OTC 2L 10s
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Original Wikitext content:
Omnitetrachordal MODMOS scales
[[2L 10s|2L+10s]]
This OTC scale pattern has two classes (with different tetrachordal divisions). Only a few other scales of the form [[OTC 2L ns|2L+ns]] are known to have this property.
temperaments: [[injera]] ?
----
===Class 1===
12 tones (5+2+5)
[[Gallery of omnitetrachordal scales#dual|Dual]] of [[OTC 10L 2s|OTC 10L+2s]]. Probably only useful for small values of L/s.
[[Gallery of omnitetrachordal scales#perfect|P]] = 0.8849491924
[[Gallery of omnitetrachordal scales#Q|Q]] = 3.8274237885 (4/3 = L+3.5s)
L = 100.00 to 600.00 cents (260.15 cents @ Q)
s = 0.00 to 100.00 cents (67.97 cents @ Q)
9/8 = 2s (0.00 to 200.00 cents)
4/3 = L+4s (500.00 to 600.00 cents)
MOS generator = s (0.00 to 100.00 cents)
MOS period = 1/2 octave (600.00 cents)
notable EDOs: 14, 16, 26, 38
{{ LsssssLsssss }} (MOS, not OTC)
{{ || }}
{{ LssssLssssss }} (OTC MODMOS) - gen chains 7,5
symmetric modes:
{{ sssLssssLsss }}
{{ ssLssssssLss }}
all modes:
|| || {{ ssLss ss ssLss }} || ||
|| || {{ sLsss ss sLsss }} || ||
|| || {{ Lssss ss Lssss }} || ||
|| {{ ss ssssL ssssL }} || || ||
|| {{ ss sssLs sssLs }} || || ||
|| {{ ss ssLss ssLss }} || || {{ ssssL ssssL ss }} ||
|| {{ ss sLsss sLsss }} || || {{ sssLs sssLs ss }} ||
|| {{ ss Lssss Lssss }} || || {{ ssLss ssLss ss }} ||
|| || || {{ sLsss sLsss ss }} ||
|| || || {{ Lssss Lssss ss }} ||
|| || {{ ssssL ss ssssL }} || ||
|| || {{ sssLs ss sssLs }} || ||
[[image:12_02_10_ssLss_ss_ssLss.png]]
----
===Class 2===
12 tones (4+4+4)
Only works at high values of L/s.
Q<span style="vertical-align: sub;">2</span> ``=`` 3.8274237885 (4/3 = L+3.5s)
P = 6.7698983847
Q<span style="vertical-align: sub;">1</span> ``=`` 9.7123729809 (4/3 = L+2.5s)
L = 100.00 to 600.00 cents (260.15 cents @ Q<span style="vertical-align: sub;">2</span>, 345.11 cents @ P, 396.09 cents @ Q<span style="vertical-align: sub;">1</span>)
s = 0.00 to 100.00 cents (67.97 cents @ Q<span style="vertical-align: sub;">2</span>, 50.98 cents @ P, 40.78 cents @ Q<span style="vertical-align: sub;">1</span>)
9/8 = 4s (0.00 to 400.00 cents)
4/3 = L+3s (400.00 to 600.00 cents)
MOS generator = s (0.00 to 100.00 cents)
MOS period = 1/2 octave (600.00 cents)
notable EDOs: 20, 22, 24
{{ LsssssLsssss }} (MOS, not OTC)
{{ | | }}
{{ LsssLsssssss }} (OTC MODMOS) - gen chains 8,4
all modes:
|| || || {{ Lsss Lsss ssss }} ||
|| || {{ sssL ssss sssL }} || ||
|| || {{ ssLs ssss ssLs }} || ||
|| || {{ sLss ssss sLss }} || ||
|| || {{ Lsss ssss Lsss }} || ||
|| {{ ssss sssL sssL }} || || ||
|| {{ ssss ssLs ssLs }} || || ||
|| {{ ssss sLss sLss }} || || ||
|| {{ ssss Lsss Lsss }} || || ||
|| || || {{ sssL sssL ssss }} ||
|| || || {{ ssLs ssLs ssss }} ||
|| || || {{ sLss sLss ssss }} ||
----
===See also===
* [[Omnitetrachordality]]
* [[Gallery of omnitetrachordal scales]]
Original HTML content:
<html><head><title>OTC 2L 10s</title></head><body>Omnitetrachordal MODMOS scales<br />
<a class="wiki_link" href="/2L%2010s">2L+10s</a><br />
<br />
This OTC scale pattern has two classes (with different tetrachordal divisions). Only a few other scales of the form <a class="wiki_link" href="/OTC%202L%20ns">2L+ns</a> are known to have this property.<br />
<br />
temperaments: <a class="wiki_link" href="/injera">injera</a> ?<br />
<br />
<hr />
<br />
<!-- ws:start:WikiTextHeadingRule:2:<h3> --><h3 id="toc0"><a name="x--Class 1"></a><!-- ws:end:WikiTextHeadingRule:2 -->Class 1</h3>
12 tones (5+2+5)<br />
<br />
<a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#dual">Dual</a> of <a class="wiki_link" href="/OTC%2010L%202s">OTC 10L+2s</a>. Probably only useful for small values of L/s.<br />
<br />
<a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect">P</a> = 0.8849491924<br />
<a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#Q">Q</a> = 3.8274237885 (4/3 = L+3.5s)<br />
<br />
L = 100.00 to 600.00 cents (260.15 cents @ Q)<br />
s = 0.00 to 100.00 cents (67.97 cents @ Q)<br />
<br />
9/8 = 2s (0.00 to 200.00 cents)<br />
4/3 = L+4s (500.00 to 600.00 cents)<br />
MOS generator = s (0.00 to 100.00 cents)<br />
MOS period = 1/2 octave (600.00 cents)<br />
<br />
notable EDOs: 14, 16, 26, 38<br />
<br />
<tt> LsssssLsssss </tt> (MOS, not OTC)<br />
<tt> || </tt><br />
<tt> LssssLssssss </tt> (OTC MODMOS) - gen chains 7,5<br />
<br />
symmetric modes:<br />
<tt> sssLssssLsss </tt><br />
<tt> ssLssssssLss </tt><br />
<br />
all modes:<br />
<table class="wiki_table">
<tr>
<td><br />
</td>
<td><tt> ssLss ss ssLss </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLsss ss sLsss </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> Lssss ss Lssss </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> ss ssssL ssssL </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> ss sssLs sssLs </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> ss ssLss ssLss </tt><br />
</td>
<td><br />
</td>
<td><tt> ssssL ssssL ss </tt><br />
</td>
</tr>
<tr>
<td><tt> ss sLsss sLsss </tt><br />
</td>
<td><br />
</td>
<td><tt> sssLs sssLs ss </tt><br />
</td>
</tr>
<tr>
<td><tt> ss Lssss Lssss </tt><br />
</td>
<td><br />
</td>
<td><tt> ssLss ssLss ss </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> sLsss sLsss ss </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> Lssss Lssss ss </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> ssssL ss ssssL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sssLs ss sssLs </tt><br />
</td>
<td><br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextLocalImageRule:213:<img src="/file/view/12_02_10_ssLss_ss_ssLss.png/589273820/12_02_10_ssLss_ss_ssLss.png" alt="" title="" /> --><img src="/file/view/12_02_10_ssLss_ss_ssLss.png/589273820/12_02_10_ssLss_ss_ssLss.png" alt="12_02_10_ssLss_ss_ssLss.png" title="12_02_10_ssLss_ss_ssLss.png" /><!-- ws:end:WikiTextLocalImageRule:213 --><br />
<br />
<hr />
<br />
<!-- ws:start:WikiTextHeadingRule:4:<h3> --><h3 id="toc1"><a name="x--Class 2"></a><!-- ws:end:WikiTextHeadingRule:4 -->Class 2</h3>
12 tones (4+4+4)<br />
<br />
Only works at high values of L/s.<br />
<br />
Q<span style="vertical-align: sub;">2</span> <!-- ws:start:WikiTextRawRule:00:``=`` -->=<!-- ws:end:WikiTextRawRule:00 --> 3.8274237885 (4/3 = L+3.5s)<br />
P = 6.7698983847<br />
Q<span style="vertical-align: sub;">1</span> <!-- ws:start:WikiTextRawRule:01:``=`` -->=<!-- ws:end:WikiTextRawRule:01 --> 9.7123729809 (4/3 = L+2.5s)<br />
<br />
L = 100.00 to 600.00 cents (260.15 cents @ Q<span style="vertical-align: sub;">2</span>, 345.11 cents @ P, 396.09 cents @ Q<span style="vertical-align: sub;">1</span>)<br />
s = 0.00 to 100.00 cents (67.97 cents @ Q<span style="vertical-align: sub;">2</span>, 50.98 cents @ P, 40.78 cents @ Q<span style="vertical-align: sub;">1</span>)<br />
<br />
9/8 = 4s (0.00 to 400.00 cents)<br />
4/3 = L+3s (400.00 to 600.00 cents)<br />
MOS generator = s (0.00 to 100.00 cents)<br />
MOS period = 1/2 octave (600.00 cents)<br />
<br />
notable EDOs: 20, 22, 24<br />
<br />
<tt> LsssssLsssss </tt> (MOS, not OTC)<br />
<tt> | | </tt><br />
<tt> LsssLsssssss </tt> (OTC MODMOS) - gen chains 8,4<br />
<br />
all modes:<br />
<table class="wiki_table">
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> Lsss Lsss ssss </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sssL ssss sssL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> ssLs ssss ssLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLss ssss sLss </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> Lsss ssss Lsss </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> ssss sssL sssL </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> ssss ssLs ssLs </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> ssss sLss sLss </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> ssss Lsss Lsss </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> sssL sssL ssss </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> ssLs ssLs ssss </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> sLss sLss ssss </tt><br />
</td>
</tr>
</table>
<br />
<hr />
<br />
<!-- ws:start:WikiTextHeadingRule:6:<h3> --><h3 id="toc2"><a name="x--See also"></a><!-- ws:end:WikiTextHeadingRule:6 -->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>