List of anomalous saturated suspensions

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This revision was by author clumma and made on 2016-08-08 17:51:50 UTC.
The original revision id was 588934502.
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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 with a capital "A" whose subscript is a tuple, where the first value is the odd limit and the second value is the index in the list for that odd limit. This is followed by an "a," "o," or "u" depending on whether the chord is ambitonal, otonal, or utonal.

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

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 with a capital &quot;A&quot; whose subscript is a tuple, where the first value is the odd limit and the second value is the index in the list for that odd limit. This is followed by an &quot;a,&quot; &quot;o,&quot; or &quot;u&quot; depending on whether the chord is ambitonal, otonal, or utonal.<br />
<br />


<table class="wiki_table">
    <tr>
        <th>ASS name<br />
</th>
        <th>Odd Limit<br />
</th>
        <th>Harmonic Series<br />
</th>
        <th>Scale<br />
</th>
        <th>Scale Name<br />
</th>
    </tr>
    <tr>
        <td>A_{9,1a}<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><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><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><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><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><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><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><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><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><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><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><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><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><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><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><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><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><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><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><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><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><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><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><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><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><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><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><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>
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