OTC 5L 7s
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 21:22:18 UTC.
- The original revision id was 590308854.
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Original Wikitext content:
Omnitetrachordal MOS scale
[[5L 7s|5L+7s]]
12 tones (5+2+5)
MOS of the helmholtz / garibaldi / [[Schismatic family|schismatic]] and [[superpyth]] temperaments, as well as Pythagorean. Very good 3/2 at almost any L/s ratio. Many modes may be pentachordally split in two ways. See also [[OTC 7L 5s|OTC 7L+5s]].
[[Gallery of omnitetrachordal scales#perfect|P]] = 1.2600167527 (L=[[2187_2048|2187/2048]], s=[[256_243|256/243]])
[[Gallery of omnitetrachordal scales#Q|Q]] = 7.9100586343 (2L+3.5s)
L = 100.00 to 240.00 cents (113.68 cents @ P, 203.91 cents @ Q)
s = 0.00 to 100.00 cents (90.23 cents @ P, 25.78 cents @ Q)
9/8 = L+s (200.00 to 240.00 cents)
4/3 = 2L+3s (480.00 to 500.00 cents)
generator = 4/3
notable EDOs: 17, 22, 27, 29, 41, 53, etc.
all modes:
|| {{ Ls LsLss LsLss }} || || ||
|| {{ sL sLssL sLssL }} || || {{ sLsLs sLsLs sL }} ||
|| {{ Ls LssLs LssLs }} || || {{ LsLss LsLss Ls }} ||
|| {{ sL ssLsL ssLsL }} || || {{ sLssL sLssL sL }} ||
|| {{ Ls sLsLs sLsLs }} || || {{ LssLs LssLs Ls }} ||
|| || || {{ ssLsL ssLsL sL }} ||
|| || {{ sLsLs sL sLsLs }} || {{ sLsLs sLsLs Ls }} ||
|| || {{ LsLss Ls LsLss }} || ||
|| || {{ sLssL sL sLssL }} || ||
|| || {{ LssLs Ls LssLs }} || ||
|| || {{ ssLsL sL ssLsL }} || ||
|| {{ sL sLsLs sLsLs }} || {{ sLsLs Ls sLsLs }} || ||
[[image:12_05_07_sLssL_sL_sLssL.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 5L 7s</title></head><body>Omnitetrachordal MOS scale<br />
<a class="wiki_link" href="/5L%207s">5L+7s</a><br />
12 tones (5+2+5)<br />
<br />
MOS of the helmholtz / garibaldi / <a class="wiki_link" href="/Schismatic%20family">schismatic</a> and <a class="wiki_link" href="/superpyth">superpyth</a> temperaments, as well as Pythagorean. Very good 3/2 at almost any L/s ratio. Many modes may be pentachordally split in two ways. See also <a class="wiki_link" href="/OTC%207L%205s">OTC 7L+5s</a>.<br />
<br />
<a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect">P</a> = 1.2600167527 (L=<a class="wiki_link" href="/2187_2048">2187/2048</a>, s=<a class="wiki_link" href="/256_243">256/243</a>)<br />
<a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#Q">Q</a> = 7.9100586343 (2L+3.5s)<br />
<br />
L = 100.00 to 240.00 cents (113.68 cents @ P, 203.91 cents @ Q)<br />
s = 0.00 to 100.00 cents (90.23 cents @ P, 25.78 cents @ Q)<br />
<br />
9/8 = L+s (200.00 to 240.00 cents)<br />
4/3 = 2L+3s (480.00 to 500.00 cents)<br />
generator = 4/3<br />
<br />
notable EDOs: 17, 22, 27, 29, 41, 53, etc.<br />
<br />
all modes:<br />
<table class="wiki_table">
<tr>
<td><tt> Ls LsLss LsLss </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> sL sLssL sLssL </tt><br />
</td>
<td><br />
</td>
<td><tt> sLsLs sLsLs sL </tt><br />
</td>
</tr>
<tr>
<td><tt> Ls LssLs LssLs </tt><br />
</td>
<td><br />
</td>
<td><tt> LsLss LsLss Ls </tt><br />
</td>
</tr>
<tr>
<td><tt> sL ssLsL ssLsL </tt><br />
</td>
<td><br />
</td>
<td><tt> sLssL sLssL sL </tt><br />
</td>
</tr>
<tr>
<td><tt> Ls sLsLs sLsLs </tt><br />
</td>
<td><br />
</td>
<td><tt> LssLs LssLs Ls </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> ssLsL ssLsL sL </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLsLs sL sLsLs </tt><br />
</td>
<td><tt> sLsLs sLsLs Ls </tt><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LsLss Ls LsLss </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> sLssL sL sLssL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> LssLs Ls LssLs </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> ssLsL sL ssLsL </tt><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><tt> sL sLsLs sLsLs </tt><br />
</td>
<td><tt> sLsLs Ls sLsLs </tt><br />
</td>
<td><br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextLocalImageRule:112:<img src="/file/view/12_05_07_sLssL_sL_sLssL.png/589273824/12_05_07_sLssL_sL_sLssL.png" alt="" title="" /> --><img src="/file/view/12_05_07_sLssL_sL_sLssL.png/589273824/12_05_07_sLssL_sL_sLssL.png" alt="12_05_07_sLssL_sL_sLssL.png" title="12_05_07_sLssL_sL_sLssL.png" /><!-- ws:end:WikiTextLocalImageRule:112 --><br />
<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>