OTC 12L 5s: Difference between revisions

Revision as of 20:50, 31 August 2016

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Original Wikitext content:

Omnitetrachordal MOS scale
[[12L 5s|12L+5s]]
17 tones (7+3+7)

Helmholtz / [[Schismatic family|schismatic]]

[[Gallery of omnitetrachordal scales#perfect|P]] = 3.8459060415 (L=[[256_243|256/243]], s=[[531441_524288|531441/524288]])
[[Gallery of omnitetrachordal scales#Q|Q]] = 29.4213422908 (4/3 = 5L+1.5s)

L = 70.59 to 100.00 cents (90.22 cents @ P, 98.60 cents @ Q)
s = 0.00 to 70.59 cents (23.46 cents @ P, 3.35 cents @ Q)

9/8 = 2L+s (200.00 to 211.76 cents)
4/3 = 5L+2s (494.12 to 500.00 cents)
generator = 4/3

notable EDOs: 29, 41, 46, 53, 65

symmetric mode: {{ LsLLLsLLsLLsLLLsL }}

all modes:
|| || {{ LsLLLsL LsL LsLLLsL }} || ||
|| || {{ sLLLsLL sLL sLLLsLL }} || ||
|| || {{ LLLsLLs LLs LLLsLLs }} || ||
|| {{ LLs LLsLLsL LLsLLsL }} || {{ LLsLLsL LsL LLsLLsL }} || ||
|| {{ LsL LsLLsLL LsLLsLL }} || {{ LsLLsLL sLL LsLLsLL }} || ||
|| {{ sLL sLLsLLL sLLsLLL }} || || ||
|| {{ LLs LLsLLLs LLsLLLs }} || || {{ LLsLLsL LLsLLsL LLs }} ||
|| {{ LsL LsLLLsL LsLLLsL }} || || {{ LsLLsLL LsLLsLL LsL }} ||
|| {{ sLL sLLLsLL sLLLsLL }} || || {{ sLLsLLL sLLsLLL sLL }} ||
|| {{ LLs LLLsLLs LLLsLLs }} || || {{ LLsLLLs LLsLLLs LLs }} ||
|| {{ LsL LLsLLsL LLsLLsL }} || || {{ LsLLLsL LsLLLsL LsL }} ||
|| {{ sLL LsLLsLL LsLLsLL }} || || {{ sLLLsLL sLLLsLL sLL }} ||
|| || || {{ LLLsLLs LLLsLLs LLs }} ||
|| || {{ LLsLLsL LLs LLsLLsL }} || {{ LLsLLsL LLsLLsL LsL }} ||
|| || {{ LsLLsLL LsL LsLLsLL }} || {{ LsLLsLL LsLLsLL sLL }} ||
|| || {{ sLLsLLL sLL sLLsLLL }} || ||
|| || {{ LLsLLLs LLs LLsLLLs }} || ||

[[image:17_12_05_LLLsLLs_LLs_LLLsLLs.png]]

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

===References===
* Noted as omnitetrachordal by Paul Erlich no later than 2002. See tuning-math list messages [[http://robertinventor.com/tuning-math/s___4/msg_3675-3699.html#3685|3685]] and [[http://robertinventor.com/tuning-math/s__11/msg_10975-10999.html#10987|10987]].

Original HTML content:

<html><head><title>OTC 12L 5s</title></head><body>Omnitetrachordal MOS scale<br />
<a class="wiki_link" href="/12L%205s">12L+5s</a><br />
17 tones (7+3+7)<br />
<br />
Helmholtz / <a class="wiki_link" href="/Schismatic%20family">schismatic</a><br />
<br />
<a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect">P</a> = 3.8459060415 (L=<a class="wiki_link" href="/256_243">256/243</a>, s=<a class="wiki_link" href="/531441_524288">531441/524288</a>)<br />
<a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#Q">Q</a> = 29.4213422908 (4/3 = 5L+1.5s)<br />
<br />
L = 70.59 to 100.00 cents (90.22 cents @ P, 98.60 cents @ Q)<br />
s = 0.00 to 70.59 cents (23.46 cents @ P, 3.35 cents @ Q)<br />
<br />
9/8 = 2L+s (200.00 to 211.76 cents)<br />
4/3 = 5L+2s (494.12 to 500.00 cents)<br />
generator = 4/3<br />
<br />
notable EDOs: 29, 41, 46, 53, 65<br />
<br />
symmetric mode: <tt> LsLLLsLLsLLsLLLsL </tt><br />
<br />
all modes:<br />


<table class="wiki_table">
    <tr>
        <td><br />
</td>
        <td><tt> LsLLLsL LsL LsLLLsL </tt><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><tt> sLLLsLL sLL sLLLsLL </tt><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><tt> LLLsLLs LLs LLLsLLs </tt><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><tt> LLs LLsLLsL LLsLLsL </tt><br />
</td>
        <td><tt> LLsLLsL LsL LLsLLsL </tt><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><tt> LsL LsLLsLL LsLLsLL </tt><br />
</td>
        <td><tt> LsLLsLL sLL LsLLsLL </tt><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><tt> sLL sLLsLLL sLLsLLL </tt><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><tt> LLs LLsLLLs LLsLLLs </tt><br />
</td>
        <td><br />
</td>
        <td><tt> LLsLLsL LLsLLsL LLs </tt><br />
</td>
    </tr>
    <tr>
        <td><tt> LsL LsLLLsL LsLLLsL </tt><br />
</td>
        <td><br />
</td>
        <td><tt> LsLLsLL LsLLsLL LsL </tt><br />
</td>
    </tr>
    <tr>
        <td><tt> sLL sLLLsLL sLLLsLL </tt><br />
</td>
        <td><br />
</td>
        <td><tt> sLLsLLL sLLsLLL sLL </tt><br />
</td>
    </tr>
    <tr>
        <td><tt> LLs LLLsLLs LLLsLLs </tt><br />
</td>
        <td><br />
</td>
        <td><tt> LLsLLLs LLsLLLs LLs </tt><br />
</td>
    </tr>
    <tr>
        <td><tt> LsL LLsLLsL LLsLLsL </tt><br />
</td>
        <td><br />
</td>
        <td><tt> LsLLLsL LsLLLsL LsL </tt><br />
</td>
    </tr>
    <tr>
        <td><tt> sLL LsLLsLL LsLLsLL </tt><br />
</td>
        <td><br />
</td>
        <td><tt> sLLLsLL sLLLsLL sLL </tt><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><tt> LLLsLLs LLLsLLs LLs </tt><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><tt> LLsLLsL LLs LLsLLsL </tt><br />
</td>
        <td><tt> LLsLLsL LLsLLsL LsL </tt><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><tt> LsLLsLL LsL LsLLsLL </tt><br />
</td>
        <td><tt> LsLLsLL LsLLsLL sLL </tt><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><tt> sLLsLLL sLL sLLsLLL </tt><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><tt> LLsLLLs LLs LLsLLLs </tt><br />
</td>
        <td><br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextLocalImageRule:152:&lt;img src=&quot;/file/view/17_12_05_LLLsLLs_LLs_LLLsLLs.png/589273876/17_12_05_LLLsLLs_LLs_LLLsLLs.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/17_12_05_LLLsLLs_LLs_LLLsLLs.png/589273876/17_12_05_LLLsLLs_LLs_LLLsLLs.png" alt="17_12_05_LLLsLLs_LLs_LLLsLLs.png" title="17_12_05_LLLsLLs_LLs_LLLsLLs.png" /><!-- ws:end:WikiTextLocalImageRule:152 --><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><br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x--References"></a><!-- ws:end:WikiTextHeadingRule:2 -->References</h3>
<ul><li>Noted as omnitetrachordal by Paul Erlich no later than 2002. See tuning-math list messages <a class="wiki_link_ext" href="http://robertinventor.com/tuning-math/s___4/msg_3675-3699.html#3685" rel="nofollow">3685</a> and <a class="wiki_link_ext" href="http://robertinventor.com/tuning-math/s__11/msg_10975-10999.html#10987" rel="nofollow">10987</a>.</li></ul></body></html>

OTC 12L 5s: Difference between revisions

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IMPORTED REVISION FROM WIKISPACES

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