OTC 2L 3s
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author spt3125 and made on 2016-08-28 20:28:09 UTC.
- The original revision id was 590306360.
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The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
Omnitetrachordal MOS scale
[[2L 3s|2L+3s]]
5 tones (2+1+2)
The classic pentatonic scale. Can include [[superpyth]], [[https://en.wikipedia.org/wiki/Pythagorean_tuning|Pythagorean]], [[meantone]], and [[Mavila Temperament Modal Harmony|mavila]] tunings. [[{$page}#ref1|(1)]]
[[Gallery of omnitetrachordal scales#perfect|P]] = 1.4424745962 (L=[[32_27|32/27]], s=9/8)
[[Gallery of omnitetrachordal scales#Q|Q]] = 4.3849491924 (4/3 = L+0.5s)
L = 240.00 to 600.00 cents (294.13 cents @ P, 447.07 cents @ Q)
s = 0.00 to 240.00 cents (203.91 cents @ P, 101.96 cents @ Q)
9/8 = s (0.00 to 240.00 cents)
4/3 = L+s (480.00 to 600.00 cents)
generator = 4/3
notable [[EDO]]s: 7, 9, 12, 16, 17, 19, 22, 26, 29, 31
symmetric mode: {{ sLsLs }}
all modes:
|| || {{ sL s sL }} || ||= [[Modal UDP Notation|1|3]] ||
|| || {{ Ls s Ls }} || ||= 3|1 ||
|| {{ s sL sL }} || || ||= 0|4 ||
|| {{ s Ls Ls }} || || {{ sL sL s }} ||= 2|2 ||
|| || || {{ Ls Ls s }} ||= 4|0 ||
[[image:05_02_03_sL_s_sL.png]]
===See also===
* [[Omnitetrachordality]]
* [[Gallery of omnitetrachordal scales]]
===References===
* [[#ref1]](1) Noted as omnitetrachordal by Paul Erlich no later than 2002. See tuning-math list messages [[http://robertinventor.com/tuning-math/s___4/msg_3675-3699.html#3685|3685]] and [[http://robertinventor.com/tuning-math/s__11/msg_10975-10999.html#10987|10987]].Original HTML content:
<html><head><title>OTC 2L 3s</title></head><body>Omnitetrachordal MOS scale<br />
<a class="wiki_link" href="/2L%203s">2L+3s</a><br />
5 tones (2+1+2)<br />
<br />
The classic pentatonic scale. Can include <a class="wiki_link" href="/superpyth">superpyth</a>, <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Pythagorean_tuning" rel="nofollow">Pythagorean</a>, <a class="wiki_link" href="/meantone">meantone</a>, and <a class="wiki_link" href="/Mavila%20Temperament%20Modal%20Harmony">mavila</a> tunings. <!-- ws:start:WikiTextVariableComponentRule:01:[[{$page}#ref1|(1)]] --><a class="wiki_link" href="/OTC%202L%203s#ref1">(1)</a><!-- ws:end:WikiTextVariableComponentRule:01 --><br />
<br />
<a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect">P</a> = 1.4424745962 (L=<a class="wiki_link" href="/32_27">32/27</a>, s=9/8)<br />
<a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#Q">Q</a> = 4.3849491924 (4/3 = L+0.5s)<br />
<br />
L = 240.00 to 600.00 cents (294.13 cents @ P, 447.07 cents @ Q)<br />
s = 0.00 to 240.00 cents (203.91 cents @ P, 101.96 cents @ Q)<br />
<br />
9/8 = s (0.00 to 240.00 cents)<br />
4/3 = L+s (480.00 to 600.00 cents)<br />
generator = 4/3<br />
<br />
notable <a class="wiki_link" href="/EDO">EDO</a>s: 7, 9, 12, 16, 17, 19, 22, 26, 29, 31<br />
<br />
symmetric mode: <tt> sLsLs </tt><br />
<br />
all modes:<br />
<table class="wiki_table">
<tr>
<td><br />
</td>
<td><tt> sL s sL </tt><br />
</td>
<td><br />
</td>
<td style="text-align: center;"> <a class="wiki_link" href="/Modal%20UDP%20Notation">1|3</a> <br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> Ls s Ls </tt><br />
</td>
<td><br />
</td>
<td style="text-align: center;">3|1<br />
</td>
</tr>
<tr>
<td><tt> s sL sL </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td style="text-align: center;">0|4<br />
</td>
</tr>
<tr>
<td><tt> s Ls Ls </tt><br />
</td>
<td><br />
</td>
<td><tt> sL sL s </tt><br />
</td>
<td style="text-align: center;">2|2<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> Ls Ls s </tt><br />
</td>
<td style="text-align: center;">4|0<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextLocalImageRule:69:<img src="/file/view/05_02_03_sL_s_sL.png/589273764/05_02_03_sL_s_sL.png" alt="" title="" /> --><img src="/file/view/05_02_03_sL_s_sL.png/589273764/05_02_03_sL_s_sL.png" alt="05_02_03_sL_s_sL.png" title="05_02_03_sL_s_sL.png" /><!-- ws:end:WikiTextLocalImageRule:69 --><br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:<h3> --><h3 id="toc0"><a name="x--See also"></a><!-- ws:end:WikiTextHeadingRule:2 -->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:4:<h3> --><h3 id="toc1"><a name="x--References"></a><!-- ws:end:WikiTextHeadingRule:4 -->References</h3>
<ul><li><!-- ws:start:WikiTextAnchorRule:6:<img src="/i/anchor.gif" class="WikiAnchor" alt="Anchor" id="wikitext@@anchor@@ref1" title="Anchor: ref1"/> --><a name="ref1"></a><!-- ws:end:WikiTextAnchorRule:6 -->(1) 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>