94edo: 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>~~2010~~-06-~~18 03~~:15:07 UTC</tt>.<br>

: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-03-25 15:06:13 UTC</tt>.<br>

: The original revision id was <tt>~~149477517~~</tt>.<br>

: The original revision id was <tt>214058154</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 94 equal temperament, often abbreviated 94-tET, 94-EDO, or 94-ET, is the scale derived by dividing the octave into 94 equally-sized steps, where each step represents a frequency ratio of 12.766 ~~cents~~. It is a remarkable all-around utility temperament, good from low prime limit to very high prime limit situations. It is the first equal temperament to be consistent though the 23-limit, and no other equal temperament is so consistent until 282 and 311 make their appearance.

<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 94 equal temperament, often abbreviated 94-tET, 94-[[EDO]], or 94-ET, is the scale derived by dividing the [[octave]] into 94 equally-sized steps, where each step represents a frequency ratio of 12.766 [[cent]]s. It is a remarkable all-around utility temperament, good from low prime limit to very high prime limit situations. It is the first equal temperament to be consistent though the [[23-limit]], and no other equal temperament is so consistent until 282 and 311 make their appearance.

The list of 23-limit commas it tempers out is huge, but it's worth noting that it tempers out 32805/32768 and is thus a schismatic system, that it tempers out 225/224 and 385/384 and so is a marvel system, and that it also tempers out 3125/3087, 4000/3969, 5120/5103 and 540/539.

Below are some 23-limit temperaments supported by 94et. It might be noted that 94, a very good tuning for garibaldi temperament, shows us how to extend it to the 23-limit.

Below are some 23-limit temperaments supported by 94et. It might be noted that 94, a very good tuning for [[garibaldi temperament]], shows us how to extend it to the 23-limit.

46&94 <<8 30 -18 -4 -28 8 -24 2 ... ||

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80&94 <<18 44 30 38 -16 18 40 28 ... ||

Temperaments for which 94 is a MOS:

Temperaments for which 94 is a [[MOS]]:

311&94 <<3 70 -42 69 -34 50 85 83...||

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</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>94edo</title></head><body>The 94 equal temperament, often abbreviated 94-tET, 94-EDO, or 94-ET, is the scale derived by dividing the octave into 94 equally-sized steps, where each step represents a frequency ratio of 12.766 ~~cents~~. It is a remarkable all-around utility temperament, good from low prime limit to very high prime limit situations. It is the first equal temperament to be consistent though the 23-limit, and no other equal temperament is so consistent until 282 and 311 make their appearance. <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>94edo</title></head><body>The 94 equal temperament, often abbreviated 94-tET, 94-<a class="wiki_link" href="/EDO">EDO</a>, or 94-ET, is the scale derived by dividing the <a class="wiki_link" href="/octave">octave</a> into 94 equally-sized steps, where each step represents a frequency ratio of 12.766 <a class="wiki_link" href="/cent">cent</a>s. It is a remarkable all-around utility temperament, good from low prime limit to very high prime limit situations. It is the first equal temperament to be consistent though the <a class="wiki_link" href="/23-limit">23-limit</a>, and no other equal temperament is so consistent until 282 and 311 make their appearance. <br />

<br />

The list of 23-limit commas it tempers out is huge, but it's worth noting that it tempers out 32805/32768 and is thus a schismatic system, that it tempers out 225/224 and 385/384 and so is a marvel system, and that it also tempers out 3125/3087, 4000/3969, 5120/5103 and 540/539.<br />

<br />

Below are some 23-limit temperaments supported by 94et. It might be noted that 94, a very good tuning for garibaldi temperament, shows us how to extend it to the 23-limit.<br />

Below are some 23-limit temperaments supported by 94et. It might be noted that 94, a very good tuning for <a class="wiki_link" href="/garibaldi%20temperament">garibaldi temperament</a>, shows us how to extend it to the 23-limit.<br />

<br />

46&amp;94 &lt;&lt;8 30 -18 -4 -28 8 -24 2 ... ||<br />

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80&amp;94 &lt;&lt;18 44 30 38 -16 18 40 28 ... ||<br />

<br />

Temperaments for which 94 is a MOS:<br />

Temperaments for which 94 is a <a class="wiki_link" href="/MOS">MOS</a>:<br />

<br />

311&amp;94 &lt;&lt;3 70 -42 69 -34 50 85 83...||<br />

422&amp;94 &lt;&lt;8 124 -18 90 -28 102 164 96 ... ||</body></html></pre></div>

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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>2010-06-18 03:15:07 UTC</tt>.<br>
+: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-03-25 15:06:13 UTC</tt>.<br>
-: The original revision id was <tt>149477517</tt>.<br>
+: The original revision id was <tt>214058154</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 94 equal temperament, often abbreviated 94-tET, 94-EDO, or 94-ET, is the scale derived by dividing the octave into 94 equally-sized steps, where each step represents a frequency ratio of 12.766 cents. It is a remarkable all-around utility temperament, good from low prime limit to very high prime limit situations. It is the first equal temperament to be consistent though the 23-limit, and no other equal temperament is so consistent until 282 and 311 make their appearance.
+<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 94 equal temperament, often abbreviated 94-tET, 94-[[EDO]], or 94-ET, is the scale derived by dividing the [[octave]] into 94 equally-sized steps, where each step represents a frequency ratio of 12.766 [[cent]]s. It is a remarkable all-around utility temperament, good from low prime limit to very high prime limit situations. It is the first equal temperament to be consistent though the [[23-limit]], and no other equal temperament is so consistent until 282 and 311 make their appearance.
 The list of 23-limit commas it tempers out is huge, but it's worth noting that it tempers out 32805/32768 and is thus a schismatic system, that it tempers out 225/224 and 385/384 and so is a marvel system, and that it also tempers out 3125/3087, 4000/3969, 5120/5103 and 540/539.
-Below are some 23-limit temperaments supported by 94et. It might be noted that 94, a very good tuning for garibaldi temperament, shows us how to extend it to the 23-limit.
+Below are some 23-limit temperaments supported by 94et. It might be noted that 94, a very good tuning for [[garibaldi temperament]], shows us how to extend it to the 23-limit.
 &amp;94 &lt;&lt;8 30 -18 -4 -28 8 -24 2 ... ||
@@ Line 24: / Line 24: @@
 &amp;94 &lt;&lt;18 44 30 38 -16 18 40 28 ... ||
-Temperaments for which 94 is a MOS:
+Temperaments for which 94 is a [[MOS]]:
 &amp;94 &lt;&lt;3 70 -42 69 -34 50 85 83...||
@@ Line 30: / Line 30: @@
 </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;94edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 94 equal temperament, often abbreviated 94-tET, 94-EDO, or 94-ET, is the scale derived by dividing the octave into 94 equally-sized steps, where each step represents a frequency ratio of 12.766 cents. It is a remarkable all-around utility temperament, good from low prime limit to very high prime limit situations. It is the first equal temperament to be consistent though the 23-limit, and no other equal temperament is so consistent until 282 and 311 make their appearance. &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;94edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 94 equal temperament, often abbreviated 94-tET, 94-&lt;a class="wiki_link" href="/EDO"&gt;EDO&lt;/a&gt;, or 94-ET, is the scale derived by dividing the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 94 equally-sized steps, where each step represents a frequency ratio of 12.766 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s. It is a remarkable all-around utility temperament, good from low prime limit to very high prime limit situations. It is the first equal temperament to be consistent though the &lt;a class="wiki_link" href="/23-limit"&gt;23-limit&lt;/a&gt;, and no other equal temperament is so consistent until 282 and 311 make their appearance. &lt;br /&gt;
 &lt;br /&gt;
 The list of 23-limit commas it tempers out is huge, but it's worth noting that it tempers out 32805/32768 and is thus a schismatic system, that it tempers out 225/224 and 385/384 and so is a marvel system, and that it also tempers out 3125/3087, 4000/3969, 5120/5103 and 540/539.&lt;br /&gt;
 &lt;br /&gt;
-Below are some 23-limit temperaments supported by 94et. It might be noted that 94, a very good tuning for garibaldi temperament, shows us how to extend it to the 23-limit.&lt;br /&gt;
+Below are some 23-limit temperaments supported by 94et. It might be noted that 94, a very good tuning for &lt;a class="wiki_link" href="/garibaldi%20temperament"&gt;garibaldi temperament&lt;/a&gt;, shows us how to extend it to the 23-limit.&lt;br /&gt;
 &lt;br /&gt;
 &amp;amp;94 &amp;lt;&amp;lt;8 30 -18 -4 -28 8 -24 2 ... ||&lt;br /&gt;
@@ Line 48: / Line 48: @@
 &amp;amp;94 &amp;lt;&amp;lt;18 44 30 38 -16 18 40 28 ... ||&lt;br /&gt;
 &lt;br /&gt;
-Temperaments for which 94 is a MOS:&lt;br /&gt;
+Temperaments for which 94 is a &lt;a class="wiki_link" href="/MOS"&gt;MOS&lt;/a&gt;:&lt;br /&gt;
 &lt;br /&gt;
 &amp;amp;94 &amp;lt;&amp;lt;3 70 -42 69 -34 50 85 83...||&lt;br /&gt;
 &amp;amp;94 &amp;lt;&amp;lt;8 124 -18 90 -28 102 164 96 ... ||&lt;/body&gt;&lt;/html&gt;</pre></div>