13edo: Difference between revisions

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<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:~~genewardsmith~~|~~genewardsmith~~]] and made on <tt>2011-11-~~23 07~~:24:12 UTC</tt>.<br>

: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-12-31 01:46:33 UTC</tt>.<br>

: The original revision id was <tt>~~278436056~~</tt>.<br>

: The original revision id was <tt>288886501</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>

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=13 tone equal temperament / 13edo=

13edo refers to a tuning system which divides the octave (frequency ratio 2:1) into 13 equal parts. The steps are of similar size to those of 12edo (albeit squashed), while the intervals between a minor third & major sixth are xenharmonic (not similar to anything available in 12edo).

13edo refers to a tuning system which divides the octave (frequency ratio 2:1) into 13 equal parts. It is the sixth [[prime numbers|prime]] edo, following [[11edo]] and coming before [[17edo]]. The steps are of similar size to those of 12edo (albeit squashed), while the intervals between a minor third & major sixth are xenharmonic (not similar to anything available in 12edo).

|| Degree || Cents ||= Approximate Ratios* || 6L1s Names || 5L3s Names || [[26edo]] names ||

|| 0 || 0 ||= 1/1 || C || C || C ||

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[[@http://www.elvenminstrel.com/music/tuning/equal/13equal/13tet.htm|Upsidedown and Backwards: Explorations in 13-tone Equal Temperament]] by [[http://www.elvenminstrel.com/|David J. Finnamore]]

[[http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/11%20-%2011.%2013%20octave.mp3|Comets Over Flatland 11]] by [[Randy Winchester]]

=Igliashon's 13-EDO diatonic approaches=

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<br />

<h1 id="toc0"><a name="x13 tone equal temperament / 13edo"></a>13 tone equal temperament / 13edo</h1>

13edo refers to a tuning system which divides the octave (frequency ratio 2:1) into 13 equal parts. The steps are of similar size to those of 12edo (albeit squashed), while the intervals between a minor third &amp; major sixth are xenharmonic (not similar to anything available in 12edo).<br />

13edo refers to a tuning system which divides the octave (frequency ratio 2:1) into 13 equal parts. It is the sixth <a class="wiki_link" href="/prime%20numbers">prime</a> edo, following <a class="wiki_link" href="/11edo">11edo</a> and coming before <a class="wiki_link" href="/17edo">17edo</a>. The steps are of similar size to those of 12edo (albeit squashed), while the intervals between a minor third &amp; major sixth are xenharmonic (not similar to anything available in 12edo).<br />

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<a class="wiki_link_ext" href="http://www.elvenminstrel.com/music/tuning/equal/13equal/13tet.htm" rel="nofollow" target="_blank">Upsidedown and Backwards: Explorations in 13-tone Equal Temperament</a> by <a class="wiki_link_ext" href="http://www.elvenminstrel.com/" rel="nofollow">David J. Finnamore</a><br />

<a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/11%20-%2011.%2013%20octave.mp3" rel="nofollow">Comets Over Flatland 11</a> by <a class="wiki_link" href="/Randy%20Winchester">Randy Winchester</a><br />

<br />

<h1 id="toc6"><a name="Igliashon's 13-EDO diatonic approaches"></a>Igliashon's 13-EDO diatonic approaches</h1>

<br />

@@ 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:genewardsmith|genewardsmith]] and made on <tt>2011-11-23 07:24:12 UTC</tt>.<br>
+: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-12-31 01:46:33 UTC</tt>.<br>
-: The original revision id was <tt>278436056</tt>.<br>
+: The original revision id was <tt>288886501</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 10: / Line 10: @@
 =13 tone equal temperament / 13edo=
-edo refers to a tuning system which divides the octave (frequency ratio 2:1) into 13 equal parts. The steps are of similar size to those of 12edo (albeit squashed), while the intervals between a minor third &amp; major sixth are xenharmonic (not similar to anything available in 12edo).
+edo refers to a tuning system which divides the octave (frequency ratio 2:1) into 13 equal parts. It is the sixth [[prime numbers|prime]] edo, following [[11edo]] and coming before [[17edo]]. The steps are of similar size to those of 12edo (albeit squashed), while the intervals between a minor third &amp; major sixth are xenharmonic (not similar to anything available in 12edo).
 || Degree || Cents ||= Approximate Ratios* || 6L1s Names || 5L3s Names || [[26edo]] names ||
 || 0 || 0 ||= 1/1 || C || C || C ||
@@ Line 62: / Line 62: @@
 [[@http://www.elvenminstrel.com/music/tuning/equal/13equal/13tet.htm|Upsidedown and Backwards: Explorations in 13-tone Equal Temperament]] by [[http://www.elvenminstrel.com/|David J. Finnamore]]
 [[http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/11%20-%2011.%2013%20octave.mp3|Comets Over Flatland 11]] by [[Randy Winchester]]
 =Igliashon's 13-EDO diatonic approaches=
@@ Line 90: / Line 91: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x13 tone equal temperament / 13edo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;13 tone equal temperament / 13edo&lt;/h1&gt;
-edo refers to a tuning system which divides the octave (frequency ratio 2:1) into 13 equal parts. The steps are of similar size to those of 12edo (albeit squashed), while the intervals between a minor third &amp;amp; major sixth are xenharmonic (not similar to anything available in 12edo).&lt;br /&gt;
+edo refers to a tuning system which divides the octave (frequency ratio 2:1) into 13 equal parts. It is the sixth &lt;a class="wiki_link" href="/prime%20numbers"&gt;prime&lt;/a&gt; edo, following &lt;a class="wiki_link" href="/11edo"&gt;11edo&lt;/a&gt; and coming before &lt;a class="wiki_link" href="/17edo"&gt;17edo&lt;/a&gt;. The steps are of similar size to those of 12edo (albeit squashed), while the intervals between a minor third &amp;amp; major sixth are xenharmonic (not similar to anything available in 12edo).&lt;br /&gt;
@@ Line 342: / Line 343: @@
 &lt;a class="wiki_link_ext" href="http://www.elvenminstrel.com/music/tuning/equal/13equal/13tet.htm" rel="nofollow" target="_blank"&gt;Upsidedown and Backwards: Explorations in 13-tone Equal Temperament&lt;/a&gt; by &lt;a class="wiki_link_ext" href="http://www.elvenminstrel.com/" rel="nofollow"&gt;David J. Finnamore&lt;/a&gt;&lt;br /&gt;
 &lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/11%20-%2011.%2013%20octave.mp3" rel="nofollow"&gt;Comets Over Flatland 11&lt;/a&gt; by &lt;a class="wiki_link" href="/Randy%20Winchester"&gt;Randy Winchester&lt;/a&gt;&lt;br /&gt;
+&lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Igliashon's 13-EDO diatonic approaches"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Igliashon's 13-EDO diatonic approaches&lt;/h1&gt;
   &lt;br /&gt;