Xenharmonic Wiki

List of anomalous saturated suspensions

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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;">{9,1a}</span> || 9 || 3:7:9:21 || 1/1 7/6 3/2 7/4 ||  ||
|| **A**<span style="vertical-align: sub;">{9,1a}</span> || 11 || 3:9:11:33 || 1/1 11/8 3/2 11/6 ||  ||
|| **A**<span style="vertical-align: sub;">{9,1a}</span> || 13 || 3:9:13:39 || 1/1 13/12 3/2 13/8 ||  ||
|| **A**<span style="vertical-align: sub;">{9,1a}</span> || 15 || 3:7:9:15:21 || 1/1 7/6 5/4 3/2 7/4 || Hendrix ||
|| **A**<span style="vertical-align: sub;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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;">{9,1a}</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>
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