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List of anomalous saturated suspensions: Difference between revisions

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Wikispaces>clumma
**Imported revision 588936646 - Original comment: **
Wikispaces>clumma
**Imported revision 588946790 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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 18:08:05 UTC</tt>.<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>588936646</tt>.<br>
: The original revision id was <tt>588946790</tt>.<br>
: The revision comment was: <tt></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>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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==Naming==
==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 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** ||
||= **Name** ||= **Odd Limit** ||= **Harmonic Series** ||= **Scale** ||= **Scale 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 ||  ||
|| || 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; || 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 ||  ||
|| **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 ||  ||
|| || 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; || 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 ||
|| **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 ||
|| || 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 || 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 ||
|| **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 ||
|| || 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 || 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 ||
|| **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 ||
|| || 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; || 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 ||
|| **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 ||
|| || 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; || 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 ||
|| **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 ||
|| || 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; || 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 ||  ||
|| **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 ||  ||
|| || 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 || 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 ||  ||
|| **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 ||  ||
|| || 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 || 3:7:9:15:21:63 || 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 ||  ||
|| **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 ||  ||
|| || 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 || 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 ||  ||
|| **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 ||  ||
|| || 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 || 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 ||  ||
|| **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 ||  ||
|| || 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 || 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 ||  ||
|| **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 ||  ||
|| || 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; || 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 ||  ||
|| **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 ||  ||
|| || 23 || 105:315:345:483:805:2415 || 1/1 24/23 6/5 3/2 36/23 12/7 ||  ||
|| **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>
</pre></div>
<h4>Original HTML content:</h4>
<h4>Original HTML content:</h4>
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&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;
&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 with 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;
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;
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Line 317: Line 317:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;br /&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;
         &lt;td&gt;21&lt;br /&gt;
         &lt;td&gt;21&lt;br /&gt;
Line 329: Line 329:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;br /&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;
         &lt;td&gt;21&lt;br /&gt;
         &lt;td&gt;21&lt;br /&gt;
Line 341: Line 341:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;br /&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;
         &lt;td&gt;21&lt;br /&gt;
         &lt;td&gt;21&lt;br /&gt;
Line 353: Line 353:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;br /&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;
         &lt;td&gt;21&lt;br /&gt;
         &lt;td&gt;21&lt;br /&gt;
Line 365: Line 365:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;br /&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;
         &lt;td&gt;21&lt;br /&gt;
         &lt;td&gt;21&lt;br /&gt;
Line 377: Line 377:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;br /&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;
         &lt;td&gt;23&lt;br /&gt;
         &lt;td&gt;23&lt;br /&gt;
Line 389: Line 389:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;br /&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;
         &lt;td&gt;23&lt;br /&gt;
         &lt;td&gt;23&lt;br /&gt;
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