Musical cells: 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:~~xenwolf~~|~~xenwolf~~]] and made on <tt>2011-08-10 04:33:01 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-08-10 14:08:08 UTC</tt>.<br>

: The original revision id was <tt>~~245196657~~</tt>.<br>

: The original revision id was <tt>245276651</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">//[[http://launch.groups.yahoo.com/group/tuning/message/100427|The corrected progression of musical cells]]// ~~- Mario Pizarro puts "imperfection of the man ear" in relation to the detectability of differences from the pure 2:1-ratio~~

<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">Musical cells is a system of [[Mario Pizarro]] for constructing [[circulating temperaments]]. Recently he has connected this to a system of stretched octaves he calls "toctaves". This is discussed on

//[[http://launch.groups.yahoo.com/group/tuning/message/100427|The corrected progression of musical cells]]//.

== ~~See~~ also ==

= Toctave =

* [[~~Toctave~~]]</pre></div>

**Toctave** (short for "True Octave") is a frequency ratio of 27 * 2^(1/4) / 16 (ca. 1205.865 cents) which Pizarro cam up with in connection with his theory of musical cells.

[[math]]

Toctave=\frac{27}{16}\sqrt[4]{2} \approx 2.0067870065670918\dots

[[math]]

This is 1/4 of a Pythagorean comma sharp.

Threads/Folders on the tuning list:

* http://launch.groups.yahoo.com/group/tuning/message/100919 - "The True Octave"

* http://launch.groups.yahoo.com/group/tuning/message/101004 - "A new equal tempered scale?"

* http://launch.groups.yahoo.com/group/tuning/files/MarioPizarro/

== see also ==

* [[Octave]]</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>musical cells</title></head><body><em><a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/100427" rel="nofollow">The corrected progression of musical cells</a></em> - ~~Mario Pizarro puts~~ &quot;~~imperfection of the man ear~~&quot; in ~~relation to the detectability~~ of ~~differences from the pure~~ 2:1~~-ratio~~<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>musical cells</title></head><body>Musical cells is a system of <a class="wiki_link" href="/Mario%20Pizarro">Mario Pizarro</a> for constructing <a class="wiki_link" href="/circulating%20temperaments">circulating temperaments</a>. Recently he has connected this to a system of stretched octaves he calls &quot;toctaves&quot;. This is discussed on<br />

<em><a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/100427" rel="nofollow">The corrected progression of musical cells</a></em>.<br />

<br />

<h1 id="toc0"><a name="Toctave"></a> Toctave </h1>

<strong>Toctave</strong> (short for &quot;True Octave&quot;) is a frequency ratio of 27 * 2^(1/4) / 16 (ca. 1205.865 cents) which Pizarro cam up with in connection with his theory of musical cells.<br />

<br />

<!-- ws:start:WikiTextMathRule:0:

[[math]]&lt;br/&gt;

Toctave=\frac{27}{16}\sqrt[4]{2} \approx 2.0067870065670918\dots&lt;br/&gt;[[math]]

--><script type="math/tex">Toctave=\frac{27}{16}\sqrt[4]{2} \approx 2.0067870065670918\dots</script><br />

<br />

This is 1/4 of a Pythagorean comma sharp.<br />

<br />

<h2 id="~~toc0~~"><a name="x-~~See~~ also"></a> ~~See~~ also </h2>

Threads/Folders on the tuning list:<br />

<ul><li><a class="wiki_link" href="/~~Toctave~~">~~Toctave~~</a></li></ul></body></html></pre></div>

<ul><li><a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/100919" rel="nofollow">http://launch.groups.yahoo.com/group/tuning/message/100919</a> - &quot;The True Octave&quot;</li><li><a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/101004" rel="nofollow">http://launch.groups.yahoo.com/group/tuning/message/101004</a> - &quot;A new equal tempered scale?&quot;</li><li><a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/files/MarioPizarro/" rel="nofollow">http://launch.groups.yahoo.com/group/tuning/files/MarioPizarro/</a></li></ul><br />

<h2 id="toc1"><a name="Toctave-see also"></a> see also </h2>

<ul><li><a class="wiki_link" href="/Octave">Octave</a></li></ul></body></html></pre></div>

@@ 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:xenwolf|xenwolf]] and made on <tt>2011-08-10 04:33:01 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-08-10 14:08:08 UTC</tt>.<br>
-: The original revision id was <tt>245196657</tt>.<br>
+: The original revision id was <tt>245276651</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">//[[http://launch.groups.yahoo.com/group/tuning/message/100427|The corrected progression of musical cells]]// - Mario Pizarro puts "imperfection of the man ear" in relation to the detectability of differences from the pure 2:1-ratio
+<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">Musical cells is a system of [[Mario Pizarro]] for constructing [[circulating temperaments]]. Recently he has connected this to a system of stretched octaves he calls "toctaves". This is discussed on
+//[[http://launch.groups.yahoo.com/group/tuning/message/100427|The corrected progression of musical cells]]//.
-== See also ==
+= Toctave =
-* [[Toctave]]</pre></div>
+**Toctave** (short for "True Octave") is a frequency ratio of 27 * 2^(1/4) / 16 (ca. 1205.865 cents) which Pizarro cam up with in connection with his theory of musical cells.
+[[math]]
+Toctave=\frac{27}{16}\sqrt[4]{2} \approx 2.0067870065670918\dots
+[[math]]
+This is 1/4 of a Pythagorean comma sharp.
+Threads/Folders on the tuning list:
+* http://launch.groups.yahoo.com/group/tuning/message/100919 - "The True Octave"
+* http://launch.groups.yahoo.com/group/tuning/message/101004 - "A new equal tempered scale?"
+* http://launch.groups.yahoo.com/group/tuning/files/MarioPizarro/
+== see also ==
+* [[Octave]]</pre></div>
 <h4>Original HTML content:</h4>
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+<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;musical cells&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Musical cells is a system of &lt;a class="wiki_link" href="/Mario%20Pizarro"&gt;Mario Pizarro&lt;/a&gt; for constructing &lt;a class="wiki_link" href="/circulating%20temperaments"&gt;circulating temperaments&lt;/a&gt;. Recently he has connected this to a system of stretched octaves he calls &amp;quot;toctaves&amp;quot;. This is discussed on&lt;br /&gt;
+&lt;em&gt;&lt;a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/100427" rel="nofollow"&gt;The corrected progression of musical cells&lt;/a&gt;&lt;/em&gt;.&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:1:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Toctave"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:1 --&gt; Toctave &lt;/h1&gt;
+&lt;strong&gt;Toctave&lt;/strong&gt; (short for &amp;quot;True Octave&amp;quot;) is a frequency ratio of 27 * 2^(1/4) / 16 (ca. 1205.865 cents) which Pizarro cam up with in connection with his theory of musical cells.&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextMathRule:0:
+[[math]]&amp;lt;br/&amp;gt;
+Toctave=\frac{27}{16}\sqrt[4]{2} \approx 2.0067870065670918\dots&amp;lt;br/&amp;gt;[[math]]
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+&lt;br /&gt;
+This is 1/4 of a Pythagorean comma sharp.&lt;br /&gt;
 &lt;br /&gt;
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+Threads/Folders on the tuning list:&lt;br /&gt;
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+&lt;ul&gt;&lt;li&gt;&lt;!-- ws:start:WikiTextUrlRule:32:http://launch.groups.yahoo.com/group/tuning/message/100919 --&gt;&lt;a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/100919" rel="nofollow"&gt;http://launch.groups.yahoo.com/group/tuning/message/100919&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:32 --&gt; - &amp;quot;The True Octave&amp;quot;&lt;/li&gt;&lt;li&gt;&lt;!-- ws:start:WikiTextUrlRule:33:http://launch.groups.yahoo.com/group/tuning/message/101004 --&gt;&lt;a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/101004" rel="nofollow"&gt;http://launch.groups.yahoo.com/group/tuning/message/101004&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:33 --&gt; - &amp;quot;A new equal tempered scale?&amp;quot;&lt;/li&gt;&lt;li&gt;&lt;!-- ws:start:WikiTextUrlRule:34:http://launch.groups.yahoo.com/group/tuning/files/MarioPizarro/ --&gt;&lt;a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/files/MarioPizarro/" rel="nofollow"&gt;http://launch.groups.yahoo.com/group/tuning/files/MarioPizarro/&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:34 --&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
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+&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Octave"&gt;Octave&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>