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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
Omnitetrachordal MOS scale
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 21:22:18 UTC</tt>.<br>
[[5L_7s|5L+7s]]
: The original revision id was <tt>590308854</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">Omnitetrachordal MOS scale
[[5L 7s|5L+7s]]
12 tones (5+2+5)
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]].
MOS of the helmholtz / garibaldi / [[Schismatic_family|schismatic]] and [[Superpyth|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#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)
 
[[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)
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)
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)
9/8 = L+s (200.00 to 240.00 cents)
4/3 = 2L+3s (480.00 to 500.00 cents)
4/3 = 2L+3s (480.00 to 500.00 cents)
generator = 4/3
generator = 4/3


Line 25: Line 24:


all modes:
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]]
{| class="wikitable"
|-
| | <tt> Ls LsLss LsLss </tt>
| |
| |
|-
| | <tt> sL sLssL sLssL </tt>
| |
| | <tt> sLsLs sLsLs sL </tt>
|-
| | <tt> Ls LssLs LssLs </tt>
| |
| | <tt> LsLss LsLss Ls </tt>
|-
| | <tt> sL ssLsL ssLsL </tt>
| |
| | <tt> sLssL sLssL sL </tt>
|-
| | <tt> Ls sLsLs sLsLs </tt>
| |
| | <tt> LssLs LssLs Ls </tt>
|-
| |
| |
| | <tt> ssLsL ssLsL sL </tt>
|-
| |
| | <tt> sLsLs sL sLsLs </tt>
| | <tt> sLsLs sLsLs Ls </tt>
|-
| |
| | <tt> LsLss Ls LsLss </tt>
| |
|-
| |
| | <tt> sLssL sL sLssL </tt>
| |
|-
| |
| | <tt> LssLs Ls LssLs </tt>
| |
|-
| |
| | <tt> ssLsL sL ssLsL </tt>
| |
|-
| | <tt> sL sLsLs sLsLs </tt>
| | <tt> sLsLs Ls sLsLs </tt>
| |
|}
 
[[File:12_05_07_sLssL_sL_sLssL.png|alt=12_05_07_sLssL_sL_sLssL.png|12_05_07_sLssL_sL_sLssL.png]]


===See also===
===See also===
* [[Omnitetrachordality]]
<ul><li>[[Omnitetrachordality|Omnitetrachordality]]</li><li>[[Gallery_of_omnitetrachordal_scales|Gallery of omnitetrachordal scales]]</li></ul>
* [[Gallery of omnitetrachordal scales]]


===References===
===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]].
<ul><li>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].</li></ul>
</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 7s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Omnitetrachordal MOS scale&lt;br /&gt;
&lt;a class="wiki_link" href="/5L%207s"&gt;5L+7s&lt;/a&gt;&lt;br /&gt;
12 tones (5+2+5)&lt;br /&gt;
&lt;br /&gt;
MOS of the helmholtz / garibaldi / &lt;a class="wiki_link" href="/Schismatic%20family"&gt;schismatic&lt;/a&gt; and &lt;a class="wiki_link" href="/superpyth"&gt;superpyth&lt;/a&gt; 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 &lt;a class="wiki_link" href="/OTC%207L%205s"&gt;OTC 7L+5s&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect"&gt;P&lt;/a&gt; = 1.2600167527 (L=&lt;a class="wiki_link" href="/2187_2048"&gt;2187/2048&lt;/a&gt;, s=&lt;a class="wiki_link" href="/256_243"&gt;256/243&lt;/a&gt;)&lt;br /&gt;
&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#Q"&gt;Q&lt;/a&gt; = 7.9100586343 (2L+3.5s)&lt;br /&gt;
&lt;br /&gt;
L = 100.00 to 240.00 cents (113.68 cents @ P, 203.91 cents @ Q)&lt;br /&gt;
s = 0.00 to 100.00 cents (90.23 cents @ P, 25.78 cents @ Q)&lt;br /&gt;
&lt;br /&gt;
9/8 = L+s (200.00 to 240.00 cents)&lt;br /&gt;
4/3 = 2L+3s (480.00 to 500.00 cents)&lt;br /&gt;
generator = 4/3&lt;br /&gt;
&lt;br /&gt;
notable EDOs: 17, 22, 27, 29, 41, 53, etc.&lt;br /&gt;
&lt;br /&gt;
all modes:&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Ls LsLss LsLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sL sLssL sLssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsLs sLsLs sL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Ls LssLs LssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLss LsLss Ls &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sL ssLsL ssLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLssL sLssL sL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Ls sLsLs sLsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LssLs LssLs Ls &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLsL ssLsL sL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsLs sL sLsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsLs sLsLs Ls &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLss Ls LsLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLssL sL sLssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LssLs Ls LssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLsL sL ssLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sL sLsLs sLsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsLs Ls sLsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:112:&amp;lt;img src=&amp;quot;/file/view/12_05_07_sLssL_sL_sLssL.png/589273824/12_05_07_sLssL_sL_sLssL.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;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" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:112 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&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:0 --&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:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x--References"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;References&lt;/h3&gt;
&lt;ul&gt;&lt;li&gt;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>
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