OTC 7L 7s: Difference between revisions

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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 22:30:14 UTC</tt>.<br>~~

[[7L_7s|7L+7s]]

~~: The original revision id was <tt>590313184</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

[[~~7L 7s~~|7L+7s]]

14 tones (6+2+6)

temperament: [[whitewood]]

temperament: [[Whitewood|whitewood]]

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 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 5L 5s~~|OTC 5L+5s]] (blackwood) and [[~~OTC 12L 12s~~|OTC 12L+12s]] (catler/compton).

<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 dual (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>

See also [[OTC_5L_5s|OTC 5L+5s]] (blackwood) and [[OTC_12L_12s|OTC 12L+12s]] (catler/compton).

[[Gallery_of_omnitetrachordal_scales#perfect|P]] = undefined (-1?)

[[~~Gallery of omnitetrachordal scales#perfect|P]] = undefined (-1?)~~

[[Gallery_of_omnitetrachordal_scales#Q|Q]] = 4.2777408456 (4/3 = 3L+2.5s)

~~[[Gallery of omnitetrachordal scales~~#Q|Q]] = 4.2777408456 (4/3 = 3L+2.5s)

L = 85.71 to 171.43 cents (138.95 cents @ Q)

s = 0.00 to 85.71 cents (32.48 cents @ Q)

9/8 = L+s (171.43 cents for any L/s)

4/3 = 3L+3s (514.29 cents for any L/s)

generator = s (0.00 to 85.71 cents)

[[~~periods and generators~~|period]] = 1/7 octave (171.43 cents)

[[periods_and_generators|period]] = 1/7 octave (171.43 cents)

notable EDOs: 21, 28, 35 (for 35edo, use L/s=3/2)

all modes:

~~|| {{ Ls LsLsLs LsLsLs }} || {{ LsLsLs Ls LsLsLs }} || {{ LsLsLs LsLsLs Ls }} ||~~

~~|| {{ sL sLsLsL sLsLsL }} || {{ sLsLsL sL sLsLsL }} || {{ sLsLsL sLsLsL sL }} ||~~

[[~~image~~:~~14_07_07_LsLsLs_Ls_LsLsLs~~.png]]

{| class="wikitable"

|-

| | <tt> Ls LsLsLs LsLsLs </tt>

| | <tt> LsLsLs Ls LsLsLs </tt>

| | <tt> LsLsLs LsLsLs Ls </tt>

|-

| | <tt> sL sLsLsL sLsLsL </tt>

| | <tt> sLsLsL sL sLsLsL </tt>

| | <tt> sLsLsL sLsLsL sL </tt>

|}

[[File:14_07_07_sLsLsL_sL_sLsLsL.png|alt=14_07_07_sLsLsL_sL_sLsLsL.png|14_07_07_sLsLsL_sL_sLsLsL.png]]

===See also===

* [[Omnitetrachordality]]

<ul><li>[[Omnitetrachordality|Omnitetrachordality]]</li><li>[[Gallery_of_omnitetrachordal_scales|Gallery of omnitetrachordal scales]]</li></ul>

* [[Gallery of omnitetrachordal scales]]

[[Category:14-tone scales]]

</~~pre~~></~~div~~>

[[Category:Tempered scales]]

~~<h4>Original HTML content~~:~~</h4>~~

[[Category:Pages with mostly numerical content]]

~~<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"><html><head><title>OTC 7L 7s</title></head><body>Omnitetrachordal MOS scale<br />

[[Category:MODMOS]]

~~<a class="wiki_link" href="/7L%207s">7L+7s</a><br />~~

[[Category:Omnitetrachordal]]

~~14 tones (6+2+6)<br />~~

[[Category:Whitewood]]

~~<br />~~

~~temperament~~: ~~<a class="wiki_link" href="/whitewood">whitewood</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 dual (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%205L%205s">OTC 5L+5s</a> (blackwood) and <a class="wiki_link" href="/OTC%2012L%2012s">OTC 12L+12s</a> (catler/compton).<br />~~

~~<br />~~

~~<a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect">P</a> = undefined (-1?)<br />~~

~~<a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#Q">Q</a> = 4.2777408456 (4/3 = 3L+2.5s)<br />~~

~~<br />~~

~~L = 85.71 to 171.43 cents (138.95 cents @ Q)<br />~~

~~s = 0.00 to 85.71 cents (32.48 cents @ Q)<br />~~

~~<br />~~

~~9/8 = L+s (171.43 cents for any L/s)<br />~~

~~4/3 = 3L+3s (514.29 cents for any L/s)<br />~~

~~generator = s (0.00 to 85.71 cents)<br />~~

~~<a class="wiki_link" href="/periods%20and%20generators">period</a> = 1/7 octave (171.43 cents)<br />~~

~~<br />~~

~~notable EDOs~~: ~~21, 28, 35 (for 35edo, use L/s=3/2)<br />~~

~~<br />~~

~~all modes~~:~~<br />~~

~~<table class="wiki_table">~~

~~<tr>~~

~~<td><tt> Ls LsLsLs LsLsLs </tt><br />~~

~~</td>~~

~~<td><tt> LsLsLs Ls LsLsLs </tt><br />~~

~~</td>~~

~~<td><tt> LsLsLs LsLsLs Ls </tt><br />~~

~~</td>~~

~~</tr>~~

~~<tr>~~

~~<td><tt> sL sLsLsL sLsLsL </tt><br />~~

~~</td>~~

~~<td><tt> sLsLsL sL sLsLsL </tt><br />~~

~~</td>~~

~~<td><tt> sLsLsL sLsLsL sL </tt><br />~~

~~</td>~~

~~</tr>~~

~~</table>~~

~~<br />~~

<img src="/file/view/14_07_07_LsLsLs_Ls_LsLsLs.png" alt="14_07_07_LsLsLs_Ls_LsLsLs.png" title="14_07_07_LsLsLs_Ls_LsLsLs.png" /><br />

~~<br />~~

~~<h3 id="toc0"><a name="x--See also"></a>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></pre></div>

@@ Line 1: / Line 1: @@
-<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 22:30:14 UTC</tt>.<br>
+[[7L_7s|7L+7s]]
-: The original revision id was <tt>590313184</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
-[[7L 7s|7L+7s]]
 tones (6+2+6)
-temperament: [[whitewood]]
+temperament: [[Whitewood|whitewood]]
 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 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 5L 5s|OTC 5L+5s]] (blackwood) and [[OTC 12L 12s|OTC 12L+12s]] (catler/compton).
+<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 dual (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>
+See also [[OTC_5L_5s|OTC 5L+5s]] (blackwood) and [[OTC_12L_12s|OTC 12L+12s]] (catler/compton).
+[[Gallery_of_omnitetrachordal_scales#perfect|P]] = undefined (-1?)
-[[Gallery of omnitetrachordal scales#perfect|P]] = undefined (-1?)
+[[Gallery_of_omnitetrachordal_scales#Q|Q]] = 4.2777408456 (4/3 = 3L+2.5s)
-[[Gallery of omnitetrachordal scales#Q|Q]] = 4.2777408456 (4/3 = 3L+2.5s)
 L = 85.71 to 171.43 cents (138.95 cents @ Q)
 s = 0.00 to 85.71 cents (32.48 cents @ Q)
 /8 = L+s (171.43 cents for any L/s)
 /3 = 3L+3s (514.29 cents for any L/s)
 generator = s (0.00 to 85.71 cents)
-[[periods and generators|period]] = 1/7 octave (171.43 cents)
+[[periods_and_generators|period]] = 1/7 octave (171.43 cents)
 notable EDOs: 21, 28, 35 (for 35edo, use L/s=3/2)
 all modes:
-|| {{ Ls LsLsLs LsLsLs }} || {{ LsLsLs Ls LsLsLs }} || {{ LsLsLs LsLsLs Ls }} ||
-|| {{ sL sLsLsL sLsLsL }} || {{ sLsLsL sL sLsLsL }} || {{ sLsLsL sLsLsL sL }} ||
-[[image:14_07_07_LsLsLs_Ls_LsLsLs.png]]
+{| class="wikitable"
+|-
+| | <tt> Ls LsLsLs LsLsLs </tt>
+| | <tt> LsLsLs Ls LsLsLs </tt>
+| | <tt> LsLsLs LsLsLs Ls </tt>
+|-
+| | <tt> sL sLsLsL sLsLsL </tt>
+| | <tt> sLsLsL sL sLsLsL </tt>
+| | <tt> sLsLsL sLsLsL sL </tt>
+|}
+[[File:14_07_07_sLsLsL_sL_sLsLsL.png|alt=14_07_07_sLsLsL_sL_sLsLsL.png|14_07_07_sLsLsL_sL_sLsLsL.png]]
 ===See also===
-* [[Omnitetrachordality]]
+<ul><li>[[Omnitetrachordality|Omnitetrachordality]]</li><li>[[Gallery_of_omnitetrachordal_scales|Gallery of omnitetrachordal scales]]</li></ul>
-* [[Gallery of omnitetrachordal scales]]
+[[Category:14-tone scales]]
-</pre></div>
+[[Category:Tempered scales]]
-<h4>Original HTML content:</h4>
+[[Category:Pages with mostly numerical content]]
-<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 7L 7s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Omnitetrachordal MOS scale&lt;br /&gt;
+[[Category:MODMOS]]
-&lt;a class="wiki_link" href="/7L%207s"&gt;7L+7s&lt;/a&gt;&lt;br /&gt;
+[[Category:Omnitetrachordal]]
-tones (6+2+6)&lt;br /&gt;
+[[Category:Whitewood]]
-&lt;br /&gt;
-temperament: &lt;a class="wiki_link" href="/whitewood"&gt;whitewood&lt;/a&gt;&lt;br /&gt;
-&lt;br /&gt;
-This scale has some unusual properties:&lt;br /&gt;
-&lt;ul&gt;&lt;li&gt;it has only two modes&lt;/li&gt;&lt;li&gt;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)&lt;/li&gt;&lt;li&gt;it is its own dual (changing all L to s, and vice versa, gives the same scale)&lt;/li&gt;&lt;li&gt;the (imperfect) tunings of 9/8 and 4/3 are independent of L/s ratio&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
-See also &lt;a class="wiki_link" href="/OTC%205L%205s"&gt;OTC 5L+5s&lt;/a&gt; (blackwood) and &lt;a class="wiki_link" href="/OTC%2012L%2012s"&gt;OTC 12L+12s&lt;/a&gt; (catler/compton).&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect"&gt;P&lt;/a&gt; = undefined (-1?)&lt;br /&gt;
-&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#Q"&gt;Q&lt;/a&gt; = 4.2777408456 (4/3 = 3L+2.5s)&lt;br /&gt;
-&lt;br /&gt;
-L = 85.71 to 171.43 cents (138.95 cents @ Q)&lt;br /&gt;
-s = 0.00 to 85.71 cents (32.48 cents @ Q)&lt;br /&gt;
-&lt;br /&gt;
-/8 = L+s (171.43 cents for any L/s)&lt;br /&gt;
-/3 = 3L+3s (514.29 cents for any L/s)&lt;br /&gt;
-generator = s (0.00 to 85.71 cents)&lt;br /&gt;
-&lt;a class="wiki_link" href="/periods%20and%20generators"&gt;period&lt;/a&gt; = 1/7 octave (171.43 cents)&lt;br /&gt;
-&lt;br /&gt;
-notable EDOs: 21, 28, 35 (for 35edo, use L/s=3/2)&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 LsLsLs LsLsLs &lt;/tt&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;tt&gt; LsLsLs Ls LsLsLs &lt;/tt&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;tt&gt; LsLsLs LsLsLs Ls &lt;/tt&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;&lt;tt&gt; sL sLsLsL sLsLsL &lt;/tt&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;tt&gt; sLsLsL sL sLsLsL &lt;/tt&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;tt&gt; sLsLsL sLsLsL sL &lt;/tt&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-&lt;/table&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:36:&amp;lt;img src=&amp;quot;/file/view/14_07_07_LsLsLs_Ls_LsLsLs.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/14_07_07_LsLsLs_Ls_LsLsLs.png" alt="14_07_07_LsLsLs_Ls_LsLsLs.png" title="14_07_07_LsLsLs_Ls_LsLsLs.png" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:36 --&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;/body&gt;&lt;/html&gt;</pre></div>