Valentine/Chords: Difference between revisions

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Wikispaces>genewardsmith
**Imported revision 288586220 - Original comment: **
Wikispaces>keenanpepper
**Imported revision 288591202 - 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:genewardsmith|genewardsmith]] and made on <tt>2011-12-27 14:46:41 UTC</tt>.<br>
: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-12-27 15:42:51 UTC</tt>.<br>
: The original revision id was <tt>288586220</tt>.<br>
: The original revision id was <tt>288591202</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>
<h4>Original Wikitext content:</h4>
<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 are listed the [[Dyadic chord|dyadic chords]] of 11-limit [[Starling temperaments#Valentine temperament-11-limit|valentine temperament]]. Typing the chords requires consideration of the fact that valentine conflates 12/11 and 11/10 and so also 11/6 and 20/11. If a transversal can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. If the chord is essentially tempered, it is analyzed in terms of the transversal which employs 11/10 and 20/11.
<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 are listed the [[Dyadic chord|dyadic chords]] of 11-limit [[Starling temperaments#Valentine%20temperament-11-limit|valentine temperament]]. Typing the chords requires consideration of the fact that valentine conflates 12/11 and 11/10 and so also 11/6 and 20/11. If a transversal can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. If the chord is essentially tempered, it is analyzed in terms of the transversal which employs 11/10 and 20/11.


If only 126/125 needs to be tempered out, the chord is labeled starling, if 121/120, biyatismic, if 176/175, valinorsmic, if 385/384, keenanismic, and if 441/440, werckismic. Chords which require any two of 121/120, 176/175 or 385/384 are labeled zeus, if they require any two of 126/125, 176/175 or 441/440, they are labeled thrush. Finally, if they require any three independent commas among those discussed above, it is labeled valentine.
If only 126/125 needs to be tempered out, the chord is labeled starling, if 121/120, biyatismic, if 176/175, valinorsmic, if 385/384, keenanismic, and if 441/440, werckismic. Chords which require any two of 121/120, 176/175 or 385/384 are labeled zeus, if they require any two of 126/125, 176/175 or 441/440, they are labeled thrush. Finally, if they require any three independent commas among those discussed above, it is labeled valentine.
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Valentine has MOS of size 15, 16, 31 and 46. It is readily observed from the list below that even the smallest of these is well-supplied with chords. Because [[Carlos Alpha]] is the generator chain of valentine in the tuning with pure 3/2's, the list below is also a list of chords of Carlos Alpha, so long as the transversals are adjusted so that the notes are in the correct octave. This means that a number in a chord listed under "chord" less than 16 corresponds to a note in the transversal which should be left unaltered, whereas the notes from 16 to 21 correspond to transversal notes which should be adjusted up an octave. Hence, tetrad 8, the 0-2-5-9 chord with transversal 1-6/5-11/8-3/2, is an essentially zeus chord of Carlos Alpha as well as valentine. On the other hand, tetrad 76, 0-10-13-18 with transversal 1-11/7-9/5-9/8, corresponds to the werckismic 1-11/7-9/5-9/4 chord of Carlos Alpha.
Valentine has MOS of size 15, 16, 31 and 46. It is readily observed from the list below that even the smallest of these is well-supplied with chords. Because [[Carlos Alpha]] is the generator chain of valentine in the tuning with pure 3/2's, the list below is also a list of chords of Carlos Alpha, so long as the transversals are adjusted so that the notes are in the correct octave. This means that a number in a chord listed under "chord" less than 16 corresponds to a note in the transversal which should be left unaltered, whereas the notes from 16 to 21 correspond to transversal notes which should be adjusted up an octave. Hence, tetrad 8, the 0-2-5-9 chord with transversal 1-6/5-11/8-3/2, is an essentially zeus chord of Carlos Alpha as well as valentine. On the other hand, tetrad 76, 0-10-13-18 with transversal 1-11/7-9/5-9/8, corresponds to the werckismic 1-11/7-9/5-9/4 chord of Carlos Alpha.


=Triads=
In other words, each chord here has an unlimited number of "voicings" in valentine temperament, but exactly one voicing in Carlos Alpha, because there are no octaves.
 
=Triads=  
|| Number || Chord || Transversal || Type ||
|| Number || Chord || Transversal || Type ||
|| 1 || 0-2-4 || 1-11/10-6/5 || otonal ||
|| 1 || 0-2-4 || 1-11/10-6/5 || otonal ||
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|| 56 || 0-18-21 || 1-9/8-9/7 || utonal ||
|| 56 || 0-18-21 || 1-9/8-9/7 || utonal ||


=Tetrads=
=Tetrads=  
|| Number || Chord || Transversal || Type ||
|| Number || Chord || Transversal || Type ||
|| 1 || 0-2-4-7 || 1-11/10-6/5-11/8 || zeus ||
|| 1 || 0-2-4-7 || 1-11/10-6/5-11/8 || zeus ||
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|| 97 || 0-13-18-21 || 1-9/5-9/8-9/7 || utonal ||
|| 97 || 0-13-18-21 || 1-9/5-9/8-9/7 || utonal ||


=Pentads=
=Pentads=  
|| Number || Chord || Transversal || Type ||
|| Number || Chord || Transversal || Type ||
|| 1 || 0-2-4-7-9 || 1-11/10-6/5-11/8-3/2 || zeus ||
|| 1 || 0-2-4-7-9 || 1-11/10-6/5-11/8-3/2 || zeus ||
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|| 65 || 0-11-13-18-21 || 1-18/11-9/5-9/8-9/7 || utonal ||
|| 65 || 0-11-13-18-21 || 1-18/11-9/5-9/8-9/7 || utonal ||


=Hexads=
=Hexads=  
|| Number || Chord || Transversal || Type ||
|| Number || Chord || Transversal || Type ||
|| 1 || 0-2-4-7-9-11 || 1-11/10-6/5-11/8-3/2-18/11 || zeus ||
|| 1 || 0-2-4-7-9-11 || 1-11/10-6/5-11/8-3/2-18/11 || zeus ||
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|| 13 || 0-8-10-13-18-21 || 1-10/7-11/7-9/5-9/8-9/7 || thrush ||
|| 13 || 0-8-10-13-18-21 || 1-10/7-11/7-9/5-9/8-9/7 || thrush ||
|| 14 || 0-8-11-13-18-21 || 1-10/7-18/11-9/5-9/8-9/7 || thrush ||
|| 14 || 0-8-11-13-18-21 || 1-10/7-18/11-9/5-9/8-9/7 || thrush ||
|| 15 || 0-9-11-13-18-21 || 1-3/2-18/11-9/5-9/8-9/7 || utonal ||
|| 15 || 0-9-11-13-18-21 || 1-3/2-18/11-9/5-9/8-9/7 || utonal ||</pre></div>
</pre></div>
<h4>Original HTML content:</h4>
<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;Chords of valentine&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Below are listed the &lt;a class="wiki_link" href="/Dyadic%20chord"&gt;dyadic chords&lt;/a&gt; of 11-limit &lt;a class="wiki_link" href="/Starling%20temperaments#Valentine temperament-11-limit"&gt;valentine temperament&lt;/a&gt;. Typing the chords requires consideration of the fact that valentine conflates 12/11 and 11/10 and so also 11/6 and 20/11. If a transversal can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. If the chord is essentially tempered, it is analyzed in terms of the transversal which employs 11/10 and 20/11.&lt;br /&gt;
<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;Chords of valentine&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Below are listed the &lt;a class="wiki_link" href="/Dyadic%20chord"&gt;dyadic chords&lt;/a&gt; of 11-limit &lt;a class="wiki_link" href="/Starling%20temperaments#Valentine%20temperament-11-limit"&gt;valentine temperament&lt;/a&gt;. Typing the chords requires consideration of the fact that valentine conflates 12/11 and 11/10 and so also 11/6 and 20/11. If a transversal can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. If the chord is essentially tempered, it is analyzed in terms of the transversal which employs 11/10 and 20/11.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
If only 126/125 needs to be tempered out, the chord is labeled starling, if 121/120, biyatismic, if 176/175, valinorsmic, if 385/384, keenanismic, and if 441/440, werckismic. Chords which require any two of 121/120, 176/175 or 385/384 are labeled zeus, if they require any two of 126/125, 176/175 or 441/440, they are labeled thrush. Finally, if they require any three independent commas among those discussed above, it is labeled valentine.&lt;br /&gt;
If only 126/125 needs to be tempered out, the chord is labeled starling, if 121/120, biyatismic, if 176/175, valinorsmic, if 385/384, keenanismic, and if 441/440, werckismic. Chords which require any two of 121/120, 176/175 or 385/384 are labeled zeus, if they require any two of 126/125, 176/175 or 441/440, they are labeled thrush. Finally, if they require any three independent commas among those discussed above, it is labeled valentine.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Valentine has MOS of size 15, 16, 31 and 46. It is readily observed from the list below that even the smallest of these is well-supplied with chords. Because &lt;a class="wiki_link" href="/Carlos%20Alpha"&gt;Carlos Alpha&lt;/a&gt; is the generator chain of valentine in the tuning with pure 3/2's, the list below is also a list of chords of Carlos Alpha, so long as the transversals are adjusted so that the notes are in the correct octave. This means that a number in a chord listed under &amp;quot;chord&amp;quot; less than 16 corresponds to a note in the transversal which should be left unaltered, whereas the notes from 16 to 21 correspond to transversal notes which should be adjusted up an octave. Hence, tetrad 8, the 0-2-5-9 chord with transversal 1-6/5-11/8-3/2, is an essentially zeus chord of Carlos Alpha as well as valentine. On the other hand, tetrad 76, 0-10-13-18 with transversal 1-11/7-9/5-9/8, corresponds to the werckismic 1-11/7-9/5-9/4 chord of Carlos Alpha.&lt;br /&gt;
Valentine has MOS of size 15, 16, 31 and 46. It is readily observed from the list below that even the smallest of these is well-supplied with chords. Because &lt;a class="wiki_link" href="/Carlos%20Alpha"&gt;Carlos Alpha&lt;/a&gt; is the generator chain of valentine in the tuning with pure 3/2's, the list below is also a list of chords of Carlos Alpha, so long as the transversals are adjusted so that the notes are in the correct octave. This means that a number in a chord listed under &amp;quot;chord&amp;quot; less than 16 corresponds to a note in the transversal which should be left unaltered, whereas the notes from 16 to 21 correspond to transversal notes which should be adjusted up an octave. Hence, tetrad 8, the 0-2-5-9 chord with transversal 1-6/5-11/8-3/2, is an essentially zeus chord of Carlos Alpha as well as valentine. On the other hand, tetrad 76, 0-10-13-18 with transversal 1-11/7-9/5-9/8, corresponds to the werckismic 1-11/7-9/5-9/4 chord of Carlos Alpha.&lt;br /&gt;
&lt;br /&gt;
In other words, each chord here has an unlimited number of &amp;quot;voicings&amp;quot; in valentine temperament, but exactly one voicing in Carlos Alpha, because there are no octaves.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Triads"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Triads&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Triads"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Triads&lt;/h1&gt;
 


&lt;table class="wiki_table"&gt;
&lt;table class="wiki_table"&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Tetrads"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Tetrads&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Tetrads"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Tetrads&lt;/h1&gt;
 


&lt;table class="wiki_table"&gt;
&lt;table class="wiki_table"&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Pentads"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Pentads&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Pentads"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Pentads&lt;/h1&gt;
 


&lt;table class="wiki_table"&gt;
&lt;table class="wiki_table"&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Hexads"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Hexads&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Hexads"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Hexads&lt;/h1&gt;
 


&lt;table class="wiki_table"&gt;
&lt;table class="wiki_table"&gt;

Revision as of 15:42, 27 December 2011

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author keenanpepper and made on 2011-12-27 15:42:51 UTC.
The original revision id was 288591202.
The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

Below are listed the [[Dyadic chord|dyadic chords]] of 11-limit [[Starling temperaments#Valentine%20temperament-11-limit|valentine temperament]]. Typing the chords requires consideration of the fact that valentine conflates 12/11 and 11/10 and so also 11/6 and 20/11. If a transversal can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. If the chord is essentially tempered, it is analyzed in terms of the transversal which employs 11/10 and 20/11.

If only 126/125 needs to be tempered out, the chord is labeled starling, if 121/120, biyatismic, if 176/175, valinorsmic, if 385/384, keenanismic, and if 441/440, werckismic. Chords which require any two of 121/120, 176/175 or 385/384 are labeled zeus, if they require any two of 126/125, 176/175 or 441/440, they are labeled thrush. Finally, if they require any three independent commas among those discussed above, it is labeled valentine.

Valentine has MOS of size 15, 16, 31 and 46. It is readily observed from the list below that even the smallest of these is well-supplied with chords. Because [[Carlos Alpha]] is the generator chain of valentine in the tuning with pure 3/2's, the list below is also a list of chords of Carlos Alpha, so long as the transversals are adjusted so that the notes are in the correct octave. This means that a number in a chord listed under "chord" less than 16 corresponds to a note in the transversal which should be left unaltered, whereas the notes from 16 to 21 correspond to transversal notes which should be adjusted up an octave. Hence, tetrad 8, the 0-2-5-9 chord with transversal 1-6/5-11/8-3/2, is an essentially zeus chord of Carlos Alpha as well as valentine. On the other hand, tetrad 76, 0-10-13-18 with transversal 1-11/7-9/5-9/8, corresponds to the werckismic 1-11/7-9/5-9/4 chord of Carlos Alpha.

In other words, each chord here has an unlimited number of "voicings" in valentine temperament, but exactly one voicing in Carlos Alpha, because there are no octaves.

=Triads= 
|| Number || Chord || Transversal || Type ||
|| 1 || 0-2-4 || 1-11/10-6/5 || otonal ||
|| 2 || 0-2-5 || 1-11/10-5/4 || valinorsmic ||
|| 3 || 0-3-5 || 1-8/7-5/4 || valinorsmic ||
|| 4 || 0-2-7 || 1-11/10-11/8 || utonal ||
|| 5 || 0-3-7 || 1-8/7-11/8 || keenanismic ||
|| 6 || 0-4-7 || 1-6/5-11/8 || keenanismic ||
|| 7 || 0-5-7 || 1-5/4-11/8 || otonal ||
|| 8 || 0-3-8 || 1-8/7-10/7 || otonal ||
|| 9 || 0-4-8 || 1-6/5-10/7 || starling ||
|| 10 || 0-5-8 || 1-5/4-10/7 || utonal ||
|| 11 || 0-2-9 || 1-12/11-3/2 || utonal ||
|| 12 || 0-4-9 || 1-6/5-3/2 || utonal ||
|| 13 || 0-5-9 || 1-5/4-3/2 || otonal ||
|| 14 || 0-7-9 || 1-11/8-3/2 || otonal ||
|| 15 || 0-2-10 || 1-11/10-11/7 || utonal ||
|| 16 || 0-3-10 || 1-8/7-11/7 || otonal ||
|| 17 || 0-5-10 || 1-5/4-11/7 || valinorsmic ||
|| 18 || 0-7-10 || 1-11/8-11/7 || utonal ||
|| 19 || 0-8-10 || 1-10/7-11/7 || otonal ||
|| 20 || 0-2-11 || 1-12/11-18/11 || otonal ||
|| 21 || 0-3-11 || 1-8/7-18/11 || werckismic ||
|| 22 || 0-4-11 || 1-6/5-18/11 || biyatismic ||
|| 23 || 0-7-11 || 1-11/8-18/11 || biyatismic ||
|| 24 || 0-8-11 || 1-10/7-18/11 || werckismic ||
|| 25 || 0-9-11 || 1-3/2-18/11 || utonal ||
|| 26 || 0-2-12 || 1-12/11-12/7 || utonal ||
|| 27 || 0-3-12 || 1-8/7-12/7 || otonal ||
|| 28 || 0-4-12 || 1-6/5-12/7 || utonal ||
|| 29 || 0-5-12 || 1-5/4-12/7 || keenanismic ||
|| 30 || 0-7-12 || 1-11/8-12/7 || keenanismic ||
|| 31 || 0-8-12 || 1-10/7-12/7 || otonal ||
|| 32 || 0-9-12 || 1-3/2-12/7 || utonal ||
|| 33 || 0-10-12 || 1-11/7-12/7 || otonal ||
|| 34 || 0-2-13 || 1-11/10-9/5 || otonal ||
|| 35 || 0-3-13 || 1-8/7-9/5 || werckismic ||
|| 36 || 0-4-13 || 1-6/5-9/5 || otonal ||
|| 37 || 0-5-13 || 1-5/4-9/5 || starling ||
|| 38 || 0-8-13 || 1-10/7-9/5 || starling ||
|| 39 || 0-9-13 || 1-3/2-9/5 || utonal ||
|| 40 || 0-10-13 || 1-11/7-9/5 || werckismic ||
|| 41 || 0-11-13 || 1-18/11-9/5 || utonal ||
|| 42 || 0-5-18 || 1-5/4-9/8 || otonal ||
|| 43 || 0-7-18 || 1-11/8-9/8 || otonal ||
|| 44 || 0-8-18 || 1-10/7-9/8 || werckismic ||
|| 45 || 0-9-18 || 1-3/2-9/8 || ambitonal ||
|| 46 || 0-10-18 || 1-11/7-9/8 || werckismic ||
|| 47 || 0-11-18 || 1-18/11-9/8 || utonal ||
|| 48 || 0-13-18 || 1-9/5-9/8 || utonal ||
|| 49 || 0-3-21 || 1-8/7-9/7 || otonal ||
|| 50 || 0-8-21 || 1-10/7-9/7 || otonal ||
|| 51 || 0-9-21 || 1-3/2-9/7 || utonal ||
|| 52 || 0-10-21 || 1-11/7-9/7 || otonal ||
|| 53 || 0-11-21 || 1-18/11-9/7 || utonal ||
|| 54 || 0-12-21 || 1-12/7-9/7 || otonal ||
|| 55 || 0-13-21 || 1-9/5-9/7 || utonal ||
|| 56 || 0-18-21 || 1-9/8-9/7 || utonal ||

=Tetrads= 
|| Number || Chord || Transversal || Type ||
|| 1 || 0-2-4-7 || 1-11/10-6/5-11/8 || zeus ||
|| 2 || 0-2-5-7 || 1-11/10-5/4-11/8 || valinorsmic ||
|| 3 || 0-3-5-7 || 1-8/7-5/4-11/8 || zeus ||
|| 4 || 0-3-5-8 || 1-8/7-5/4-10/7 || valinorsmic ||
|| 5 || 0-2-4-9 || 1-12/11-6/5-3/2 || utonal ||
|| 6 || 0-2-5-9 || 1-11/10-5/4-3/2 || zeus ||
|| 7 || 0-2-7-9 || 1-11/10-11/8-3/2 || biyatismic ||
|| 8 || 0-4-7-9 || 1-6/5-11/8-3/2 || zeus ||
|| 9 || 0-5-7-9 || 1-5/4-11/8-3/2 || otonal ||
|| 10 || 0-2-5-10 || 1-11/10-5/4-11/7 || valinorsmic ||
|| 11 || 0-3-5-10 || 1-8/7-5/4-11/7 || valinorsmic ||
|| 12 || 0-2-7-10 || 1-11/10-11/8-11/7 || utonal ||
|| 13 || 0-3-7-10 || 1-8/7-11/8-11/7 || keenanismic ||
|| 14 || 0-5-7-10 || 1-5/4-11/8-11/7 || valinorsmic ||
|| 15 || 0-3-8-10 || 1-8/7-10/7-11/7 || otonal ||
|| 16 || 0-5-8-10 || 1-5/4-10/7-11/7 || valinorsmic ||
|| 17 || 0-2-4-11 || 1-11/10-6/5-18/11 || biyatismic ||
|| 18 || 0-2-7-11 || 1-11/10-11/8-18/11 || biyatismic ||
|| 19 || 0-3-7-11 || 1-8/7-11/8-18/11 || valentine ||
|| 20 || 0-4-7-11 || 1-6/5-11/8-18/11 || zeus ||
|| 21 || 0-3-8-11 || 1-8/7-10/7-18/11 || werckismic ||
|| 22 || 0-4-8-11 || 1-6/5-10/7-18/11 || valentine ||
|| 23 || 0-2-9-11 || 1-12/11-3/2-18/11 || ambitonal ||
|| 24 || 0-4-9-11 || 1-6/5-3/2-18/11 || biyatismic ||
|| 25 || 0-7-9-11 || 1-11/8-3/2-18/11 || biyatismic ||
|| 26 || 0-2-4-12 || 1-12/11-6/5-12/7 || utonal ||
|| 27 || 0-2-5-12 || 1-11/10-5/4-12/7 || zeus ||
|| 28 || 0-3-5-12 || 1-8/7-5/4-12/7 || zeus ||
|| 29 || 0-2-7-12 || 1-11/10-11/8-12/7 || zeus ||
|| 30 || 0-3-7-12 || 1-8/7-11/8-12/7 || keenanismic ||
|| 31 || 0-4-7-12 || 1-6/5-11/8-12/7 || keenanismic ||
|| 32 || 0-5-7-12 || 1-5/4-11/8-12/7 || keenanismic ||
|| 33 || 0-3-8-12 || 1-8/7-10/7-12/7 || otonal ||
|| 34 || 0-4-8-12 || 1-6/5-10/7-12/7 || starling ||
|| 35 || 0-5-8-12 || 1-5/4-10/7-12/7 || keenanismic ||
|| 36 || 0-2-9-12 || 1-12/11-3/2-12/7 || utonal ||
|| 37 || 0-4-9-12 || 1-6/5-3/2-12/7 || utonal ||
|| 38 || 0-5-9-12 || 1-5/4-3/2-12/7 || keenanismic ||
|| 39 || 0-7-9-12 || 1-11/8-3/2-12/7 || zeus ||
|| 40 || 0-2-10-12 || 1-11/10-11/7-12/7 || biyatismic ||
|| 41 || 0-3-10-12 || 1-8/7-11/7-12/7 || otonal ||
|| 42 || 0-5-10-12 || 1-5/4-11/7-12/7 || zeus ||
|| 43 || 0-7-10-12 || 1-11/8-11/7-12/7 || zeus ||
|| 44 || 0-8-10-12 || 1-10/7-11/7-12/7 || otonal ||
|| 45 || 0-2-4-13 || 1-11/10-6/5-9/5 || otonal ||
|| 46 || 0-2-5-13 || 1-11/10-5/4-9/5 || thrush ||
|| 47 || 0-3-5-13 || 1-8/7-5/4-9/5 || thrush ||
|| 48 || 0-3-8-13 || 1-8/7-10/7-9/5 || thrush ||
|| 49 || 0-4-8-13 || 1-6/5-10/7-9/5 || starling ||
|| 50 || 0-5-8-13 || 1-5/4-10/7-9/5 || starling ||
|| 51 || 0-2-9-13 || 1-11/10-3/2-9/5 || biyatismic ||
|| 52 || 0-4-9-13 || 1-6/5-3/2-9/5 || ambitonal ||
|| 53 || 0-5-9-13 || 1-5/4-3/2-9/5 || starling ||
|| 54 || 0-2-10-13 || 1-11/10-11/7-9/5 || werckismic ||
|| 55 || 0-3-10-13 || 1-8/7-11/7-9/5 || werckismic ||
|| 56 || 0-5-10-13 || 1-5/4-11/7-9/5 || thrush ||
|| 57 || 0-8-10-13 || 1-10/7-11/7-9/5 || thrush ||
|| 58 || 0-2-11-13 || 1-11/10-18/11-9/5 || biyatismic ||
|| 59 || 0-3-11-13 || 1-8/7-18/11-9/5 || werckismic ||
|| 60 || 0-4-11-13 || 1-6/5-18/11-9/5 || biyatismic ||
|| 61 || 0-8-11-13 || 1-10/7-18/11-9/5 || thrush ||
|| 62 || 0-9-11-13 || 1-3/2-18/11-9/5 || utonal ||
|| 63 || 0-5-7-18 || 1-5/4-11/8-9/8 || otonal ||
|| 64 || 0-5-8-18 || 1-5/4-10/7-9/8 || werckismic ||
|| 65 || 0-5-9-18 || 1-5/4-3/2-9/8 || otonal ||
|| 66 || 0-7-9-18 || 1-11/8-3/2-9/8 || otonal ||
|| 67 || 0-5-10-18 || 1-5/4-11/7-9/8 || thrush ||
|| 68 || 0-7-10-18 || 1-11/8-11/7-9/8 || werckismic ||
|| 69 || 0-8-10-18 || 1-10/7-11/7-9/8 || werckismic ||
|| 70 || 0-7-11-18 || 1-11/8-18/11-9/8 || biyatismic ||
|| 71 || 0-8-11-18 || 1-10/7-18/11-9/8 || werckismic ||
|| 72 || 0-9-11-18 || 1-3/2-18/11-9/8 || utonal ||
|| 73 || 0-5-13-18 || 1-5/4-9/5-9/8 || starling ||
|| 74 || 0-8-13-18 || 1-10/7-9/5-9/8 || thrush ||
|| 75 || 0-9-13-18 || 1-3/2-9/5-9/8 || utonal ||
|| 76 || 0-10-13-18 || 1-11/7-9/5-9/8 || werckismic ||
|| 77 || 0-11-13-18 || 1-18/11-9/5-9/8 || utonal ||
|| 78 || 0-3-8-21 || 1-8/7-10/7-9/7 || otonal ||
|| 79 || 0-3-10-21 || 1-8/7-11/7-9/7 || otonal ||
|| 80 || 0-8-10-21 || 1-10/7-11/7-9/7 || otonal ||
|| 81 || 0-3-11-21 || 1-8/7-18/11-9/7 || werckismic ||
|| 82 || 0-8-11-21 || 1-10/7-18/11-9/7 || werckismic ||
|| 83 || 0-9-11-21 || 1-3/2-18/11-9/7 || utonal ||
|| 84 || 0-3-12-21 || 1-8/7-12/7-9/7 || otonal ||
|| 85 || 0-8-12-21 || 1-10/7-12/7-9/7 || otonal ||
|| 86 || 0-9-12-21 || 1-3/2-12/7-9/7 || ambitonal ||
|| 87 || 0-10-12-21 || 1-11/7-12/7-9/7 || otonal ||
|| 88 || 0-3-13-21 || 1-8/7-9/5-9/7 || werckismic ||
|| 89 || 0-8-13-21 || 1-10/7-9/5-9/7 || starling ||
|| 90 || 0-9-13-21 || 1-3/2-9/5-9/7 || utonal ||
|| 91 || 0-10-13-21 || 1-11/7-9/5-9/7 || werckismic ||
|| 92 || 0-11-13-21 || 1-18/11-9/5-9/7 || utonal ||
|| 93 || 0-8-18-21 || 1-10/7-9/8-9/7 || werckismic ||
|| 94 || 0-9-18-21 || 1-3/2-9/8-9/7 || utonal ||
|| 95 || 0-10-18-21 || 1-11/7-9/8-9/7 || werckismic ||
|| 96 || 0-11-18-21 || 1-18/11-9/8-9/7 || utonal ||
|| 97 || 0-13-18-21 || 1-9/5-9/8-9/7 || utonal ||

=Pentads= 
|| Number || Chord || Transversal || Type ||
|| 1 || 0-2-4-7-9 || 1-11/10-6/5-11/8-3/2 || zeus ||
|| 2 || 0-2-5-7-9 || 1-11/10-5/4-11/8-3/2 || zeus ||
|| 3 || 0-2-5-7-10 || 1-11/10-5/4-11/8-11/7 || valinorsmic ||
|| 4 || 0-3-5-7-10 || 1-8/7-5/4-11/8-11/7 || zeus ||
|| 5 || 0-3-5-8-10 || 1-8/7-5/4-10/7-11/7 || valinorsmic ||
|| 6 || 0-2-4-7-11 || 1-11/10-6/5-11/8-18/11 || zeus ||
|| 7 || 0-2-4-9-11 || 1-11/10-6/5-3/2-18/11 || biyatismic ||
|| 8 || 0-2-7-9-11 || 1-11/10-11/8-3/2-18/11 || biyatismic ||
|| 9 || 0-4-7-9-11 || 1-6/5-11/8-3/2-18/11 || zeus ||
|| 10 || 0-2-4-7-12 || 1-11/10-6/5-11/8-12/7 || zeus ||
|| 11 || 0-2-5-7-12 || 1-11/10-5/4-11/8-12/7 || zeus ||
|| 12 || 0-3-5-7-12 || 1-8/7-5/4-11/8-12/7 || zeus ||
|| 13 || 0-3-5-8-12 || 1-8/7-5/4-10/7-12/7 || zeus ||
|| 14 || 0-2-4-9-12 || 1-12/11-6/5-3/2-12/7 || utonal ||
|| 15 || 0-2-5-9-12 || 1-11/10-5/4-3/2-12/7 || zeus ||
|| 16 || 0-2-7-9-12 || 1-11/10-11/8-3/2-12/7 || zeus ||
|| 17 || 0-4-7-9-12 || 1-6/5-11/8-3/2-12/7 || zeus ||
|| 18 || 0-5-7-9-12 || 1-5/4-11/8-3/2-12/7 || zeus ||
|| 19 || 0-2-5-10-12 || 1-11/10-5/4-11/7-12/7 || zeus ||
|| 20 || 0-3-5-10-12 || 1-8/7-5/4-11/7-12/7 || zeus ||
|| 21 || 0-2-7-10-12 || 1-11/10-11/8-11/7-12/7 || zeus ||
|| 22 || 0-3-7-10-12 || 1-8/7-11/8-11/7-12/7 || zeus ||
|| 23 || 0-5-7-10-12 || 1-5/4-11/8-11/7-12/7 || zeus ||
|| 24 || 0-3-8-10-12 || 1-8/7-10/7-11/7-12/7 || otonal ||
|| 25 || 0-5-8-10-12 || 1-5/4-10/7-11/7-12/7 || zeus ||
|| 26 || 0-3-5-8-13 || 1-8/7-5/4-10/7-9/5 || thrush ||
|| 27 || 0-2-4-9-13 || 1-11/10-6/5-3/2-9/5 || biyatismic ||
|| 28 || 0-2-5-9-13 || 1-11/10-5/4-3/2-9/5 || valentine ||
|| 29 || 0-2-5-10-13 || 1-11/10-5/4-11/7-9/5 || thrush ||
|| 30 || 0-3-5-10-13 || 1-8/7-5/4-11/7-9/5 || thrush ||
|| 31 || 0-3-8-10-13 || 1-8/7-10/7-11/7-9/5 || thrush ||
|| 32 || 0-5-8-10-13 || 1-5/4-10/7-11/7-9/5 || thrush ||
|| 33 || 0-2-4-11-13 || 1-11/10-6/5-18/11-9/5 || biyatismic ||
|| 34 || 0-3-8-11-13 || 1-8/7-10/7-18/11-9/5 || thrush ||
|| 35 || 0-4-8-11-13 || 1-6/5-10/7-18/11-9/5 || valentine ||
|| 36 || 0-2-9-11-13 || 1-11/10-3/2-18/11-9/5 || biyatismic ||
|| 37 || 0-4-9-11-13 || 1-6/5-3/2-18/11-9/5 || biyatismic ||
|| 38 || 0-5-7-9-18 || 1-5/4-11/8-3/2-9/8 || otonal ||
|| 39 || 0-5-7-10-18 || 1-5/4-11/8-11/7-9/8 || thrush ||
|| 40 || 0-5-8-10-18 || 1-5/4-10/7-11/7-9/8 || thrush ||
|| 41 || 0-7-9-11-18 || 1-11/8-3/2-18/11-9/8 || biyatismic ||
|| 42 || 0-5-8-13-18 || 1-5/4-10/7-9/5-9/8 || thrush ||
|| 43 || 0-5-9-13-18 || 1-5/4-3/2-9/5-9/8 || starling ||
|| 44 || 0-5-10-13-18 || 1-5/4-11/7-9/5-9/8 || thrush ||
|| 45 || 0-8-10-13-18 || 1-10/7-11/7-9/5-9/8 || thrush ||
|| 46 || 0-8-11-13-18 || 1-10/7-18/11-9/5-9/8 || thrush ||
|| 47 || 0-9-11-13-18 || 1-3/2-18/11-9/5-9/8 || utonal ||
|| 48 || 0-3-8-10-21 || 1-8/7-10/7-11/7-9/7 || otonal ||
|| 49 || 0-3-8-11-21 || 1-8/7-10/7-18/11-9/7 || werckismic ||
|| 50 || 0-3-8-12-21 || 1-8/7-10/7-12/7-9/7 || otonal ||
|| 51 || 0-3-10-12-21 || 1-8/7-11/7-12/7-9/7 || otonal ||
|| 52 || 0-8-10-12-21 || 1-10/7-11/7-12/7-9/7 || otonal ||
|| 53 || 0-3-8-13-21 || 1-8/7-10/7-9/5-9/7 || thrush ||
|| 54 || 0-3-10-13-21 || 1-8/7-11/7-9/5-9/7 || werckismic ||
|| 55 || 0-8-10-13-21 || 1-10/7-11/7-9/5-9/7 || thrush ||
|| 56 || 0-3-11-13-21 || 1-8/7-18/11-9/5-9/7 || werckismic ||
|| 57 || 0-8-11-13-21 || 1-10/7-18/11-9/5-9/7 || thrush ||
|| 58 || 0-9-11-13-21 || 1-3/2-18/11-9/5-9/7 || utonal ||
|| 59 || 0-8-10-18-21 || 1-10/7-11/7-9/8-9/7 || werckismic ||
|| 60 || 0-8-11-18-21 || 1-10/7-18/11-9/8-9/7 || werckismic ||
|| 61 || 0-9-11-18-21 || 1-3/2-18/11-9/8-9/7 || utonal ||
|| 62 || 0-8-13-18-21 || 1-10/7-9/5-9/8-9/7 || thrush ||
|| 63 || 0-9-13-18-21 || 1-3/2-9/5-9/8-9/7 || utonal ||
|| 64 || 0-10-13-18-21 || 1-11/7-9/5-9/8-9/7 || werckismic ||
|| 65 || 0-11-13-18-21 || 1-18/11-9/5-9/8-9/7 || utonal ||

=Hexads= 
|| Number || Chord || Transversal || Type ||
|| 1 || 0-2-4-7-9-11 || 1-11/10-6/5-11/8-3/2-18/11 || zeus ||
|| 2 || 0-2-4-7-9-12 || 1-11/10-6/5-11/8-3/2-12/7 || zeus ||
|| 3 || 0-2-5-7-9-12 || 1-11/10-5/4-11/8-3/2-12/7 || zeus ||
|| 4 || 0-2-5-7-10-12 || 1-11/10-5/4-11/8-11/7-12/7 || zeus ||
|| 5 || 0-3-5-7-10-12 || 1-8/7-5/4-11/8-11/7-12/7 || zeus ||
|| 6 || 0-3-5-8-10-12 || 1-8/7-5/4-10/7-11/7-12/7 || zeus ||
|| 7 || 0-3-5-8-10-13 || 1-8/7-5/4-10/7-11/7-9/5 || thrush ||
|| 8 || 0-2-4-9-11-13 || 1-11/10-6/5-3/2-18/11-9/5 || biyatismic ||
|| 9 || 0-5-8-10-13-18 || 1-5/4-10/7-11/7-9/5-9/8 || thrush ||
|| 10 || 0-3-8-10-12-21 || 1-8/7-10/7-11/7-12/7-9/7 || otonal ||
|| 11 || 0-3-8-10-13-21 || 1-8/7-10/7-11/7-9/5-9/7 || thrush ||
|| 12 || 0-3-8-11-13-21 || 1-8/7-10/7-18/11-9/5-9/7 || thrush ||
|| 13 || 0-8-10-13-18-21 || 1-10/7-11/7-9/5-9/8-9/7 || thrush ||
|| 14 || 0-8-11-13-18-21 || 1-10/7-18/11-9/5-9/8-9/7 || thrush ||
|| 15 || 0-9-11-13-18-21 || 1-3/2-18/11-9/5-9/8-9/7 || utonal ||

Original HTML content:

<html><head><title>Chords of valentine</title></head><body>Below are listed the <a class="wiki_link" href="/Dyadic%20chord">dyadic chords</a> of 11-limit <a class="wiki_link" href="/Starling%20temperaments#Valentine%20temperament-11-limit">valentine temperament</a>. Typing the chords requires consideration of the fact that valentine conflates 12/11 and 11/10 and so also 11/6 and 20/11. If a transversal can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. If the chord is essentially tempered, it is analyzed in terms of the transversal which employs 11/10 and 20/11.<br />
<br />
If only 126/125 needs to be tempered out, the chord is labeled starling, if 121/120, biyatismic, if 176/175, valinorsmic, if 385/384, keenanismic, and if 441/440, werckismic. Chords which require any two of 121/120, 176/175 or 385/384 are labeled zeus, if they require any two of 126/125, 176/175 or 441/440, they are labeled thrush. Finally, if they require any three independent commas among those discussed above, it is labeled valentine.<br />
<br />
Valentine has MOS of size 15, 16, 31 and 46. It is readily observed from the list below that even the smallest of these is well-supplied with chords. Because <a class="wiki_link" href="/Carlos%20Alpha">Carlos Alpha</a> is the generator chain of valentine in the tuning with pure 3/2's, the list below is also a list of chords of Carlos Alpha, so long as the transversals are adjusted so that the notes are in the correct octave. This means that a number in a chord listed under &quot;chord&quot; less than 16 corresponds to a note in the transversal which should be left unaltered, whereas the notes from 16 to 21 correspond to transversal notes which should be adjusted up an octave. Hence, tetrad 8, the 0-2-5-9 chord with transversal 1-6/5-11/8-3/2, is an essentially zeus chord of Carlos Alpha as well as valentine. On the other hand, tetrad 76, 0-10-13-18 with transversal 1-11/7-9/5-9/8, corresponds to the werckismic 1-11/7-9/5-9/4 chord of Carlos Alpha.<br />
<br />
In other words, each chord here has an unlimited number of &quot;voicings&quot; in valentine temperament, but exactly one voicing in Carlos Alpha, because there are no octaves.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Triads"></a><!-- ws:end:WikiTextHeadingRule:0 -->Triads</h1>
 

<table class="wiki_table">
    <tr>
        <td>Number<br />
</td>
        <td>Chord<br />
</td>
        <td>Transversal<br />
</td>
        <td>Type<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>0-2-4<br />
</td>
        <td>1-11/10-6/5<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>0-2-5<br />
</td>
        <td>1-11/10-5/4<br />
</td>
        <td>valinorsmic<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>0-3-5<br />
</td>
        <td>1-8/7-5/4<br />
</td>
        <td>valinorsmic<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>0-2-7<br />
</td>
        <td>1-11/10-11/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>0-3-7<br />
</td>
        <td>1-8/7-11/8<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>0-4-7<br />
</td>
        <td>1-6/5-11/8<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>0-5-7<br />
</td>
        <td>1-5/4-11/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>0-3-8<br />
</td>
        <td>1-8/7-10/7<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>0-4-8<br />
</td>
        <td>1-6/5-10/7<br />
</td>
        <td>starling<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>0-5-8<br />
</td>
        <td>1-5/4-10/7<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>0-2-9<br />
</td>
        <td>1-12/11-3/2<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>0-4-9<br />
</td>
        <td>1-6/5-3/2<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>0-5-9<br />
</td>
        <td>1-5/4-3/2<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>0-7-9<br />
</td>
        <td>1-11/8-3/2<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>0-2-10<br />
</td>
        <td>1-11/10-11/7<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>0-3-10<br />
</td>
        <td>1-8/7-11/7<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>0-5-10<br />
</td>
        <td>1-5/4-11/7<br />
</td>
        <td>valinorsmic<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>0-7-10<br />
</td>
        <td>1-11/8-11/7<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>0-8-10<br />
</td>
        <td>1-10/7-11/7<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>0-2-11<br />
</td>
        <td>1-12/11-18/11<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>0-3-11<br />
</td>
        <td>1-8/7-18/11<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>0-4-11<br />
</td>
        <td>1-6/5-18/11<br />
</td>
        <td>biyatismic<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>0-7-11<br />
</td>
        <td>1-11/8-18/11<br />
</td>
        <td>biyatismic<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>0-8-11<br />
</td>
        <td>1-10/7-18/11<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>0-9-11<br />
</td>
        <td>1-3/2-18/11<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>0-2-12<br />
</td>
        <td>1-12/11-12/7<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>0-3-12<br />
</td>
        <td>1-8/7-12/7<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>0-4-12<br />
</td>
        <td>1-6/5-12/7<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>0-5-12<br />
</td>
        <td>1-5/4-12/7<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td>0-7-12<br />
</td>
        <td>1-11/8-12/7<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>0-8-12<br />
</td>
        <td>1-10/7-12/7<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>32<br />
</td>
        <td>0-9-12<br />
</td>
        <td>1-3/2-12/7<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>0-10-12<br />
</td>
        <td>1-11/7-12/7<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>34<br />
</td>
        <td>0-2-13<br />
</td>
        <td>1-11/10-9/5<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>35<br />
</td>
        <td>0-3-13<br />
</td>
        <td>1-8/7-9/5<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>36<br />
</td>
        <td>0-4-13<br />
</td>
        <td>1-6/5-9/5<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>37<br />
</td>
        <td>0-5-13<br />
</td>
        <td>1-5/4-9/5<br />
</td>
        <td>starling<br />
</td>
    </tr>
    <tr>
        <td>38<br />
</td>
        <td>0-8-13<br />
</td>
        <td>1-10/7-9/5<br />
</td>
        <td>starling<br />
</td>
    </tr>
    <tr>
        <td>39<br />
</td>
        <td>0-9-13<br />
</td>
        <td>1-3/2-9/5<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>40<br />
</td>
        <td>0-10-13<br />
</td>
        <td>1-11/7-9/5<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>41<br />
</td>
        <td>0-11-13<br />
</td>
        <td>1-18/11-9/5<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>42<br />
</td>
        <td>0-5-18<br />
</td>
        <td>1-5/4-9/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>43<br />
</td>
        <td>0-7-18<br />
</td>
        <td>1-11/8-9/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>44<br />
</td>
        <td>0-8-18<br />
</td>
        <td>1-10/7-9/8<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>45<br />
</td>
        <td>0-9-18<br />
</td>
        <td>1-3/2-9/8<br />
</td>
        <td>ambitonal<br />
</td>
    </tr>
    <tr>
        <td>46<br />
</td>
        <td>0-10-18<br />
</td>
        <td>1-11/7-9/8<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>47<br />
</td>
        <td>0-11-18<br />
</td>
        <td>1-18/11-9/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>48<br />
</td>
        <td>0-13-18<br />
</td>
        <td>1-9/5-9/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>49<br />
</td>
        <td>0-3-21<br />
</td>
        <td>1-8/7-9/7<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>50<br />
</td>
        <td>0-8-21<br />
</td>
        <td>1-10/7-9/7<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>51<br />
</td>
        <td>0-9-21<br />
</td>
        <td>1-3/2-9/7<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>52<br />
</td>
        <td>0-10-21<br />
</td>
        <td>1-11/7-9/7<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>53<br />
</td>
        <td>0-11-21<br />
</td>
        <td>1-18/11-9/7<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>54<br />
</td>
        <td>0-12-21<br />
</td>
        <td>1-12/7-9/7<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>55<br />
</td>
        <td>0-13-21<br />
</td>
        <td>1-9/5-9/7<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>56<br />
</td>
        <td>0-18-21<br />
</td>
        <td>1-9/8-9/7<br />
</td>
        <td>utonal<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Tetrads"></a><!-- ws:end:WikiTextHeadingRule:2 -->Tetrads</h1>
 

<table class="wiki_table">
    <tr>
        <td>Number<br />
</td>
        <td>Chord<br />
</td>
        <td>Transversal<br />
</td>
        <td>Type<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>0-2-4-7<br />
</td>
        <td>1-11/10-6/5-11/8<br />
</td>
        <td>zeus<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>0-2-5-7<br />
</td>
        <td>1-11/10-5/4-11/8<br />
</td>
        <td>valinorsmic<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>0-3-5-7<br />
</td>
        <td>1-8/7-5/4-11/8<br />
</td>
        <td>zeus<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>0-3-5-8<br />
</td>
        <td>1-8/7-5/4-10/7<br />
</td>
        <td>valinorsmic<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>0-2-4-9<br />
</td>
        <td>1-12/11-6/5-3/2<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>0-2-5-9<br />
</td>
        <td>1-11/10-5/4-3/2<br />
</td>
        <td>zeus<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>0-2-7-9<br />
</td>
        <td>1-11/10-11/8-3/2<br />
</td>
        <td>biyatismic<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>0-4-7-9<br />
</td>
        <td>1-6/5-11/8-3/2<br />
</td>
        <td>zeus<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>0-5-7-9<br />
</td>
        <td>1-5/4-11/8-3/2<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>0-2-5-10<br />
</td>
        <td>1-11/10-5/4-11/7<br />
</td>
        <td>valinorsmic<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>0-3-5-10<br />
</td>
        <td>1-8/7-5/4-11/7<br />
</td>
        <td>valinorsmic<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>0-2-7-10<br />
</td>
        <td>1-11/10-11/8-11/7<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>0-3-7-10<br />
</td>
        <td>1-8/7-11/8-11/7<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>0-5-7-10<br />
</td>
        <td>1-5/4-11/8-11/7<br />
</td>
        <td>valinorsmic<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>0-3-8-10<br />
</td>
        <td>1-8/7-10/7-11/7<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>0-5-8-10<br />
</td>
        <td>1-5/4-10/7-11/7<br />
</td>
        <td>valinorsmic<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>0-2-4-11<br />
</td>
        <td>1-11/10-6/5-18/11<br />
</td>
        <td>biyatismic<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>0-2-7-11<br />
</td>
        <td>1-11/10-11/8-18/11<br />
</td>
        <td>biyatismic<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>0-3-7-11<br />
</td>
        <td>1-8/7-11/8-18/11<br />
</td>
        <td>valentine<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>0-4-7-11<br />
</td>
        <td>1-6/5-11/8-18/11<br />
</td>
        <td>zeus<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>0-3-8-11<br />
</td>
        <td>1-8/7-10/7-18/11<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>0-4-8-11<br />
</td>
        <td>1-6/5-10/7-18/11<br />
</td>
        <td>valentine<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>0-2-9-11<br />
</td>
        <td>1-12/11-3/2-18/11<br />
</td>
        <td>ambitonal<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>0-4-9-11<br />
</td>
        <td>1-6/5-3/2-18/11<br />
</td>
        <td>biyatismic<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>0-7-9-11<br />
</td>
        <td>1-11/8-3/2-18/11<br />
</td>
        <td>biyatismic<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>0-2-4-12<br />
</td>
        <td>1-12/11-6/5-12/7<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>0-2-5-12<br />
</td>
        <td>1-11/10-5/4-12/7<br />
</td>
        <td>zeus<br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>0-3-5-12<br />
</td>
        <td>1-8/7-5/4-12/7<br />
</td>
        <td>zeus<br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>0-2-7-12<br />
</td>
        <td>1-11/10-11/8-12/7<br />
</td>
        <td>zeus<br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td>0-3-7-12<br />
</td>
        <td>1-8/7-11/8-12/7<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>0-4-7-12<br />
</td>
        <td>1-6/5-11/8-12/7<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>32<br />
</td>
        <td>0-5-7-12<br />
</td>
        <td>1-5/4-11/8-12/7<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>0-3-8-12<br />
</td>
        <td>1-8/7-10/7-12/7<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>34<br />
</td>
        <td>0-4-8-12<br />
</td>
        <td>1-6/5-10/7-12/7<br />
</td>
        <td>starling<br />
</td>
    </tr>
    <tr>
        <td>35<br />
</td>
        <td>0-5-8-12<br />
</td>
        <td>1-5/4-10/7-12/7<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>36<br />
</td>
        <td>0-2-9-12<br />
</td>
        <td>1-12/11-3/2-12/7<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>37<br />
</td>
        <td>0-4-9-12<br />
</td>
        <td>1-6/5-3/2-12/7<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>38<br />
</td>
        <td>0-5-9-12<br />
</td>
        <td>1-5/4-3/2-12/7<br />
</td>
        <td>keenanismic<br />
</td>
    </tr>
    <tr>
        <td>39<br />
</td>
        <td>0-7-9-12<br />
</td>
        <td>1-11/8-3/2-12/7<br />
</td>
        <td>zeus<br />
</td>
    </tr>
    <tr>
        <td>40<br />
</td>
        <td>0-2-10-12<br />
</td>
        <td>1-11/10-11/7-12/7<br />
</td>
        <td>biyatismic<br />
</td>
    </tr>
    <tr>
        <td>41<br />
</td>
        <td>0-3-10-12<br />
</td>
        <td>1-8/7-11/7-12/7<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>42<br />
</td>
        <td>0-5-10-12<br />
</td>
        <td>1-5/4-11/7-12/7<br />
</td>
        <td>zeus<br />
</td>
    </tr>
    <tr>
        <td>43<br />
</td>
        <td>0-7-10-12<br />
</td>
        <td>1-11/8-11/7-12/7<br />
</td>
        <td>zeus<br />
</td>
    </tr>
    <tr>
        <td>44<br />
</td>
        <td>0-8-10-12<br />
</td>
        <td>1-10/7-11/7-12/7<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>45<br />
</td>
        <td>0-2-4-13<br />
</td>
        <td>1-11/10-6/5-9/5<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>46<br />
</td>
        <td>0-2-5-13<br />
</td>
        <td>1-11/10-5/4-9/5<br />
</td>
        <td>thrush<br />
</td>
    </tr>
    <tr>
        <td>47<br />
</td>
        <td>0-3-5-13<br />
</td>
        <td>1-8/7-5/4-9/5<br />
</td>
        <td>thrush<br />
</td>
    </tr>
    <tr>
        <td>48<br />
</td>
        <td>0-3-8-13<br />
</td>
        <td>1-8/7-10/7-9/5<br />
</td>
        <td>thrush<br />
</td>
    </tr>
    <tr>
        <td>49<br />
</td>
        <td>0-4-8-13<br />
</td>
        <td>1-6/5-10/7-9/5<br />
</td>
        <td>starling<br />
</td>
    </tr>
    <tr>
        <td>50<br />
</td>
        <td>0-5-8-13<br />
</td>
        <td>1-5/4-10/7-9/5<br />
</td>
        <td>starling<br />
</td>
    </tr>
    <tr>
        <td>51<br />
</td>
        <td>0-2-9-13<br />
</td>
        <td>1-11/10-3/2-9/5<br />
</td>
        <td>biyatismic<br />
</td>
    </tr>
    <tr>
        <td>52<br />
</td>
        <td>0-4-9-13<br />
</td>
        <td>1-6/5-3/2-9/5<br />
</td>
        <td>ambitonal<br />
</td>
    </tr>
    <tr>
        <td>53<br />
</td>
        <td>0-5-9-13<br />
</td>
        <td>1-5/4-3/2-9/5<br />
</td>
        <td>starling<br />
</td>
    </tr>
    <tr>
        <td>54<br />
</td>
        <td>0-2-10-13<br />
</td>
        <td>1-11/10-11/7-9/5<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>55<br />
</td>
        <td>0-3-10-13<br />
</td>
        <td>1-8/7-11/7-9/5<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>56<br />
</td>
        <td>0-5-10-13<br />
</td>
        <td>1-5/4-11/7-9/5<br />
</td>
        <td>thrush<br />
</td>
    </tr>
    <tr>
        <td>57<br />
</td>
        <td>0-8-10-13<br />
</td>
        <td>1-10/7-11/7-9/5<br />
</td>
        <td>thrush<br />
</td>
    </tr>
    <tr>
        <td>58<br />
</td>
        <td>0-2-11-13<br />
</td>
        <td>1-11/10-18/11-9/5<br />
</td>
        <td>biyatismic<br />
</td>
    </tr>
    <tr>
        <td>59<br />
</td>
        <td>0-3-11-13<br />
</td>
        <td>1-8/7-18/11-9/5<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>60<br />
</td>
        <td>0-4-11-13<br />
</td>
        <td>1-6/5-18/11-9/5<br />
</td>
        <td>biyatismic<br />
</td>
    </tr>
    <tr>
        <td>61<br />
</td>
        <td>0-8-11-13<br />
</td>
        <td>1-10/7-18/11-9/5<br />
</td>
        <td>thrush<br />
</td>
    </tr>
    <tr>
        <td>62<br />
</td>
        <td>0-9-11-13<br />
</td>
        <td>1-3/2-18/11-9/5<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>63<br />
</td>
        <td>0-5-7-18<br />
</td>
        <td>1-5/4-11/8-9/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>64<br />
</td>
        <td>0-5-8-18<br />
</td>
        <td>1-5/4-10/7-9/8<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>65<br />
</td>
        <td>0-5-9-18<br />
</td>
        <td>1-5/4-3/2-9/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>66<br />
</td>
        <td>0-7-9-18<br />
</td>
        <td>1-11/8-3/2-9/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>67<br />
</td>
        <td>0-5-10-18<br />
</td>
        <td>1-5/4-11/7-9/8<br />
</td>
        <td>thrush<br />
</td>
    </tr>
    <tr>
        <td>68<br />
</td>
        <td>0-7-10-18<br />
</td>
        <td>1-11/8-11/7-9/8<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>69<br />
</td>
        <td>0-8-10-18<br />
</td>
        <td>1-10/7-11/7-9/8<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>70<br />
</td>
        <td>0-7-11-18<br />
</td>
        <td>1-11/8-18/11-9/8<br />
</td>
        <td>biyatismic<br />
</td>
    </tr>
    <tr>
        <td>71<br />
</td>
        <td>0-8-11-18<br />
</td>
        <td>1-10/7-18/11-9/8<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>72<br />
</td>
        <td>0-9-11-18<br />
</td>
        <td>1-3/2-18/11-9/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>73<br />
</td>
        <td>0-5-13-18<br />
</td>
        <td>1-5/4-9/5-9/8<br />
</td>
        <td>starling<br />
</td>
    </tr>
    <tr>
        <td>74<br />
</td>
        <td>0-8-13-18<br />
</td>
        <td>1-10/7-9/5-9/8<br />
</td>
        <td>thrush<br />
</td>
    </tr>
    <tr>
        <td>75<br />
</td>
        <td>0-9-13-18<br />
</td>
        <td>1-3/2-9/5-9/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>76<br />
</td>
        <td>0-10-13-18<br />
</td>
        <td>1-11/7-9/5-9/8<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>77<br />
</td>
        <td>0-11-13-18<br />
</td>
        <td>1-18/11-9/5-9/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>78<br />
</td>
        <td>0-3-8-21<br />
</td>
        <td>1-8/7-10/7-9/7<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>79<br />
</td>
        <td>0-3-10-21<br />
</td>
        <td>1-8/7-11/7-9/7<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>80<br />
</td>
        <td>0-8-10-21<br />
</td>
        <td>1-10/7-11/7-9/7<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>81<br />
</td>
        <td>0-3-11-21<br />
</td>
        <td>1-8/7-18/11-9/7<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>82<br />
</td>
        <td>0-8-11-21<br />
</td>
        <td>1-10/7-18/11-9/7<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>83<br />
</td>
        <td>0-9-11-21<br />
</td>
        <td>1-3/2-18/11-9/7<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>84<br />
</td>
        <td>0-3-12-21<br />
</td>
        <td>1-8/7-12/7-9/7<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>85<br />
</td>
        <td>0-8-12-21<br />
</td>
        <td>1-10/7-12/7-9/7<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>86<br />
</td>
        <td>0-9-12-21<br />
</td>
        <td>1-3/2-12/7-9/7<br />
</td>
        <td>ambitonal<br />
</td>
    </tr>
    <tr>
        <td>87<br />
</td>
        <td>0-10-12-21<br />
</td>
        <td>1-11/7-12/7-9/7<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>88<br />
</td>
        <td>0-3-13-21<br />
</td>
        <td>1-8/7-9/5-9/7<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>89<br />
</td>
        <td>0-8-13-21<br />
</td>
        <td>1-10/7-9/5-9/7<br />
</td>
        <td>starling<br />
</td>
    </tr>
    <tr>
        <td>90<br />
</td>
        <td>0-9-13-21<br />
</td>
        <td>1-3/2-9/5-9/7<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>91<br />
</td>
        <td>0-10-13-21<br />
</td>
        <td>1-11/7-9/5-9/7<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>92<br />
</td>
        <td>0-11-13-21<br />
</td>
        <td>1-18/11-9/5-9/7<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>93<br />
</td>
        <td>0-8-18-21<br />
</td>
        <td>1-10/7-9/8-9/7<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>94<br />
</td>
        <td>0-9-18-21<br />
</td>
        <td>1-3/2-9/8-9/7<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>95<br />
</td>
        <td>0-10-18-21<br />
</td>
        <td>1-11/7-9/8-9/7<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>96<br />
</td>
        <td>0-11-18-21<br />
</td>
        <td>1-18/11-9/8-9/7<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>97<br />
</td>
        <td>0-13-18-21<br />
</td>
        <td>1-9/5-9/8-9/7<br />
</td>
        <td>utonal<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Pentads"></a><!-- ws:end:WikiTextHeadingRule:4 -->Pentads</h1>
 

<table class="wiki_table">
    <tr>
        <td>Number<br />
</td>
        <td>Chord<br />
</td>
        <td>Transversal<br />
</td>
        <td>Type<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>0-2-4-7-9<br />
</td>
        <td>1-11/10-6/5-11/8-3/2<br />
</td>
        <td>zeus<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>0-2-5-7-9<br />
</td>
        <td>1-11/10-5/4-11/8-3/2<br />
</td>
        <td>zeus<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>0-2-5-7-10<br />
</td>
        <td>1-11/10-5/4-11/8-11/7<br />
</td>
        <td>valinorsmic<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>0-3-5-7-10<br />
</td>
        <td>1-8/7-5/4-11/8-11/7<br />
</td>
        <td>zeus<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>0-3-5-8-10<br />
</td>
        <td>1-8/7-5/4-10/7-11/7<br />
</td>
        <td>valinorsmic<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>0-2-4-7-11<br />
</td>
        <td>1-11/10-6/5-11/8-18/11<br />
</td>
        <td>zeus<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>0-2-4-9-11<br />
</td>
        <td>1-11/10-6/5-3/2-18/11<br />
</td>
        <td>biyatismic<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>0-2-7-9-11<br />
</td>
        <td>1-11/10-11/8-3/2-18/11<br />
</td>
        <td>biyatismic<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>0-4-7-9-11<br />
</td>
        <td>1-6/5-11/8-3/2-18/11<br />
</td>
        <td>zeus<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>0-2-4-7-12<br />
</td>
        <td>1-11/10-6/5-11/8-12/7<br />
</td>
        <td>zeus<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>0-2-5-7-12<br />
</td>
        <td>1-11/10-5/4-11/8-12/7<br />
</td>
        <td>zeus<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>0-3-5-7-12<br />
</td>
        <td>1-8/7-5/4-11/8-12/7<br />
</td>
        <td>zeus<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>0-3-5-8-12<br />
</td>
        <td>1-8/7-5/4-10/7-12/7<br />
</td>
        <td>zeus<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>0-2-4-9-12<br />
</td>
        <td>1-12/11-6/5-3/2-12/7<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>0-2-5-9-12<br />
</td>
        <td>1-11/10-5/4-3/2-12/7<br />
</td>
        <td>zeus<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>0-2-7-9-12<br />
</td>
        <td>1-11/10-11/8-3/2-12/7<br />
</td>
        <td>zeus<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>0-4-7-9-12<br />
</td>
        <td>1-6/5-11/8-3/2-12/7<br />
</td>
        <td>zeus<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>0-5-7-9-12<br />
</td>
        <td>1-5/4-11/8-3/2-12/7<br />
</td>
        <td>zeus<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>0-2-5-10-12<br />
</td>
        <td>1-11/10-5/4-11/7-12/7<br />
</td>
        <td>zeus<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>0-3-5-10-12<br />
</td>
        <td>1-8/7-5/4-11/7-12/7<br />
</td>
        <td>zeus<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>0-2-7-10-12<br />
</td>
        <td>1-11/10-11/8-11/7-12/7<br />
</td>
        <td>zeus<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>0-3-7-10-12<br />
</td>
        <td>1-8/7-11/8-11/7-12/7<br />
</td>
        <td>zeus<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>0-5-7-10-12<br />
</td>
        <td>1-5/4-11/8-11/7-12/7<br />
</td>
        <td>zeus<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>0-3-8-10-12<br />
</td>
        <td>1-8/7-10/7-11/7-12/7<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>0-5-8-10-12<br />
</td>
        <td>1-5/4-10/7-11/7-12/7<br />
</td>
        <td>zeus<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>0-3-5-8-13<br />
</td>
        <td>1-8/7-5/4-10/7-9/5<br />
</td>
        <td>thrush<br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>0-2-4-9-13<br />
</td>
        <td>1-11/10-6/5-3/2-9/5<br />
</td>
        <td>biyatismic<br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>0-2-5-9-13<br />
</td>
        <td>1-11/10-5/4-3/2-9/5<br />
</td>
        <td>valentine<br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>0-2-5-10-13<br />
</td>
        <td>1-11/10-5/4-11/7-9/5<br />
</td>
        <td>thrush<br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td>0-3-5-10-13<br />
</td>
        <td>1-8/7-5/4-11/7-9/5<br />
</td>
        <td>thrush<br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>0-3-8-10-13<br />
</td>
        <td>1-8/7-10/7-11/7-9/5<br />
</td>
        <td>thrush<br />
</td>
    </tr>
    <tr>
        <td>32<br />
</td>
        <td>0-5-8-10-13<br />
</td>
        <td>1-5/4-10/7-11/7-9/5<br />
</td>
        <td>thrush<br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>0-2-4-11-13<br />
</td>
        <td>1-11/10-6/5-18/11-9/5<br />
</td>
        <td>biyatismic<br />
</td>
    </tr>
    <tr>
        <td>34<br />
</td>
        <td>0-3-8-11-13<br />
</td>
        <td>1-8/7-10/7-18/11-9/5<br />
</td>
        <td>thrush<br />
</td>
    </tr>
    <tr>
        <td>35<br />
</td>
        <td>0-4-8-11-13<br />
</td>
        <td>1-6/5-10/7-18/11-9/5<br />
</td>
        <td>valentine<br />
</td>
    </tr>
    <tr>
        <td>36<br />
</td>
        <td>0-2-9-11-13<br />
</td>
        <td>1-11/10-3/2-18/11-9/5<br />
</td>
        <td>biyatismic<br />
</td>
    </tr>
    <tr>
        <td>37<br />
</td>
        <td>0-4-9-11-13<br />
</td>
        <td>1-6/5-3/2-18/11-9/5<br />
</td>
        <td>biyatismic<br />
</td>
    </tr>
    <tr>
        <td>38<br />
</td>
        <td>0-5-7-9-18<br />
</td>
        <td>1-5/4-11/8-3/2-9/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>39<br />
</td>
        <td>0-5-7-10-18<br />
</td>
        <td>1-5/4-11/8-11/7-9/8<br />
</td>
        <td>thrush<br />
</td>
    </tr>
    <tr>
        <td>40<br />
</td>
        <td>0-5-8-10-18<br />
</td>
        <td>1-5/4-10/7-11/7-9/8<br />
</td>
        <td>thrush<br />
</td>
    </tr>
    <tr>
        <td>41<br />
</td>
        <td>0-7-9-11-18<br />
</td>
        <td>1-11/8-3/2-18/11-9/8<br />
</td>
        <td>biyatismic<br />
</td>
    </tr>
    <tr>
        <td>42<br />
</td>
        <td>0-5-8-13-18<br />
</td>
        <td>1-5/4-10/7-9/5-9/8<br />
</td>
        <td>thrush<br />
</td>
    </tr>
    <tr>
        <td>43<br />
</td>
        <td>0-5-9-13-18<br />
</td>
        <td>1-5/4-3/2-9/5-9/8<br />
</td>
        <td>starling<br />
</td>
    </tr>
    <tr>
        <td>44<br />
</td>
        <td>0-5-10-13-18<br />
</td>
        <td>1-5/4-11/7-9/5-9/8<br />
</td>
        <td>thrush<br />
</td>
    </tr>
    <tr>
        <td>45<br />
</td>
        <td>0-8-10-13-18<br />
</td>
        <td>1-10/7-11/7-9/5-9/8<br />
</td>
        <td>thrush<br />
</td>
    </tr>
    <tr>
        <td>46<br />
</td>
        <td>0-8-11-13-18<br />
</td>
        <td>1-10/7-18/11-9/5-9/8<br />
</td>
        <td>thrush<br />
</td>
    </tr>
    <tr>
        <td>47<br />
</td>
        <td>0-9-11-13-18<br />
</td>
        <td>1-3/2-18/11-9/5-9/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>48<br />
</td>
        <td>0-3-8-10-21<br />
</td>
        <td>1-8/7-10/7-11/7-9/7<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>49<br />
</td>
        <td>0-3-8-11-21<br />
</td>
        <td>1-8/7-10/7-18/11-9/7<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>50<br />
</td>
        <td>0-3-8-12-21<br />
</td>
        <td>1-8/7-10/7-12/7-9/7<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>51<br />
</td>
        <td>0-3-10-12-21<br />
</td>
        <td>1-8/7-11/7-12/7-9/7<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>52<br />
</td>
        <td>0-8-10-12-21<br />
</td>
        <td>1-10/7-11/7-12/7-9/7<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>53<br />
</td>
        <td>0-3-8-13-21<br />
</td>
        <td>1-8/7-10/7-9/5-9/7<br />
</td>
        <td>thrush<br />
</td>
    </tr>
    <tr>
        <td>54<br />
</td>
        <td>0-3-10-13-21<br />
</td>
        <td>1-8/7-11/7-9/5-9/7<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>55<br />
</td>
        <td>0-8-10-13-21<br />
</td>
        <td>1-10/7-11/7-9/5-9/7<br />
</td>
        <td>thrush<br />
</td>
    </tr>
    <tr>
        <td>56<br />
</td>
        <td>0-3-11-13-21<br />
</td>
        <td>1-8/7-18/11-9/5-9/7<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>57<br />
</td>
        <td>0-8-11-13-21<br />
</td>
        <td>1-10/7-18/11-9/5-9/7<br />
</td>
        <td>thrush<br />
</td>
    </tr>
    <tr>
        <td>58<br />
</td>
        <td>0-9-11-13-21<br />
</td>
        <td>1-3/2-18/11-9/5-9/7<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>59<br />
</td>
        <td>0-8-10-18-21<br />
</td>
        <td>1-10/7-11/7-9/8-9/7<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>60<br />
</td>
        <td>0-8-11-18-21<br />
</td>
        <td>1-10/7-18/11-9/8-9/7<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>61<br />
</td>
        <td>0-9-11-18-21<br />
</td>
        <td>1-3/2-18/11-9/8-9/7<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>62<br />
</td>
        <td>0-8-13-18-21<br />
</td>
        <td>1-10/7-9/5-9/8-9/7<br />
</td>
        <td>thrush<br />
</td>
    </tr>
    <tr>
        <td>63<br />
</td>
        <td>0-9-13-18-21<br />
</td>
        <td>1-3/2-9/5-9/8-9/7<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>64<br />
</td>
        <td>0-10-13-18-21<br />
</td>
        <td>1-11/7-9/5-9/8-9/7<br />
</td>
        <td>werckismic<br />
</td>
    </tr>
    <tr>
        <td>65<br />
</td>
        <td>0-11-13-18-21<br />
</td>
        <td>1-18/11-9/5-9/8-9/7<br />
</td>
        <td>utonal<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Hexads"></a><!-- ws:end:WikiTextHeadingRule:6 -->Hexads</h1>
 

<table class="wiki_table">
    <tr>
        <td>Number<br />
</td>
        <td>Chord<br />
</td>
        <td>Transversal<br />
</td>
        <td>Type<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>0-2-4-7-9-11<br />
</td>
        <td>1-11/10-6/5-11/8-3/2-18/11<br />
</td>
        <td>zeus<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>0-2-4-7-9-12<br />
</td>
        <td>1-11/10-6/5-11/8-3/2-12/7<br />
</td>
        <td>zeus<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>0-2-5-7-9-12<br />
</td>
        <td>1-11/10-5/4-11/8-3/2-12/7<br />
</td>
        <td>zeus<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>0-2-5-7-10-12<br />
</td>
        <td>1-11/10-5/4-11/8-11/7-12/7<br />
</td>
        <td>zeus<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>0-3-5-7-10-12<br />
</td>
        <td>1-8/7-5/4-11/8-11/7-12/7<br />
</td>
        <td>zeus<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>0-3-5-8-10-12<br />
</td>
        <td>1-8/7-5/4-10/7-11/7-12/7<br />
</td>
        <td>zeus<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>0-3-5-8-10-13<br />
</td>
        <td>1-8/7-5/4-10/7-11/7-9/5<br />
</td>
        <td>thrush<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>0-2-4-9-11-13<br />
</td>
        <td>1-11/10-6/5-3/2-18/11-9/5<br />
</td>
        <td>biyatismic<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>0-5-8-10-13-18<br />
</td>
        <td>1-5/4-10/7-11/7-9/5-9/8<br />
</td>
        <td>thrush<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>0-3-8-10-12-21<br />
</td>
        <td>1-8/7-10/7-11/7-12/7-9/7<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>0-3-8-10-13-21<br />
</td>
        <td>1-8/7-10/7-11/7-9/5-9/7<br />
</td>
        <td>thrush<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>0-3-8-11-13-21<br />
</td>
        <td>1-8/7-10/7-18/11-9/5-9/7<br />
</td>
        <td>thrush<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>0-8-10-13-18-21<br />
</td>
        <td>1-10/7-11/7-9/5-9/8-9/7<br />
</td>
        <td>thrush<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>0-8-11-13-18-21<br />
</td>
        <td>1-10/7-18/11-9/5-9/8-9/7<br />
</td>
        <td>thrush<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>0-9-11-13-18-21<br />
</td>
        <td>1-3/2-18/11-9/5-9/8-9/7<br />
</td>
        <td>utonal<br />
</td>
    </tr>
</table>

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