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OTC 5L 2s

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Original Wikitext content:

Omnitetrachordal MOS scale
[[5L 2s|5L+2s]]
7 tones (3+1+3)

The classic diatonic scale ([[meantone]], Pythagorean, [[superpyth]]). [[{$page}#ref1|(1)]]

[[Gallery of omnitetrachordal scales#perfect|P]] = 2.2600167527 (L=9/8, s=[[256_243|256/243]])

L = 171.43 to 240.00 cents (203.91 cents @ P)
s = 0.00 to 171.43 cents (90.22 cents @ P)

9/8 = L (171.43 to 240.00 cents)
4/3 = 2L+s (480.00 to 514.29 cents)
generator = 3L+s (685.71 to 720.00 cents)

notable EDOs: 12, 17, 19, 22, 26, 29, 31, etc.

symmetric mode: LsLLLsL

all modes:
|| || {{ LLs L LLs }} || || Ionian ||=  5|1  ||
|| || {{ LsL L LsL }} || || Dorian ||= 3|3 ||
|| || {{ sLL L sLL }} || || Phrygian ||= 1|5 ||
|| {{ L LLs LLs }} || || || Lydian ||= 6|0 ||
|| {{ L LsL LsL }} || || {{ LLs LLs L }} || Mixolydian ||= 4|2 ||
|| {{ L sLL sLL }} || || {{ LsL LsL L }} || Aeolian ||= 2|4 ||
|| || || {{ sLL sLL L }} || Locrian ||= 0|6 ||

all modes in [[Modal UDP Notation|UDP]] order:
|| {{ L LLs LLs }} || || || Lydian ||=  6|0  ||
|| || {{ LLs L LLs }} || || Ionian ||= 5|1 ||
|| {{ L LsL LsL }} || || {{ LLs LLs L }} || Mixolydian ||= 4|2 ||
|| || {{ LsL L LsL }} || || Dorian ||= 3|3 ||
|| {{ L sLL sLL }} || || {{ LsL LsL L }} || Aeolian ||= 2|4 ||
|| || {{ sLL L sLL }} || || Phrygian ||= 1|5 ||
|| || || {{ sLL sLL L }} || Locrian ||= 0|6 ||

[[image:07_05_02_LsL_L_Ls.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 5L 2s</title></head><body>Omnitetrachordal MOS scale<br />
<a class="wiki_link" href="/5L%202s">5L+2s</a><br />
7 tones (3+1+3)<br />
<br />
The classic diatonic scale (<a class="wiki_link" href="/meantone">meantone</a>, Pythagorean, <a class="wiki_link" href="/superpyth">superpyth</a>). <!-- ws:start:WikiTextVariableComponentRule:01:[[{$page}#ref1|(1)]] --><a class="wiki_link" href="/OTC%205L%202s#ref1">(1)</a><!-- ws:end:WikiTextVariableComponentRule:01 --><br />
<br />
<a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect">P</a> = 2.2600167527 (L=9/8, s=<a class="wiki_link" href="/256_243">256/243</a>)<br />
<br />
L = 171.43 to 240.00 cents (203.91 cents @ P)<br />
s = 0.00 to 171.43 cents (90.22 cents @ P)<br />
<br />
9/8 = L (171.43 to 240.00 cents)<br />
4/3 = 2L+s (480.00 to 514.29 cents)<br />
generator = 3L+s (685.71 to 720.00 cents)<br />
<br />
notable EDOs: 12, 17, 19, 22, 26, 29, 31, etc.<br />
<br />
symmetric mode: LsLLLsL<br />
<br />
all modes:<br />


<table class="wiki_table">
    <tr>
        <td><br />
</td>
        <td><tt> LLs L LLs </tt><br />
</td>
        <td><br />
</td>
        <td>Ionian<br />
</td>
        <td style="text-align: center;"> 5|1 <br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><tt> LsL L LsL </tt><br />
</td>
        <td><br />
</td>
        <td>Dorian<br />
</td>
        <td style="text-align: center;">3|3<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><tt> sLL L sLL </tt><br />
</td>
        <td><br />
</td>
        <td>Phrygian<br />
</td>
        <td style="text-align: center;">1|5<br />
</td>
    </tr>
    <tr>
        <td><tt> L LLs LLs </tt><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>Lydian<br />
</td>
        <td style="text-align: center;">6|0<br />
</td>
    </tr>
    <tr>
        <td><tt> L LsL LsL </tt><br />
</td>
        <td><br />
</td>
        <td><tt> LLs LLs L </tt><br />
</td>
        <td>Mixolydian<br />
</td>
        <td style="text-align: center;">4|2<br />
</td>
    </tr>
    <tr>
        <td><tt> L sLL sLL </tt><br />
</td>
        <td><br />
</td>
        <td><tt> LsL LsL L </tt><br />
</td>
        <td>Aeolian<br />
</td>
        <td style="text-align: center;">2|4<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><tt> sLL sLL L </tt><br />
</td>
        <td>Locrian<br />
</td>
        <td style="text-align: center;">0|6<br />
</td>
    </tr>
</table>

<br />
all modes in <a class="wiki_link" href="/Modal%20UDP%20Notation">UDP</a> order:<br />


<table class="wiki_table">
    <tr>
        <td><tt> L LLs LLs </tt><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>Lydian<br />
</td>
        <td style="text-align: center;"> 6|0 <br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><tt> LLs L LLs </tt><br />
</td>
        <td><br />
</td>
        <td>Ionian<br />
</td>
        <td style="text-align: center;">5|1<br />
</td>
    </tr>
    <tr>
        <td><tt> L LsL LsL </tt><br />
</td>
        <td><br />
</td>
        <td><tt> LLs LLs L </tt><br />
</td>
        <td>Mixolydian<br />
</td>
        <td style="text-align: center;">4|2<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><tt> LsL L LsL </tt><br />
</td>
        <td><br />
</td>
        <td>Dorian<br />
</td>
        <td style="text-align: center;">3|3<br />
</td>
    </tr>
    <tr>
        <td><tt> L sLL sLL </tt><br />
</td>
        <td><br />
</td>
        <td><tt> LsL LsL L </tt><br />
</td>
        <td>Aeolian<br />
</td>
        <td style="text-align: center;">2|4<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><tt> sLL L sLL </tt><br />
</td>
        <td><br />
</td>
        <td>Phrygian<br />
</td>
        <td style="text-align: center;">1|5<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><tt> sLL sLL L </tt><br />
</td>
        <td>Locrian<br />
</td>
        <td style="text-align: center;">0|6<br />
</td>
    </tr>
</table>

<br />
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<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><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:&lt;h3&gt; --><h3 id="toc1"><a name="x--References"></a><!-- ws:end:WikiTextHeadingRule:4 -->References</h3>
<ul><li><!-- ws:start:WikiTextAnchorRule:6:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@ref1&quot; title=&quot;Anchor: ref1&quot;/&gt; --><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>
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