Musical cells: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
'''Musical cells''' is a system of [[Mario_Pizarro|Mario Pizarro]] for constructing [[Circulating_Temperaments|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]''.
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>2011-08-21 12:15:36 UTC</tt>.<br>
: The original revision id was <tt>247394293</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">**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]]//.


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


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


This is 1/4 of a Pythagorean comma sharp.
This is 1/4 of a Pythagorean comma sharp.


Threads/Folders on the tuning list:
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?"
<ul><li>[http://launch.groups.yahoo.com/group/tuning/message/100919 http://launch.groups.yahoo.com/group/tuning/message/100919] - "The True Octave"</li><li>[http://launch.groups.yahoo.com/group/tuning/message/101004 http://launch.groups.yahoo.com/group/tuning/message/101004] - "A new equal tempered scale?"</li><li>[http://launch.groups.yahoo.com/group/tuning/files/MarioPizarro/ http://launch.groups.yahoo.com/group/tuning/files/MarioPizarro/]</li></ul>
* http://launch.groups.yahoo.com/group/tuning/files/MarioPizarro/


== see also ==
== see also ==
* [[Octave]]</pre></div>
<ul><li>[[Octave|Octave]]</li></ul>     [[Category:stub]]
<h4>Original HTML content:</h4>
[[Category:todo:add_definition]]
<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;&lt;strong&gt;Musical cells&lt;/strong&gt; 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;&lt;strong&gt;toctaves&lt;/strong&gt;&amp;quot;. This is discussed on &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;
[[Category:todo:expand]]
&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 came 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]]
--&gt;&lt;script type="math/tex"&gt;Toctave=\frac{27}{16}\sqrt[4]{2} \approx 2.0067870065670918\dots&lt;/script&gt;&lt;!-- ws:end:WikiTextMathRule:0 --&gt;&lt;br /&gt;
&lt;br /&gt;
This is 1/4 of a Pythagorean comma sharp.&lt;br /&gt;
&lt;br /&gt;
Threads/Folders on the tuning list:&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;&lt;!-- ws:start:WikiTextUrlRule:31: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:31 --&gt; - &amp;quot;The True Octave&amp;quot;&lt;/li&gt;&lt;li&gt;&lt;!-- ws:start:WikiTextUrlRule:32: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:32 --&gt; - &amp;quot;A new equal tempered scale?&amp;quot;&lt;/li&gt;&lt;li&gt;&lt;!-- ws:start:WikiTextUrlRule:33: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:33 --&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:3:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Toctave-see also"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:3 --&gt; see also &lt;/h2&gt;
&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>

Revision as of 00:00, 17 July 2018

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 The corrected progression of musical cells.

Toctave

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

[math]\displaystyle{ 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:

see also