OTC 12L 12s
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Omnitetrachordal MOS and MODMOS scale
[[12L 12s|12L+12s]]
24 tones (10+4+10)
[[Pythagorean family|catler, compton]]; 3 forms
Form 1 (MOS) 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)
See also [[OTC 5L 5s|OTC 5L+5s]] (blackwood) and [[OTC 7L 7s|OTC 7L+7s]] (whitewood), which have similar properties.
For all 3 forms:
* the (imperfect) tunings of 9/8 and 4/3 are independent of L/s ratio
Forms 2 and 3 are duals.
[[Gallery of omnitetrachordal scales#perfect|P]] = undefined (-1?)
[[Gallery of omnitetrachordal scales#Q|Q]] = 24.5754362493 (4/3 = 5L+4.5s)
L = 50.00 to 100.00 cents (96.09 cents @ Q)
s = 0.00 to 50.00 cents (3.91 cents @ Q)
9/8 = 2L+2s (200.00 cents, for any L/s)
4/3 = 5L+5s (500.00 cents, for any L/s)
MOS generator = s (0.00 to 50.00 cents)
MOS period = 1/12 octave (100.00 cents)
notable EDOs: 36, 48, 60, 72, 84
{{ LsLsLsLsLsLsLsLsLsLsLsLs }} (OTC form 1, MOS)
{{ | || || || || | }}
{{ ssLsLLssLLssLsLLssLLssLL }} (form 2, MODMOS) - gc 3,3,3,2,3,3,2; 5o ;; pc 12,2,2; 8o
{{ || || }}
{{ ssLLsLssLLssLLsLssLLssLL }} (form 3, MODMOS) - gc 3,3,3,2,3,3,2; 5o ;; pc 12,2,2; 8o
{{ | |||| || |||| || | }}
{{ LsLsLsLsLsLsLsLsLsLsLsLs }} (form 1)
all modes, form 1:
|| {{ LsLs LsLsLsLsLs LsLsLsLsLs }} || {{ LsLsLsLsLs LsLs LsLsLsLsLs }} || {{ LsLsLsLsLs LsLsLsLsLs LsLs }} ||
|| {{ sLsL sLsLsLsLsL sLsLsLsLsL }} || {{ sLsLsLsLsL sLsL sLsLsLsLsL }} || {{ sLsLsLsLsL sLsLsLsLsL sLsL }} ||
all modes, form 2:
|| || || {{ ssLsLLssLL ssLsLLssLL ssLL }} ||
|| || || {{ sLsLLssLLs sLsLLssLLs sLLs }} ||
|| || || {{ LsLLssLLss LsLLssLLss LLss }} ||
|| || {{ sLLssLLssL sLLs sLLssLLssL }} || {{ sLLssLLssL sLLssLLssL LssL }} ||
|| || {{ LLssLLssLs LLss LLssLLssLs }} || ||
|| || {{ LssLLssLsL LssL LssLLssLsL }} || ||
|| || {{ ssLLssLsLL ssLL ssLLssLsLL }} || ||
|| || {{ sLLssLsLLs sLLs sLLssLsLLs }} || ||
|| || {{ LLssLsLLss LLss LLssLsLLss }} || ||
|| || {{ LssLsLLssL LssL LssLsLLssL }} || ||
|| || {{ ssLsLLssLL ssLL ssLsLLssLL }} || ||
|| || {{ sLsLLssLLs sLLs sLsLLssLLs }} || ||
|| || {{ LsLLssLLss LLss LsLLssLLss }} || ||
|| {{ sLLs sLLssLLssL sLLssLLssL }} || {{ sLLssLLssL LssL sLLssLLssL }} || ||
|| {{ LLss LLssLLssLs LLssLLssLs }} || || ||
|| {{ LssL LssLLssLsL LssLLssLsL }} || || ||
|| {{ ssLL ssLLssLsLL ssLLssLsLL }} || || ||
|| {{ sLLs sLLssLsLLs sLLssLsLLs }} || || {{ sLLssLLssL sLLssLLssL sLLs }} ||
|| {{ LLss LLssLsLLss LLssLsLLss }} || || {{ LLssLLssLs LLssLLssLs LLss }} ||
|| {{ LssL LssLsLLssL LssLsLLssL }} || || {{ LssLLssLsL LssLLssLsL LssL }} ||
|| {{ ssLL ssLsLLssLL ssLsLLssLL }} || || {{ ssLLssLsLL ssLLssLsLL ssLL }} ||
|| {{ sLLs sLsLLssLLs sLsLLssLLs }} || || {{ sLLssLsLLs sLLssLsLLs sLLs }} ||
|| {{ LLss LsLLssLLss LsLLssLLss }} || || {{ LLssLsLLss LLssLsLLss LLss }} ||
|| {{ LssL sLLssLLssL sLLssLLssL }} || || {{ LssLsLLssL LssLsLLssL LssL }} ||
all modes, form 3:
|| {{ ssLL sLssLLssLL sLssLLssLL }} || || {{ ssLLsLssLL ssLLsLssLL ssLL }} ||
|| {{ sLLs LssLLssLLs LssLLssLLs }} || || {{ sLLsLssLLs sLLsLssLLs sLLs }} ||
|| || || {{ LLsLssLLss LLsLssLLss LLss }} ||
|| || || {{ LsLssLLssL LsLssLLssL LssL }} ||
|| || || {{ sLssLLssLL sLssLLssLL ssLL }} ||
|| || {{ LssLLssLLs LssL LssLLssLLs }} || {{ LssLLssLLs LssLLssLLs sLLs }} ||
|| || {{ ssLLssLLsL ssLL ssLLssLLsL }} || ||
|| || {{ sLLssLLsLs sLLs sLLssLLsLs }} || ||
|| || {{ LLssLLsLss LLss LLssLLsLss }} || ||
|| || {{ LssLLsLssL LssL LssLLsLssL }} || ||
|| || {{ ssLLsLssLL ssLL ssLLsLssLL }} || ||
|| || {{ sLLsLssLLs sLLs sLLsLssLLs }} || ||
|| || {{ LLsLssLLss LLss LLsLssLLss }} || ||
|| || {{ LsLssLLssL LssL LsLssLLssL }} || ||
|| || {{ sLssLLssLL ssLL sLssLLssLL }} || ||
|| {{ LssL LssLLssLLs LssLLssLLs }} || {{ LssLLssLLs sLLs LssLLssLLs }} || ||
|| {{ ssLL ssLLssLLsL ssLLssLLsL }} || || ||
|| {{ sLLs sLLssLLsLs sLLssLLsLs }} || || ||
|| {{ LLss LLssLLsLss LLssLLsLss }} || || ||
|| {{ LssL LssLLsLssL LssLLsLssL }} || || {{ LssLLssLLs LssLLssLLs LssL }} ||
|| {{ ssLL ssLLsLssLL ssLLsLssLL }} || || {{ ssLLssLLsL ssLLssLLsL ssLL }} ||
|| {{ sLLs sLLsLssLLs sLLsLssLLs }} || || {{ sLLssLLsLs sLLssLLsLs sLLs }} ||
|| {{ LLss LLsLssLLss LLsLssLLss }} || || {{ LLssLLsLss LLssLLsLss LLss }} ||
|| {{ LssL LsLssLLssL LsLssLLssL }} || || {{ LssLLsLssL LssLLsLssL LssL }} ||
===See also===
* [[Omnitetrachordality]]
* [[Gallery of omnitetrachordal scales]]
Original HTML content:
<html><head><title>OTC 12L 12s</title></head><body>Omnitetrachordal MOS and MODMOS scale<br />
<a class="wiki_link" href="/12L%2012s">12L+12s</a><br />
24 tones (10+4+10)<br />
<br />
<a class="wiki_link" href="/Pythagorean%20family">catler, compton</a>; 3 forms<br />
<br />
Form 1 (MOS) 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></ul><br />
See also <a class="wiki_link" href="/OTC%205L%205s">OTC 5L+5s</a> (blackwood) and <a class="wiki_link" href="/OTC%207L%207s">OTC 7L+7s</a> (whitewood), which have similar properties.<br />
<br />
For all 3 forms:<br />
<ul><li>the (imperfect) tunings of 9/8 and 4/3 are independent of L/s ratio</li></ul><br />
Forms 2 and 3 are duals.<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> = 24.5754362493 (4/3 = 5L+4.5s)<br />
<br />
L = 50.00 to 100.00 cents (96.09 cents @ Q)<br />
s = 0.00 to 50.00 cents (3.91 cents @ Q)<br />
<br />
9/8 = 2L+2s (200.00 cents, for any L/s)<br />
4/3 = 5L+5s (500.00 cents, for any L/s)<br />
MOS generator = s (0.00 to 50.00 cents)<br />
MOS period = 1/12 octave (100.00 cents)<br />
<br />
notable EDOs: 36, 48, 60, 72, 84<br />
<br />
<tt> LsLsLsLsLsLsLsLsLsLsLsLs </tt> (OTC form 1, MOS)<br />
<tt> | || || || || | </tt><br />
<tt> ssLsLLssLLssLsLLssLLssLL </tt> (form 2, MODMOS) - gc 3,3,3,2,3,3,2; 5o ;; pc 12,2,2; 8o<br />
<tt> || || </tt><br />
<tt> ssLLsLssLLssLLsLssLLssLL </tt> (form 3, MODMOS) - gc 3,3,3,2,3,3,2; 5o ;; pc 12,2,2; 8o<br />
<tt> | |||| || |||| || | </tt><br />
<tt> LsLsLsLsLsLsLsLsLsLsLsLs </tt> (form 1)<br />
<br />
all modes, form 1:<br />
<table class="wiki_table">
<tr>
<td><tt> LsLs LsLsLsLsLs LsLsLsLsLs </tt><br />
</td>
<td><tt> LsLsLsLsLs LsLs LsLsLsLsLs </tt><br />
</td>
<td><tt> LsLsLsLsLs LsLsLsLsLs LsLs </tt><br />
</td>
</tr>
<tr>
<td><tt> sLsL sLsLsLsLsL sLsLsLsLsL </tt><br />
</td>
<td><tt> sLsLsLsLsL sLsL sLsLsLsLsL </tt><br />
</td>
<td><tt> sLsLsLsLsL sLsLsLsLsL sLsL </tt><br />
</td>
</tr>
</table>
<br />
all modes, form 2:<br />
<table class="wiki_table">
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> ssLsLLssLL ssLsLLssLL ssLL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> sLsLLssLLs sLsLLssLLs sLLs </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> LsLLssLLss LsLLssLLss LLss </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLLssLLssL sLLs sLLssLLssL </tt><br />
</td>
<td><tt> sLLssLLssL sLLssLLssL LssL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LLssLLssLs LLss LLssLLssLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LssLLssLsL LssL LssLLssLsL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> ssLLssLsLL ssLL ssLLssLsLL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLLssLsLLs sLLs sLLssLsLLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LLssLsLLss LLss LLssLsLLss </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LssLsLLssL LssL LssLsLLssL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> ssLsLLssLL ssLL ssLsLLssLL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLsLLssLLs sLLs sLsLLssLLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LsLLssLLss LLss LsLLssLLss </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> sLLs sLLssLLssL sLLssLLssL </tt><br />
</td>
<td><tt> sLLssLLssL LssL sLLssLLssL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> LLss LLssLLssLs LLssLLssLs </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> LssL LssLLssLsL LssLLssLsL </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> ssLL ssLLssLsLL ssLLssLsLL </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> sLLs sLLssLsLLs sLLssLsLLs </tt><br />
</td>
<td><br />
</td>
<td><tt> sLLssLLssL sLLssLLssL sLLs </tt><br />
</td>
</tr>
<tr>
<td><tt> LLss LLssLsLLss LLssLsLLss </tt><br />
</td>
<td><br />
</td>
<td><tt> LLssLLssLs LLssLLssLs LLss </tt><br />
</td>
</tr>
<tr>
<td><tt> LssL LssLsLLssL LssLsLLssL </tt><br />
</td>
<td><br />
</td>
<td><tt> LssLLssLsL LssLLssLsL LssL </tt><br />
</td>
</tr>
<tr>
<td><tt> ssLL ssLsLLssLL ssLsLLssLL </tt><br />
</td>
<td><br />
</td>
<td><tt> ssLLssLsLL ssLLssLsLL ssLL </tt><br />
</td>
</tr>
<tr>
<td><tt> sLLs sLsLLssLLs sLsLLssLLs </tt><br />
</td>
<td><br />
</td>
<td><tt> sLLssLsLLs sLLssLsLLs sLLs </tt><br />
</td>
</tr>
<tr>
<td><tt> LLss LsLLssLLss LsLLssLLss </tt><br />
</td>
<td><br />
</td>
<td><tt> LLssLsLLss LLssLsLLss LLss </tt><br />
</td>
</tr>
<tr>
<td><tt> LssL sLLssLLssL sLLssLLssL </tt><br />
</td>
<td><br />
</td>
<td><tt> LssLsLLssL LssLsLLssL LssL </tt><br />
</td>
</tr>
</table>
<br />
all modes, form 3:<br />
<table class="wiki_table">
<tr>
<td><tt> ssLL sLssLLssLL sLssLLssLL </tt><br />
</td>
<td><br />
</td>
<td><tt> ssLLsLssLL ssLLsLssLL ssLL </tt><br />
</td>
</tr>
<tr>
<td><tt> sLLs LssLLssLLs LssLLssLLs </tt><br />
</td>
<td><br />
</td>
<td><tt> sLLsLssLLs sLLsLssLLs sLLs </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> LLsLssLLss LLsLssLLss LLss </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> LsLssLLssL LsLssLLssL LssL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> sLssLLssLL sLssLLssLL ssLL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LssLLssLLs LssL LssLLssLLs </tt><br />
</td>
<td><tt> LssLLssLLs LssLLssLLs sLLs </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> ssLLssLLsL ssLL ssLLssLLsL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLLssLLsLs sLLs sLLssLLsLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LLssLLsLss LLss LLssLLsLss </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LssLLsLssL LssL LssLLsLssL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> ssLLsLssLL ssLL ssLLsLssLL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLLsLssLLs sLLs sLLsLssLLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LLsLssLLss LLss LLsLssLLss </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LsLssLLssL LssL LsLssLLssL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLssLLssLL ssLL sLssLLssLL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> LssL LssLLssLLs LssLLssLLs </tt><br />
</td>
<td><tt> LssLLssLLs sLLs LssLLssLLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> ssLL ssLLssLLsL ssLLssLLsL </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> sLLs sLLssLLsLs sLLssLLsLs </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> LLss LLssLLsLss LLssLLsLss </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> LssL LssLLsLssL LssLLsLssL </tt><br />
</td>
<td><br />
</td>
<td><tt> LssLLssLLs LssLLssLLs LssL </tt><br />
</td>
</tr>
<tr>
<td><tt> ssLL ssLLsLssLL ssLLsLssLL </tt><br />
</td>
<td><br />
</td>
<td><tt> ssLLssLLsL ssLLssLLsL ssLL </tt><br />
</td>
</tr>
<tr>
<td><tt> sLLs sLLsLssLLs sLLsLssLLs </tt><br />
</td>
<td><br />
</td>
<td><tt> sLLssLLsLs sLLssLLsLs sLLs </tt><br />
</td>
</tr>
<tr>
<td><tt> LLss LLsLssLLss LLsLssLLss </tt><br />
</td>
<td><br />
</td>
<td><tt> LLssLLsLss LLssLLsLss LLss </tt><br />
</td>
</tr>
<tr>
<td><tt> LssL LsLssLLssL LsLssLLssL </tt><br />
</td>
<td><br />
</td>
<td><tt> LssLLsLssL LssLLsLssL LssL </tt><br />
</td>
</tr>
</table>
<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></body></html>