List of anomalous saturated suspensions: Difference between revisions

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Wikispaces>clumma
**Imported revision 588946842 - Original comment: **
Wikispaces>Sarzadoce
**Imported revision 588947298 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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 21:41:39 UTC</tt>.<br>
: This revision was by author [[User:Sarzadoce|Sarzadoce]] and made on <tt>2016-08-08 22:00:43 UTC</tt>.<br>
: The original revision id was <tt>588946842</tt>.<br>
: The original revision id was <tt>588947298</tt>.<br>
: The revision comment was: <tt></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>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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<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.
<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==
==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 by a capital "A" whose subscript is a tuple, where the first value is its odd limit and the second value is its 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.
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 by a capital "A" whose subscript is a tuple, where the first value is its odd limit and the second value is its 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.


||= **Name** ||= **Odd Limit** ||= **Harmonic Series** ||= **Scale** ||= **Scale Name** ||
||= **Name** ||= **Odd Limit** ||= **Harmonic Series** ||= **Scale** ||= **Scale Name** ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt; ||= 9 || 3:5:9:15 || 1/1 6/5 3/2 9/5 || ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt; || 9 || 3:5:9:15 || 1/1 6/5 3/2 9/5 ||   ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt; ||= 9 || 3:7:9:21 || 1/1 7/6 3/2 7/4 || ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{9,2a}&lt;/span&gt; || 9 || 3:7:9:21 || 1/1 7/6 3/2 7/4 ||   ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt; ||= 11 || 3:9:11:33 || 1/1 11/8 3/2 11/6 || ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{11,1a}&lt;/span&gt; || 11 || 3:9:11:33 || 1/1 11/8 3/2 11/6 ||   ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt; ||= 13 || 3:9:13:39 || 1/1 13/12 3/2 13/8 || ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{13,1a}&lt;/span&gt; || 13 || 3:9:13:39 || 1/1 13/12 3/2 13/8 ||   ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt; ||= 15 || 3:7:9:15:21 || 1/1 7/6 5/4 3/2 7/4 || Hendrix ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{15,1o}&lt;/span&gt; || 15 || 3:7:9:15:21 || 1/1 7/6 5/4 3/2 7/4 || Hendrix ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt; ||= 15 || 15:21:35:45:105 || 1/1 7/6 7/5 3/2 7/4 || Inverted Hendrix ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{15,1u}&lt;/span&gt; || 15 || 15:21:35:45:105 || 1/1 7/6 7/5 3/2 7/4 || Inverted Hendrix ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt; ||= 15 || 3:9:11:15:33 || 1/1 5/4 11/8 3/2 11/6 || 11-Hendrix ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{15,2o}&lt;/span&gt; || 15 || 3:9:11:15:33 || 1/1 5/4 11/8 3/2 11/6 || 11-Hendrix ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt; ||= 15 || 15:33:45:55:165 || 1/1 11/10 11/8 3/2 11/6 || Inverted 11-Hendrix ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{15,2u}&lt;/span&gt; || 15 || 15:33:45:55:165 || 1/1 11/10 11/8 3/2 11/6 || Inverted 11-Hendrix ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt; ||= 15 || 3:9:13:15:39 || 1/1 13/12 5/4 3/2 13/8 || 13-Hendrix ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{15,3o}&lt;/span&gt; || 15 || 3:9:13:15:39 || 1/1 13/12 5/4 3/2 13/8 || 13-Hendrix ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt; ||= 15 || 15:39:45:65:195 || 1/1 13/12 13/10 3/2 13/8 || Inverted 13-Hendrix ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{15,3u}&lt;/span&gt; || 15 || 15:39:45:65:195 || 1/1 13/12 13/10 3/2 13/8 || Inverted 13-Hendrix ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt; ||= 17 || 3:9:15:17:51 || 1/1 17/16 5/4 17/12 3/2 || 17-Hendrix ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{17,1o}&lt;/span&gt; || 17 || 3:9:15:17:51 || 1/1 17/16 5/4 17/12 3/2 || 17-Hendrix ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt; ||= 17 || 15:45:51:85:255 || 1/1 17/16 17/12 3/2 17/10 || Inverted 17-Hendrix ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{17,1u}&lt;/span&gt; || 17 || 15:45:51:85:255 || 1/1 17/16 17/12 3/2 17/10 || Inverted 17-Hendrix ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt; ||= 19 || 3:9:15:19:57 || 1/1 19/16 5/4 3/2 19/12 || 19-Hendrix ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{19,1o}&lt;/span&gt; || 19 || 3:9:15:19:57 || 1/1 19/16 5/4 3/2 19/12 || 19-Hendrix ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt; ||= 19 || 15:45:57:95:285 || 1/1 19/16 3/2 19/12 19/10 || Inverted 19-Hendrix ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{19,1u}&lt;/span&gt; || 19 || 15:45:57:95:285 || 1/1 19/16 3/2 19/12 19/10 || Inverted 19-Hendrix ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt; ||= 21 || 5:15:21:35:45:105 || 1/1 21/20 9/8 21/16 3/2 7/4 || ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{21,1o}&lt;/span&gt; || 21 || 3:5:9:15:21:45 || 1/1 15/14 9/8 9/7 3/2 12/7 ||   ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt; ||= 21 || 3:5:9:15:21:45 || 1/1 15/14 9/8 9/7 3/2 12/7 || ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{21,1u}&lt;/span&gt; || 21 || 7:15:21:35:63:105 || 1/1 15/14 9/8 5/4 3/2 15/8 ||   ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt; ||= 21 || 7:15:21:35:63:105 || 1/1 15/14 9/8 5/4 3/2 15/8 || ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{21,2o}&lt;/span&gt; || 21 || 3:7:9:15:21:63 || 1/1 21/20 9/8 6/5 3/2 9/5 ||   ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt; ||= 21 || 3:7:9:15:21:63 || 1/1 21/20 9/8 6/5 3/2 9/5 || ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{21,2u}&lt;/span&gt; || 21 || 5:15:21:35:45:105 || 1/1 21/20 9/8 21/16 3/2 7/4 ||   ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt; ||= 21 || 3:9:11:15:21:33 || 1/1 5/4 11/8 3/2 7/4 11/6 || ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{21,3o}&lt;/span&gt; || 21 || 3:9:11:15:21:33 || 1/1 5/4 11/8 3/2 7/4 11/6 ||   ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt; ||= 21 || 105:165:231:315:385:1155 || 1/1 12/11 6/5 3/2 18/11 12/7 || ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{21,3u}&lt;/span&gt; || 21 || 105:165:231:315:385:1155 || 1/1 12/11 6/5 3/2 18/11 12/7 ||   ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt; ||= 21 || 3:9:13:15:21:39 || 1/1 13/12 5/4 3/2 13/8 7/4 || ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{21,4o}&lt;/span&gt; || 21 || 3:9:13:15:21:39 || 1/1 13/12 5/4 3/2 13/8 7/4 ||   ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt; ||= 21 || 105:195:273:315:455:1365 || 1/1 6/5 18/13 3/2 12/7 24/13 || ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{21,4u}&lt;/span&gt; || 21 || 105:195:273:315:455:1365 || 1/1 6/5 18/13 3/2 12/7 24/13 ||   ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt; ||= 21 || 3:9:15:17:21:51 || 1/1 17/16 5/4 17/12 3/2 7/4 || ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{21,5o}&lt;/span&gt; || 21 || 3:9:15:17:21:51 || 1/1 17/16 5/4 17/12 3/2 7/4 ||   ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt; ||= 21 || 105:255:315:357:595:1785 || 1/1 18/17 6/5 24/17 3/2 12/7 || ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{21,5u}&lt;/span&gt; || 21 || 105:255:315:357:595:1785 || 1/1 18/17 6/5 24/17 3/2 12/7 ||   ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt; ||= 21 || 3:9:15:19:21:57 || 1/1 19/16 5/4 3/2 19/12 7/4 || ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{21,6o}&lt;/span&gt; || 21 || 3:9:15:19:21:57 || 1/1 19/16 5/4 3/2 19/12 7/4 ||   ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt; ||= 21 || 105:285:315:399:665:1995 || 1/1 6/5 24/19 3/2 12/7 36/19 || ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{21,6u}&lt;/span&gt; || 21 || 105:285:315:399:665:1995 || 1/1 6/5 24/19 3/2 12/7 36/19 ||   ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt; ||= 23 || 3:9:15:21:23:69 || 1/1 5/4 23/16 3/2 7/4 23/12 || ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{23,1o}&lt;/span&gt; || 23 || 3:9:15:21:23:69 || 1/1 5/4 23/16 3/2 7/4 23/12 ||   ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt; ||= 23 || 105:315:345:483:805:2415 || 1/1 24/23 6/5 3/2 36/23 12/7 || ||
|| **A**&lt;span style="vertical-align: sub;"&gt;{23,1u}&lt;/span&gt; || 23 || 105:315:345:483:805:2415 || 1/1 24/23 6/5 3/2 36/23 12/7 ||   ||</pre></div>
</pre></div>
<h4>Original HTML content:</h4>
<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;
<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;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;!-- 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;
&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 by a capital &amp;quot;A&amp;quot; whose subscript is a tuple, where the first value is its odd limit and the second value is its 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;
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 by a capital &amp;quot;A&amp;quot; whose subscript is a tuple, where the first value is its odd limit and the second value is its 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;
&lt;br /&gt;
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         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;9&lt;br /&gt;
         &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;3:5:9:15&lt;br /&gt;
         &lt;td&gt;3:5:9:15&lt;br /&gt;
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     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{9,2a}&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;9&lt;br /&gt;
         &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;3:7:9:21&lt;br /&gt;
         &lt;td&gt;3:7:9:21&lt;br /&gt;
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     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{11,1a}&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;11&lt;br /&gt;
         &lt;td&gt;11&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;3:9:11:33&lt;br /&gt;
         &lt;td&gt;3:9:11:33&lt;br /&gt;
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     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{13,1a}&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;13&lt;br /&gt;
         &lt;td&gt;13&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;3:9:13:39&lt;br /&gt;
         &lt;td&gt;3:9:13:39&lt;br /&gt;
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     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{15,1o}&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;15&lt;br /&gt;
         &lt;td&gt;15&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;3:7:9:15:21&lt;br /&gt;
         &lt;td&gt;3:7:9:15:21&lt;br /&gt;
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     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{15,1u}&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;15&lt;br /&gt;
         &lt;td&gt;15&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;15:21:35:45:105&lt;br /&gt;
         &lt;td&gt;15:21:35:45:105&lt;br /&gt;
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     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{15,2o}&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;15&lt;br /&gt;
         &lt;td&gt;15&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;3:9:11:15:33&lt;br /&gt;
         &lt;td&gt;3:9:11:15:33&lt;br /&gt;
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     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{15,2u}&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;15&lt;br /&gt;
         &lt;td&gt;15&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;15:33:45:55:165&lt;br /&gt;
         &lt;td&gt;15:33:45:55:165&lt;br /&gt;
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     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{15,3o}&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;15&lt;br /&gt;
         &lt;td&gt;15&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;3:9:13:15:39&lt;br /&gt;
         &lt;td&gt;3:9:13:15:39&lt;br /&gt;
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     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{15,3u}&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;15&lt;br /&gt;
         &lt;td&gt;15&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;15:39:45:65:195&lt;br /&gt;
         &lt;td&gt;15:39:45:65:195&lt;br /&gt;
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     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{17,1o}&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;17&lt;br /&gt;
         &lt;td&gt;17&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;3:9:15:17:51&lt;br /&gt;
         &lt;td&gt;3:9:15:17:51&lt;br /&gt;
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     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{17,1u}&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;17&lt;br /&gt;
         &lt;td&gt;17&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;15:45:51:85:255&lt;br /&gt;
         &lt;td&gt;15:45:51:85:255&lt;br /&gt;
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     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{19,1o}&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;19&lt;br /&gt;
         &lt;td&gt;19&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;3:9:15:19:57&lt;br /&gt;
         &lt;td&gt;3:9:15:19:57&lt;br /&gt;
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     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{19,1u}&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;19&lt;br /&gt;
         &lt;td&gt;19&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;15:45:57:95:285&lt;br /&gt;
         &lt;td&gt;15:45:57:95:285&lt;br /&gt;
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     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{21,1o}&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;21&lt;br /&gt;
         &lt;td&gt;21&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;5:15:21:35:45:105&lt;br /&gt;
         &lt;td&gt;3:5:9:15:21:45&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;1/1 21/20 9/8 21/16 3/2 7/4&lt;br /&gt;
         &lt;td&gt;1/1 15/14 9/8 9/7 3/2 12/7&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
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     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{21,1u}&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;21&lt;br /&gt;
         &lt;td&gt;21&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;3:5:9:15:21:45&lt;br /&gt;
         &lt;td&gt;7:15:21:35:63:105&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;1/1 15/14 9/8 9/7 3/2 12/7&lt;br /&gt;
         &lt;td&gt;1/1 15/14 9/8 5/4 3/2 15/8&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
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     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{21,2o}&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;21&lt;br /&gt;
         &lt;td&gt;21&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;7:15:21:35:63:105&lt;br /&gt;
         &lt;td&gt;3:7:9:15:21:63&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;1/1 15/14 9/8 5/4 3/2 15/8&lt;br /&gt;
         &lt;td&gt;1/1 21/20 9/8 6/5 3/2 9/5&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
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     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{21,2u}&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;21&lt;br /&gt;
         &lt;td&gt;21&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;3:7:9:15:21:63&lt;br /&gt;
         &lt;td&gt;5:15:21:35:45:105&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;1/1 21/20 9/8 6/5 3/2 9/5&lt;br /&gt;
         &lt;td&gt;1/1 21/20 9/8 21/16 3/2 7/4&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
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     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{21,3o}&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;21&lt;br /&gt;
         &lt;td&gt;21&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;3:9:11:15:21:33&lt;br /&gt;
         &lt;td&gt;3:9:11:15:21:33&lt;br /&gt;
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     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{21,3u}&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;21&lt;br /&gt;
         &lt;td&gt;21&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;105:165:231:315:385:1155&lt;br /&gt;
         &lt;td&gt;105:165:231:315:385:1155&lt;br /&gt;
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     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{21,4o}&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;21&lt;br /&gt;
         &lt;td&gt;21&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;3:9:13:15:21:39&lt;br /&gt;
         &lt;td&gt;3:9:13:15:21:39&lt;br /&gt;
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     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{21,4u}&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;21&lt;br /&gt;
         &lt;td&gt;21&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;105:195:273:315:455:1365&lt;br /&gt;
         &lt;td&gt;105:195:273:315:455:1365&lt;br /&gt;
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     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{21,5o}&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;21&lt;br /&gt;
         &lt;td&gt;21&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;3:9:15:17:21:51&lt;br /&gt;
         &lt;td&gt;3:9:15:17:21:51&lt;br /&gt;
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     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{21,5u}&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;21&lt;br /&gt;
         &lt;td&gt;21&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;105:255:315:357:595:1785&lt;br /&gt;
         &lt;td&gt;105:255:315:357:595:1785&lt;br /&gt;
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     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{21,6o}&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;21&lt;br /&gt;
         &lt;td&gt;21&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;3:9:15:19:21:57&lt;br /&gt;
         &lt;td&gt;3:9:15:19:21:57&lt;br /&gt;
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     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{21,6u}&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;21&lt;br /&gt;
         &lt;td&gt;21&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;105:285:315:399:665:1995&lt;br /&gt;
         &lt;td&gt;105:285:315:399:665:1995&lt;br /&gt;
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     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{23,1o}&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;23&lt;br /&gt;
         &lt;td&gt;23&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;3:9:15:21:23:69&lt;br /&gt;
         &lt;td&gt;3:9:15:21:23:69&lt;br /&gt;
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     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{9,1a}&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;span style="vertical-align: sub;"&gt;{23,1u}&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;23&lt;br /&gt;
         &lt;td&gt;23&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;105:315:345:483:805:2415&lt;br /&gt;
         &lt;td&gt;105:315:345:483:805:2415&lt;br /&gt;

Revision as of 22:00, 8 August 2016

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author Sarzadoce and made on 2016-08-08 22:00:43 UTC.
The original revision id was 588947298.
The revision comment was:

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Original Wikitext content:

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 by a capital "A" whose subscript is a tuple, where the first value is its odd limit and the second value is its 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.

||= **Name** ||= **Odd Limit** ||= **Harmonic Series** ||= **Scale** ||= **Scale Name** ||
|| **A**<span style="vertical-align: sub;">{9,1a}</span> || 9 || 3:5:9:15 || 1/1 6/5 3/2 9/5 ||   ||
|| **A**<span style="vertical-align: sub;">{9,2a}</span> || 9 || 3:7:9:21 || 1/1 7/6 3/2 7/4 ||   ||
|| **A**<span style="vertical-align: sub;">{11,1a}</span> || 11 || 3:9:11:33 || 1/1 11/8 3/2 11/6 ||   ||
|| **A**<span style="vertical-align: sub;">{13,1a}</span> || 13 || 3:9:13:39 || 1/1 13/12 3/2 13/8 ||   ||
|| **A**<span style="vertical-align: sub;">{15,1o}</span> || 15 || 3:7:9:15:21 || 1/1 7/6 5/4 3/2 7/4 || Hendrix ||
|| **A**<span style="vertical-align: sub;">{15,1u}</span> || 15 || 15:21:35:45:105 || 1/1 7/6 7/5 3/2 7/4 || Inverted Hendrix ||
|| **A**<span style="vertical-align: sub;">{15,2o}</span> || 15 || 3:9:11:15:33 || 1/1 5/4 11/8 3/2 11/6 || 11-Hendrix ||
|| **A**<span style="vertical-align: sub;">{15,2u}</span> || 15 || 15:33:45:55:165 || 1/1 11/10 11/8 3/2 11/6 || Inverted 11-Hendrix ||
|| **A**<span style="vertical-align: sub;">{15,3o}</span> || 15 || 3:9:13:15:39 || 1/1 13/12 5/4 3/2 13/8 || 13-Hendrix ||
|| **A**<span style="vertical-align: sub;">{15,3u}</span> || 15 || 15:39:45:65:195 || 1/1 13/12 13/10 3/2 13/8 || Inverted 13-Hendrix ||
|| **A**<span style="vertical-align: sub;">{17,1o}</span> || 17 || 3:9:15:17:51 || 1/1 17/16 5/4 17/12 3/2 || 17-Hendrix ||
|| **A**<span style="vertical-align: sub;">{17,1u}</span> || 17 || 15:45:51:85:255 || 1/1 17/16 17/12 3/2 17/10 || Inverted 17-Hendrix ||
|| **A**<span style="vertical-align: sub;">{19,1o}</span> || 19 || 3:9:15:19:57 || 1/1 19/16 5/4 3/2 19/12 || 19-Hendrix ||
|| **A**<span style="vertical-align: sub;">{19,1u}</span> || 19 || 15:45:57:95:285 || 1/1 19/16 3/2 19/12 19/10 || Inverted 19-Hendrix ||
|| **A**<span style="vertical-align: sub;">{21,1o}</span> || 21 || 3:5:9:15:21:45 || 1/1 15/14 9/8 9/7 3/2 12/7 ||   ||
|| **A**<span style="vertical-align: sub;">{21,1u}</span> || 21 || 7:15:21:35:63:105 || 1/1 15/14 9/8 5/4 3/2 15/8 ||   ||
|| **A**<span style="vertical-align: sub;">{21,2o}</span> || 21 || 3:7:9:15:21:63 || 1/1 21/20 9/8 6/5 3/2 9/5 ||   ||
|| **A**<span style="vertical-align: sub;">{21,2u}</span> || 21 || 5:15:21:35:45:105 || 1/1 21/20 9/8 21/16 3/2 7/4 ||   ||
|| **A**<span style="vertical-align: sub;">{21,3o}</span> || 21 || 3:9:11:15:21:33 || 1/1 5/4 11/8 3/2 7/4 11/6 ||   ||
|| **A**<span style="vertical-align: sub;">{21,3u}</span> || 21 || 105:165:231:315:385:1155 || 1/1 12/11 6/5 3/2 18/11 12/7 ||   ||
|| **A**<span style="vertical-align: sub;">{21,4o}</span> || 21 || 3:9:13:15:21:39 || 1/1 13/12 5/4 3/2 13/8 7/4 ||   ||
|| **A**<span style="vertical-align: sub;">{21,4u}</span> || 21 || 105:195:273:315:455:1365 || 1/1 6/5 18/13 3/2 12/7 24/13 ||   ||
|| **A**<span style="vertical-align: sub;">{21,5o}</span> || 21 || 3:9:15:17:21:51 || 1/1 17/16 5/4 17/12 3/2 7/4 ||   ||
|| **A**<span style="vertical-align: sub;">{21,5u}</span> || 21 || 105:255:315:357:595:1785 || 1/1 18/17 6/5 24/17 3/2 12/7 ||   ||
|| **A**<span style="vertical-align: sub;">{21,6o}</span> || 21 || 3:9:15:19:21:57 || 1/1 19/16 5/4 3/2 19/12 7/4 ||   ||
|| **A**<span style="vertical-align: sub;">{21,6u}</span> || 21 || 105:285:315:399:665:1995 || 1/1 6/5 24/19 3/2 12/7 36/19 ||   ||
|| **A**<span style="vertical-align: sub;">{23,1o}</span> || 23 || 3:9:15:21:23:69 || 1/1 5/4 23/16 3/2 7/4 23/12 ||   ||
|| **A**<span style="vertical-align: sub;">{23,1u}</span> || 23 || 105:315:345:483:805:2415 || 1/1 24/23 6/5 3/2 36/23 12/7 ||   ||

Original HTML content:

<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 />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Naming"></a><!-- ws:end:WikiTextHeadingRule:0 -->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 by a capital &quot;A&quot; whose subscript is a tuple, where the first value is its odd limit and the second value is its 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 />


<table class="wiki_table">
    <tr>
        <td style="text-align: center;"><strong>Name</strong><br />
</td>
        <td style="text-align: center;"><strong>Odd Limit</strong><br />
</td>
        <td style="text-align: center;"><strong>Harmonic Series</strong><br />
</td>
        <td style="text-align: center;"><strong>Scale</strong><br />
</td>
        <td style="text-align: center;"><strong>Scale Name</strong><br />
</td>
    </tr>
    <tr>
        <td><strong>A</strong><span style="vertical-align: sub;">{9,1a}</span><br />
</td>
        <td>9<br />
</td>
        <td>3:5:9:15<br />
</td>
        <td>1/1 6/5 3/2 9/5<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><strong>A</strong><span style="vertical-align: sub;">{9,2a}</span><br />
</td>
        <td>9<br />
</td>
        <td>3:7:9:21<br />
</td>
        <td>1/1 7/6 3/2 7/4<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><strong>A</strong><span style="vertical-align: sub;">{11,1a}</span><br />
</td>
        <td>11<br />
</td>
        <td>3:9:11:33<br />
</td>
        <td>1/1 11/8 3/2 11/6<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><strong>A</strong><span style="vertical-align: sub;">{13,1a}</span><br />
</td>
        <td>13<br />
</td>
        <td>3:9:13:39<br />
</td>
        <td>1/1 13/12 3/2 13/8<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><strong>A</strong><span style="vertical-align: sub;">{15,1o}</span><br />
</td>
        <td>15<br />
</td>
        <td>3:7:9:15:21<br />
</td>
        <td>1/1 7/6 5/4 3/2 7/4<br />
</td>
        <td>Hendrix<br />
</td>
    </tr>
    <tr>
        <td><strong>A</strong><span style="vertical-align: sub;">{15,1u}</span><br />
</td>
        <td>15<br />
</td>
        <td>15:21:35:45:105<br />
</td>
        <td>1/1 7/6 7/5 3/2 7/4<br />
</td>
        <td>Inverted Hendrix<br />
</td>
    </tr>
    <tr>
        <td><strong>A</strong><span style="vertical-align: sub;">{15,2o}</span><br />
</td>
        <td>15<br />
</td>
        <td>3:9:11:15:33<br />
</td>
        <td>1/1 5/4 11/8 3/2 11/6<br />
</td>
        <td>11-Hendrix<br />
</td>
    </tr>
    <tr>
        <td><strong>A</strong><span style="vertical-align: sub;">{15,2u}</span><br />
</td>
        <td>15<br />
</td>
        <td>15:33:45:55:165<br />
</td>
        <td>1/1 11/10 11/8 3/2 11/6<br />
</td>
        <td>Inverted 11-Hendrix<br />
</td>
    </tr>
    <tr>
        <td><strong>A</strong><span style="vertical-align: sub;">{15,3o}</span><br />
</td>
        <td>15<br />
</td>
        <td>3:9:13:15:39<br />
</td>
        <td>1/1 13/12 5/4 3/2 13/8<br />
</td>
        <td>13-Hendrix<br />
</td>
    </tr>
    <tr>
        <td><strong>A</strong><span style="vertical-align: sub;">{15,3u}</span><br />
</td>
        <td>15<br />
</td>
        <td>15:39:45:65:195<br />
</td>
        <td>1/1 13/12 13/10 3/2 13/8<br />
</td>
        <td>Inverted 13-Hendrix<br />
</td>
    </tr>
    <tr>
        <td><strong>A</strong><span style="vertical-align: sub;">{17,1o}</span><br />
</td>
        <td>17<br />
</td>
        <td>3:9:15:17:51<br />
</td>
        <td>1/1 17/16 5/4 17/12 3/2<br />
</td>
        <td>17-Hendrix<br />
</td>
    </tr>
    <tr>
        <td><strong>A</strong><span style="vertical-align: sub;">{17,1u}</span><br />
</td>
        <td>17<br />
</td>
        <td>15:45:51:85:255<br />
</td>
        <td>1/1 17/16 17/12 3/2 17/10<br />
</td>
        <td>Inverted 17-Hendrix<br />
</td>
    </tr>
    <tr>
        <td><strong>A</strong><span style="vertical-align: sub;">{19,1o}</span><br />
</td>
        <td>19<br />
</td>
        <td>3:9:15:19:57<br />
</td>
        <td>1/1 19/16 5/4 3/2 19/12<br />
</td>
        <td>19-Hendrix<br />
</td>
    </tr>
    <tr>
        <td><strong>A</strong><span style="vertical-align: sub;">{19,1u}</span><br />
</td>
        <td>19<br />
</td>
        <td>15:45:57:95:285<br />
</td>
        <td>1/1 19/16 3/2 19/12 19/10<br />
</td>
        <td>Inverted 19-Hendrix<br />
</td>
    </tr>
    <tr>
        <td><strong>A</strong><span style="vertical-align: sub;">{21,1o}</span><br />
</td>
        <td>21<br />
</td>
        <td>3:5:9:15:21:45<br />
</td>
        <td>1/1 15/14 9/8 9/7 3/2 12/7<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><strong>A</strong><span style="vertical-align: sub;">{21,1u}</span><br />
</td>
        <td>21<br />
</td>
        <td>7:15:21:35:63:105<br />
</td>
        <td>1/1 15/14 9/8 5/4 3/2 15/8<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><strong>A</strong><span style="vertical-align: sub;">{21,2o}</span><br />
</td>
        <td>21<br />
</td>
        <td>3:7:9:15:21:63<br />
</td>
        <td>1/1 21/20 9/8 6/5 3/2 9/5<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><strong>A</strong><span style="vertical-align: sub;">{21,2u}</span><br />
</td>
        <td>21<br />
</td>
        <td>5:15:21:35:45:105<br />
</td>
        <td>1/1 21/20 9/8 21/16 3/2 7/4<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><strong>A</strong><span style="vertical-align: sub;">{21,3o}</span><br />
</td>
        <td>21<br />
</td>
        <td>3:9:11:15:21:33<br />
</td>
        <td>1/1 5/4 11/8 3/2 7/4 11/6<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><strong>A</strong><span style="vertical-align: sub;">{21,3u}</span><br />
</td>
        <td>21<br />
</td>
        <td>105:165:231:315:385:1155<br />
</td>
        <td>1/1 12/11 6/5 3/2 18/11 12/7<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><strong>A</strong><span style="vertical-align: sub;">{21,4o}</span><br />
</td>
        <td>21<br />
</td>
        <td>3:9:13:15:21:39<br />
</td>
        <td>1/1 13/12 5/4 3/2 13/8 7/4<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><strong>A</strong><span style="vertical-align: sub;">{21,4u}</span><br />
</td>
        <td>21<br />
</td>
        <td>105:195:273:315:455:1365<br />
</td>
        <td>1/1 6/5 18/13 3/2 12/7 24/13<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><strong>A</strong><span style="vertical-align: sub;">{21,5o}</span><br />
</td>
        <td>21<br />
</td>
        <td>3:9:15:17:21:51<br />
</td>
        <td>1/1 17/16 5/4 17/12 3/2 7/4<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><strong>A</strong><span style="vertical-align: sub;">{21,5u}</span><br />
</td>
        <td>21<br />
</td>
        <td>105:255:315:357:595:1785<br />
</td>
        <td>1/1 18/17 6/5 24/17 3/2 12/7<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><strong>A</strong><span style="vertical-align: sub;">{21,6o}</span><br />
</td>
        <td>21<br />
</td>
        <td>3:9:15:19:21:57<br />
</td>
        <td>1/1 19/16 5/4 3/2 19/12 7/4<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><strong>A</strong><span style="vertical-align: sub;">{21,6u}</span><br />
</td>
        <td>21<br />
</td>
        <td>105:285:315:399:665:1995<br />
</td>
        <td>1/1 6/5 24/19 3/2 12/7 36/19<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><strong>A</strong><span style="vertical-align: sub;">{23,1o}</span><br />
</td>
        <td>23<br />
</td>
        <td>3:9:15:21:23:69<br />
</td>
        <td>1/1 5/4 23/16 3/2 7/4 23/12<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><strong>A</strong><span style="vertical-align: sub;">{23,1u}</span><br />
</td>
        <td>23<br />
</td>
        <td>105:315:345:483:805:2415<br />
</td>
        <td>1/1 24/23 6/5 3/2 36/23 12/7<br />
</td>
        <td><br />
</td>
    </tr>
</table>

</body></html>