OTC 5L 5s
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 20:54:05 UTC.
- The original revision id was 590307632.
- The revision comment was:
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
[[5L 5s|5L+5s]]
10 tones (4+2+4)
temperament: [[blackwood]]
This scale 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 [[Gallery of omnitetrachordal scales#dual|dual]] (changing all L to s, and vice versa, gives the same scale)
* the (imperfect) tunings of 9/8 and 4/3 are independent of L/s ratio
See also [[OTC 7L 7s|OTC 7L+7s]] (whitewood) and [[OTC 12L 12s|OTC 12L+12s]] (catler/compton), which have similar properties.
[[Gallery of omnitetrachordal scales#perfect|P]] = undefined (or -1?)
[[Gallery of omnitetrachordal scales#Q|Q]] = 5.6500418817 (4/3 = 2L+2.5s)
L = 120.00 to 240.00 cents (203.91 cents @ Q)
s = 0.00 to 120.00 cents (36.09 cents @ Q)
9/8 = L+s (240.00 cents for any L/s)
4/3 = 2L+2s (480.00 cents for any L/s)
generator = s (0.00 to 120.00 cents)
[[periods and generators|period]] = 1/5 octave (240.00 cents)
notable EDOs: 15, 20, 25
all modes:
|| {{ Ls LsLs LsLs }} || {{ LsLs Ls LsLs }} || {{ LsLs LsLs Ls }} ||
|| {{ sL sLsL sLsL }} || {{ sLsL sL sLsL }} || {{ sLsL sLsL sL }} ||
[[image:10_05_05_LsLs_Ls_LsLs.png]]
===See also===
* [[Omnitetrachordality]]
* [[Gallery of omnitetrachordal scales]]
Original HTML content:
<html><head><title>OTC 5L 5s</title></head><body>Omnitetrachordal MOS scale<br />
<a class="wiki_link" href="/5L%205s">5L+5s</a><br />
10 tones (4+2+4)<br />
<br />
temperament: <a class="wiki_link" href="/blackwood">blackwood</a><br />
<br />
This scale 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 <a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#dual">dual</a> (changing all L to s, and vice versa, gives the same scale)</li><li>the (imperfect) tunings of 9/8 and 4/3 are independent of L/s ratio</li></ul><br />
See also <a class="wiki_link" href="/OTC%207L%207s">OTC 7L+7s</a> (whitewood) and <a class="wiki_link" href="/OTC%2012L%2012s">OTC 12L+12s</a> (catler/compton), which have similar properties.<br />
<br />
<a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect">P</a> = undefined (or -1?)<br />
<a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#Q">Q</a> = 5.6500418817 (4/3 = 2L+2.5s)<br />
<br />
L = 120.00 to 240.00 cents (203.91 cents @ Q)<br />
s = 0.00 to 120.00 cents (36.09 cents @ Q)<br />
<br />
9/8 = L+s (240.00 cents for any L/s)<br />
4/3 = 2L+2s (480.00 cents for any L/s)<br />
generator = s (0.00 to 120.00 cents)<br />
<a class="wiki_link" href="/periods%20and%20generators">period</a> = 1/5 octave (240.00 cents)<br />
<br />
notable EDOs: 15, 20, 25<br />
<br />
all modes:<br />
<table class="wiki_table">
<tr>
<td><tt> Ls LsLs LsLs </tt><br />
</td>
<td><tt> LsLs Ls LsLs </tt><br />
</td>
<td><tt> LsLs LsLs Ls </tt><br />
</td>
</tr>
<tr>
<td><tt> sL sLsL sLsL </tt><br />
</td>
<td><tt> sLsL sL sLsL </tt><br />
</td>
<td><tt> sLsL sLsL sL </tt><br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextLocalImageRule:36:<img src="/file/view/10_05_05_LsLs_Ls_LsLs.png/589273800/10_05_05_LsLs_Ls_LsLs.png" alt="" title="" /> --><img src="/file/view/10_05_05_LsLs_Ls_LsLs.png/589273800/10_05_05_LsLs_Ls_LsLs.png" alt="10_05_05_LsLs_Ls_LsLs.png" title="10_05_05_LsLs_Ls_LsLs.png" /><!-- ws:end:WikiTextLocalImageRule:36 --><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></body></html>