OTC 7L 7s: Difference between revisions

Revision as of 21:44, 2 September 2016

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Original Wikitext content:

Omnitetrachordal MOS scale
[[7L 7s|7L+7s]]
14 tones (6+2+6)

temperament: [[whitewood]]

This scale has some unusual properties:
* it has only two modes
* either mode may be split in any of the three possible omnitetrachordal ways (9/8-4/3-4/3, 4/3-9/8-4/3, 4/3-4/3-9/8)
* it is its own dual (changing all L to s, and vice versa, gives the same scale)
* the (imperfect) tunings of 9/8 and 4/3 are independent of L/s ratio

See also [[OTC 5L 5s|OTC 5L+5s]] (blackwood) and [[OTC 12L 12s|OTC 12L+12s]] (catler/compton).

[[Gallery of omnitetrachordal scales#perfect|P]] = undefined (-1?)
[[Gallery of omnitetrachordal scales#Q|Q]] = 4.2777408456 (4/3 = 3L+2.5s)

L = 85.71 to 171.43 cents (138.95 cents @ Q)
s = 0.00 to 85.71 cents (32.48 cents @ Q)

9/8 = L+s (171.43 cents for any L/s)
4/3 = 3L+3s (514.29 cents for any L/s)
generator = s (0.00 to 85.71 cents)
[[periods and generators|period]] = 1/7 octave (171.43 cents)

notable EDOs: 21, 28, 35 (for 35edo, use L/s=3/2)

all modes:
|| {{ Ls LsLsLs LsLsLs }} || {{ LsLsLs Ls LsLsLs }} || {{ LsLsLs LsLsLs Ls }} ||
|| {{ sL sLsLsL sLsLsL }} || {{ sLsLsL sL sLsLsL }} || {{ sLsLsL sLsLsL sL }} ||

[[image:14_07_07_sLsLsL_sL_sLsLsL.png]]

===See also===
* [[Omnitetrachordality]]
* [[Gallery of omnitetrachordal scales]]

Original HTML content:

<html><head><title>OTC 7L 7s</title></head><body>Omnitetrachordal MOS scale<br />
<a class="wiki_link" href="/7L%207s">7L+7s</a><br />
14 tones (6+2+6)<br />
<br />
temperament: <a class="wiki_link" href="/whitewood">whitewood</a><br />
<br />
This scale has some unusual properties:<br />
<ul><li>it has only two modes</li><li>either mode may be split in any of the three possible omnitetrachordal ways (9/8-4/3-4/3, 4/3-9/8-4/3, 4/3-4/3-9/8)</li><li>it is its own dual (changing all L to s, and vice versa, gives the same scale)</li><li>the (imperfect) tunings of 9/8 and 4/3 are independent of L/s ratio</li></ul><br />
See also <a class="wiki_link" href="/OTC%205L%205s">OTC 5L+5s</a> (blackwood) and <a class="wiki_link" href="/OTC%2012L%2012s">OTC 12L+12s</a> (catler/compton).<br />
<br />
<a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect">P</a> = undefined (-1?)<br />
<a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#Q">Q</a> = 4.2777408456 (4/3 = 3L+2.5s)<br />
<br />
L = 85.71 to 171.43 cents (138.95 cents @ Q)<br />
s = 0.00 to 85.71 cents (32.48 cents @ Q)<br />
<br />
9/8 = L+s (171.43 cents for any L/s)<br />
4/3 = 3L+3s (514.29 cents for any L/s)<br />
generator = s (0.00 to 85.71 cents)<br />
<a class="wiki_link" href="/periods%20and%20generators">period</a> = 1/7 octave (171.43 cents)<br />
<br />
notable EDOs: 21, 28, 35 (for 35edo, use L/s=3/2)<br />
<br />
all modes:<br />


<table class="wiki_table">
    <tr>
        <td><tt> Ls LsLsLs LsLsLs </tt><br />
</td>
        <td><tt> LsLsLs Ls LsLsLs </tt><br />
</td>
        <td><tt> LsLsLs LsLsLs Ls </tt><br />
</td>
    </tr>
    <tr>
        <td><tt> sL sLsLsL sLsLsL </tt><br />
</td>
        <td><tt> sLsLsL sL sLsLsL </tt><br />
</td>
        <td><tt> sLsLsL sLsLsL sL </tt><br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextLocalImageRule:36:&lt;img src=&quot;/file/view/14_07_07_sLsLsL_sL_sLsLsL.png/590988812/14_07_07_sLsLsL_sL_sLsLsL.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/14_07_07_sLsLsL_sL_sLsLsL.png/590988812/14_07_07_sLsLsL_sL_sLsLsL.png" alt="14_07_07_sLsLsL_sL_sLsLsL.png" title="14_07_07_sLsLsL_sL_sLsLsL.png" /><!-- ws:end:WikiTextLocalImageRule:36 --><br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h3&gt; --><h3 id="toc0"><a name="x--See also"></a><!-- ws:end:WikiTextHeadingRule:0 -->See also</h3>
<ul><li><a class="wiki_link" href="/Omnitetrachordality">Omnitetrachordality</a></li><li><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales">Gallery of omnitetrachordal scales</a></li></ul></body></html>

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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:spt3125|spt3125]] and made on <tt>2016-08-28 22:30:14 UTC</tt>.<br>
+: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2016-09-02 21:44:45 UTC</tt>.<br>
-: The original revision id was <tt>590313184</tt>.<br>
+: The original revision id was <tt>590989008</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 37: / Line 37: @@
 || {{ sL sLsLsL sLsLsL }} || {{ sLsLsL sL sLsLsL }} || {{ sLsLsL sLsLsL sL }} ||
-[[image:14_07_07_LsLsLs_Ls_LsLsLs.png]]
+[[image:14_07_07_sLsLsL_sL_sLsLsL.png]]
 ===See also===
 * [[Omnitetrachordality]]
-* [[Gallery of omnitetrachordal scales]]
+* [[Gallery of omnitetrachordal scales]]</pre></div>
-</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;OTC 7L 7s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Omnitetrachordal MOS scale&lt;br /&gt;
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 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:36:&amp;lt;img src=&amp;quot;/file/view/14_07_07_LsLsLs_Ls_LsLsLs.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/14_07_07_LsLsLs_Ls_LsLsLs.png" alt="14_07_07_LsLsLs_Ls_LsLsLs.png" title="14_07_07_LsLsLs_Ls_LsLsLs.png" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:36 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:36:&amp;lt;img src=&amp;quot;/file/view/14_07_07_sLsLsL_sL_sLsLsL.png/590988812/14_07_07_sLsLsL_sL_sLsLsL.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/14_07_07_sLsLsL_sL_sLsLsL.png/590988812/14_07_07_sLsLsL_sL_sLsLsL.png" alt="14_07_07_sLsLsL_sL_sLsLsL.png" title="14_07_07_sLsLsL_sL_sLsLsL.png" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:36 --&gt;&lt;br /&gt;
 &lt;br /&gt;
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 &lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Omnitetrachordality"&gt;Omnitetrachordality&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales"&gt;Gallery of omnitetrachordal scales&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

OTC 7L 7s: Difference between revisions

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