List of anomalous saturated suspensions: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
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 that is also an ASS.
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>2016-08-09 01:00:44 UTC</tt>.<br>
: The original revision id was <tt>588951872</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 that is also an ASS.


==Formal names==  
==Formal names==


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.


||= **Formal Name** ||= **Odd Limit** ||= **Harmonic Series** ||= **Scale** ||= **Common Name** ||
{| class="wikitable"
|| **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 || Minor 7th Chord  ||
|-
|| **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 || Septimal Minor 7th Chord ||
| style="text-align:center;" | '''Formal Name'''
|| **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 ||   ||
| style="text-align:center;" | '''Odd Limit'''
|| **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 ||   ||
| style="text-align:center;" | '''Harmonic Series'''
|| **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 ||
| style="text-align:center;" | '''Scale'''
|| **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 ||
| style="text-align:center;" | '''Common Name'''
|| **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;{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'''<span style="vertical-align: sub;">{9,1a}</span>
|| **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 ||
| | 9
|| **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 ||
| | 3:5:9:15
|| **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 ||
| | 1/1 6/5 3/2 9/5
|| **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 ||
| | Minor 7th Chord
|| **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;{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'''<span style="vertical-align: sub;">{9,2a}</span>
|| **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 ||   ||
| | 9
|| **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 ||   ||
| | 3:7:9:21
|| **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 ||   ||
| | 1/1 7/6 3/2 7/4
|| **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 ||   ||
| | Septimal Minor 7th Chord
|| **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;{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'''<span style="vertical-align: sub;">{11,1a}</span>
|| **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 ||   ||
| | 11
|| **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 ||   ||
| | 3:9:11:33
|| **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 ||   ||
| | 1/1 11/8 3/2 11/6
|| **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;{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;{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'''<span style="vertical-align: sub;">{13,1a}</span>
|| **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 ||   ||
| | 13
|| **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>
| | 3:9:13:39
<h4>Original HTML content:</h4>
| | 1/1 13/12 3/2 13/8
<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 that 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-Formal names"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Formal names&lt;/h2&gt;
| | '''A'''<span style="vertical-align: sub;">{15,1o}</span>
&lt;br /&gt;
| | 15
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;
| | 3:7:9:15:21
&lt;br /&gt;
| | 1/1 7/6 5/4 3/2 7/4
 
| | Hendrix
 
|-
&lt;table class="wiki_table"&gt;
| | '''A'''<span style="vertical-align: sub;">{15,1u}</span>
    &lt;tr&gt;
| | 15
        &lt;td style="text-align: center;"&gt;&lt;strong&gt;Formal Name&lt;/strong&gt;&lt;br /&gt;
| | 15:21:35:45:105
&lt;/td&gt;
| | 1/1 7/6 7/5 3/2 7/4
        &lt;td style="text-align: center;"&gt;&lt;strong&gt;Odd Limit&lt;/strong&gt;&lt;br /&gt;
| | Inverted Hendrix
&lt;/td&gt;
|-
        &lt;td style="text-align: center;"&gt;&lt;strong&gt;Harmonic Series&lt;/strong&gt;&lt;br /&gt;
| | '''A'''<span style="vertical-align: sub;">{15,2o}</span>
&lt;/td&gt;
| | 15
        &lt;td style="text-align: center;"&gt;&lt;strong&gt;Scale&lt;/strong&gt;&lt;br /&gt;
| | 3:9:11:15:33
&lt;/td&gt;
| | 1/1 5/4 11/8 3/2 11/6
        &lt;td style="text-align: center;"&gt;&lt;strong&gt;Common Name&lt;/strong&gt;&lt;br /&gt;
| | 11-Hendrix
&lt;/td&gt;
|-
    &lt;/tr&gt;
| | '''A'''<span style="vertical-align: sub;">{15,2u}</span>
    &lt;tr&gt;
| | 15
        &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;
| | 15:33:45:55:165
&lt;/td&gt;
| | 1/1 11/10 11/8 3/2 11/6
        &lt;td&gt;9&lt;br /&gt;
| | Inverted 11-Hendrix
&lt;/td&gt;
|-
        &lt;td&gt;3:5:9:15&lt;br /&gt;
| | '''A'''<span style="vertical-align: sub;">{15,3o}</span>
&lt;/td&gt;
| | 15
        &lt;td&gt;1/1 6/5 3/2 9/5&lt;br /&gt;
| | 3:9:13:15:39
&lt;/td&gt;
| | 1/1 13/12 5/4 3/2 13/8
        &lt;td&gt;Minor 7th Chord&lt;br /&gt;
| | 13-Hendrix
&lt;/td&gt;
|-
    &lt;/tr&gt;
| | '''A'''<span style="vertical-align: sub;">{15,3u}</span>
    &lt;tr&gt;
| | 15
        &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;
| | 15:39:45:65:195
&lt;/td&gt;
| | 1/1 13/12 13/10 3/2 13/8
        &lt;td&gt;9&lt;br /&gt;
| | Inverted 13-Hendrix
&lt;/td&gt;
|-
        &lt;td&gt;3:7:9:21&lt;br /&gt;
| | '''A'''<span style="vertical-align: sub;">{17,1o}</span>
&lt;/td&gt;
| | 17
        &lt;td&gt;1/1 7/6 3/2 7/4&lt;br /&gt;
| | 3:9:15:17:51
&lt;/td&gt;
| | 1/1 17/16 5/4 17/12 3/2
        &lt;td&gt;Septimal Minor 7th Chord&lt;br /&gt;
| | 17-Hendrix
&lt;/td&gt;
|-
    &lt;/tr&gt;
| | '''A'''<span style="vertical-align: sub;">{17,1u}</span>
    &lt;tr&gt;
| | 17
        &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;
| | 15:45:51:85:255
&lt;/td&gt;
| | 1/1 17/16 17/12 3/2 17/10
        &lt;td&gt;11&lt;br /&gt;
| | Inverted 17-Hendrix
&lt;/td&gt;
|-
        &lt;td&gt;3:9:11:33&lt;br /&gt;
| | '''A'''<span style="vertical-align: sub;">{19,1o}</span>
&lt;/td&gt;
| | 19
        &lt;td&gt;1/1 11/8 3/2 11/6&lt;br /&gt;
| | 3:9:15:19:57
&lt;/td&gt;
| | 1/1 19/16 5/4 3/2 19/12
        &lt;td&gt;&lt;br /&gt;
| | 19-Hendrix
&lt;/td&gt;
|-
    &lt;/tr&gt;
| | '''A'''<span style="vertical-align: sub;">{19,1u}</span>
    &lt;tr&gt;
| | 19
        &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;
| | 15:45:57:95:285
&lt;/td&gt;
| | 1/1 19/16 3/2 19/12 19/10
        &lt;td&gt;13&lt;br /&gt;
| | Inverted 19-Hendrix
&lt;/td&gt;
|-
        &lt;td&gt;3:9:13:39&lt;br /&gt;
| | '''A'''<span style="vertical-align: sub;">{21,1o}</span>
&lt;/td&gt;
| | 21
        &lt;td&gt;1/1 13/12 3/2 13/8&lt;br /&gt;
| | 3:5:9:15:21:45
&lt;/td&gt;
| | 1/1 15/14 9/8 9/7 3/2 12/7
        &lt;td&gt;&lt;br /&gt;
| |  
&lt;/td&gt;
|-
    &lt;/tr&gt;
| | '''A'''<span style="vertical-align: sub;">{21,1u}</span>
    &lt;tr&gt;
| | 21
        &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;
| | 7:15:21:35:63:105
&lt;/td&gt;
| | 1/1 15/14 9/8 5/4 3/2 15/8
        &lt;td&gt;15&lt;br /&gt;
| |  
&lt;/td&gt;
|-
        &lt;td&gt;3:7:9:15:21&lt;br /&gt;
| | '''A'''<span style="vertical-align: sub;">{21,2o}</span>
&lt;/td&gt;
| | 21
        &lt;td&gt;1/1 7/6 5/4 3/2 7/4&lt;br /&gt;
| | 3:7:9:15:21:63
&lt;/td&gt;
| | 1/1 21/20 9/8 6/5 3/2 9/5
        &lt;td&gt;Hendrix&lt;br /&gt;
| |  
&lt;/td&gt;
|-
    &lt;/tr&gt;
| | '''A'''<span style="vertical-align: sub;">{21,2u}</span>
    &lt;tr&gt;
| | 21
        &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;
| | 5:15:21:35:45:105
&lt;/td&gt;
| | 1/1 21/20 9/8 21/16 3/2 7/4
        &lt;td&gt;15&lt;br /&gt;
| |  
&lt;/td&gt;
|-
        &lt;td&gt;15:21:35:45:105&lt;br /&gt;
| | '''A'''<span style="vertical-align: sub;">{21,3o}</span>
&lt;/td&gt;
| | 21
        &lt;td&gt;1/1 7/6 7/5 3/2 7/4&lt;br /&gt;
| | 3:9:11:15:21:33
&lt;/td&gt;
| | 1/1 5/4 11/8 3/2 7/4 11/6
        &lt;td&gt;Inverted Hendrix&lt;br /&gt;
| |  
&lt;/td&gt;
|-
    &lt;/tr&gt;
| | '''A'''<span style="vertical-align: sub;">{21,3u}</span>
    &lt;tr&gt;
| | 21
        &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;
| | 105:165:231:315:385:1155
&lt;/td&gt;
| | 1/1 12/11 6/5 3/2 18/11 12/7
        &lt;td&gt;15&lt;br /&gt;
| |  
&lt;/td&gt;
|-
        &lt;td&gt;3:9:11:15:33&lt;br /&gt;
| | '''A'''<span style="vertical-align: sub;">{21,4o}</span>
&lt;/td&gt;
| | 21
        &lt;td&gt;1/1 5/4 11/8 3/2 11/6&lt;br /&gt;
| | 3:9:13:15:21:39
&lt;/td&gt;
| | 1/1 13/12 5/4 3/2 13/8 7/4
        &lt;td&gt;11-Hendrix&lt;br /&gt;
| |  
&lt;/td&gt;
|-
    &lt;/tr&gt;
| | '''A'''<span style="vertical-align: sub;">{21,4u}</span>
    &lt;tr&gt;
| | 21
        &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;
| | 105:195:273:315:455:1365
&lt;/td&gt;
| | 1/1 6/5 18/13 3/2 12/7 24/13
        &lt;td&gt;15&lt;br /&gt;
| |  
&lt;/td&gt;
|-
        &lt;td&gt;15:33:45:55:165&lt;br /&gt;
| | '''A'''<span style="vertical-align: sub;">{21,5o}</span>
&lt;/td&gt;
| | 21
        &lt;td&gt;1/1 11/10 11/8 3/2 11/6&lt;br /&gt;
| | 3:9:15:17:21:51
&lt;/td&gt;
| | 1/1 17/16 5/4 17/12 3/2 7/4
        &lt;td&gt;Inverted 11-Hendrix&lt;br /&gt;
| |  
&lt;/td&gt;
|-
    &lt;/tr&gt;
| | '''A'''<span style="vertical-align: sub;">{21,5u}</span>
    &lt;tr&gt;
| | 21
        &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;
| | 105:255:315:357:595:1785
&lt;/td&gt;
| | 1/1 18/17 6/5 24/17 3/2 12/7
        &lt;td&gt;15&lt;br /&gt;
| |  
&lt;/td&gt;
|-
        &lt;td&gt;3:9:13:15:39&lt;br /&gt;
| | '''A'''<span style="vertical-align: sub;">{21,6o}</span>
&lt;/td&gt;
| | 21
        &lt;td&gt;1/1 13/12 5/4 3/2 13/8&lt;br /&gt;
| | 3:9:15:19:21:57
&lt;/td&gt;
| | 1/1 19/16 5/4 3/2 19/12 7/4
        &lt;td&gt;13-Hendrix&lt;br /&gt;
| |  
&lt;/td&gt;
|-
    &lt;/tr&gt;
| | '''A'''<span style="vertical-align: sub;">{21,6u}</span>
    &lt;tr&gt;
| | 21
        &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;
| | 105:285:315:399:665:1995
&lt;/td&gt;
| | 1/1 6/5 24/19 3/2 12/7 36/19
        &lt;td&gt;15&lt;br /&gt;
| |  
&lt;/td&gt;
|-
        &lt;td&gt;15:39:45:65:195&lt;br /&gt;
| | '''A'''<span style="vertical-align: sub;">{23,1o}</span>
&lt;/td&gt;
| | 23
        &lt;td&gt;1/1 13/12 13/10 3/2 13/8&lt;br /&gt;
| | 3:9:15:21:23:69
&lt;/td&gt;
| | 1/1 5/4 23/16 3/2 7/4 23/12
        &lt;td&gt;Inverted 13-Hendrix&lt;br /&gt;
| |  
&lt;/td&gt;
|-
    &lt;/tr&gt;
| | '''A'''<span style="vertical-align: sub;">{23,1u}</span>
    &lt;tr&gt;
| | 23
        &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;
| | 105:315:345:483:805:2415
&lt;/td&gt;
| | 1/1 24/23 6/5 3/2 36/23 12/7
        &lt;td&gt;17&lt;br /&gt;
| |
&lt;/td&gt;
|}
        &lt;td&gt;3:9:15:17:51&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1 17/16 5/4 17/12 3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;17-Hendrix&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&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;17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15:45:51:85:255&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1 17/16 17/12 3/2 17/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Inverted 17-Hendrix&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&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;19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3:9:15:19:57&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1 19/16 5/4 3/2 19/12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;19-Hendrix&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&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;19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15:45:57:95:285&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1 19/16 3/2 19/12 19/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Inverted 19-Hendrix&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&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;21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3:5:9:15:21:45&lt;br /&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;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&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;21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7:15:21:35:63:105&lt;br /&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;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&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;21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3:7:9:15:21:63&lt;br /&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;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&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;21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5:15:21:35:45:105&lt;br /&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;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&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;21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3:9:11:15:21:33&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1 5/4 11/8 3/2 7/4 11/6&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;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;21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;105:165:231:315:385:1155&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1 12/11 6/5 3/2 18/11 12/7&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;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;21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3:9:13:15:21:39&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1 13/12 5/4 3/2 13/8 7/4&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;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;21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;105:195:273:315:455:1365&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1 6/5 18/13 3/2 12/7 24/13&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;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;21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3:9:15:17:21:51&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1 17/16 5/4 17/12 3/2 7/4&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;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;21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;105:255:315:357:595:1785&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1 18/17 6/5 24/17 3/2 12/7&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;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;21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3:9:15:19:21:57&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1 19/16 5/4 3/2 19/12 7/4&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;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;21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;105:285:315:399:665:1995&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1 6/5 24/19 3/2 12/7 36/19&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;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;23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3:9:15:21:23:69&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1 5/4 23/16 3/2 7/4 23/12&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;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;23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;105:315:345:483:805:2415&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1 24/23 6/5 3/2 36/23 12/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

Below is a complete list of Anomalous Saturated Suspensions through the 23-limit. Each chord listed is either ambitonal or has a o/utonal inverse that is also an ASS.

Formal names

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.

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