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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>
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| : This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-08-21 12:15:36 UTC</tt>.<br>
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| : The original revision id was <tt>247394293</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext 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;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]]//.
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| = 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. |
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| [[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]]
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| This is 1/4 of a Pythagorean comma sharp. | | This is 1/4 of a Pythagorean comma sharp. |
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| Threads/Folders on the tuning list: | | Threads/Folders on the tuning list: |
| * http://launch.groups.yahoo.com/group/tuning/message/100919 - "The True Octave"
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| * 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/
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| == 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"><html><head><title>musical cells</title></head><body><strong>Musical cells</strong> 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;<strong>toctaves</strong>&quot;. This is discussed on <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 />
| | [[Category:todo:expand]] |
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| <!-- ws:start:WikiTextHeadingRule:1:&lt;h1&gt; --><h1 id="toc0"><a name="Toctave"></a><!-- ws:end:WikiTextHeadingRule:1 --> Toctave </h1>
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| <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 came up with in connection with his theory of musical cells.<br />
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| <!-- ws:start:WikiTextMathRule:0:
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| [[math]]&lt;br/&gt; | |
| Toctave=\frac{27}{16}\sqrt[4]{2} \approx 2.0067870065670918\dots&lt;br/&gt;[[math]]
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| --><script type="math/tex">Toctave=\frac{27}{16}\sqrt[4]{2} \approx 2.0067870065670918\dots</script><!-- ws:end:WikiTextMathRule:0 --><br />
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| This is 1/4 of a Pythagorean comma sharp.<br />
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| Threads/Folders on the tuning list:<br />
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| <ul><li><!-- ws:start:WikiTextUrlRule:31:http://launch.groups.yahoo.com/group/tuning/message/100919 --><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><!-- ws:end:WikiTextUrlRule:31 --> - &quot;The True Octave&quot;</li><li><!-- ws:start:WikiTextUrlRule:32:http://launch.groups.yahoo.com/group/tuning/message/101004 --><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><!-- ws:end:WikiTextUrlRule:32 --> - &quot;A new equal tempered scale?&quot;</li><li><!-- ws:start:WikiTextUrlRule:33:http://launch.groups.yahoo.com/group/tuning/files/MarioPizarro/ --><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><!-- ws:end:WikiTextUrlRule:33 --></li></ul><br />
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| <!-- ws:start:WikiTextHeadingRule:3:&lt;h2&gt; --><h2 id="toc1"><a name="Toctave-see also"></a><!-- ws:end:WikiTextHeadingRule:3 --> see also </h2>
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| <ul><li><a class="wiki_link" href="/Octave">Octave</a></li></ul></body></html></pre></div>
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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