OTC 5L 2s: Difference between revisions

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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 />
<!-- ws:start:WikiTextLocalImageRule:189:&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:189 --><br />
<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>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2016-08-28 20:15:21 UTC</tt>.<br>
+: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2016-08-28 20:20:58 UTC</tt>.<br>
-: The original revision id was <tt>590305916</tt>.<br>
+: The original revision id was <tt>590306118</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
 <h4>Original Wikitext content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">[[5L 2s|5L+2s]] / 7 tones (3+1+3)
+<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">Omnitetrachordal MOS scale
-Classic diatonic MOS scale ([[meantone]], Pythagorean, [[superpyth]]). [[{$page}#ref1|(1)]]
+[[5L 2s|5L+2s]]
+tones (3+1+3)
+The classic diatonic scale ([[meantone]], Pythagorean, [[superpyth]]). [[{$page}#ref1|(1)]]
 [[Gallery of omnitetrachordal scales#perfect|P]] = 2.2600167527 (L=9/8, s=[[256_243|256/243]])
@@ Line 42: / Line 45: @@
 [[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]].</pre></div>
 <h4>Original HTML content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;OTC 5L 2s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;a class="wiki_link" href="/5L%202s"&gt;5L+2s&lt;/a&gt; / 7 tones (3+1+3)&lt;br /&gt;
+<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;OTC 5L 2s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Omnitetrachordal MOS scale&lt;br /&gt;
-Classic diatonic MOS scale (&lt;a class="wiki_link" href="/meantone"&gt;meantone&lt;/a&gt;, Pythagorean, &lt;a class="wiki_link" href="/superpyth"&gt;superpyth&lt;/a&gt;). &lt;!-- ws:start:WikiTextVariableComponentRule:01:[[{$page}#ref1|(1)]] --&gt;&lt;a class="wiki_link" href="/OTC%205L%202s#ref1"&gt;(1)&lt;/a&gt;&lt;!-- ws:end:WikiTextVariableComponentRule:01 --&gt;&lt;br /&gt;
+&lt;a class="wiki_link" href="/5L%202s"&gt;5L+2s&lt;/a&gt;&lt;br /&gt;
+tones (3+1+3)&lt;br /&gt;
+&lt;br /&gt;
+The classic diatonic scale (&lt;a class="wiki_link" href="/meantone"&gt;meantone&lt;/a&gt;, Pythagorean, &lt;a class="wiki_link" href="/superpyth"&gt;superpyth&lt;/a&gt;). &lt;!-- ws:start:WikiTextVariableComponentRule:01:[[{$page}#ref1|(1)]] --&gt;&lt;a class="wiki_link" href="/OTC%205L%202s#ref1"&gt;(1)&lt;/a&gt;&lt;!-- ws:end:WikiTextVariableComponentRule:01 --&gt;&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect"&gt;P&lt;/a&gt; = 2.2600167527 (L=9/8, s=&lt;a class="wiki_link" href="/256_243"&gt;256/243&lt;/a&gt;)&lt;br /&gt;
@@ Line 242: / Line 253: @@
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:179:&amp;lt;img src=&amp;quot;/file/view/07_05_02_LsL_L_Ls.png/589273784/07_05_02_LsL_L_Ls.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;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" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:179 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:189:&amp;lt;img src=&amp;quot;/file/view/07_05_02_LsL_L_Ls.png/589273784/07_05_02_LsL_L_Ls.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;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" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:189 --&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;ul&gt;&lt;li&gt;&lt;!-- ws:start:WikiTextAnchorRule:2:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@ref1&amp;quot; title=&amp;quot;Anchor: ref1&amp;quot;/&amp;gt; --&gt;&lt;a name="ref1"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:2 --&gt;(1) Noted as omnitetrachordal by Paul Erlich no later than 2002. See tuning-math list messages &lt;a class="wiki_link_ext" href="http://robertinventor.com/tuning-math/s___4/msg_3675-3699.html#3685" rel="nofollow"&gt;3685&lt;/a&gt; and &lt;a class="wiki_link_ext" href="http://robertinventor.com/tuning-math/s__11/msg_10975-10999.html#10987" rel="nofollow"&gt;10987&lt;/a&gt;.&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
+&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc0"&gt;&lt;a name="x--See also"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;See also&lt;/h3&gt;
+&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Omnitetrachordality"&gt;Omnitetrachordality&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales"&gt;Gallery of omnitetrachordal scales&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x--References"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;References&lt;/h3&gt;
+&lt;ul&gt;&lt;li&gt;&lt;!-- ws:start:WikiTextAnchorRule:6:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@ref1&amp;quot; title=&amp;quot;Anchor: ref1&amp;quot;/&amp;gt; --&gt;&lt;a name="ref1"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:6 --&gt;(1) Noted as omnitetrachordal by Paul Erlich no later than 2002. See tuning-math list messages &lt;a class="wiki_link_ext" href="http://robertinventor.com/tuning-math/s___4/msg_3675-3699.html#3685" rel="nofollow"&gt;3685&lt;/a&gt; and &lt;a class="wiki_link_ext" href="http://robertinventor.com/tuning-math/s__11/msg_10975-10999.html#10987" rel="nofollow"&gt;10987&lt;/a&gt;.&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

OTC 5L 2s: Difference between revisions

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