List of anomalous saturated suspensions: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
Below is a complete list of [[anomalous saturated suspension]]s through the [[23-odd-limit]]. Each chord listed is either [[Otonality and utonality|ambitonal]] or has a [[Otonality and utonality|o/utonal]] inverse that is also an anomalous saturated suspension.
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 21:39:43 UTC</tt>.<br>
: The original revision id was <tt>588946790</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==


== 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.


||= **Name** ||= **Odd Limit** ||= **Harmonic Series** ||= **Scale** ||= **Scale Name** ||
Every chord has a plausible [[Chord homonym|homonym]]. The alternate root is bolded in the scale. The Color Names column names the homonym for some of the chords. For example, if the first chord is Cg7, it has as a homonym gEby6.
|| **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;{9,1a}&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;{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;{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;{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;{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;{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;{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;{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;{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;{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;{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;{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;{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;{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;{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;{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;{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;{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;{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;{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;{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;{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;{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;{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;{9,1a}&lt;/span&gt; || 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 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;


{| class="wikitable"
|-
! Formal name
! Odd limit
! Harmonic series
! Scale
! [[Color name]]
! Common name
|-
| '''A'''<span style="vertical-align: sub;">{9,1a}</span>
| 9
| 3:5:9:15
| 1/1 '''6/5''' 3/2 9/5
| g7 = y6
| Minor 7th Chord
|-
| '''A'''<span style="vertical-align: sub;">{9,2a}</span>
| 9
| 3:7:9:21
| 1/1 '''7/6''' 3/2 7/4
| z7 = r6
| Septimal Minor 7th Chord
|-
| '''A'''<span style="vertical-align: sub;">{11,1a}</span>
| 11
| 3:9:11:33
| 1/1 11/8 3/2 '''11/6'''
| 1o7(1o4) = 1u6(1u2)
|
|-
| '''A'''<span style="vertical-align: sub;">{13,1a}</span>
| 13
| 3:9:13:39
| 1/1 '''13/12''' 3/2 13/8
| 3o6(3o2) = 3u7(3u4)
|
|-
| '''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
| h7,z10 = r6,ry8
| 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
| z7,zg5 = r6,g3
| 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'''
| y,1o7,1o11 = 1u6,1u9(1uy4)
| 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'''
| 1o7(1o4)1og9 = g,1u6,1u9
| 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
| y,3o6,3o9 = 3u7(3u4)3uy9
| 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
| 3o6,3o9(3og4) = g,3u7,3u11
| 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
| y,17o9,17o12
| 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
| 17og7(17o2)17o12
| 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'''
| 19o6,y3 = 19u7,19uy5
| 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
| 19o6,19og8 = 19u7,g3
| Inverted 19-Hendrix
|-
| '''A'''<span style="vertical-align: sub;">{21,1o}</span>
| 21
| 3:5:9:15:21:45
| 1/1 5/4 3/2 '''5/3''' 7/4 15/8
| y6,z7,y7 = g9,zg9
|
|-
| '''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
| y9,ry8 = g7,g6,r6
|
|-
| '''A'''<span style="vertical-align: sub;">{21,2o}</span>
| 21
| 3:7:9:15:21:63
| 1/1 '''7/6''' 5/4 21/16 3/2 7/4
| h7,z10,z11 = r6,ry8,9
| Hendrix add11?
|-
| '''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'''
| z9(z4)zg9 = z6,4,zg5 = r6,g3,r9
| blues scale
|-
| '''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'''
| h7,1o7,1o11
|
|-
| '''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
| s6,1u6,1u9
|
|-
| '''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
| h7,3o6,3o9
|
|-
| '''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'''
| s6,3u4,3u7
|
|-
| '''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
| h7,17o9,17o12
| dom7b9#11
|-
| '''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
| s6,17u8,17u11
| min6b9#11
|-
| '''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
| 19o6,y3,z7
| dom7#9b13
|-
| '''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
| 19u7,g3,r6
| maj7#9,13
|-
| '''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'''
| h7,23o5,23o8
|
|-
| '''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
| s6,23u5,23u8
|
|}


&lt;table class="wiki_table"&gt;
== External links ==
    &lt;tr&gt;
* [http://x31eq.com/ass.htm Graham Breed's list]
        &lt;td style="text-align: center;"&gt;&lt;strong&gt;Name&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;strong&gt;Odd Limit&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;strong&gt;Harmonic Series&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;strong&gt;Scale&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;strong&gt;Scale Name&lt;/strong&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;{9,1a}&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3:5:9:15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1 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;{9,1a}&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3:7:9:21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1 7/6 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;{9,1a}&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3:9:11:33&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1 11/8 3/2 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;{9,1a}&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3:9:13:39&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1 13/12 3/2 13/8&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;{9,1a}&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3:7:9:15:21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1 7/6 5/4 3/2 7/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;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;{9,1a}&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15:21:35:45:105&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1 7/6 7/5 3/2 7/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Inverted 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;{9,1a}&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3:9:11:15:33&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1 5/4 11/8 3/2 11/6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11-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;{9,1a}&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15:33:45:55:165&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1 11/10 11/8 3/2 11/6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Inverted 11-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;{9,1a}&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3:9:13:15:39&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1 13/12 5/4 3/2 13/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13-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;{9,1a}&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15:39:45:65:195&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1 13/12 13/10 3/2 13/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Inverted 13-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;{9,1a}&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &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;{9,1a}&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;{9,1a}&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;{9,1a}&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;{9,1a}&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;{9,1a}&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;{9,1a}&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;{9,1a}&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;{9,1a}&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;{9,1a}&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;{9,1a}&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;{9,1a}&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;{9,1a}&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;{9,1a}&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;{9,1a}&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;{9,1a}&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;{9,1a}&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;{9,1a}&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>
[[Category:Lists of chords]]
[[Category:Dyadic chords]]

Latest revision as of 22:11, 22 December 2024

Below is a complete list of anomalous saturated suspensions through the 23-odd-limit. Each chord listed is either ambitonal or has a o/utonal inverse that is also an anomalous saturated suspension.

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.

Every chord has a plausible homonym. The alternate root is bolded in the scale. The Color Names column names the homonym for some of the chords. For example, if the first chord is Cg7, it has as a homonym gEby6.

Formal name Odd limit Harmonic series Scale Color name Common name
A{9,1a} 9 3:5:9:15 1/1 6/5 3/2 9/5 g7 = y6 Minor 7th Chord
A{9,2a} 9 3:7:9:21 1/1 7/6 3/2 7/4 z7 = r6 Septimal Minor 7th Chord
A{11,1a} 11 3:9:11:33 1/1 11/8 3/2 11/6 1o7(1o4) = 1u6(1u2)
A{13,1a} 13 3:9:13:39 1/1 13/12 3/2 13/8 3o6(3o2) = 3u7(3u4)
A{15,1o} 15 3:7:9:15:21 1/1 7/6 5/4 3/2 7/4 h7,z10 = r6,ry8 Hendrix
A{15,1u} 15 15:21:35:45:105 1/1 7/6 7/5 3/2 7/4 z7,zg5 = r6,g3 Inverted Hendrix
A{15,2o} 15 3:9:11:15:33 1/1 5/4 11/8 3/2 11/6 y,1o7,1o11 = 1u6,1u9(1uy4) 11-Hendrix
A{15,2u} 15 15:33:45:55:165 1/1 11/10 11/8 3/2 11/6 1o7(1o4)1og9 = g,1u6,1u9 Inverted 11-Hendrix
A{15,3o} 15 3:9:13:15:39 1/1 13/12 5/4 3/2 13/8 y,3o6,3o9 = 3u7(3u4)3uy9 13-Hendrix
A{15,3u} 15 15:39:45:65:195 1/1 13/12 13/10 3/2 13/8 3o6,3o9(3og4) = g,3u7,3u11 Inverted 13-Hendrix
A{17,1o} 17 3:9:15:17:51 1/1 17/16 5/4 17/12 3/2 y,17o9,17o12 17-Hendrix
A{17,1u} 17 15:45:51:85:255 1/1 17/16 17/12 3/2 17/10 17og7(17o2)17o12 Inverted 17-Hendrix
A{19,1o} 19 3:9:15:19:57 1/1 19/16 5/4 3/2 19/12 19o6,y3 = 19u7,19uy5 19-Hendrix
A{19,1u} 19 15:45:57:95:285 1/1 19/16 3/2 19/12 19/10 19o6,19og8 = 19u7,g3 Inverted 19-Hendrix
A{21,1o} 21 3:5:9:15:21:45 1/1 5/4 3/2 5/3 7/4 15/8 y6,z7,y7 = g9,zg9
A{21,1u} 21 7:15:21:35:63:105 1/1 15/14 9/8 5/4 3/2 15/8 y9,ry8 = g7,g6,r6
A{21,2o} 21 3:7:9:15:21:63 1/1 7/6 5/4 21/16 3/2 7/4 h7,z10,z11 = r6,ry8,9 Hendrix add11?
A{21,2u} 21 5:15:21:35:45:105 1/1 21/20 9/8 21/16 3/2 7/4 z9(z4)zg9 = z6,4,zg5 = r6,g3,r9 blues scale
A{21,3o} 21 3:9:11:15:21:33 1/1 5/4 11/8 3/2 7/4 11/6 h7,1o7,1o11
A{21,3u} 21 105:165:231:315:385:1155 1/1 12/11 6/5 3/2 18/11 12/7 s6,1u6,1u9
A{21,4o} 21 3:9:13:15:21:39 1/1 13/12 5/4 3/2 13/8 7/4 h7,3o6,3o9
A{21,4u} 21 105:195:273:315:455:1365 1/1 6/5 18/13 3/2 12/7 24/13 s6,3u4,3u7
A{21,5o} 21 3:9:15:17:21:51 1/1 17/16 5/4 17/12 3/2 7/4 h7,17o9,17o12 dom7b9#11
A{21,5u} 21 105:255:315:357:595:1785 1/1 18/17 6/5 24/17 3/2 12/7 s6,17u8,17u11 min6b9#11
A{21,6o} 21 3:9:15:19:21:57 1/1 19/16 5/4 3/2 19/12 7/4 19o6,y3,z7 dom7#9b13
A{21,6u} 21 105:285:315:399:665:1995 1/1 6/5 24/19 3/2 12/7 36/19 19u7,g3,r6 maj7#9,13
A{23,1o} 23 3:9:15:21:23:69 1/1 5/4 23/16 3/2 7/4 23/12 h7,23o5,23o8
A{23,1u} 23 105:315:345:483:805:2415 1/1 24/23 6/5 3/2 36/23 12/7 s6,23u5,23u8

External links

Retrieved from "https://en.xen.wiki/index.php?title=List_of_anomalous_saturated_suspensions&oldid=172452"