OTC 7L 5s
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Original Wikitext content:
Omnitetrachordal MOS scale
[[7L 5s|7L+5s]]
12 tones (5+2+5)
MOS of the [[meantone]] and [[Meantone family#Flattone|flattone]] temperaments (slightly flat 3/2). [[Gallery of omnitetrachordal scales#perfect|Imperfect]], but very usable at any L/s ratio. Many modes may be pentachordally split in two ways.
[[Gallery of omnitetrachordal scales#perfect|P]] = 0.7936402416
[[Gallery of omnitetrachordal scales#Q|Q]] = 6.0713810872 (4/3 = 3L+1.5s)
L = 100.00 to 171.43 cents (153.38 cents @ Q)
s = 0.00 to 100.00 cents (25.26 cents @ Q)
9/8 = L+s (171.43 to 200.00 cents)
4/3 = 3L+2s (500.00 to 514.29 cents)
generator = 4/3
notable EDOs: 19, 26, 31, 33, 43, 45, 50, etc.
all modes:
|| || {{ sLLsL sL sLLsL }} || ||
|| || {{ LLsLs Ls LLsLs }} || ||
|| {{ Ls LsLsL LsLsL }} || {{ LsLsL sL LsLsL }} || ||
|| {{ sL sLsLL sLsLL }} || || ||
|| {{ Ls LsLLs LsLLs }} || || {{ LsLsL LsLsL Ls }} ||
|| {{ sL sLLsL sLLsL }} || || {{ sLsLL sLsLL sL }} ||
|| {{ Ls LLsLs LLsLs }} || || {{ LsLLs LsLLs Ls }} ||
|| {{ sL LsLsL LsLsL }} || || {{ sLLsL sLLsL sL }} ||
|| || || {{ LLsLs LLsLs Ls }} ||
|| || {{ LsLsL Ls LsLsL }} || {{ LsLsL LsLsL sL }} ||
|| || {{ sLsLL sL sLsLL }} || ||
|| || {{ LsLLs Ls LsLLs }} || ||
[[image:12_07_05_LsLLs_Ls_LsLLs.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 7L 5s</title></head><body>Omnitetrachordal MOS scale<br />
<a class="wiki_link" href="/7L%205s">7L+5s</a><br />
12 tones (5+2+5)<br />
<br />
MOS of the <a class="wiki_link" href="/meantone">meantone</a> and <a class="wiki_link" href="/Meantone%20family#Flattone">flattone</a> temperaments (slightly flat 3/2). <a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect">Imperfect</a>, but very usable at any L/s ratio. Many modes may be pentachordally split in two ways.<br />
<br />
<a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect">P</a> = 0.7936402416<br />
<a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#Q">Q</a> = 6.0713810872 (4/3 = 3L+1.5s)<br />
<br />
L = 100.00 to 171.43 cents (153.38 cents @ Q)<br />
s = 0.00 to 100.00 cents (25.26 cents @ Q)<br />
<br />
9/8 = L+s (171.43 to 200.00 cents)<br />
4/3 = 3L+2s (500.00 to 514.29 cents)<br />
generator = 4/3<br />
<br />
notable EDOs: 19, 26, 31, 33, 43, 45, 50, etc.<br />
<br />
all modes:<br />
<table class="wiki_table">
<tr>
<td><br />
</td>
<td><tt> sLLsL sL sLLsL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LLsLs Ls LLsLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> Ls LsLsL LsLsL </tt><br />
</td>
<td><tt> LsLsL sL LsLsL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> sL sLsLL sLsLL </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> Ls LsLLs LsLLs </tt><br />
</td>
<td><br />
</td>
<td><tt> LsLsL LsLsL Ls </tt><br />
</td>
</tr>
<tr>
<td><tt> sL sLLsL sLLsL </tt><br />
</td>
<td><br />
</td>
<td><tt> sLsLL sLsLL sL </tt><br />
</td>
</tr>
<tr>
<td><tt> Ls LLsLs LLsLs </tt><br />
</td>
<td><br />
</td>
<td><tt> LsLLs LsLLs Ls </tt><br />
</td>
</tr>
<tr>
<td><tt> sL LsLsL LsLsL </tt><br />
</td>
<td><br />
</td>
<td><tt> sLLsL sLLsL sL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> LLsLs LLsLs Ls </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LsLsL Ls LsLsL </tt><br />
</td>
<td><tt> LsLsL LsLsL sL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLsLL sL sLsLL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LsLLs Ls LsLLs </tt><br />
</td>
<td><br />
</td>
</tr>
</table>
<br />
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<br />
<!-- ws:start:WikiTextHeadingRule:0:<h3> --><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:<h3> --><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>