80edo: 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:~~phylingual~~|~~phylingual~~]] and made on <tt>2012-07-~~17 20~~:42:07 UTC</tt>.<br>

: This revision was by author [[User:guest|guest]] and made on <tt>2012-08-28 13:30:23 UTC</tt>.<br>

: The original revision id was <tt>~~353605850~~</tt>.<br>

: The original revision id was <tt>360478464</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 //80 equal temperament//, often abbreviated 80-tET, 80-EDO, or 80-ET, is the scale derived by dividing the octave into 80 equally-sized steps. Each step represents a frequency ratio of exactly 15 [[cent]]s. 80et is the first equal temperament that represents the [[19-limit]] [[tonality diamond]] [[consistent]]ly (it barely manages to do so), and in fact represents the 21 odd limit tonality diamond consistently also.

<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 //80 equal temperament//, often abbreviated 80-tET, 80-EDO, or 80-ET, is the scale derived by dividing the octave into 80 equally-sized steps. Each step represents a frequency ratio of exactly 15 [[xenharmonic/cent|cent]]s. 80et is the first equal temperament that represents the [[xenharmonic/19-limit|19-limit]] [[xenharmonic/tonality diamond|tonality diamond]] [[xenharmonic/consistent|consistent]]ly (it barely manages to do so), and in fact represents the 21 odd limit tonality diamond consistently also.

80 et [[tempering out|tempers out]] 136/135, 169/168, 176/175, 190/189, 221/220, 256/255, 286/285, 289/288, 325/324, 351/350, 352/351, 361/360, 364/363, 400/399, 456/455, 476/475, 540/539, 561/560, 595/594, 715/714, 936/935, 969/968, 1001/1000, 1275/1274, 1331/1330, 1445/1444, 1521/1520, 1540/1539 and 1729/1728, not to mention such important non-superparticular commas as 2048/2025, 4000/3969, 1728/1715 and 3136/3125.

80 et [[xenharmonic/tempering out|tempers out]] 136/135, 169/168, 176/175, 190/189, 221/220, 256/255, 286/285, 289/288, 325/324, 351/350, 352/351, 361/360, 364/363, 400/399, 456/455, 476/475, 540/539, 561/560, 595/594, 715/714, 936/935, 969/968, 1001/1000, 1275/1274, 1331/1330, 1445/1444, 1521/1520, 1540/1539 and 1729/1728, not to mention such important non-superparticular commas as 2048/2025, 4000/3969, 1728/1715 and 3136/3125.

80 supports a profusion of 19-limit (and lower) rank two temperaments which have mostly not been explored. We might mention:

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41&80 <<7 26 25 -3 -24 -33 20 ... ||

In each case, the numbers joined by an ampersand represent 19-limit [[Patent val|patent vals]] (meaning obtained by rounding to the nearest integer) and the first and most important part of the wedgie is given.

In each case, the numbers joined by an ampersand represent 19-limit [[xenharmonic/Patent val|patent vals]] (meaning obtained by rounding to the nearest integer) and the first and most important part of the wedgie is given.

=Intervals of 80edo=

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|| 30 || 450 || 13/10, 22/17 ||

|| 31 || 465 || 17/13 ||

|| 32 || 480 || 21/16, 25/19 ||

|| 32 || 480 || (21/16), 25/19 ||

|| 33 || 495 || 4/3 ||

|| 34 || 510 || ||

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*based on treating 80edo as a 19-limit temperament; other approaches are possible.</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>80edo</title></head><body>The <em>80 equal temperament</em>, often abbreviated 80-tET, 80-EDO, or 80-ET, is the scale derived by dividing the octave into 80 equally-sized steps. Each step represents a frequency ratio of exactly 15 <a class="wiki_link" href="/cent">cent</a>s. 80et is the first equal temperament that represents the <a class="wiki_link" href="/19-limit">19-limit</a> <a class="wiki_link" href="/tonality%20diamond">tonality diamond</a> <a class="wiki_link" href="/consistent">consistent</a>ly (it barely manages to do so), and in fact represents the 21 odd limit tonality diamond consistently also.<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>80edo</title></head><body>The <em>80 equal temperament</em>, often abbreviated 80-tET, 80-EDO, or 80-ET, is the scale derived by dividing the octave into 80 equally-sized steps. Each step represents a frequency ratio of exactly 15 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/cent">cent</a>s. 80et is the first equal temperament that represents the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/19-limit">19-limit</a> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/tonality%20diamond">tonality diamond</a> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/consistent">consistent</a>ly (it barely manages to do so), and in fact represents the 21 odd limit tonality diamond consistently also.<br />

<br />

80 et <a class="wiki_link" href="/tempering%20out">tempers out</a> 136/135, 169/168, 176/175, 190/189, 221/220, 256/255, 286/285, 289/288, 325/324, 351/350, 352/351, 361/360, 364/363, 400/399, 456/455, 476/475, 540/539, 561/560, 595/594, 715/714, 936/935, 969/968, 1001/1000, 1275/1274, 1331/1330, 1445/1444, 1521/1520, 1540/1539 and 1729/1728, not to mention such important non-superparticular commas as 2048/2025, 4000/3969, 1728/1715 and 3136/3125.<br />

80 et <a class="wiki_link" href="http://xenharmonic.wikispaces.com/tempering%20out">tempers out</a> 136/135, 169/168, 176/175, 190/189, 221/220, 256/255, 286/285, 289/288, 325/324, 351/350, 352/351, 361/360, 364/363, 400/399, 456/455, 476/475, 540/539, 561/560, 595/594, 715/714, 936/935, 969/968, 1001/1000, 1275/1274, 1331/1330, 1445/1444, 1521/1520, 1540/1539 and 1729/1728, not to mention such important non-superparticular commas as 2048/2025, 4000/3969, 1728/1715 and 3136/3125.<br />

<br />

80 supports a profusion of 19-limit (and lower) rank two temperaments which have mostly not been explored. We might mention:<br />

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41&amp;80 &lt;&lt;7 26 25 -3 -24 -33 20 ... ||<br />

<br />

In each case, the numbers joined by an ampersand represent 19-limit <a class="wiki_link" href="/Patent%20val">patent vals</a> (meaning obtained by rounding to the nearest integer) and the first and most important part of the wedgie is given.<br />

In each case, the numbers joined by an ampersand represent 19-limit <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Patent%20val">patent vals</a> (meaning obtained by rounding to the nearest integer) and the first and most important part of the wedgie is given.<br />

<br />

<h1 id="toc0"><a name="Intervals of 80edo"></a>Intervals of 80edo</h1>

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</td>

</td>

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@@ 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:phylingual|phylingual]] and made on <tt>2012-07-17 20:42:07 UTC</tt>.<br>
+: This revision was by author [[User:guest|guest]] and made on <tt>2012-08-28 13:30:23 UTC</tt>.<br>
-: The original revision id was <tt>353605850</tt>.<br>
+: The original revision id was <tt>360478464</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 //80 equal temperament//, often abbreviated 80-tET, 80-EDO, or 80-ET, is the scale derived by dividing the octave into 80 equally-sized steps. Each step represents a frequency ratio of exactly 15 [[cent]]s. 80et is the first equal temperament that represents the [[19-limit]] [[tonality diamond]] [[consistent]]ly (it barely manages to do so), and in fact represents the 21 odd limit tonality diamond consistently also.
+<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 //80 equal temperament//, often abbreviated 80-tET, 80-EDO, or 80-ET, is the scale derived by dividing the octave into 80 equally-sized steps. Each step represents a frequency ratio of exactly 15 [[xenharmonic/cent|cent]]s. 80et is the first equal temperament that represents the [[xenharmonic/19-limit|19-limit]] [[xenharmonic/tonality diamond|tonality diamond]] [[xenharmonic/consistent|consistent]]ly (it barely manages to do so), and in fact represents the 21 odd limit tonality diamond consistently also.
-et [[tempering out|tempers out]] 136/135, 169/168, 176/175, 190/189, 221/220, 256/255, 286/285, 289/288, 325/324, 351/350, 352/351, 361/360, 364/363, 400/399, 456/455, 476/475, 540/539, 561/560, 595/594, 715/714, 936/935, 969/968, 1001/1000, 1275/1274, 1331/1330, 1445/1444, 1521/1520, 1540/1539 and 1729/1728, not to mention such important non-superparticular commas as 2048/2025, 4000/3969, 1728/1715 and 3136/3125.
+et [[xenharmonic/tempering out|tempers out]] 136/135, 169/168, 176/175, 190/189, 221/220, 256/255, 286/285, 289/288, 325/324, 351/350, 352/351, 361/360, 364/363, 400/399, 456/455, 476/475, 540/539, 561/560, 595/594, 715/714, 936/935, 969/968, 1001/1000, 1275/1274, 1331/1330, 1445/1444, 1521/1520, 1540/1539 and 1729/1728, not to mention such important non-superparticular commas as 2048/2025, 4000/3969, 1728/1715 and 3136/3125.
 supports a profusion of 19-limit (and lower) rank two temperaments which have mostly not been explored. We might mention:
@@ Line 22: / Line 22: @@
 &amp;80 &lt;&lt;7 26 25 -3 -24 -33 20 ... ||
-In each case, the numbers joined by an ampersand represent 19-limit [[Patent val|patent vals]] (meaning obtained by rounding to the nearest integer) and the first and most important part of the wedgie is given.
+In each case, the numbers joined by an ampersand represent 19-limit [[xenharmonic/Patent val|patent vals]] (meaning obtained by rounding to the nearest integer) and the first and most important part of the wedgie is given.
 =Intervals of 80edo=
@@ Line 58: / Line 58: @@
 || 30 || 450 || 13/10, 22/17 ||
 || 31 || 465 || 17/13 ||
-|| 32 || 480 || 21/16, 25/19 ||
+|| 32 || 480 || (21/16), 25/19 ||
 || 33 || 495 || 4/3 ||
 || 34 || 510 ||   ||
@@ Line 69: / Line 69: @@
 *based on treating 80edo as a 19-limit temperament; other approaches are possible.</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;80edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;80 equal temperament&lt;/em&gt;, often abbreviated 80-tET, 80-EDO, or 80-ET, is the scale derived by dividing the octave into 80 equally-sized steps. Each step represents a frequency ratio of exactly 15 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s. 80et is the first equal temperament that represents the &lt;a class="wiki_link" href="/19-limit"&gt;19-limit&lt;/a&gt; &lt;a class="wiki_link" href="/tonality%20diamond"&gt;tonality diamond&lt;/a&gt; &lt;a class="wiki_link" href="/consistent"&gt;consistent&lt;/a&gt;ly (it barely manages to do so), and in fact represents the 21 odd limit tonality diamond consistently also.&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;80edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;80 equal temperament&lt;/em&gt;, often abbreviated 80-tET, 80-EDO, or 80-ET, is the scale derived by dividing the octave into 80 equally-sized steps. Each step represents a frequency ratio of exactly 15 &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/cent"&gt;cent&lt;/a&gt;s. 80et is the first equal temperament that represents the &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/19-limit"&gt;19-limit&lt;/a&gt; &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/tonality%20diamond"&gt;tonality diamond&lt;/a&gt; &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/consistent"&gt;consistent&lt;/a&gt;ly (it barely manages to do so), and in fact represents the 21 odd limit tonality diamond consistently also.&lt;br /&gt;
 &lt;br /&gt;
-et &lt;a class="wiki_link" href="/tempering%20out"&gt;tempers out&lt;/a&gt; 136/135, 169/168, 176/175, 190/189, 221/220, 256/255, 286/285, 289/288, 325/324, 351/350, 352/351, 361/360, 364/363, 400/399, 456/455, 476/475, 540/539, 561/560, 595/594, 715/714, 936/935, 969/968, 1001/1000, 1275/1274, 1331/1330, 1445/1444, 1521/1520, 1540/1539 and 1729/1728, not to mention such important non-superparticular commas as 2048/2025, 4000/3969, 1728/1715 and 3136/3125.&lt;br /&gt;
+et &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/tempering%20out"&gt;tempers out&lt;/a&gt; 136/135, 169/168, 176/175, 190/189, 221/220, 256/255, 286/285, 289/288, 325/324, 351/350, 352/351, 361/360, 364/363, 400/399, 456/455, 476/475, 540/539, 561/560, 595/594, 715/714, 936/935, 969/968, 1001/1000, 1275/1274, 1331/1330, 1445/1444, 1521/1520, 1540/1539 and 1729/1728, not to mention such important non-superparticular commas as 2048/2025, 4000/3969, 1728/1715 and 3136/3125.&lt;br /&gt;
 &lt;br /&gt;
 supports a profusion of 19-limit (and lower) rank two temperaments which have mostly not been explored. We might mention:&lt;br /&gt;
@@ Line 85: / Line 85: @@
 &amp;amp;80 &amp;lt;&amp;lt;7 26 25 -3 -24 -33 20 ... ||&lt;br /&gt;
 &lt;br /&gt;
-In each case, the numbers joined by an ampersand represent 19-limit &lt;a class="wiki_link" href="/Patent%20val"&gt;patent vals&lt;/a&gt; (meaning obtained by rounding to the nearest integer) and the first and most important part of the wedgie is given.&lt;br /&gt;
+In each case, the numbers joined by an ampersand represent 19-limit &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Patent%20val"&gt;patent vals&lt;/a&gt; (meaning obtained by rounding to the nearest integer) and the first and most important part of the wedgie is given.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Intervals of 80edo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Intervals of 80edo&lt;/h1&gt;
@@ Line 360: / Line 360: @@
          &lt;td&gt;480&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;21/16, 25/19&lt;br /&gt;
+         &lt;td&gt;(21/16), 25/19&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;