OTC 5L 2s

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This revision was by author spt3125 and made on 2016-08-28 20:15:21 UTC.
The original revision id was 590305916.
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:

[[5L 2s|5L+2s]] / 7 tones (3+1+3)
Classic diatonic MOS 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]]

* [[#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><a class="wiki_link" href="/5L%202s">5L+2s</a> / 7 tones (3+1+3)<br />
Classic diatonic MOS 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 />
<!-- ws:start:WikiTextLocalImageRule:179:&lt;img src=&quot;/file/view/07_05_02_LsL_L_Ls.png/589273784/07_05_02_LsL_L_Ls.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/07_05_02_LsL_L_Ls.png/589273784/07_05_02_LsL_L_Ls.png" alt="07_05_02_LsL_L_Ls.png" title="07_05_02_LsL_L_Ls.png" /><!-- ws:end:WikiTextLocalImageRule:179 --><br />
<br />
<ul><li><!-- ws:start:WikiTextAnchorRule:2:&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:2 -->(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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