%29.jpg" alt="external image 14edo+guitar+%282%29.jpg" title="external image 14edo+guitar+%282%29.jpg" style="height: 256px; width: 750px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:468 --&gt;&lt;br /&gt;
+  &lt;!-- ws:start:WikiTextRemoteImageRule:404:&amp;lt;img src=&amp;quot;http://4.bp.blogspot.com/_7rDA1Q80rL8/S9M8H2YTpaI/AAAAAAAAAHM/Qkxp5gioOF0/s1600/14edo+guitar+%282%29.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 256px; width: 750px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://4.bp.blogspot.com/_7rDA1Q80rL8/S9M8H2YTpaI/AAAAAAAAAHM/Qkxp5gioOF0/s1600/14edo+guitar+%282%29.jpg" alt="external image 14edo+guitar+%282%29.jpg" title="external image 14edo+guitar+%282%29.jpg" style="height: 256px; width: 750px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:404 --&gt;&lt;br /&gt;
 &lt;em&gt;A Tetradecaphonic Guitar. 14-EDO Guitar by Ron Sword.&lt;/em&gt;&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="x14 tone equal temperament-Books:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;&lt;strong&gt;Books:&lt;/strong&gt;&lt;/h2&gt;
-  &lt;!-- ws:start:WikiTextLocalImageRule:467:&amp;lt;img src=&amp;quot;/file/view/Libro_Tetradecaf%C3%B3nico.PNG/163539671/360x431/Libro_Tetradecaf%C3%B3nico.PNG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 431px; width: 360px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/Libro_Tetradecaf%C3%B3nico.PNG/163539671/360x431/Libro_Tetradecaf%C3%B3nico.PNG" alt="Libro_Tetradecafónico.PNG" title="Libro_Tetradecafónico.PNG" style="height: 431px; width: 360px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:467 --&gt;&lt;br /&gt;
+  &lt;!-- ws:start:WikiTextLocalImageRule:403:&amp;lt;img src=&amp;quot;/file/view/Libro_Tetradecaf%C3%B3nico.PNG/163539671/360x431/Libro_Tetradecaf%C3%B3nico.PNG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 431px; width: 360px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/Libro_Tetradecaf%C3%B3nico.PNG/163539671/360x431/Libro_Tetradecaf%C3%B3nico.PNG" alt="Libro_Tetradecafónico.PNG" title="Libro_Tetradecafónico.PNG" style="height: 431px; width: 360px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:403 --&gt;&lt;br /&gt;
 &lt;em&gt;Sword, Ron. &amp;quot;Tetradecaphonic Scales for Guitar&amp;quot; IAAA Press. First Ed: June 2009.&lt;/em&gt;&lt;br /&gt;
 &lt;br /&gt;

14edo: Difference between revisions

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