14edo: Difference between revisions

Revision as of 16:30, 24 March 2015

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[[toc|flat]]
=**Intervals**= 
|| **DEGREE** || **NOTE**
**NAME** || **CENTS**
**<span style="background-color: #ffffff;">DMS</span>** ||= **Approximate**
**Ratios 1``*``** ||= **Approximate**
**Ratios 2** **``**``** ||= Nearest
Harmonic || Interval Type ||
|| 0 || C || 0 ||= 1/1 ||= 1/1 ||= 1 || Unison ||
|| 1 || C^, Dv || 85.714
25°42'51" ||= 20/19, 19/18, 18/17 ||= 22/21, 28/27, 21/20 ||= 67 || Narrow Minor 2nd ||
|| 2 || D || 171.429
<span style="background-color: #ffffff;">51°25'43"</span> ||= 11/10, 10/9, 19/17 ||= 9/8, 10/9, 11/10,
12/11 ||= 71 || Neutral 2nd, or
Narrow Major 2nd ||
|| 3· || D^, Ev || 257.143
77°8'34" ||= 22/19, 20/17 ||= 7/6, 8/7 ||= 37 || Subminor 3rd ||
|| 4 || E || 342.857
<span style="background-color: #ffffff;">102°51'26"</span> ||= 11/9, 17/14 ||= 11/9, 5/4, 6/5 ||= 39 || Neutral 3rd ||
|| 5· || E^, Fv || 428.571
<span style="line-height: 15.6000003814697px;">128°34'17"</span> ||= 9/7, 14/11, 22/17 ||= 9/7, 14/11 ||= 41 || Supermajor 3rd ||
|| 6 || F || 51<span style="line-height: 1.5;">4.286</span>
<span style="background-color: #ffffff;">154°17'9"</span> ||= 19/14 ||= 4/3,11/8 ||= 43 || Wide 4th ||
|| 7· || F^, Gv || 600
180° ||= 7/5, 10/7 ||= 7/5, 10/7 ||= 91 || Tritone ||
|| 8 || G || 685.714
<span style="background-color: #ffffff;">205°42'51"</span> ||= 28/19 ||= 3/2, 16/11 ||= 95 || Narrow 5th ||
|| 9· || G^, Av || 771.429
231°25'43" ||= 14/9, 11/7, 17/11 ||=   ||= 25 || Subminor 6th ||
|| 10 || A || 857.143
<span style="background-color: #ffffff;">257°8'34"</span> ||= 18/11 ||= 18/11, 8/5, 5/3 ||= 105 || Neutral 6th ||
|| 11· || A^, Bv || 942.857
282°51'26" ||= 19/11, 17/10 ||= 12/7, 7/4 ||= 55 || Supermajor 6th ||
|| 12 || B || 1028.571
<span style="background-color: #ffffff;">308°34'17"</span> ||= 20/11, 9/5, 34/19 ||= 16/9, 9/5, 20/11,
11/6 ||= 29 || Neutral 7th, or
Wide Minor 7th ||
|| 13 || B^, Cv || 1114.286
234°17'9" ||= 19/10, 36/19, 17/9 ||= 21/11, 27/14, 40/21 ||= 61 || Wide Major 7th ||
|| 14··(or 0) || C || 1200
360° ||= 2/1 ||= 2/1 ||= 2 || Octave ||
``*``based on treating 14-EDO as a 2.7/5.9/5.11/5.17/5.19/5 [[subgroup]]; other approaches are possible.
<span style="display: block; text-align: center;">``**``</span>
based on treating 14edo as an 11-limit temperament
[[media type="custom" key="24802838"]]

[[file:14ed2-001.svg]]

=Rank two temperaments= 
[[xenharmonic/List of 14edo rank two temperaments by badness|List of 14edo rank two temperaments by badness]]

=Harmony= 
The character of 14-EDO does not well serve those seeking low-limit JI approaches, with the exception of 5:7:9:11:17:19 (which is quite well approximated, relative to other JI approximations of the low-numbered EDOs). However, the ratios 7/5, 7/6, 9/7, 10/7, 10/9, 11/7, 11/9, and 11/10 are all recognizably approximated, and if you accept that 14edo offers approximations of these intervals, you end up with a low-complexity, high-damage 11-limit temperament where the commas listed at the bottom of this page are tempered out. This leads to some of the bizarre equivalences described in the second "Approximate Ratios" column in the table above.

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.

=Notation= 
[[Ivor Darreg]] wrote in [[http://sonic-arts.org/darreg/dar15.htm|this article]]:

//The 14-tone scale presents a new situation: while one might use ordinary sharps and flats in addition to conventional naturals for the notes of the 7-tone-equal temperament, it would be misleading and confusing to do so, because there is a 7-tone circle of fifths (admittedly quite distorted) already notatable and nameable as F C G D A E B in the usual manner. But there is no 14-tone circle of fifths. There is simply a second set of 7 fifths in a circle which does not intersect the with the first set. Thus is we think of B-flat and B, or B-natural and F-sharp, the 14-tone-system interval would NOT be a fifth of that system and would not sound like one, since B F would be the very same kind of distorted fifth that C G or A E happens to be in 7 or 14. Our suggestion is to call the new notes of 14, the second set of 7, F* C* G* D* A* E* B*, and use asterisks or arrows or whatever you please on the staff. Or just number the tones as for 13.//

The following chart (made by [[Tútim Dennsuul Wafiil|TDW]]) shows this recommendation as "standard notation" as well as a proposed alternative.

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

=Images= 

[[image:14edo wheel.png width="343" height="343"]]

=Commas= 
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 ||=   ||

=**[[modes|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>


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

=**Compositions**= 
[[http://split-notes.com/004/|NANA WODORI]] by knowsur
[[http://micro.soonlabel.com/0-praxis/audio/August/august_03_thereminnards.mp3|Thereminnards]] by Ralph Lewis
Pendula (for amplified trombone) by Philip Schuessler
[[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]]
<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]]
[[http://archive.org/download/tranSentient/tranSentient.mp3|tranSentient]] by [[Jon Lyle Smith]]
[[http://archive.org/download/TheSpectrumOfDesire/the_spectrum_of_desire.mp3|the spectrum of desire]] 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://youtu.be/mHyaW1fVWsg|Medicine Wheel]] by Mark Allan Barnes
[[http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/Fourteen_EDO_CBobro_r8b.mp3|Fourteen EDO]] by [[Cameron Bobro]]

Original HTML content:

<html><head><title>14edo</title></head><body><!-- ws:start:WikiTextTocRule:23:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --><a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --> | <a href="#Rank two temperaments">Rank two temperaments</a><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --> | <a href="#Harmony">Harmony</a><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --> | <a href="#Notation">Notation</a><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --> | <a href="#Images">Images</a><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --> | <a href="#Modes">Modes</a><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --> | <a href="#Books">Books</a><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --> | <a href="#Compositions">Compositions</a><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: -->
<!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextHeadingRule:5:&lt;h1&gt; --><h1 id="toc0"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:5 --><strong>Intervals</strong></h1>
 

<table class="wiki_table">
    <tr>
        <td><strong>DEGREE</strong><br />
</td>
        <td><strong>NOTE</strong><br />
<strong>NAME</strong><br />
</td>
        <td><strong>CENTS</strong><br />
<strong><span style="background-color: #ffffff;">DMS</span></strong><br />
</td>
        <td style="text-align: center;"><strong>Approximate</strong><br />
<strong>Ratios 1<!-- ws:start:WikiTextRawRule:00:``*`` -->*<!-- ws:end:WikiTextRawRule:00 --></strong><br />
</td>
        <td style="text-align: center;"><strong>Approximate</strong><br />
<strong>Ratios 2</strong> <strong><!-- ws:start:WikiTextRawRule:01:``**`` -->**<!-- ws:end:WikiTextRawRule:01 --></strong><br />
</td>
        <td style="text-align: center;">Nearest<br />
Harmonic<br />
</td>
        <td>Interval Type<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;">1/1<br />
</td>
        <td style="text-align: center;">1<br />
</td>
        <td>Unison<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>C^, Dv<br />
</td>
        <td>85.714<br />
25°42'51&quot;<br />
</td>
        <td style="text-align: center;">20/19, 19/18, 18/17<br />
</td>
        <td style="text-align: center;">22/21, 28/27, 21/20<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 />
<span style="background-color: #ffffff;">51°25'43&quot;</span><br />
</td>
        <td style="text-align: center;">11/10, 10/9, 19/17<br />
</td>
        <td style="text-align: center;">9/8, 10/9, 11/10,<br />
12/11<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^, Ev<br />
</td>
        <td>257.143<br />
77°8'34&quot;<br />
</td>
        <td style="text-align: center;">22/19, 20/17<br />
</td>
        <td style="text-align: center;">7/6, 8/7<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 />
<span style="background-color: #ffffff;">102°51'26&quot;</span><br />
</td>
        <td style="text-align: center;">11/9, 17/14<br />
</td>
        <td style="text-align: center;">11/9, 5/4, 6/5<br />
</td>
        <td style="text-align: center;">39<br />
</td>
        <td>Neutral 3rd<br />
</td>
    </tr>
    <tr>
        <td>5·<br />
</td>
        <td>E^, Fv<br />
</td>
        <td>428.571<br />
<span style="line-height: 15.6000003814697px;">128°34'17&quot;</span><br />
</td>
        <td style="text-align: center;">9/7, 14/11, 22/17<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>51<span style="line-height: 1.5;">4.286</span><br />
<span style="background-color: #ffffff;">154°17'9&quot;</span><br />
</td>
        <td style="text-align: center;">19/14<br />
</td>
        <td style="text-align: center;">4/3,11/8<br />
</td>
        <td style="text-align: center;">43<br />
</td>
        <td>Wide 4th<br />
</td>
    </tr>
    <tr>
        <td>7·<br />
</td>
        <td>F^, Gv<br />
</td>
        <td>600<br />
180°<br />
</td>
        <td style="text-align: center;">7/5, 10/7<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 />
<span style="background-color: #ffffff;">205°42'51&quot;</span><br />
</td>
        <td style="text-align: center;">28/19<br />
</td>
        <td style="text-align: center;">3/2, 16/11<br />
</td>
        <td style="text-align: center;">95<br />
</td>
        <td>Narrow 5th<br />
</td>
    </tr>
    <tr>
        <td>9·<br />
</td>
        <td>G^, Av<br />
</td>
        <td>771.429<br />
231°25'43&quot;<br />
</td>
        <td style="text-align: center;">14/9, 11/7, 17/11<br />
</td>
        <td style="text-align: center;"><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 />
<span style="background-color: #ffffff;">257°8'34&quot;</span><br />
</td>
        <td style="text-align: center;">18/11<br />
</td>
        <td style="text-align: center;">18/11, 8/5, 5/3<br />
</td>
        <td style="text-align: center;">105<br />
</td>
        <td>Neutral 6th<br />
</td>
    </tr>
    <tr>
        <td>11·<br />
</td>
        <td>A^, Bv<br />
</td>
        <td>942.857<br />
282°51'26&quot;<br />
</td>
        <td style="text-align: center;">19/11, 17/10<br />
</td>
        <td style="text-align: center;">12/7, 7/4<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 />
<span style="background-color: #ffffff;">308°34'17&quot;</span><br />
</td>
        <td style="text-align: center;">20/11, 9/5, 34/19<br />
</td>
        <td style="text-align: center;">16/9, 9/5, 20/11,<br />
11/6<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^, Cv<br />
</td>
        <td>1114.286<br />
234°17'9&quot;<br />
</td>
        <td style="text-align: center;">19/10, 36/19, 17/9<br />
</td>
        <td style="text-align: center;">21/11, 27/14, 40/21<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 />
360°<br />
</td>
        <td style="text-align: center;">2/1<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>

<!-- ws:start:WikiTextRawRule:02:``*`` -->*<!-- ws:end:WikiTextRawRule:02 -->based on treating 14-EDO as a 2.7/5.9/5.11/5.17/5.19/5 <a class="wiki_link" href="/subgroup">subgroup</a>; other approaches are possible.<br />
<span style="display: block; text-align: center;"><!-- ws:start:WikiTextRawRule:03:``**`` -->**<!-- ws:end:WikiTextRawRule:03 --></span><br />
based on treating 14edo as an 11-limit temperament<br />
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<!-- ws:start:WikiTextHeadingRule:7:&lt;h1&gt; --><h1 id="toc1"><a name="Rank two temperaments"></a><!-- ws:end:WikiTextHeadingRule:7 -->Rank two temperaments</h1>
 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/List%20of%2014edo%20rank%20two%20temperaments%20by%20badness">List of 14edo rank two temperaments by badness</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:9:&lt;h1&gt; --><h1 id="toc2"><a name="Harmony"></a><!-- ws:end:WikiTextHeadingRule:9 -->Harmony</h1>
 The character of 14-EDO does not well serve those seeking low-limit JI approaches, with the exception of 5:7:9:11:17:19 (which is quite well approximated, relative to other JI approximations of the low-numbered EDOs). However, the ratios 7/5, 7/6, 9/7, 10/7, 10/9, 11/7, 11/9, and 11/10 are all recognizably approximated, and if you accept that 14edo offers approximations of these intervals, you end up with a low-complexity, high-damage 11-limit temperament where the commas listed at the bottom of this page are tempered out. This leads to some of the bizarre equivalences described in the second &quot;Approximate Ratios&quot; column in the table above.<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 />
<!-- ws:start:WikiTextHeadingRule:11:&lt;h1&gt; --><h1 id="toc3"><a name="Notation"></a><!-- ws:end:WikiTextHeadingRule:11 -->Notation</h1>
 <a class="wiki_link" href="/Ivor%20Darreg">Ivor Darreg</a> wrote in <a class="wiki_link_ext" href="http://sonic-arts.org/darreg/dar15.htm" rel="nofollow">this article</a>:<br />
<br />
<em>The 14-tone scale presents a new situation: while one might use ordinary sharps and flats in addition to conventional naturals for the notes of the 7-tone-equal temperament, it would be misleading and confusing to do so, because there is a 7-tone circle of fifths (admittedly quite distorted) already notatable and nameable as F C G D A E B in the usual manner. But there is no 14-tone circle of fifths. There is simply a second set of 7 fifths in a circle which does not intersect the with the first set. Thus is we think of B-flat and B, or B-natural and F-sharp, the 14-tone-system interval would NOT be a fifth of that system and would not sound like one, since B F would be the very same kind of distorted fifth that C G or A E happens to be in 7 or 14. Our suggestion is to call the new notes of 14, the second set of 7, F* C* G* D* A* E* B*, and use asterisks or arrows or whatever you please on the staff. Or just number the tones as for 13.</em><br />
<br />
The following chart (made by <a class="wiki_link" href="/T%C3%BAtim%20Dennsuul%20Wafiil">TDW</a>) shows this recommendation as &quot;standard notation&quot; as well as a proposed alternative.<br />
<br />
<!-- ws:start:WikiTextLocalImageRule:450:&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:450 --><br />
<br />
<!-- ws:start:WikiTextHeadingRule:13:&lt;h1&gt; --><h1 id="toc4"><a name="Images"></a><!-- ws:end:WikiTextHeadingRule:13 -->Images</h1>
 <br />
<!-- ws:start:WikiTextLocalImageRule:451:&lt;img src=&quot;/file/view/14edo%20wheel.png/516971016/343x343/14edo%20wheel.png&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 343px; width: 343px;&quot; /&gt; --><img src="/file/view/14edo%20wheel.png/516971016/343x343/14edo%20wheel.png" alt="14edo wheel.png" title="14edo wheel.png" style="height: 343px; width: 343px;" /><!-- ws:end:WikiTextLocalImageRule:451 --><br />
<br />
<!-- ws:start:WikiTextHeadingRule:15:&lt;h1&gt; --><h1 id="toc5"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:15 -->Commas</h1>
 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:17:&lt;h1&gt; --><h1 id="toc6"><a name="Modes"></a><!-- ws:end:WikiTextHeadingRule:17 --><strong><a class="wiki_link" href="/modes">Modes</a></strong></h1>
 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 />
<br />
<!-- ws:start:WikiTextHeadingRule:19:&lt;h1&gt; --><h1 id="toc7"><a name="Books"></a><!-- ws:end:WikiTextHeadingRule:19 -->Books</h1>
 <!-- ws:start:WikiTextLocalImageRule:452:&lt;img src=&quot;/file/view/Libro_Tetradecaf%C3%B3nico.PNG/163539671/Libro_Tetradecaf%C3%B3nico.PNG&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/Libro_Tetradecaf%C3%B3nico.PNG/163539671/Libro_Tetradecaf%C3%B3nico.PNG" alt="Libro_Tetradecafónico.PNG" title="Libro_Tetradecafónico.PNG" /><!-- ws:end:WikiTextLocalImageRule:452 --><br />
<em>Sword, Ron. &quot;Tetradecaphonic Scales for Guitar&quot; IAAA Press. First Ed: June 2009.</em><br />
<br />
<!-- ws:start:WikiTextHeadingRule:21:&lt;h1&gt; --><h1 id="toc8"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:21 --><strong>Compositions</strong></h1>
 <a class="wiki_link_ext" href="http://split-notes.com/004/" rel="nofollow">NANA WODORI</a> by knowsur<br />
<a class="wiki_link_ext" href="http://micro.soonlabel.com/0-praxis/audio/August/august_03_thereminnards.mp3" rel="nofollow">Thereminnards</a> by Ralph Lewis<br />
Pendula (for amplified trombone) by Philip Schuessler<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><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="http://archive.org/download/tranSentient/tranSentient.mp3" rel="nofollow">tranSentient</a> by <a class="wiki_link" href="/Jon%20Lyle%20Smith">Jon Lyle Smith</a><br />
<a class="wiki_link_ext" href="http://archive.org/download/TheSpectrumOfDesire/the_spectrum_of_desire.mp3" rel="nofollow">the spectrum of desire</a> 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://youtu.be/mHyaW1fVWsg" rel="nofollow">Medicine Wheel</a> by Mark Allan Barnes<br />
<a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/Fourteen_EDO_CBobro_r8b.mp3" rel="nofollow">Fourteen EDO</a> by <a class="wiki_link" href="/Cameron%20Bobro">Cameron Bobro</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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2014-07-24 11:11:53 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-03-24 16:30:02 UTC</tt>.<br>
-: The original revision id was <tt>516971060</tt>.<br>
+: The original revision id was <tt>545189974</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: @@
 =**Intervals**=
 || **DEGREE** || **NOTE**
-**NAME** || **CENTS** ||= **Approximate**
+**NAME** || **CENTS**
+**&lt;span style="background-color: #ffffff;"&gt;DMS&lt;/span&gt;** ||= **Approximate**
 **Ratios 1``*``** ||= **Approximate**
 **Ratios 2** **``**``** ||= Nearest
 Harmonic || Interval Type ||
 || 0 || C || 0 ||= 1/1 ||= 1/1 ||= 1 || Unison ||
-|| 1 || C^, Dv || 85.714 ||= 20/19, 19/18, 18/17 ||= 22/21, 28/27, 21/20 ||= 67 || Narrow Minor 2nd ||
+|| 1 || C^, Dv || 85.714
-|| 2 || D || 171.429 ||= 11/10, 10/9, 19/17 ||= 9/8, 10/9, 11/10,
+°42'51" ||= 20/19, 19/18, 18/17 ||= 22/21, 28/27, 21/20 ||= 67 || Narrow Minor 2nd ||
+|| 2 || D || 171.429
+&lt;span style="background-color: #ffffff;"&gt;51°25'43"&lt;/span&gt; ||= 11/10, 10/9, 19/17 ||= 9/8, 10/9, 11/10,
 /11 ||= 71 || Neutral 2nd, or
 Narrow Major 2nd ||
-|| 3· || D^, Ev || 257.143 ||= 22/19, 20/17 ||= 7/6, 8/7 ||= 37 || Subminor 3rd ||
+|| 3· || D^, Ev || 257.143
-|| 4 || E || 342.857 ||= 11/9, 17/14 ||= 11/9, 5/4, 6/5 ||= 39 || Neutral 3rd ||
+°8'34" ||= 22/19, 20/17 ||= 7/6, 8/7 ||= 37 || Subminor 3rd ||
-|| 5· || E^, Fv || 428.571 ||= 9/7, 14/11, 22/17 ||= 9/7, 14/11 ||= 41 || Supermajor 3rd ||
+|| 4 || E || 342.857
-|| 6 || F || 514.286 ||= 19/14 ||= 4/3,11/8 ||= 43 || Wide 4th ||
+&lt;span style="background-color: #ffffff;"&gt;102°51'26"&lt;/span&gt; ||= 11/9, 17/14 ||= 11/9, 5/4, 6/5 ||= 39 || Neutral 3rd ||
-|| 7· || F^, Gv || 600 ||= 7/5, 10/7 ||= 7/5, 10/7 ||= 91 || Tritone ||
+|| 5· || E^, Fv || 428.571
-|| 8 || G || 685.714 ||= 28/19 ||= 3/2, 16/11 ||= 95 || Narrow 5th ||
+&lt;span style="line-height: 15.6000003814697px;"&gt;128°34'17"&lt;/span&gt; ||= 9/7, 14/11, 22/17 ||= 9/7, 14/11 ||= 41 || Supermajor 3rd ||
-|| 9· || G^, Av || 771.429 ||= 14/9, 11/7, 17/11 ||= 11/7, 14/9 ||= 25 || Subminor 6th ||
+|| 6 || F || 51&lt;span style="line-height: 1.5;"&gt;4.286&lt;/span&gt;
-|| 10 || A || 857.143 ||= 18/11 ||= 18/11, 8/5, 5/3 ||= 105 || Neutral 6th ||
+&lt;span style="background-color: #ffffff;"&gt;154°17'9"&lt;/span&gt; ||= 19/14 ||= 4/3,11/8 ||= 43 || Wide 4th ||
-|| 11· || A^, Bv || 942.857 ||= 19/11, 17/10 ||= 12/7, 7/4 ||= 55 || Supermajor 6th ||
+|| 7· || F^, Gv || 600
-|| 12 || B || 1028.571 ||= 20/11, 9/5, 34/19 ||= 16/9, 9/5, 20/11,
+° ||= 7/5, 10/7 ||= 7/5, 10/7 ||= 91 || Tritone ||
+|| 8 || G || 685.714
+&lt;span style="background-color: #ffffff;"&gt;205°42'51"&lt;/span&gt; ||= 28/19 ||= 3/2, 16/11 ||= 95 || Narrow 5th ||
+|| 9· || G^, Av || 771.429
+°25'43" ||= 14/9, 11/7, 17/11 ||=   ||= 25 || Subminor 6th ||
+|| 10 || A || 857.143
+&lt;span style="background-color: #ffffff;"&gt;257°8'34"&lt;/span&gt; ||= 18/11 ||= 18/11, 8/5, 5/3 ||= 105 || Neutral 6th ||
+|| 11· || A^, Bv || 942.857
+°51'26" ||= 19/11, 17/10 ||= 12/7, 7/4 ||= 55 || Supermajor 6th ||
+|| 12 || B || 1028.571
+&lt;span style="background-color: #ffffff;"&gt;308°34'17"&lt;/span&gt; ||= 20/11, 9/5, 34/19 ||= 16/9, 9/5, 20/11,
 /6 ||= 29 || Neutral 7th, or
 Wide Minor 7th ||
-|| 13 || B^, Cv || 1114.286 ||= 19/10, 36/19, 17/9 ||= 21/11, 27/14, 40/21 ||= 61 || Wide Major 7th ||
+|| 13 || B^, Cv || 1114.286
-|| 14··(or 0) || C || 1200 ||= 2/1 ||= 2/1 ||= 2 || Octave ||
+°17'9" ||= 19/10, 36/19, 17/9 ||= 21/11, 27/14, 40/21 ||= 61 || Wide Major 7th ||
+|| 14··(or 0) || C || 1200
+° ||= 2/1 ||= 2/1 ||= 2 || Octave ||
 ``*``based on treating 14-EDO as a 2.7/5.9/5.11/5.17/5.19/5 [[subgroup]]; other approaches are possible.
-**&lt;span style="text-align: center;"&gt;``**`` &lt;/span&gt;**based on treating 14edo as an 11-limit temperament
+&lt;span style="display: block; text-align: center;"&gt;``**``&lt;/span&gt;
+based on treating 14edo as an 11-limit temperament
 [[media type="custom" key="24802838"]]
@@ Line 135: / Line 151: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;strong&gt;CENTS&lt;/strong&gt;&lt;br /&gt;
+&lt;strong&gt;&lt;span style="background-color: #ffffff;"&gt;DMS&lt;/span&gt;&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;
@@ Line 170: / Line 187: @@
 &lt;/td&gt;
          &lt;td&gt;85.714&lt;br /&gt;
+°42'51&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;20/19, 19/18, 18/17&lt;br /&gt;
@@ Line 186: / Line 204: @@
 &lt;/td&gt;
          &lt;td&gt;171.429&lt;br /&gt;
+&lt;span style="background-color: #ffffff;"&gt;51°25'43&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;11/10, 10/9, 19/17&lt;br /&gt;
@@ Line 204: / Line 223: @@
 &lt;/td&gt;
          &lt;td&gt;257.143&lt;br /&gt;
+°8'34&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;22/19, 20/17&lt;br /&gt;
@@ Line 220: / Line 240: @@
 &lt;/td&gt;
          &lt;td&gt;342.857&lt;br /&gt;
+&lt;span style="background-color: #ffffff;"&gt;102°51'26&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;11/9, 17/14&lt;br /&gt;
@@ Line 236: / Line 257: @@
 &lt;/td&gt;
          &lt;td&gt;428.571&lt;br /&gt;
+&lt;span style="line-height: 15.6000003814697px;"&gt;128°34'17&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;9/7, 14/11, 22/17&lt;br /&gt;
@@ Line 251: / Line 273: @@
          &lt;td&gt;F&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;514.286&lt;br /&gt;
+         &lt;td&gt;51&lt;span style="line-height: 1.5;"&gt;4.286&lt;/span&gt;&lt;br /&gt;
+&lt;span style="background-color: #ffffff;"&gt;154°17'9&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;19/14&lt;br /&gt;
@@ Line 268: / Line 291: @@
 &lt;/td&gt;
          &lt;td&gt;600&lt;br /&gt;
+°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;7/5, 10/7&lt;br /&gt;
@@ Line 284: / Line 308: @@
 &lt;/td&gt;
          &lt;td&gt;685.714&lt;br /&gt;
+&lt;span style="background-color: #ffffff;"&gt;205°42'51&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;28/19&lt;br /&gt;
@@ Line 300: / Line 325: @@
 &lt;/td&gt;
          &lt;td&gt;771.429&lt;br /&gt;
+°25'43&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;14/9, 11/7, 17/11&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;11/7, 14/9&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;25&lt;br /&gt;
@@ Line 316: / Line 342: @@
 &lt;/td&gt;
          &lt;td&gt;857.143&lt;br /&gt;
+&lt;span style="background-color: #ffffff;"&gt;257°8'34&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;18/11&lt;br /&gt;
@@ Line 332: / Line 359: @@
 &lt;/td&gt;
          &lt;td&gt;942.857&lt;br /&gt;
+°51'26&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;19/11, 17/10&lt;br /&gt;
@@ Line 348: / Line 376: @@
 &lt;/td&gt;
          &lt;td&gt;1028.571&lt;br /&gt;
+&lt;span style="background-color: #ffffff;"&gt;308°34'17&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;20/11, 9/5, 34/19&lt;br /&gt;
@@ Line 366: / Line 395: @@
 &lt;/td&gt;
          &lt;td&gt;1114.286&lt;br /&gt;
+°17'9&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;19/10, 36/19, 17/9&lt;br /&gt;
@@ Line 382: / Line 412: @@
 &lt;/td&gt;
          &lt;td&gt;1200&lt;br /&gt;
+°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;2/1&lt;br /&gt;
@@ Line 395: / Line 426: @@
 &lt;!-- ws:start:WikiTextRawRule:02:``*`` --&gt;*&lt;!-- ws:end:WikiTextRawRule:02 --&gt;based on treating 14-EDO as a 2.7/5.9/5.11/5.17/5.19/5 &lt;a class="wiki_link" href="/subgroup"&gt;subgroup&lt;/a&gt;; other approaches are possible.&lt;br /&gt;
-&lt;strong&gt;&lt;span style="text-align: center;"&gt;&lt;!-- ws:start:WikiTextRawRule:03:``**`` --&gt;**&lt;!-- ws:end:WikiTextRawRule:03 --&gt; &lt;/span&gt;&lt;/strong&gt;based on treating 14edo as an 11-limit temperament&lt;br /&gt;
+&lt;span style="display: block; text-align: center;"&gt;&lt;!-- ws:start:WikiTextRawRule:03:``**`` --&gt;**&lt;!-- ws:end:WikiTextRawRule:03 --&gt;&lt;/span&gt;&lt;br /&gt;
+based on treating 14edo as an 11-limit temperament&lt;br /&gt;
 &lt;!-- ws:start:WikiTextMediaRule:4:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/custom/24802838?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;24802838&amp;amp;quot;&amp;quot; title=&amp;quot;Custom Media&amp;quot;/&amp;gt; --&gt;&lt;object id="example" type="image/svg+xml" data="http://xenharmonic.wikispaces.com/file/view/14ed2-001.svg"&gt;alt : Your browser has no SVG support.&lt;/object&gt;&lt;!-- ws:end:WikiTextMediaRule:4 --&gt;&lt;br /&gt;
 &lt;br /&gt;

14edo: Difference between revisions

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