68edo: Difference between revisions

Revision as of 11:04, 7 December 2016

IMPORTED REVISION FROM WIKISPACES

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This revision was by author JosephRuhf and made on 2016-12-07 11:04:55 UTC.

The original revision id was 601622606.

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Original Wikitext content:

The //68 equal temperament//, often abbreviated 68-tET, 68-EDO, or 68-ET, is the scale derived by dividing the octave into 68 equally-sized steps. Each step represents a frequency ratio of 17.65 cents; this is half of the step size of [[34edo]], which does well in the 5-limit but not so well in the 7-limit, and one quarter the size of [[17edo]], which does well in the [[3-limit]], but not so well in the [[5-limit]]. The luck continues; 68 is a strong [[7-limit]] system, but does not do as well for in [[11-limit]]; though it's certainly usable for that purpose, it does not represent the 11-limit diamond [[consistent]]ly.

As a 7-limit system it tempers out 2048/2025, 245/243, 4000/3969, 15625/15552, 3136/3125, 6144/6125 and 2401/2400. It supports octacot, shrutar, hemiwuerschmidt, hemikleismic, clyde and neptune temperaments, and supplies the optimal patent val for 11-limit hemikleismic. It is a sharp-tending system, with the third, fifth and seventh harmonics all sharp.

Diatonic scales:
Negative comma: [[tel:14 14 -1 14 14 14 -1|14 14 -1 14 14 14 -1]] (E is sharper than F, and B is sharper than C5)
Superpyth: [[tel:12 12 4 12 12 12 4|12 12 4 12 12 12 4]]
Flattone: [[tel:10 10 9 10 10 10 9|10 10 9 10 10 10 9]]
Inverse: 8 [[tel:8 14 8 8 8 14|8 14 8 8 8 14]]

Original HTML content:

<html><head><title>68edo</title></head><body>The <em>68 equal temperament</em>, often abbreviated 68-tET, 68-EDO, or 68-ET, is the scale derived by dividing the octave into 68 equally-sized steps. Each step represents a frequency ratio of 17.65 cents; this is half of the step size of <a class="wiki_link" href="/34edo">34edo</a>, which does well in the 5-limit but not so well in the 7-limit, and one quarter the size of <a class="wiki_link" href="/17edo">17edo</a>, which does well in the <a class="wiki_link" href="/3-limit">3-limit</a>, but not so well in the <a class="wiki_link" href="/5-limit">5-limit</a>. The luck continues; 68 is a strong <a class="wiki_link" href="/7-limit">7-limit</a> system, but does not do as well for in <a class="wiki_link" href="/11-limit">11-limit</a>; though it's certainly usable for that purpose, it does not represent the 11-limit diamond <a class="wiki_link" href="/consistent">consistent</a>ly.<br />
<br />
As a 7-limit system it tempers out 2048/2025, 245/243, 4000/3969, 15625/15552, 3136/3125, 6144/6125 and 2401/2400. It supports octacot, shrutar, hemiwuerschmidt, hemikleismic, clyde and neptune temperaments, and supplies the optimal patent val for 11-limit hemikleismic. It is a sharp-tending system, with the third, fifth and seventh harmonics all sharp.<br />
<br />
Diatonic scales:<br />
Negative comma: <a class="wiki_link" href="http://tel.wikispaces.com/14%2014%20-1%2014%2014%2014%20-1">14 14 -1 14 14 14 -1</a> (E is sharper than F, and B is sharper than C5)<br />
Superpyth: <a class="wiki_link" href="http://tel.wikispaces.com/12%2012%204%2012%2012%2012%204">12 12 4 12 12 12 4</a><br />
Flattone: <a class="wiki_link" href="http://tel.wikispaces.com/10%2010%209%2010%2010%2010%209">10 10 9 10 10 10 9</a><br />
Inverse: 8 <a class="wiki_link" href="http://tel.wikispaces.com/8%2014%208%208%208%2014">8 14 8 8 8 14</a></body></html>

@@ 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:PiotrGrochowski|PiotrGrochowski]] and made on <tt>2016-09-17 04:36:46 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-07 11:04:55 UTC</tt>.<br>
-: The original revision id was <tt>592459868</tt>.<br>
+: The original revision id was <tt>601622606</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 11: / Line 11: @@
 Diatonic scales:
-Negative semitone: 14 14 -1 14 14 14 -1 (E is sharper than F, and B is sharper than C5)
+Negative comma: [[tel:14 14 -1 14 14 14 -1|14 14 -1 14 14 14 -1]] (E is sharper than F, and B is sharper than C5)
-Superpyth: 12 12 4 12 12 12 4
+Superpyth: [[tel:12 12 4 12 12 12 4|12 12 4 12 12 12 4]]
-Flattone: 10 10 9 10 10 10 9
+Flattone: [[tel:10 10 9 10 10 10 9|10 10 9 10 10 10 9]]
-Inverse: 8 8 14 8 8 8 14</pre></div>
+Inverse: 8 [[tel:8 14 8 8 8 14|8 14 8 8 8 14]]</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;68edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;68 equal temperament&lt;/em&gt;, often abbreviated 68-tET, 68-EDO, or 68-ET, is the scale derived by dividing the octave into 68 equally-sized steps. Each step represents a frequency ratio of 17.65 cents; this is half of the step size of &lt;a class="wiki_link" href="/34edo"&gt;34edo&lt;/a&gt;, which does well in the 5-limit but not so well in the 7-limit, and one quarter the size of &lt;a class="wiki_link" href="/17edo"&gt;17edo&lt;/a&gt;, which does well in the &lt;a class="wiki_link" href="/3-limit"&gt;3-limit&lt;/a&gt;, but not so well in the &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt;. The luck continues; 68 is a strong &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt; system, but does not do as well for in &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt;; though it's certainly usable for that purpose, it does not represent the 11-limit diamond &lt;a class="wiki_link" href="/consistent"&gt;consistent&lt;/a&gt;ly.&lt;br /&gt;
@@ Line 21: / Line 21: @@
 &lt;br /&gt;
 Diatonic scales:&lt;br /&gt;
-Negative semitone: 14 14 -1 14 14 14 -1 (E is sharper than F, and B is sharper than C5)&lt;br /&gt;
+Negative comma: &lt;a class="wiki_link" href="http://tel.wikispaces.com/14%2014%20-1%2014%2014%2014%20-1"&gt;14 14 -1 14 14 14 -1&lt;/a&gt; (E is sharper than F, and B is sharper than C5)&lt;br /&gt;
-Superpyth: 12 12 4 12 12 12 4&lt;br /&gt;
+Superpyth: &lt;a class="wiki_link" href="http://tel.wikispaces.com/12%2012%204%2012%2012%2012%204"&gt;12 12 4 12 12 12 4&lt;/a&gt;&lt;br /&gt;
-Flattone: 10 10 9 10 10 10 9&lt;br /&gt;
+Flattone: &lt;a class="wiki_link" href="http://tel.wikispaces.com/10%2010%209%2010%2010%2010%209"&gt;10 10 9 10 10 10 9&lt;/a&gt;&lt;br /&gt;
-Inverse: 8 8 14 8 8 8 14&lt;/body&gt;&lt;/html&gt;</pre></div>
+Inverse: 8 &lt;a class="wiki_link" href="http://tel.wikispaces.com/8%2014%208%208%208%2014"&gt;8 14 8 8 8 14&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

68edo: Difference between revisions

Revision as of 11:04, 7 December 2016

IMPORTED REVISION FROM WIKISPACES

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