30edo: 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:~~Osmiorisbendi~~|~~Osmiorisbendi~~]] and made on <tt>~~2011~~-06-~~24 18~~:12:27 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-05-28 17:00:24 UTC</tt>.<br>

: The original revision id was <tt>~~238636367~~</tt>.<br>

: The original revision id was <tt>340221728</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">The //30 equal division// divides the octave into 30 equal steps of precisely 40 cents each. Its [[patent val]] is a doubled version of the patent val for [[15edo]] through the 11-limit, so 30 can be viewed as a [[contorted]] version of 15. ~~However, 5\30 is 200 cents, which is a good (and familiar) approximation~~ for ~~9/8, and hence 30 can be viewed inconsistently, as having a 9' at 95\30 as well as a 9 at 96\30.~~

<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">The //30 equal division// divides the octave into 30 equal steps of precisely 40 cents each. Its [[patent val]] is a doubled version of the patent val for [[15edo]] through the 11-limit, so 30 can be viewed as a [[contorted]] version of 15. In the 13-limit it supplies the optimal patent val for [[Trienstonic clan#Quindecic|quindecic temperament]]

Instead of the 18\30 fifth of 720 cents, 30 also makes available a 17\30 fifth of 680 cents. This is an ideal tuning for pelogic (5-limit mavila), which tempers out 135/128. When 30 is used for pelogic, 5\30 can again be used inconsistently as a 9/8.

However, 5\30 is 200 cents, which is a good (and familiar) approximation for 9/8, and hence 30 can be viewed inconsistently, as having a 9' at 95\30 as well as a 9 at 96\30. Instead of the 18\30 fifth of 720 cents, 30 also makes available a 17\30 fifth of 680 cents. This is an ideal tuning for pelogic (5-limit mavila), which tempers out 135/128. When 30 is used for pelogic, 5\30 can again be used inconsistently as a 9/8.

Below is a plot of the Z function around 30:

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|| 29 || 1160 ||</pre></div>

<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"><html><head><title>30edo</title></head><body>The <em>30 equal division</em> divides the octave into 30 equal steps of precisely 40 cents each. Its <a class="wiki_link" href="/patent%20val">patent val</a> is a doubled version of the patent val for <a class="wiki_link" href="/15edo">15edo</a> through the 11-limit, so 30 can be viewed as a <a class="wiki_link" href="/contorted">contorted</a> version of 15. ~~However, 5\30 is 200 cents, which is~~ a ~~good (and familiar) approximation for 9~~/~~8, and hence 30 can be viewed inconsistently, as having a 9' at 95\30 as well as~~ a ~~9 at 96\30.~~<br />

<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"><html><head><title>30edo</title></head><body>The <em>30 equal division</em> divides the octave into 30 equal steps of precisely 40 cents each. Its <a class="wiki_link" href="/patent%20val">patent val</a> is a doubled version of the patent val for <a class="wiki_link" href="/15edo">15edo</a> through the 11-limit, so 30 can be viewed as a <a class="wiki_link" href="/contorted">contorted</a> version of 15. In the 13-limit it supplies the optimal patent val for <a class="wiki_link" href="/Trienstonic%20clan#Quindecic">quindecic temperament</a><br />

<br />

Instead of the 18\30 fifth of 720 cents, 30 also makes available a 17\30 fifth of 680 cents. This is an ideal tuning for pelogic (5-limit mavila), which tempers out 135/128. When 30 is used for pelogic, 5\30 can again be used inconsistently as a 9/8.<br />

However, 5\30 is 200 cents, which is a good (and familiar) approximation for 9/8, and hence 30 can be viewed inconsistently, as having a 9' at 95\30 as well as a 9 at 96\30. Instead of the 18\30 fifth of 720 cents, 30 also makes available a 17\30 fifth of 680 cents. This is an ideal tuning for pelogic (5-limit mavila), which tempers out 135/128. When 30 is used for pelogic, 5\30 can again be used inconsistently as a 9/8.<br />

<br />

Below is a plot of the Z function around 30:<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:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2011-06-24 18:12:27 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-05-28 17:00:24 UTC</tt>.<br>
-: The original revision id was <tt>238636367</tt>.<br>
+: The original revision id was <tt>340221728</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">The //30 equal division// divides the octave into 30 equal steps of precisely 40 cents each. Its [[patent val]] is a doubled version of the patent val for [[15edo]] through the 11-limit, so 30 can be viewed as a [[contorted]] version of 15. However, 5\30 is 200 cents, which is a good (and familiar) approximation for 9/8, and hence 30 can be viewed inconsistently, as having a 9' at 95\30 as well as a 9 at 96\30.
+<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">The //30 equal division// divides the octave into 30 equal steps of precisely 40 cents each. Its [[patent val]] is a doubled version of the patent val for [[15edo]] through the 11-limit, so 30 can be viewed as a [[contorted]] version of 15. In the 13-limit it supplies the optimal patent val for [[Trienstonic clan#Quindecic|quindecic temperament]]
-Instead of the 18\30 fifth of 720 cents, 30 also makes available a 17\30 fifth of 680 cents. This is an ideal tuning for pelogic (5-limit mavila), which tempers out 135/128. When 30 is used for pelogic, 5\30 can again be used inconsistently as a 9/8.
+However, 5\30 is 200 cents, which is a good (and familiar) approximation for 9/8, and hence 30 can be viewed inconsistently, as having a 9' at 95\30 as well as a 9 at 96\30. Instead of the 18\30 fifth of 720 cents, 30 also makes available a 17\30 fifth of 680 cents. This is an ideal tuning for pelogic (5-limit mavila), which tempers out 135/128. When 30 is used for pelogic, 5\30 can again be used inconsistently as a 9/8.
 Below is a plot of the Z function around 30:
@@ Line 73: / Line 73: @@
 || 29 || 1160 ||</pre></div>
 <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;30edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;30 equal division&lt;/em&gt; divides the octave into 30 equal steps of precisely 40 cents each. Its &lt;a class="wiki_link" href="/patent%20val"&gt;patent val&lt;/a&gt; is a doubled version of the patent val for &lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt; through the 11-limit, so 30 can be viewed as a &lt;a class="wiki_link" href="/contorted"&gt;contorted&lt;/a&gt; version of 15. However, 5\30 is 200 cents, which is a good (and familiar) approximation for 9/8, and hence 30 can be viewed inconsistently, as having a 9' at 95\30 as well as a 9 at 96\30.&lt;br /&gt;
+<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;30edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;30 equal division&lt;/em&gt; divides the octave into 30 equal steps of precisely 40 cents each. Its &lt;a class="wiki_link" href="/patent%20val"&gt;patent val&lt;/a&gt; is a doubled version of the patent val for &lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt; through the 11-limit, so 30 can be viewed as a &lt;a class="wiki_link" href="/contorted"&gt;contorted&lt;/a&gt; version of 15. In the 13-limit it supplies the optimal patent val for &lt;a class="wiki_link" href="/Trienstonic%20clan#Quindecic"&gt;quindecic temperament&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
-Instead of the 18\30 fifth of 720 cents, 30 also makes available a 17\30 fifth of 680 cents. This is an ideal tuning for pelogic (5-limit mavila), which tempers out 135/128. When 30 is used for pelogic, 5\30 can again be used inconsistently as a 9/8.&lt;br /&gt;
+However, 5\30 is 200 cents, which is a good (and familiar) approximation for 9/8, and hence 30 can be viewed inconsistently, as having a 9' at 95\30 as well as a 9 at 96\30. Instead of the 18\30 fifth of 720 cents, 30 also makes available a 17\30 fifth of 680 cents. This is an ideal tuning for pelogic (5-limit mavila), which tempers out 135/128. When 30 is used for pelogic, 5\30 can again be used inconsistently as a 9/8.&lt;br /&gt;
 &lt;br /&gt;
 Below is a plot of the Z function around 30:&lt;br /&gt;