List of anomalous saturated suspensions: Difference between revisions

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<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:clumma|clumma]] and made on <tt>2016-08-08 17:39:25 UTC</tt>.<br>

: This revision was by author [[User:clumma|clumma]] and made on <tt>2016-08-08 17:51:50 UTC</tt>.<br>

: The original revision id was <tt>~~588933770~~</tt>.<br>

: The original revision id was <tt>588934502</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">Below is a complete list of [[http://x31eq.com/ass.htm|Anomalous Saturated Suspensions]] through the 23-limit. Each chord listed is either ambitonal, or has a [[Otonality and utonality|o/utonal]] inverse which is also an ASS.

==Naming==

For each odd limit we can list ambitonal chords in lexicographic order by harmonic series representation, along with o/utonal chord pairs according to the harmonic series representation of the otonal chord in the pair. Each chord is then designated with a capital "A" whose subscript is a tuple, where the first value is the odd limit and the second value is the index in the list for that odd limit. This is followed by an "a," "o," or "u" depending on whether the chord is ambitonal, otonal, or utonal.

||~ ASS name ||~ Odd Limit ||~ Harmonic Series ||~ Scale ||~ Scale Name ||

|| || 9 || 3:5:9:15 || 1/1 6/5 3/2 9/5 || ||

|| A_{9,1a} || 9 || 3:5:9:15 || 1/1 6/5 3/2 9/5 || ||

|| || 9 || 3:7:9:21 || 1/1 7/6 3/2 7/4 || ||

|| || 11 || 3:9:11:33 || 1/1 11/8 3/2 11/6 || ||

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|| || 21 || 105:285:315:399:665:1995 || 1/1 6/5 24/19 3/2 12/7 36/19 || ||

|| || 23 || 3:9:15:21:23:69 || 1/1 5/4 23/16 3/2 7/4 23/12 || ||

|| || 23 || 105:315:345:483:805:2415 || 1/1 24/23 6/5 3/2 36/23 12/7 || ||</pre></div>

|| || 23 || 105:315:345:483:805:2415 || 1/1 24/23 6/5 3/2 36/23 12/7 || ||

</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"><html><head><title>Anomalous Saturated Suspensions</title></head><body>Below is a complete list of <a class="wiki_link_ext" href="http://x31eq.com/ass.htm" rel="nofollow">Anomalous Saturated Suspensions</a> through the 23-limit. Each chord listed is either ambitonal, or has a <a class="wiki_link" href="/Otonality%20and%20utonality">o/utonal</a> inverse which is also an ASS.<br />

<br />

<h2 id="toc0"><a name="x-Naming"></a>Naming</h2>

<br />

For each odd limit we can list ambitonal chords in lexicographic order by harmonic series representation, along with o/utonal chord pairs according to the harmonic series representation of the otonal chord in the pair. Each chord is then designated with a capital &quot;A&quot; whose subscript is a tuple, where the first value is the odd limit and the second value is the index in the list for that odd limit. This is followed by an &quot;a,&quot; &quot;o,&quot; or &quot;u&quot; depending on whether the chord is ambitonal, otonal, or utonal.<br />

<br />

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@@ 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:clumma|clumma]] and made on <tt>2016-08-08 17:39:25 UTC</tt>.<br>
+: This revision was by author [[User:clumma|clumma]] and made on <tt>2016-08-08 17:51:50 UTC</tt>.<br>
-: The original revision id was <tt>588933770</tt>.<br>
+: The original revision id was <tt>588934502</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">Below is a complete list of [[http://x31eq.com/ass.htm|Anomalous Saturated Suspensions]] through the 23-limit. Each chord listed is either ambitonal, or has a [[Otonality and utonality|o/utonal]] inverse which is also an ASS.
+==Naming==
+For each odd limit we can list ambitonal chords in lexicographic order by harmonic series representation, along with o/utonal chord pairs according to the harmonic series representation of the otonal chord in the pair. Each chord is then designated with a capital "A" whose subscript is a tuple, where the first value is the odd limit and the second value is the index in the list for that odd limit. This is followed by an "a," "o," or "u" depending on whether the chord is ambitonal, otonal, or utonal.
 ||~ ASS name ||~ Odd Limit ||~ Harmonic Series ||~ Scale ||~ Scale Name ||
-||  || 9 || 3:5:9:15 || 1/1 6/5 3/2 9/5 ||  ||
+|| A_{9,1a} || 9 || 3:5:9:15 || 1/1 6/5 3/2 9/5 ||  ||
 ||  || 9 || 3:7:9:21 || 1/1 7/6 3/2 7/4 ||  ||
 ||  || 11 || 3:9:11:33 || 1/1 11/8 3/2 11/6 ||  ||
@@ Line 36: / Line 40: @@
 ||  || 21 || 105:285:315:399:665:1995 || 1/1 6/5 24/19 3/2 12/7 36/19 ||  ||
 ||  || 23 || 3:9:15:21:23:69 || 1/1 5/4 23/16 3/2 7/4 23/12 ||  ||
-||  || 23 || 105:315:345:483:805:2415 || 1/1 24/23 6/5 3/2 36/23 12/7 ||  ||</pre></div>
+||  || 23 || 105:315:345:483:805:2415 || 1/1 24/23 6/5 3/2 36/23 12/7 ||  ||
+</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;Anomalous Saturated Suspensions&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Below is a complete list of &lt;a class="wiki_link_ext" href="http://x31eq.com/ass.htm" rel="nofollow"&gt;Anomalous Saturated Suspensions&lt;/a&gt; through the 23-limit. Each chord listed is either ambitonal, or has a &lt;a class="wiki_link" href="/Otonality%20and%20utonality"&gt;o/utonal&lt;/a&gt; inverse which is also an ASS.&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Naming"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Naming&lt;/h2&gt;
+&lt;br /&gt;
+For each odd limit we can list ambitonal chords in lexicographic order by harmonic series representation, along with o/utonal chord pairs according to the harmonic series representation of the otonal chord in the pair. Each chord is then designated with a capital &amp;quot;A&amp;quot; whose subscript is a tuple, where the first value is the odd limit and the second value is the index in the list for that odd limit. This is followed by an &amp;quot;a,&amp;quot; &amp;quot;o,&amp;quot; or &amp;quot;u&amp;quot; depending on whether the chord is ambitonal, otonal, or utonal.&lt;br /&gt;
 &lt;br /&gt;
@@ Line 56: / Line 65: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;A_{9,1a}&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;9&lt;br /&gt;