10edo: Difference between revisions

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:~~guest~~|~~guest~~]] and made on <tt>2011-09-~~18 15~~:43:53 UTC</tt>.<br>

: This revision was by author [[User:igliashon|igliashon]] and made on <tt>2011-09-20 19:39:35 UTC</tt>.<br>

: The original revision id was <tt>~~255331488~~</tt>.<br>

: The original revision id was <tt>256314300</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 19:

|| 2 || 240 || 15/13, 8/7 || second/third ||

|| 3 || 360 || 16/13 || large neutral third ||

|| 4 || 480 || 64/49, 169/128 || smaller fourth ~~33/25~~ ||

|| 4 || 480 || 64/49, 169/128 || smaller fourth ||

|| 5 || 600 || 91/64, 169/120 || tritone ||

|| 6 || 720 || 49/32, 256/169 || bigger fifth ~~50/33~~ ||

|| 6 || 720 || 49/32, 256/169 || bigger fifth ||

|| 7 || 840 || 13/8 || neutral sixth ||

|| 8 || 960 || 7/4, 26/15, 125/72 || sixth/seventh ||

Line 27:

|| 10 || 1200 || 2/1 || octave ||

*based on treating 10-EDO as a 2.7.13.15 subgroup temperament.

=Linear temperaments=

||~ Periods

Line 73:

Line 74:

[[file:decexperiment.ogg]]3 tracks made in ZynAddSubFx simply mixed in Audacity (cenobyte)

=**Instruments**=

10-EDO lends itself exceptionally well to guitar (and other fretted strings), on account of the fact that five of its flat 4ths (at 480 cents) exactly spans two octaves (480*5=2400), meaning the open strings can be uniformly tuned in 4ths. This allows for greater uniformity in chord and scale fingering patterns than in 12-TET, making it exceptionally easy to learn. For instance, the fingering for an "E" chord would be 0-2-2-1-0-0 (low to high), an "A" chord would be 0-0-2-2-1-0, and a "D" chord would be 1-0-0-2-2-1. This is also the case in all EDOs which are multiples of 5, but in 10-EDO it is particularly simple.

[[image:Decaphonic_Classic_Guitar.png caption="A Decaphonic (10-EDO) Classical Guitar"]][[image:decaphonic-uke.JPG width="526" height="406"]][[media type="custom" key="10021077"]]</pre></div>

Line 144:

Line 147:

</td>

<td>smaller fourth ~~33/25~~<br />

<td>smaller fourth<br />

</td>

</tr>

Line 164:

Line 167:

</td>

<td>bigger fifth ~~50/33~~<br />

<td>bigger fifth<br />

</td>

</tr>

Line 210:

Line 213:

*based on treating 10-EDO as a 2.7.13.15 subgroup temperament.<br />

<br />

<h1 id="toc1"><a name="Linear temperaments"></a>Linear temperaments</h1>

Line 608:

Line 612:

<h1 id="toc4"><a name="Instruments"></a><strong>Instruments</strong></h1>

<br />

10-EDO lends itself exceptionally well to guitar (and other fretted strings), on account of the fact that five of its flat 4ths (at 480 cents) exactly spans two octaves (480*5=2400), meaning the open strings can be uniformly tuned in 4ths. This allows for greater uniformity in chord and scale fingering patterns than in 12-TET, making it exceptionally easy to learn. For instance, the fingering for an &quot;E&quot; chord would be 0-2-2-1-0-0 (low to high), an &quot;A&quot; chord would be 0-0-2-2-1-0, and a &quot;D&quot; chord would be 1-0-0-2-2-1. This is also the case in all EDOs which are multiples of 5, but in 10-EDO it is particularly simple.<br />

<br />

<table class="captionBox"><tr><td class="captionedImage"><img src="/file/view/Decaphonic_Classic_Guitar.png/234752078/Decaphonic_Classic_Guitar.png" alt="Decaphonic_Classic_Guitar.png" title="Decaphonic_Classic_Guitar.png" /></td></tr><tr><td class="imageCaption">A Decaphonic (10-EDO) Classical Guitar</td></tr></table><img src="/file/view/decaphonic-uke.JPG/251070060/526x406/decaphonic-uke.JPG" alt="decaphonic-uke.JPG" title="decaphonic-uke.JPG" style="height: 406px; width: 526px;" /><script type="text/javascript" src="http://webplayer.yahooapis.com/player.js">

</script></body></html></pre></div>

@@ 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:guest|guest]] and made on <tt>2011-09-18 15:43:53 UTC</tt>.<br>
+: This revision was by author [[User:igliashon|igliashon]] and made on <tt>2011-09-20 19:39:35 UTC</tt>.<br>
-: The original revision id was <tt>255331488</tt>.<br>
+: The original revision id was <tt>256314300</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 19: / Line 19: @@
 || 2 || 240 || 15/13, 8/7 || second/third ||
 || 3 || 360 || 16/13 || large neutral third ||
-|| 4 || 480 || 64/49, 169/128 || smaller fourth 33/25 ||
+|| 4 || 480 || 64/49, 169/128 || smaller fourth ||
 || 5 || 600 || 91/64, 169/120 || tritone ||
-|| 6 || 720 || 49/32, 256/169 || bigger fifth 50/33 ||
+|| 6 || 720 || 49/32, 256/169 || bigger fifth ||
 || 7 || 840 || 13/8 || neutral sixth ||
 || 8 || 960 || 7/4, 26/15, 125/72 || sixth/seventh ||
@@ Line 27: / Line 27: @@
 || 10 || 1200 || 2/1 || octave ||
 *based on treating 10-EDO as a 2.7.13.15 subgroup temperament.
 =Linear temperaments=
 ||~ Periods
@@ Line 73: / Line 74: @@
 [[file:decexperiment.ogg]]3 tracks made in ZynAddSubFx simply mixed in Audacity (cenobyte)
 =**Instruments**=
+-EDO lends itself exceptionally well to guitar (and other fretted strings), on account of the fact that five of its flat 4ths (at 480 cents) exactly spans two octaves (480*5=2400), meaning the open strings can be uniformly tuned in 4ths. This allows for greater uniformity in chord and scale fingering patterns than in 12-TET, making it exceptionally easy to learn. For instance, the fingering for an "E" chord would be 0-2-2-1-0-0 (low to high), an "A" chord would be 0-0-2-2-1-0, and a "D" chord would be 1-0-0-2-2-1. This is also the case in all EDOs which are multiples of 5, but in 10-EDO it is particularly simple.
 [[image:Decaphonic_Classic_Guitar.png caption="A Decaphonic (10-EDO) Classical Guitar"]][[image:decaphonic-uke.JPG width="526" height="406"]][[media type="custom" key="10021077"]]</pre></div>
@@ Line 144: / Line 147: @@
          &lt;td&gt;64/49, 169/128&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;smaller fourth 33/25&lt;br /&gt;
+         &lt;td&gt;smaller fourth&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 164: / Line 167: @@
          &lt;td&gt;49/32, 256/169&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;bigger fifth 50/33&lt;br /&gt;
+         &lt;td&gt;bigger fifth&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 210: / Line 213: @@
 *based on treating 10-EDO as a 2.7.13.15 subgroup temperament.&lt;br /&gt;
+&lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:3:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Linear temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:3 --&gt;Linear temperaments&lt;/h1&gt;
@@ Line 608: / Line 612: @@
 &lt;!-- ws:start:WikiTextHeadingRule:9:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Instruments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:9 --&gt;&lt;strong&gt;Instruments&lt;/strong&gt;&lt;/h1&gt;
   &lt;br /&gt;
+-EDO lends itself exceptionally well to guitar (and other fretted strings), on account of the fact that five of its flat 4ths (at 480 cents) exactly spans two octaves (480*5=2400), meaning the open strings can be uniformly tuned in 4ths. This allows for greater uniformity in chord and scale fingering patterns than in 12-TET, making it exceptionally easy to learn. For instance, the fingering for an &amp;quot;E&amp;quot; chord would be 0-2-2-1-0-0 (low to high), an &amp;quot;A&amp;quot; chord would be 0-0-2-2-1-0, and a &amp;quot;D&amp;quot; chord would be 1-0-0-2-2-1. This is also the case in all EDOs which are multiples of 5, but in 10-EDO it is particularly simple.&lt;br /&gt;
+&lt;br /&gt;
 &lt;!-- ws:start:WikiTextLocalImageRule:515:&amp;lt;img src=&amp;quot;/file/view/Decaphonic_Classic_Guitar.png/234752078/Decaphonic_Classic_Guitar.png&amp;quot; alt=&amp;quot;A Decaphonic (10-EDO) Classical Guitar&amp;quot; title=&amp;quot;A Decaphonic (10-EDO) Classical Guitar&amp;quot; /&amp;gt; --&gt;&lt;table class="captionBox"&gt;&lt;tr&gt;&lt;td class="captionedImage"&gt;&lt;img src="/file/view/Decaphonic_Classic_Guitar.png/234752078/Decaphonic_Classic_Guitar.png" alt="Decaphonic_Classic_Guitar.png" title="Decaphonic_Classic_Guitar.png" /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td class="imageCaption"&gt;A Decaphonic (10-EDO) Classical Guitar&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;!-- ws:end:WikiTextLocalImageRule:515 --&gt;&lt;!-- ws:start:WikiTextLocalImageRule:516:&amp;lt;img src=&amp;quot;/file/view/decaphonic-uke.JPG/251070060/526x406/decaphonic-uke.JPG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 406px; width: 526px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/decaphonic-uke.JPG/251070060/526x406/decaphonic-uke.JPG" alt="decaphonic-uke.JPG" title="decaphonic-uke.JPG" style="height: 406px; width: 526px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:516 --&gt;&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/custom/10021077?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;10021077&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;
 &lt;/script&gt;&lt;!-- ws:end:WikiTextMediaRule:0 --&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>