List of anomalous saturated suspensions: Difference between revisions

Revision as of 22:15, 8 August 2016

IMPORTED REVISION FROM WIKISPACES

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This revision was by author Sarzadoce and made on 2016-08-08 22:15:35 UTC.

The original revision id was 588947750.

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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.

||= **Formal Name** ||= **Odd Limit** ||= **Harmonic Series** ||= **Scale** ||= **Common Name** ||
|| **A**<span style="vertical-align: sub;">{9,1a}</span> || 9 || 3:5:9:15 || 1/1 6/5 3/2 9/5 || 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 || 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 ||   ||
|| **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>Formal 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>Common 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>Minor 7th Chord<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>Septimal Minor 7th Chord<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>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:Sarzadoce|Sarzadoce]] and made on <tt>2016-08-08 22:00:43 UTC</tt>.<br>
+: This revision was by author [[User:Sarzadoce|Sarzadoce]] and made on <tt>2016-08-08 22:15:35 UTC</tt>.<br>
-: The original revision id was <tt>588947298</tt>.<br>
+: The original revision id was <tt>588947750</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>
@@ Line 12: / Line 12: @@
 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** ||
+||= **Formal Name** ||= **Odd Limit** ||= **Harmonic Series** ||= **Scale** ||= **Common 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 || 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 ||   ||
+|| **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  ||
 || **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;{13,1a}&lt;/span&gt; || 13 || 3:9:13:39 || 1/1 13/12 3/2 13/8 ||   ||
@@ Line 52: / Line 52: @@
 &lt;table class="wiki_table"&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;&lt;strong&gt;Name&lt;/strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;strong&gt;Formal 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;
@@ Line 60: / Line 60: @@
          &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 style="text-align: center;"&gt;&lt;strong&gt;Common Name&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 72: / Line 72: @@
          &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;Minor 7th Chord&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 84: / Line 84: @@
          &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;Septimal Minor 7th Chord&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;

List of anomalous saturated suspensions: Difference between revisions

Revision as of 22:15, 8 August 2016

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

Original HTML content:

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