OTC 2L 8s
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Original Wikitext content:
Omnitetrachordal MODMOS scale
[[2L 8s|2L+8s]]
10 tones (4+2+4)
[[Pajara]] [[MODMOS]]. Best at lower ratios of L/s.
[[Gallery of omnitetrachordal scales#perfect|P]] = 1.8849491924
[[Gallery of omnitetrachordal scales#Q|Q]] = 4.8274237885 (4/3 = L+2.5s)
L = 120.00 to 600.00 cents (192.18 cents @ P, 328.12 cents @ Q)
s = 0.00 to 120.00 cents (101.96 cents @ P, 67.97 cents @ Q)
9/8 = 2s (0.00 to 240.00 cents)
4/3 = L+3s (480.00 to 600.00 cents)
[[MOS]] generator = s (0.00 to 120.00 cents)
MOS [[periods and generators|period]] = 1/2 octave (600.00 cents)
notable EDOs: 12, 14, 16, 22, 26
{{ LssssLssss }} (MOS, not OTC)
{{ || }}
{{ LsssssLsss }} (OTC MODMOS) - gen chains 6,4
modes:
|| || {{ sssL ss sssL }} || || Standard Pentachordal Minor ||
|| || {{ ssLs ss ssLs }} || || - ||
|| || {{ sLss ss sLss }} || || Alternate Pentachordal Major ||
|| || {{ Lsss ss Lsss }} || || - ||
|| {{ ss sssL sssL }} || || || - ||
|| {{ ss ssLs ssLs }} || || || Alternate Pentachordal Minor ||
|| {{ ss sLss sLss }} || || {{ sssL sssL ss }} || - ||
|| {{ ss Lsss Lsss }} || || {{ ssLs ssLs ss }} || Standard Pentachordal Major ||
|| || || {{ sLss sLss ss }} || - ||
|| || || {{ Lsss Lsss ss }} || - ||
(The names of the modes are Paul Erlich's - see [[http://lumma.org/tuning/erlich/erlich-decatonic.pdf]].)
[[image:10_02_08_sLss_ss_sLss.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 2L 8s</title></head><body>Omnitetrachordal MODMOS scale<br />
<a class="wiki_link" href="/2L%208s">2L+8s</a><br />
10 tones (4+2+4)<br />
<br />
<a class="wiki_link" href="/Pajara">Pajara</a> <a class="wiki_link" href="/MODMOS">MODMOS</a>. Best at lower ratios of L/s.<br />
<br />
<a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect">P</a> = 1.8849491924<br />
<a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#Q">Q</a> = 4.8274237885 (4/3 = L+2.5s)<br />
<br />
L = 120.00 to 600.00 cents (192.18 cents @ P, 328.12 cents @ Q)<br />
s = 0.00 to 120.00 cents (101.96 cents @ P, 67.97 cents @ Q)<br />
<br />
9/8 = 2s (0.00 to 240.00 cents)<br />
4/3 = L+3s (480.00 to 600.00 cents)<br />
<a class="wiki_link" href="/MOS">MOS</a> generator = s (0.00 to 120.00 cents)<br />
MOS <a class="wiki_link" href="/periods%20and%20generators">period</a> = 1/2 octave (600.00 cents)<br />
<br />
notable EDOs: 12, 14, 16, 22, 26<br />
<br />
<tt> LssssLssss </tt> (MOS, not OTC)<br />
<tt> || </tt> <br />
<tt> LsssssLsss </tt> (OTC MODMOS) - gen chains 6,4<br />
<br />
modes:<br />
<table class="wiki_table">
<tr>
<td><br />
</td>
<td><tt> sssL ss sssL </tt><br />
</td>
<td><br />
</td>
<td>Standard Pentachordal Minor<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> ssLs ss ssLs </tt><br />
</td>
<td><br />
</td>
<td>-<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLss ss sLss </tt><br />
</td>
<td><br />
</td>
<td>Alternate Pentachordal Major<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> Lsss ss Lsss </tt><br />
</td>
<td><br />
</td>
<td>-<br />
</td>
</tr>
<tr>
<td><tt> ss sssL sssL </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>-<br />
</td>
</tr>
<tr>
<td><tt> ss ssLs ssLs </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>Alternate Pentachordal Minor<br />
</td>
</tr>
<tr>
<td><tt> ss sLss sLss </tt><br />
</td>
<td><br />
</td>
<td><tt> sssL sssL ss </tt><br />
</td>
<td>-<br />
</td>
</tr>
<tr>
<td><tt> ss Lsss Lsss </tt><br />
</td>
<td><br />
</td>
<td><tt> ssLs ssLs ss </tt><br />
</td>
<td>Standard Pentachordal Major<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> sLss sLss ss </tt><br />
</td>
<td>-<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> Lsss Lsss ss </tt><br />
</td>
<td>-<br />
</td>
</tr>
</table>
(The names of the modes are Paul Erlich's - see <a class="wiki_link_ext" href="http://lumma.org/tuning/erlich/erlich-decatonic.pdf" rel="nofollow">http://lumma.org/tuning/erlich/erlich-decatonic.pdf</a>.)<br />
<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>