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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<span style="display: block; text-align: right;">[[6平均律|日本語]]</span>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2017-07-22 19:11:04 UTC</tt>.<br>
: The original revision id was <tt>615831797</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">&lt;span style="display: block; text-align: right;"&gt;[[6平均律|日本語]]
&lt;/span&gt;
=6 Equal Divisions of the Octave=
==="whole tone"===


**6-edo** divides the 1200-[[cents|cent]] octave into 6 equal parts, making its smallest interval exactly 200¢, or the sixth root of 2.
=6 Equal Divisions of the Octave=


==Related EDOs==  
==="whole tone"===
* Superset: [[2edo]], [[3edo]]
* Supersets: [[12edo]], [[18edo]], [[24edo]]...
* Neighbours: [[5edo]], [[7edo]]


==Notation==
'''6-edo''' divides the 1200-[[cents|cent]] octave into 6 equal parts, making its smallest interval exactly 200¢, or the sixth root of 2.
* Notatable on a five-line staff with standard.


==Music==  
==Related EDOs==
[[http://www.uvnitr.cz/flaoyg/forgotten_works/dvandva.html|Dvandva]] by Milan Guštar.
<ul><li>Superset: [[2edo|2edo]], [[3edo|3edo]]</li><li>Supersets: [[12edo|12edo]], [[18edo|18edo]], [[24edo|24edo]]...</li><li>Neighbours: [[5edo|5edo]], [[7edo|7edo]]</li></ul>
[[http://micro.soonlabel.com/6edo/the-good-boundless-03.mp3|The Good Boundless]] by Chris Vaisvil


==Commas==  
==Notation==
6 EDO tempers out the following commas. (Note: This assumes val &lt; 6 10 14 17 21 22 |.)
<ul><li>Notatable on a five-line staff with standard.</li></ul>
||~ Comma ||~ Value (cents) ||~ Name ||~ Second Name ||~ Val ||
 
||= 32/27 ||&gt; 294.13 || Pythagorean minor third ||  || | 5 -3 &gt; ||
==Music==
||= 128/125 ||&gt; 41.06 || Diesis || Augmented Comma || | 7 0 -3 &gt; ||
[http://www.uvnitr.cz/flaoyg/forgotten_works/dvandva.html Dvandva] by Milan Guštar.
||= 3125/3072 ||&gt; 29.61 || Small Diesis || Magic Comma || | -10 -1 5 &gt; ||
||= 393216/390625 ||&gt; 11.45 || Wuerschmidt Comma ||  || | 17 1 -8 &gt; ||
||= 2783927/2773137 ||&gt; 6.72 || Mutt Comma ||  || | -44 -3 21 &gt; ||
||= 49/48 ||&gt; 35.70 || Slendro Diesis ||  || | -4 -1 0 2 &gt; ||
||= 50/49 ||&gt; 34.98 || Tritonic Diesis || Jubilisma || | 1 0 2 -2 &gt; ||
||= 3136/3125 ||&gt; 6.08 || Hemimean ||  || | 6 0 -5 2 &gt; ||
||= 6144/6125 ||&gt; 5.36 || Porwell ||  || | 11 1 -3 -2 &gt; ||
||= 2401/2400 ||&gt; 0.72 || Breedsma ||  || | -5 -1 -2 4 &gt; ||
||= 121/120 ||&gt; 14.37 || Biyatisma ||  || | -3 -1 -1 0 2 &gt; ||
||= 176/175 ||&gt; 9.86 || Valinorsma ||  || | 4 0 -2 -1 1 &gt; ||
||= 385/384 ||&gt; 4.50 || Keenanisma ||  || | -7 -1 1 1 1 &gt; ||


[[media type="custom" key="15381610"]]</pre></div>
[http://micro.soonlabel.com/6edo/the-good-boundless-03.mp3 The Good Boundless] by Chris Vaisvil
<h4>Original HTML content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;6edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;span style="display: block; text-align: right;"&gt;&lt;a class="wiki_link" href="/6%E5%B9%B3%E5%9D%87%E5%BE%8B"&gt;日本語&lt;/a&gt;&lt;br /&gt;
&lt;/span&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:1:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x6 Equal Divisions of the Octave"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:1 --&gt;6 Equal Divisions of the Octave&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:3:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x6 Equal Divisions of the Octave--&amp;quot;whole tone&amp;quot;"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:3 --&gt;&amp;quot;whole tone&amp;quot;&lt;/h3&gt;
&lt;br /&gt;
&lt;strong&gt;6-edo&lt;/strong&gt; divides the 1200-&lt;a class="wiki_link" href="/cents"&gt;cent&lt;/a&gt; octave into 6 equal parts, making its smallest interval exactly 200¢, or the sixth root of 2.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:5:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x6 Equal Divisions of the Octave-Related EDOs"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:5 --&gt;Related EDOs&lt;/h2&gt;
&lt;ul&gt;&lt;li&gt;Superset: &lt;a class="wiki_link" href="/2edo"&gt;2edo&lt;/a&gt;, &lt;a class="wiki_link" href="/3edo"&gt;3edo&lt;/a&gt;&lt;/li&gt;&lt;li&gt;Supersets: &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;, &lt;a class="wiki_link" href="/18edo"&gt;18edo&lt;/a&gt;, &lt;a class="wiki_link" href="/24edo"&gt;24edo&lt;/a&gt;...&lt;/li&gt;&lt;li&gt;Neighbours: &lt;a class="wiki_link" href="/5edo"&gt;5edo&lt;/a&gt;, &lt;a class="wiki_link" href="/7edo"&gt;7edo&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:7:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x6 Equal Divisions of the Octave-Notation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:7 --&gt;Notation&lt;/h2&gt;
&lt;ul&gt;&lt;li&gt;Notatable on a five-line staff with standard.&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:9:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="x6 Equal Divisions of the Octave-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:9 --&gt;Music&lt;/h2&gt;
&lt;a class="wiki_link_ext" href="http://www.uvnitr.cz/flaoyg/forgotten_works/dvandva.html" rel="nofollow"&gt;Dvandva&lt;/a&gt; by Milan Guštar.&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/6edo/the-good-boundless-03.mp3" rel="nofollow"&gt;The Good Boundless&lt;/a&gt; by Chris Vaisvil&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:11:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="x6 Equal Divisions of the Octave-Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:11 --&gt;Commas&lt;/h2&gt;
6 EDO tempers out the following commas. (Note: This assumes val &amp;lt; 6 10 14 17 21 22 |.)&lt;br /&gt;


==Commas==
6 EDO tempers out the following commas. (Note: This assumes val &lt; 6 10 14 17 21 22 |.)


&lt;table class="wiki_table"&gt;
{| class="wikitable"
    &lt;tr&gt;
|-
        &lt;th&gt;Comma&lt;br /&gt;
! | Comma
&lt;/th&gt;
! | Value (cents)
        &lt;th&gt;Value (cents)&lt;br /&gt;
! | Name
&lt;/th&gt;
! | Second Name
        &lt;th&gt;Name&lt;br /&gt;
! | Val
&lt;/th&gt;
|-
        &lt;th&gt;Second Name&lt;br /&gt;
| style="text-align:center;" | 32/27
&lt;/th&gt;
| style="text-align:right;" | 294.13
        &lt;th&gt;Val&lt;br /&gt;
| | Pythagorean minor third
&lt;/th&gt;
| |
    &lt;/tr&gt;
| | | 5 -3 &gt;
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;32/27&lt;br /&gt;
| style="text-align:center;" | 128/125
&lt;/td&gt;
| style="text-align:right;" | 41.06
        &lt;td style="text-align: right;"&gt;294.13&lt;br /&gt;
| | Diesis
&lt;/td&gt;
| | Augmented Comma
        &lt;td&gt;Pythagorean minor third&lt;br /&gt;
| | | 7 0 -3 &gt;
&lt;/td&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| style="text-align:center;" | 3125/3072
&lt;/td&gt;
| style="text-align:right;" | 29.61
        &lt;td&gt;| 5 -3 &amp;gt;&lt;br /&gt;
| | Small Diesis
&lt;/td&gt;
| | Magic Comma
    &lt;/tr&gt;
| | | -10 -1 5 &gt;
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;128/125&lt;br /&gt;
| style="text-align:center;" | 393216/390625
&lt;/td&gt;
| style="text-align:right;" | 11.45
        &lt;td style="text-align: right;"&gt;41.06&lt;br /&gt;
| | Wuerschmidt Comma
&lt;/td&gt;
| |
        &lt;td&gt;Diesis&lt;br /&gt;
| | | 17 1 -8 &gt;
&lt;/td&gt;
|-
        &lt;td&gt;Augmented Comma&lt;br /&gt;
| style="text-align:center;" | 2783927/2773137
&lt;/td&gt;
| style="text-align:right;" | 6.72
        &lt;td&gt;| 7 0 -3 &amp;gt;&lt;br /&gt;
| | Mutt Comma
&lt;/td&gt;
| |
    &lt;/tr&gt;
| | | -44 -3 21 &gt;
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;3125/3072&lt;br /&gt;
| style="text-align:center;" | 49/48
&lt;/td&gt;
| style="text-align:right;" | 35.70
        &lt;td style="text-align: right;"&gt;29.61&lt;br /&gt;
| | Slendro Diesis
&lt;/td&gt;
| |
        &lt;td&gt;Small Diesis&lt;br /&gt;
| | | -4 -1 0 2 &gt;
&lt;/td&gt;
|-
        &lt;td&gt;Magic Comma&lt;br /&gt;
| style="text-align:center;" | 50/49
&lt;/td&gt;
| style="text-align:right;" | 34.98
        &lt;td&gt;| -10 -1 5 &amp;gt;&lt;br /&gt;
| | Tritonic Diesis
&lt;/td&gt;
| | Jubilisma
    &lt;/tr&gt;
| | | 1 0 2 -2 &gt;
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;393216/390625&lt;br /&gt;
| style="text-align:center;" | 3136/3125
&lt;/td&gt;
| style="text-align:right;" | 6.08
        &lt;td style="text-align: right;"&gt;11.45&lt;br /&gt;
| | Hemimean
&lt;/td&gt;
| |
        &lt;td&gt;Wuerschmidt Comma&lt;br /&gt;
| | | 6 0 -5 2 &gt;
&lt;/td&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| style="text-align:center;" | 6144/6125
&lt;/td&gt;
| style="text-align:right;" | 5.36
        &lt;td&gt;| 17 1 -8 &amp;gt;&lt;br /&gt;
| | Porwell
&lt;/td&gt;
| |
    &lt;/tr&gt;
| | | 11 1 -3 -2 &gt;
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;2783927/2773137&lt;br /&gt;
| style="text-align:center;" | 2401/2400
&lt;/td&gt;
| style="text-align:right;" | 0.72
        &lt;td style="text-align: right;"&gt;6.72&lt;br /&gt;
| | Breedsma
&lt;/td&gt;
| |
        &lt;td&gt;Mutt Comma&lt;br /&gt;
| | | -5 -1 -2 4 &gt;
&lt;/td&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| style="text-align:center;" | 121/120
&lt;/td&gt;
| style="text-align:right;" | 14.37
        &lt;td&gt;| -44 -3 21 &amp;gt;&lt;br /&gt;
| | Biyatisma
&lt;/td&gt;
| |
    &lt;/tr&gt;
| | | -3 -1 -1 0 2 &gt;
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;49/48&lt;br /&gt;
| style="text-align:center;" | 176/175
&lt;/td&gt;
| style="text-align:right;" | 9.86
        &lt;td style="text-align: right;"&gt;35.70&lt;br /&gt;
| | Valinorsma
&lt;/td&gt;
| |
        &lt;td&gt;Slendro Diesis&lt;br /&gt;
| | | 4 0 -2 -1 1 &gt;
&lt;/td&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| style="text-align:center;" | 385/384
&lt;/td&gt;
| style="text-align:right;" | 4.50
        &lt;td&gt;| -4 -1 0 2 &amp;gt;&lt;br /&gt;
| | Keenanisma
&lt;/td&gt;
| |
    &lt;/tr&gt;
| | | -7 -1 1 1 1 &gt;
    &lt;tr&gt;
|}
        &lt;td style="text-align: center;"&gt;50/49&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;34.98&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Tritonic Diesis&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Jubilisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 1 0 2 -2 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3136/3125&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;6.08&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Hemimean&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 6 0 -5 2 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;6144/6125&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;5.36&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Porwell&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 11 1 -3 -2 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;2401/2400&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;0.72&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Breedsma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -5 -1 -2 4 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;121/120&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;14.37&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Biyatisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -3 -1 -1 0 2 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;176/175&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;9.86&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Valinorsma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 4 0 -2 -1 1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;385/384&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;4.50&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Keenanisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -7 -1 1 1 1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
[[Category:6-tone]]
&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/custom/15381610?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;15381610&amp;amp;quot;&amp;quot; title=&amp;quot;Custom Media&amp;quot;/&amp;gt; --&gt;&lt;script type="text/javascript" src="http://webplayer.yahooapis.com/player.js"&gt;
[[Category:6edo]]
&lt;/script&gt;&lt;!-- ws:end:WikiTextMediaRule:0 --&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
[[Category:edo]]
[[Category:listen]]
[[Category:macrotonal]]
[[Category:scale]]
[[Category:subgroup]]
[[Category:todo:unify_precision]]

Revision as of 00:00, 17 July 2018

日本語

6 Equal Divisions of the Octave

"whole tone"

6-edo divides the 1200-cent octave into 6 equal parts, making its smallest interval exactly 200¢, or the sixth root of 2.

Related EDOs

Notation

  • Notatable on a five-line staff with standard.

Music

Dvandva by Milan Guštar.

The Good Boundless by Chris Vaisvil

Commas

6 EDO tempers out the following commas. (Note: This assumes val < 6 10 14 17 21 22 |.)

Comma Value (cents) Name Second Name Val
32/27 294.13 Pythagorean minor third | 5 -3 >
128/125 41.06 Diesis Augmented Comma | 7 0 -3 >
3125/3072 29.61 Small Diesis Magic Comma | -10 -1 5 >
393216/390625 11.45 Wuerschmidt Comma | 17 1 -8 >
2783927/2773137 6.72 Mutt Comma | -44 -3 21 >
49/48 35.70 Slendro Diesis | -4 -1 0 2 >
50/49 34.98 Tritonic Diesis Jubilisma | 1 0 2 -2 >
3136/3125 6.08 Hemimean | 6 0 -5 2 >
6144/6125 5.36 Porwell | 11 1 -3 -2 >
2401/2400 0.72 Breedsma | -5 -1 -2 4 >
121/120 14.37 Biyatisma | -3 -1 -1 0 2 >
176/175 9.86 Valinorsma | 4 0 -2 -1 1 >
385/384 4.50 Keenanisma | -7 -1 1 1 1 >
Retrieved from "https://en.xen.wiki/index.php?title=6edo&oldid=957"