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Wikispaces>genewardsmith
**Imported revision 526796008 - Original comment: **
Wikispaces>jdfreivald
**Imported revision 531298704 - Original comment: Added 41 EDO notation and audio examples of the triads.**
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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>2014-10-16 13:05:37 UTC</tt>.<br>
: This revision was by author [[User:jdfreivald|jdfreivald]] and made on <tt>2014-11-16 21:55:21 UTC</tt>.<br>
: The original revision id was <tt>526796008</tt>.<br>
: The original revision id was <tt>531298704</tt>.<br>
: The revision comment was: <tt></tt><br>
: The revision comment was: <tt>Added 41 EDO notation and audio examples of the triads.</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 [[Gamelismic clan#Miracle|miracle temperament]]. They are listed in order of increasing [[Graham complexity]], with hash complexity used to break ties. For any linear temperament, if we chose a generator, we may put any octave-equivalent chord of the temperament in a canonical form by representing it as a set of nonnegative integers, starting with 0, which are the number of generator steps giving an octave-equivalent note class in the chord. If S is such a set, the sum Σ 2^s for all s∊S provides a unique odd number encoding the chord, and the logarithm base two of this number is the hash complexity, listed under the heading "Hash" below. The floor of hash complexity, that is, the greatest integer less than the hash complexity, is equal to the Graham complexity. The heading "transversal" shows a JI chord whose intervals temper to the marvel chord. Under "type" it says otonal if it is an essentially just chord best understood in terms of the overtone series, utonal if it is the inversion of an otonal chord, and ambitonal if it can equally well be seen as otonal or utonal. The other names denote types of essentially tempered chord, giving the least amount of tempering needed to define the chord, so that if for example it says "werckismic" only 441/440 needs to be tempered out. Also, "marvel" denotes 9 odd limit (7-limit) marvel, whereas "unimarvel" means 11-limit marvel. The generator used below is the standard choice for miracle temperament, the secor. 16/15~15/14. However, it should be noted that the choice of generator does not effect the list of chords, only how those chords are interpreted. Does 0-7-13 denote the major triad or the minor triad? It's on the list of chords either way, but with a secor generator it's the major triad.
<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 [[Gamelismic clan#Miracle|miracle temperament]]. They are listed in order of increasing [[Graham complexity]], with hash complexity used to break ties. For any linear temperament, if we chose a generator, we may put any octave-equivalent chord of the temperament in a canonical form by representing it as a set of nonnegative integers, starting with 0, which are the number of generator steps giving an octave-equivalent note class in the chord. If S is such a set, the sum Σ 2^s for all s∊S provides a unique odd number encoding the chord, and the logarithm base two of this number is the hash complexity, listed under the heading "Hash" below. The floor of hash complexity, that is, the greatest integer less than the hash complexity, is equal to the Graham complexity. The heading "transversal" shows a JI chord whose intervals temper to the marvel chord. Under "type" it says otonal if it is an essentially just chord best understood in terms of the overtone series, utonal if it is the inversion of an otonal chord, and ambitonal if it can equally well be seen as otonal or utonal. The other names denote types of essentially tempered chord, giving the least amount of tempering needed to define the chord, so that if for example it says "werckismic" only 441/440 needs to be tempered out. Also, "marvel" denotes 9 odd limit (7-limit) marvel, whereas "unimarvel" means 11-limit marvel. The generator used below is the standard choice for miracle temperament, the secor. 16/15~15/14. However, it should be noted that the choice of generator does not effect the list of chords, only how those chords are interpreted. Does 0-7-13 denote the major triad or the minor triad? It's on the list of chords either way, but with a secor generator it's the major triad.


=Triads=
=Triads=  
Each of the triads below has three inversions. All three inversions for all 63 chords are notated in this [[@http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads.pdf|PDF]] (uses 41 EDO sagittal notation) and can be heard using [[http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads-piano.mp3|piano]], [[http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads-oud.mp3|oud]], or [[http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads-sine-waves.mp3|sine wave]] timbres (all links in MP3 format). Finally, here is a [[http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads.mid|tuned MIDI file]].
|| Number || Chord || Transversal || Type || Hash ||
|| Number || Chord || Transversal || Type || Hash ||
|| 1 || 0-2-5 || 1-8/7-7/5 || werckismic || 5.209453 ||
|| 1 || 0-2-5 || 1-8/7-7/5 || werckismic || 5.209453 ||
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|| 63 || 0-19-22 || 1-9/5-11/10 || otonal || 22.169925 ||
|| 63 || 0-19-22 || 1-9/5-11/10 || otonal || 22.169925 ||


=Tetrads=
=Tetrads=  
|| Number || Chord || Transversal || Type || Hash ||
|| Number || Chord || Transversal || Type || Hash ||
|| 1 || 0-2-5-7 || 1-8/7-7/5-8/5 || werckismic || 7.366322 ||
|| 1 || 0-2-5-7 || 1-8/7-7/5-8/5 || werckismic || 7.366322 ||
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|| 111 || 0-17-19-22 || 1-11/7-9/5-11/10 || werckismic || 22.209454 ||
|| 111 || 0-17-19-22 || 1-11/7-9/5-11/10 || werckismic || 22.209454 ||


=Pentads=
=Pentads=  
|| Number || Chord || Transversal || Type || Hash ||
|| Number || Chord || Transversal || Type || Hash ||
|| 1 || 0-3-6-9-12 || 1-11/9-3/2-11/6-9/8 || rastmic || 12.192601 ||
|| 1 || 0-3-6-9-12 || 1-11/9-3/2-11/6-9/8 || rastmic || 12.192601 ||
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|| 73 || 0-14-17-19-22 || 1-9/7-11/7-9/5-11/10 || jove || 22.214319 ||
|| 73 || 0-14-17-19-22 || 1-9/7-11/7-9/5-11/10 || jove || 22.214319 ||


=Hexads=
=Hexads=  
|| Number || Chord || Transversal || Type || Hash ||
|| Number || Chord || Transversal || Type || Hash ||
|| 1 || 0-3-6-9-12-15 || 1-11/9-3/2-11/6-9/8-11/8 || rastmic || 15.192640 ||
|| 1 || 0-3-6-9-12-15 || 1-11/9-3/2-11/6-9/8-11/8 || rastmic || 15.192640 ||
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|| 12 || 0-5-7-13-19-22 || 1-7/5-8/5-6/5-9/5-11/10 || otonal || 22.172477 ||
|| 12 || 0-5-7-13-19-22 || 1-7/5-8/5-6/5-9/5-11/10 || otonal || 22.172477 ||
|| 13 || 0-5-7-14-19-22 || 1-7/5-8/5-9/7-9/5-11/10 || unimarvel || 22.174975 ||
|| 13 || 0-5-7-14-19-22 || 1-7/5-8/5-9/7-9/5-11/10 || unimarvel || 22.174975 ||
|| 14 || 0-5-14-17-19-22 || 1-7/5-9/7-11/7-9/5-11/10 || jove || 22.214329 ||
|| 14 || 0-5-14-17-19-22 || 1-7/5-9/7-11/7-9/5-11/10 || jove || 22.214329 ||</pre></div>
 
</pre></div>
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<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 miracle&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="/Gamelismic%20clan#Miracle"&gt;miracle temperament&lt;/a&gt;. They are listed in order of increasing &lt;a class="wiki_link" href="/Graham%20complexity"&gt;Graham complexity&lt;/a&gt;, with hash complexity used to break ties. For any linear temperament, if we chose a generator, we may put any octave-equivalent chord of the temperament in a canonical form by representing it as a set of nonnegative integers, starting with 0, which are the number of generator steps giving an octave-equivalent note class in the chord. If S is such a set, the sum Σ 2^s for all s∊S provides a unique odd number encoding the chord, and the logarithm base two of this number is the hash complexity, listed under the heading &amp;quot;Hash&amp;quot; below. The floor of hash complexity, that is, the greatest integer less than the hash complexity, is equal to the Graham complexity. The heading &amp;quot;transversal&amp;quot; shows a JI chord whose intervals temper to the marvel chord. Under &amp;quot;type&amp;quot; it says otonal if it is an essentially just chord best understood in terms of the overtone series, utonal if it is the inversion of an otonal chord, and ambitonal if it can equally well be seen as otonal or utonal. The other names denote types of essentially tempered chord, giving the least amount of tempering needed to define the chord, so that if for example it says &amp;quot;werckismic&amp;quot; only 441/440 needs to be tempered out. Also, &amp;quot;marvel&amp;quot; denotes 9 odd limit (7-limit) marvel, whereas &amp;quot;unimarvel&amp;quot; means 11-limit marvel. The generator used below is the standard choice for miracle temperament, the secor. 16/15~15/14. However, it should be noted that the choice of generator does not effect the list of chords, only how those chords are interpreted. Does 0-7-13 denote the major triad or the minor triad? It's on the list of chords either way, but with a secor generator it's the major triad.&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 miracle&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="/Gamelismic%20clan#Miracle"&gt;miracle temperament&lt;/a&gt;. They are listed in order of increasing &lt;a class="wiki_link" href="/Graham%20complexity"&gt;Graham complexity&lt;/a&gt;, with hash complexity used to break ties. For any linear temperament, if we chose a generator, we may put any octave-equivalent chord of the temperament in a canonical form by representing it as a set of nonnegative integers, starting with 0, which are the number of generator steps giving an octave-equivalent note class in the chord. If S is such a set, the sum Σ 2^s for all s∊S provides a unique odd number encoding the chord, and the logarithm base two of this number is the hash complexity, listed under the heading &amp;quot;Hash&amp;quot; below. The floor of hash complexity, that is, the greatest integer less than the hash complexity, is equal to the Graham complexity. The heading &amp;quot;transversal&amp;quot; shows a JI chord whose intervals temper to the marvel chord. Under &amp;quot;type&amp;quot; it says otonal if it is an essentially just chord best understood in terms of the overtone series, utonal if it is the inversion of an otonal chord, and ambitonal if it can equally well be seen as otonal or utonal. The other names denote types of essentially tempered chord, giving the least amount of tempering needed to define the chord, so that if for example it says &amp;quot;werckismic&amp;quot; only 441/440 needs to be tempered out. Also, &amp;quot;marvel&amp;quot; denotes 9 odd limit (7-limit) marvel, whereas &amp;quot;unimarvel&amp;quot; means 11-limit marvel. The generator used below is the standard choice for miracle temperament, the secor. 16/15~15/14. However, it should be noted that the choice of generator does not effect the list of chords, only how those chords are interpreted. Does 0-7-13 denote the major triad or the minor triad? It's on the list of chords either way, but with a secor generator it's the major triad.&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;
Each of the triads below has three inversions. All three inversions for all 63 chords are notated in this &lt;a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads.pdf" rel="nofollow" target="_blank"&gt;PDF&lt;/a&gt; (uses 41 EDO sagittal notation) and can be heard using &lt;a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads-piano.mp3" rel="nofollow"&gt;piano&lt;/a&gt;, &lt;a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads-oud.mp3" rel="nofollow"&gt;oud&lt;/a&gt;, or &lt;a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads-sine-waves.mp3" rel="nofollow"&gt;sine wave&lt;/a&gt; timbres (all links in MP3 format). Finally, here is a &lt;a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads.mid" rel="nofollow"&gt;tuned MIDI file&lt;/a&gt;.&lt;br /&gt;




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&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;
 


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&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;
 


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&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;
 


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Revision as of 21:55, 16 November 2014

IMPORTED REVISION FROM WIKISPACES

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

This revision was by author jdfreivald and made on 2014-11-16 21:55:21 UTC.
The original revision id was 531298704.
The revision comment was: Added 41 EDO notation and audio examples of the triads.

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 [[Gamelismic clan#Miracle|miracle temperament]]. They are listed in order of increasing [[Graham complexity]], with hash complexity used to break ties. For any linear temperament, if we chose a generator, we may put any octave-equivalent chord of the temperament in a canonical form by representing it as a set of nonnegative integers, starting with 0, which are the number of generator steps giving an octave-equivalent note class in the chord. If S is such a set, the sum Σ 2^s for all s∊S provides a unique odd number encoding the chord, and the logarithm base two of this number is the hash complexity, listed under the heading "Hash" below. The floor of hash complexity, that is, the greatest integer less than the hash complexity, is equal to the Graham complexity. The heading "transversal" shows a JI chord whose intervals temper to the marvel chord. Under "type" it says otonal if it is an essentially just chord best understood in terms of the overtone series, utonal if it is the inversion of an otonal chord, and ambitonal if it can equally well be seen as otonal or utonal. The other names denote types of essentially tempered chord, giving the least amount of tempering needed to define the chord, so that if for example it says "werckismic" only 441/440 needs to be tempered out. Also, "marvel" denotes 9 odd limit (7-limit) marvel, whereas "unimarvel" means 11-limit marvel. The generator used below is the standard choice for miracle temperament, the secor. 16/15~15/14. However, it should be noted that the choice of generator does not effect the list of chords, only how those chords are interpreted. Does 0-7-13 denote the major triad or the minor triad? It's on the list of chords either way, but with a secor generator it's the major triad.

=Triads= 
Each of the triads below has three inversions. All three inversions for all 63 chords are notated in this [[@http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads.pdf|PDF]] (uses 41 EDO sagittal notation) and can be heard using [[http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads-piano.mp3|piano]], [[http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads-oud.mp3|oud]], or [[http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads-sine-waves.mp3|sine wave]] timbres (all links in MP3 format). Finally, here is a [[http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads.mid|tuned MIDI file]].
|| Number || Chord || Transversal || Type || Hash ||
|| 1 || 0-2-5 || 1-8/7-7/5 || werckismic || 5.209453 ||
|| 2 || 0-3-5 || 1-11/9-7/5 || werckismic || 5.357552 ||
|| 3 || 0-3-6 || 1-11/9-3/2 || rastmic || 6.189825 ||
|| 4 || 0-2-7 || 1-8/7-8/5 || utonal || 7.055282 ||
|| 5 || 0-5-7 || 1-7/5-8/5 || otonal || 7.330917 ||
|| 6 || 0-2-8 || 1-8/7-12/7 || otonal || 8.027906 ||
|| 7 || 0-3-8 || 1-11/9-12/7 || swetismic || 8.049849 ||
|| 8 || 0-5-8 || 1-7/5-12/7 || swetismic || 8.174926 ||
|| 9 || 0-6-8 || 1-3/2-12/7 || utonal || 8.326429 ||
|| 10 || 0-2-9 || 1-8/7-11/6 || keenanismic || 9.014020 ||
|| 11 || 0-3-9 || 1-11/9-11/6 || utonal || 9.025140 ||
|| 12 || 0-6-9 || 1-3/2-11/6 || otonal || 9.172428 ||
|| 13 || 0-7-9 || 1-8/5-11/6 || keenanismic || 9.324181 ||
|| 14 || 0-3-12 || 1-11/9-9/8 || rastmic || 12.003167 ||
|| 15 || 0-5-12 || 1-7/5-9/8 || marvel || 12.011577 ||
|| 16 || 0-6-12 || 1-3/2-9/8 || ambitonal || 12.022715 ||
|| 17 || 0-7-12 || 1-8/5-9/8 || marvel || 12.044736 ||
|| 18 || 0-9-12 || 1-11/6-9/8 || rastmic || 12.170238 ||
|| 19 || 0-5-13 || 1-7/5-6/5 || otonal || 13.005800 ||
|| 20 || 0-6-13 || 1-3/2-6/5 || utonal || 13.011402 ||
|| 21 || 0-7-13 || 1-8/5-6/5 || otonal || 13.022541 ||
|| 22 || 0-8-13 || 1-12/7-6/5 || utonal || 13.044565 ||
|| 23 || 0-2-14 || 1-8/7-9/7 || otonal || 14.000440 ||
|| 24 || 0-5-14 || 1-7/5-9/7 || swetismic || 14.002903 ||
|| 25 || 0-6-14 || 1-3/2-9/7 || utonal || 14.005712 ||
|| 26 || 0-7-14 || 1-8/5-9/7 || marvel || 14.011315 ||
|| 27 || 0-8-14 || 1-12/7-9/7 || otonal || 14.022455 ||
|| 28 || 0-9-14 || 1-11/6-9/7 || swetismic || 14.04448 ||
|| 29 || 0-12-14 || 1-9/8-9/7 || utonal || 14.321999 ||
|| 30 || 0-2-15 || 1-8/7-11/8 || keenanismic || 15.000220 ||
|| 31 || 0-3-15 || 1-11/9-11/8 || utonal || 15.000396 ||
|| 32 || 0-6-15 || 1-3/2-11/8 || otonal || 15.002859 ||
|| 33 || 0-7-15 || 1-8/5-11/8 || keenanismic || 15.005660 ||
|| 34 || 0-8-15 || 1-12/7-11/8 || keenanismic || 15.011271 ||
|| 35 || 0-9-15 || 1-11/6-11/8 || utonal || 15.022411 ||
|| 36 || 0-12-15 || 1-9/8-11/8 || otonal || 15.169964 ||
|| 37 || 0-13-15 || 1-6/5-11/8 || keenanismic || 15.321963 ||
|| 38 || 0-2-17 || 1-8/7-11/7 || otonal || 17.000055 ||
|| 39 || 0-3-17 || 1-11/9-11/7 || utonal || 17.000099 ||
|| 40 || 0-5-17 || 1-7/5-11/7 || werckismic || 17.000363 ||
|| 41 || 0-8-17 || 1-12/7-11/7 || otonal || 17.002826 ||
|| 42 || 0-9-17 || 1-11/6-11/7 || utonal || 17.005636 ||
|| 43 || 0-12-17 || 1-9/8-11/7 || werckismic || 17.0444 ||
|| 44 || 0-14-17 || 1-9/7-11/7 || otonal || 17.169935 ||
|| 45 || 0-15-17 || 1-11/8-11/7 || utonal || 17.321937 ||
|| 46 || 0-2-19 || 1-8/7-9/5 || werckismic || 19.000014 ||
|| 47 || 0-5-19 || 1-7/5-9/5 || otonal || 19.000091 ||
|| 48 || 0-6-19 || 1-3/2-9/5 || utonal || 19.000179 ||
|| 49 || 0-7-19 || 1-8/5-9/5 || otonal || 19.000355 ||
|| 50 || 0-12-19 || 1-9/8-9/5 || utonal || 19.011230 ||
|| 51 || 0-13-19 || 1-6/5-9/5 || otonal || 19.022371 ||
|| 52 || 0-14-19 || 1-9/7-9/5 || utonal || 19.044397 ||
|| 53 || 0-17-19 || 1-11/7-9/5 || werckismic || 19.321930 ||
|| 54 || 0-3-22 || 1-11/9-11/10 || utonal || 22.000003 ||
|| 55 || 0-5-22 || 1-7/5-11/10 || otonal || 22.000011 ||
|| 56 || 0-7-22 || 1-8/5-11/10 || otonal || 22.000044 ||
|| 57 || 0-8-22 || 1-12/7-11/10 || swetismic || 22.000088 ||
|| 58 || 0-9-22 || 1-11/6-11/10 || utonal || 22.000176 ||
|| 59 || 0-13-22 || 1-6/5-11/10 || otonal || 22.002815 ||
|| 60 || 0-14-22 || 1-9/7-11/10 || swetismic || 22.005625 ||
|| 61 || 0-15-22 || 1-11/8-11/10 || utonal || 22.011228 ||
|| 62 || 0-17-22 || 1-11/7-11/10 || utonal || 22.044394 ||
|| 63 || 0-19-22 || 1-9/5-11/10 || otonal || 22.169925 ||

=Tetrads= 
|| Number || Chord || Transversal || Type || Hash ||
|| 1 || 0-2-5-7 || 1-8/7-7/5-8/5 || werckismic || 7.366322 ||
|| 2 || 0-2-5-8 || 1-8/7-7/5-12/7 || jove || 8.194757 ||
|| 3 || 0-3-5-8 || 1-11/9-7/5-12/7 || jove || 8.214319 ||
|| 4 || 0-3-6-8 || 1-11/9-3/2-12/7 || jove || 8.361944 ||
|| 5 || 0-3-6-9 || 1-11/9-3/2-11/6 || rastmic || 9.192293 ||
|| 6 || 0-2-7-9 || 1-8/7-8/5-11/6 || keenanismic || 9.333155 ||
|| 7 || 0-3-5-12 || 1-11/9-7/5-9/8 || miracle || 12.014369 ||
|| 8 || 0-3-6-12 || 1-11/9-3/2-9/8 || rastmic || 12.025486 ||
|| 9 || 0-5-7-12 || 1-7/5-8/5-9/8 || marvel || 12.055621 ||
|| 10 || 0-3-9-12 || 1-11/9-11/6-9/8 || rastmic || 12.172740 ||
|| 11 || 0-6-9-12 || 1-3/2-11/6-9/8 || rastmic || 12.190133 ||
|| 12 || 0-7-9-12 || 1-8/5-11/6-9/8 || miracle || 12.209758 ||
|| 13 || 0-5-7-13 || 1-7/5-8/5-6/5 || otonal || 13.028079 ||
|| 14 || 0-5-8-13 || 1-7/5-12/7-6/5 || swetismic || 13.050019 ||
|| 15 || 0-6-8-13 || 1-3/2-12/7-6/5 || utonal || 13.055452 ||
|| 16 || 0-2-5-14 || 1-8/7-7/5-9/7 || jove || 14.003254 ||
|| 17 || 0-2-7-14 || 1-8/7-8/5-9/7 || marvel || 14.011664 ||
|| 18 || 0-5-7-14 || 1-7/5-8/5-9/7 || unimarvel || 14.014108 ||
|| 19 || 0-2-8-14 || 1-8/7-12/7-9/7 || otonal || 14.022801 ||
|| 20 || 0-5-8-14 || 1-7/5-12/7-9/7 || swetismic || 14.025226 ||
|| 21 || 0-6-8-14 || 1-3/2-12/7-9/7 || ambitonal || 14.027992 ||
|| 22 || 0-2-9-14 || 1-8/7-11/6-9/7 || unimarvel || 14.044821 ||
|| 23 || 0-6-9-14 || 1-3/2-11/6-9/7 || swetismic || 14.049934 ||
|| 24 || 0-7-9-14 || 1-8/5-11/6-9/7 || unimarvel || 14.055367 ||
|| 25 || 0-5-12-14 || 1-7/5-9/8-9/7 || unimarvel || 14.324251 ||
|| 26 || 0-6-12-14 || 1-3/2-9/8-9/7 || utonal || 14.326500 ||
|| 27 || 0-7-12-14 || 1-8/5-9/8-9/7 || marvel || 14.330987 ||
|| 28 || 0-9-12-14 || 1-11/6-9/8-9/7 || jove || 14.357621 ||
|| 29 || 0-3-6-15 || 1-11/9-3/2-11/8 || rastmic || 15.003210 ||
|| 30 || 0-2-7-15 || 1-8/7-8/5-11/8 || keenanismic || 15.005844 ||
|| 31 || 0-2-8-15 || 1-8/7-12/7-11/8 || keenanismic || 15.011446 ||
|| 32 || 0-3-8-15 || 1-11/9-12/7-11/8 || unimarvel || 15.011620 ||
|| 33 || 0-6-8-15 || 1-3/2-12/7-11/8 || keenanismic || 15.014064 ||
|| 34 || 0-2-9-15 || 1-8/7-11/6-11/8 || keenanismic || 15.022585 ||
|| 35 || 0-3-9-15 || 1-11/9-11/6-11/8 || utonal || 15.022758 ||
|| 36 || 0-6-9-15 || 1-3/2-11/6-11/8 || ambitonal || 15.025183 ||
|| 37 || 0-7-9-15 || 1-8/5-11/6-11/8 || keenanismic || 15.027949 ||
|| 38 || 0-3-12-15 || 1-11/9-9/8-11/8 || rastmic || 15.170277 ||
|| 39 || 0-6-12-15 || 1-3/2-9/8-11/8 || otonal || 15.172467 ||
|| 40 || 0-7-12-15 || 1-8/5-9/8-11/8 || unimarvel || 15.174965 ||
|| 41 || 0-9-12-15 || 1-11/6-9/8-11/8 || rastmic || 15.189863 ||
|| 42 || 0-6-13-15 || 1-3/2-6/5-11/8 || keenanismic || 15.324216 ||
|| 43 || 0-7-13-15 || 1-8/5-6/5-11/8 || keenanismic || 15.326465 ||
|| 44 || 0-8-13-15 || 1-12/7-6/5-11/8 || keenanismic || 15.330952 ||
|| 45 || 0-2-5-17 || 1-8/7-7/5-11/7 || werckismic || 17.000407 ||
|| 46 || 0-3-5-17 || 1-11/9-7/5-11/7 || werckismic || 17.000451 ||
|| 47 || 0-2-8-17 || 1-8/7-12/7-11/7 || otonal || 17.002870 ||
|| 48 || 0-3-8-17 || 1-11/9-12/7-11/7 || swetismic || 17.002914 ||
|| 49 || 0-5-8-17 || 1-7/5-12/7-11/7 || jove || 17.003177 ||
|| 50 || 0-2-9-17 || 1-8/7-11/6-11/7 || keenanismic || 17.005679 ||
|| 51 || 0-3-9-17 || 1-11/9-11/6-11/7 || utonal || 17.005723 ||
|| 52 || 0-3-12-17 || 1-11/9-9/8-11/7 || jove || 17.044490 ||
|| 53 || 0-5-12-17 || 1-7/5-9/8-11/7 || prodigy || 17.044746 ||
|| 54 || 0-9-12-17 || 1-11/6-9/8-11/7 || jove || 17.049859 ||
|| 55 || 0-2-14-17 || 1-8/7-9/7-11/7 || otonal || 17.169974 ||
|| 56 || 0-5-14-17 || 1-7/5-9/7-11/7 || jove || 17.170248 ||
|| 57 || 0-8-14-17 || 1-12/7-9/7-11/7 || otonal || 17.172437 ||
|| 58 || 0-9-14-17 || 1-11/6-9/7-11/7 || swetismic || 17.174935 ||
|| 59 || 0-12-14-17 || 1-9/8-9/7-11/7 || werckismic || 17.209463 ||
|| 60 || 0-2-15-17 || 1-8/7-11/8-11/7 || keenanismic || 17.321972 ||
|| 61 || 0-3-15-17 || 1-11/9-11/8-11/7 || utonal || 17.322007 ||
|| 62 || 0-8-15-17 || 1-12/7-11/8-11/7 || keenanismic || 17.324189 ||
|| 63 || 0-9-15-17 || 1-11/6-11/8-11/7 || utonal || 17.326438 ||
|| 64 || 0-12-15-17 || 1-9/8-11/8-11/7 || werckismic || 17.357561 ||
|| 65 || 0-2-5-19 || 1-8/7-7/5-9/5 || werckismic || 19.000102 ||
|| 66 || 0-2-7-19 || 1-8/7-8/5-9/5 || werckismic || 19.000366 ||
|| 67 || 0-5-7-19 || 1-7/5-8/5-9/5 || otonal || 19.000443 ||
|| 68 || 0-5-12-19 || 1-7/5-9/8-9/5 || marvel || 19.011317 ||
|| 69 || 0-6-12-19 || 1-3/2-9/8-9/5 || utonal || 19.011405 ||
|| 70 || 0-7-12-19 || 1-8/5-9/8-9/5 || marvel || 19.011579 ||
|| 71 || 0-5-13-19 || 1-7/5-6/5-9/5 || otonal || 19.022457 ||
|| 72 || 0-6-13-19 || 1-3/2-6/5-9/5 || ambitonal || 19.022544 ||
|| 73 || 0-7-13-19 || 1-8/5-6/5-9/5 || otonal || 19.022717 ||
|| 74 || 0-2-14-19 || 1-8/7-9/7-9/5 || werckismic || 19.044407 ||
|| 75 || 0-5-14-19 || 1-7/5-9/7-9/5 || swetismic || 19.044482 ||
|| 76 || 0-6-14-19 || 1-3/2-9/7-9/5 || utonal || 19.044568 ||
|| 77 || 0-7-14-19 || 1-8/5-9/7-9/5 || marvel || 19.044738 ||
|| 78 || 0-12-14-19 || 1-9/8-9/7-9/5 || utonal || 19.055285 ||
|| 79 || 0-2-17-19 || 1-8/7-11/7-9/5 || werckismic || 19.321939 ||
|| 80 || 0-5-17-19 || 1-7/5-11/7-9/5 || werckismic || 19.322001 ||
|| 81 || 0-12-17-19 || 1-9/8-11/7-9/5 || werckismic || 19.330919 ||
|| 82 || 0-14-17-19 || 1-9/7-11/7-9/5 || werckismic || 19.357554 ||
|| 83 || 0-3-5-22 || 1-11/9-7/5-11/10 || werckismic || 22.000014 ||
|| 84 || 0-5-7-22 || 1-7/5-8/5-11/10 || otonal || 22.000055 ||
|| 85 || 0-3-8-22 || 1-11/9-12/7-11/10 || swetismic || 22.000091 ||
|| 86 || 0-5-8-22 || 1-7/5-12/7-11/10 || swetismic || 22.000099 ||
|| 87 || 0-3-9-22 || 1-11/9-11/6-11/10 || utonal || 22.000179 ||
|| 88 || 0-7-9-22 || 1-8/5-11/6-11/10 || keenanismic || 22.000220 ||
|| 89 || 0-5-13-22 || 1-7/5-6/5-11/10 || otonal || 22.002826 ||
|| 90 || 0-7-13-22 || 1-8/5-6/5-11/10 || otonal || 22.002859 ||
|| 91 || 0-8-13-22 || 1-12/7-6/5-11/10 || swetismic || 22.002903 ||
|| 92 || 0-5-14-22 || 1-7/5-9/7-11/10 || swetismic || 22.005636 ||
|| 93 || 0-7-14-22 || 1-8/5-9/7-11/10 || unimarvel || 22.005669 ||
|| 94 || 0-8-14-22 || 1-12/7-9/7-11/10 || swetismic || 22.005713 ||
|| 95 || 0-9-14-22 || 1-11/6-9/7-11/10 || swetismic || 22.005800 ||
|| 96 || 0-3-15-22 || 1-11/9-11/8-11/10 || utonal || 22.011230 ||
|| 97 || 0-7-15-22 || 1-8/5-11/8-11/10 || keenanismic || 22.011271 ||
|| 98 || 0-8-15-22 || 1-12/7-11/8-11/10 || unimarvel || 22.011315 ||
|| 99 || 0-9-15-22 || 1-11/6-11/8-11/10 || utonal || 22.011402 ||
|| 100 || 0-13-15-22 || 1-6/5-11/8-11/10 || keenanismic || 22.014021 ||
|| 101 || 0-3-17-22 || 1-11/9-11/7-11/10 || utonal || 22.044397 ||
|| 102 || 0-5-17-22 || 1-7/5-11/7-11/10 || werckismic || 22.044405 ||
|| 103 || 0-8-17-22 || 1-12/7-11/7-11/10 || swetismic || 22.044480 ||
|| 104 || 0-9-17-22 || 1-11/6-11/7-11/10 || utonal || 22.044565 ||
|| 105 || 0-14-17-22 || 1-9/7-11/7-11/10 || swetismic || 22.049849 ||
|| 106 || 0-15-17-22 || 1-11/8-11/7-11/10 || utonal || 22.055283 ||
|| 107 || 0-5-19-22 || 1-7/5-9/5-11/10 || otonal || 22.169935 ||
|| 108 || 0-7-19-22 || 1-8/5-9/5-11/10 || otonal || 22.169964 ||
|| 109 || 0-13-19-22 || 1-6/5-9/5-11/10 || otonal || 22.172428 ||
|| 110 || 0-14-19-22 || 1-9/7-9/5-11/10 || swetismic || 22.174926 ||
|| 111 || 0-17-19-22 || 1-11/7-9/5-11/10 || werckismic || 22.209454 ||

=Pentads= 
|| Number || Chord || Transversal || Type || Hash ||
|| 1 || 0-3-6-9-12 || 1-11/9-3/2-11/6-9/8 || rastmic || 12.192601 ||
|| 2 || 0-2-5-7-14 || 1-8/7-7/5-8/5-9/7 || miracle || 14.014456 ||
|| 3 || 0-2-5-8-14 || 1-8/7-7/5-12/7-9/7 || jove || 14.025572 ||
|| 4 || 0-2-7-9-14 || 1-8/7-8/5-11/6-9/7 || unimarvel || 14.055706 ||
|| 5 || 0-5-7-12-14 || 1-7/5-8/5-9/8-9/7 || unimarvel || 14.333225 ||
|| 6 || 0-6-9-12-14 || 1-3/2-11/6-9/8-9/7 || jove || 14.362012 ||
|| 7 || 0-7-9-12-14 || 1-8/5-11/6-9/8-9/7 || miracle || 14.366391 ||
|| 8 || 0-3-6-8-15 || 1-11/9-3/2-12/7-11/8 || miracle || 15.014413 ||
|| 9 || 0-3-6-9-15 || 1-11/9-3/2-11/6-11/8 || rastmic || 15.025529 ||
|| 10 || 0-2-7-9-15 || 1-8/7-8/5-11/6-11/8 || keenanismic || 15.028122 ||
|| 11 || 0-3-6-12-15 || 1-11/9-3/2-9/8-11/8 || rastmic || 15.172779 ||
|| 12 || 0-3-9-12-15 || 1-11/9-11/6-9/8-11/8 || rastmic || 15.190172 ||
|| 13 || 0-6-9-12-15 || 1-3/2-11/6-9/8-11/8 || rastmic || 15.192331 ||
|| 14 || 0-7-9-12-15 || 1-8/5-11/6-9/8-11/8 || miracle || 15.194795 ||
|| 15 || 0-6-8-13-15 || 1-3/2-12/7-6/5-11/8 || keenanismic || 15.333190 ||
|| 16 || 0-2-5-8-17 || 1-8/7-7/5-12/7-11/7 || jove || 17.003221 ||
|| 17 || 0-3-5-8-17 || 1-11/9-7/5-12/7-11/7 || jove || 17.003265 ||
|| 18 || 0-3-5-12-17 || 1-11/9-7/5-9/8-11/7 || miracle || 17.044832 ||
|| 19 || 0-3-9-12-17 || 1-11/9-11/6-9/8-11/7 || jove || 17.049944 ||
|| 20 || 0-2-5-14-17 || 1-8/7-7/5-9/7-11/7 || jove || 17.170287 ||
|| 21 || 0-2-8-14-17 || 1-8/7-12/7-9/7-11/7 || otonal || 17.172476 ||
|| 22 || 0-5-8-14-17 || 1-7/5-12/7-9/7-11/7 || jove || 17.172750 ||
|| 23 || 0-2-9-14-17 || 1-8/7-11/6-9/7-11/7 || unimarvel || 17.174974 ||
|| 24 || 0-5-12-14-17 || 1-7/5-9/8-9/7-11/7 || miracle || 17.209767 ||
|| 25 || 0-9-12-14-17 || 1-11/6-9/8-9/7-11/7 || jove || 17.214329 ||
|| 26 || 0-2-8-15-17 || 1-8/7-12/7-11/8-11/7 || keenanismic || 17.324225 ||
|| 27 || 0-3-8-15-17 || 1-11/9-12/7-11/8-11/7 || unimarvel || 17.324260 ||
|| 28 || 0-2-9-15-17 || 1-8/7-11/6-11/8-11/7 || keenanismic || 17.326473 ||
|| 29 || 0-3-9-15-17 || 1-11/9-11/6-11/8-11/7 || utonal || 17.326508 ||
|| 30 || 0-3-12-15-17 || 1-11/9-9/8-11/8-11/7 || jove || 17.357629 ||
|| 31 || 0-9-12-15-17 || 1-11/6-9/8-11/8-11/7 || jove || 17.361952 ||
|| 32 || 0-2-5-7-19 || 1-8/7-7/5-8/5-9/5 || werckismic || 19.000454 ||
|| 33 || 0-5-7-12-19 || 1-7/5-8/5-9/8-9/5 || marvel || 19.011667 ||
|| 34 || 0-5-7-13-19 || 1-7/5-8/5-6/5-9/5 || otonal || 19.022804 ||
|| 35 || 0-2-5-14-19 || 1-8/7-7/5-9/7-9/5 || jove || 19.044493 ||
|| 36 || 0-2-7-14-19 || 1-8/7-8/5-9/7-9/5 || prodigy || 19.044749 ||
|| 37 || 0-5-7-14-19 || 1-7/5-8/5-9/7-9/5 || unimarvel || 19.044824 ||
|| 38 || 0-5-12-14-19 || 1-7/5-9/8-9/7-9/5 || unimarvel || 19.055370 ||
|| 39 || 0-6-12-14-19 || 1-3/2-9/8-9/7-9/5 || utonal || 19.055455 ||
|| 40 || 0-7-12-14-19 || 1-8/5-9/8-9/7-9/5 || marvel || 19.055624 ||
|| 41 || 0-2-5-17-19 || 1-8/7-7/5-11/7-9/5 || werckismic || 19.322010 ||
|| 42 || 0-5-12-17-19 || 1-7/5-9/8-11/7-9/5 || prodigy || 19.330989 ||
|| 43 || 0-2-14-17-19 || 1-8/7-9/7-11/7-9/5 || werckismic || 19.357563 ||
|| 44 || 0-5-14-17-19 || 1-7/5-9/7-11/7-9/5 || jove || 19.357623 ||
|| 45 || 0-12-14-17-19 || 1-9/8-9/7-11/7-9/5 || werckismic || 19.366324 ||
|| 46 || 0-3-5-8-22 || 1-11/9-7/5-12/7-11/10 || jove || 22.000102 ||
|| 47 || 0-5-7-13-22 || 1-7/5-8/5-6/5-11/10 || otonal || 22.002870 ||
|| 48 || 0-5-8-13-22 || 1-7/5-12/7-6/5-11/10 || swetismic || 22.002914 ||
|| 49 || 0-5-7-14-22 || 1-7/5-8/5-9/7-11/10 || unimarvel || 22.005680 ||
|| 50 || 0-5-8-14-22 || 1-7/5-12/7-9/7-11/10 || swetismic || 22.005724 ||
|| 51 || 0-7-9-14-22 || 1-8/5-11/6-9/7-11/10 || unimarvel || 22.005844 ||
|| 52 || 0-3-8-15-22 || 1-11/9-12/7-11/8-11/10 || unimarvel || 22.011318 ||
|| 53 || 0-3-9-15-22 || 1-11/9-11/6-11/8-11/10 || utonal || 22.011405 ||
|| 54 || 0-7-9-15-22 || 1-8/5-11/6-11/8-11/10 || keenanismic || 22.011446 ||
|| 55 || 0-7-13-15-22 || 1-8/5-6/5-11/8-11/10 || keenanismic || 22.014064 ||
|| 56 || 0-8-13-15-22 || 1-12/7-6/5-11/8-11/10 || unimarvel || 22.014108 ||
|| 57 || 0-3-5-17-22 || 1-11/9-7/5-11/7-11/10 || werckismic || 22.044408 ||
|| 58 || 0-3-8-17-22 || 1-11/9-12/7-11/7-11/10 || swetismic || 22.044483 ||
|| 59 || 0-5-8-17-22 || 1-7/5-12/7-11/7-11/10 || jove || 22.044491 ||
|| 60 || 0-3-9-17-22 || 1-11/9-11/6-11/7-11/10 || utonal || 22.044568 ||
|| 61 || 0-5-14-17-22 || 1-7/5-9/7-11/7-11/10 || jove || 22.049860 ||
|| 62 || 0-8-14-17-22 || 1-12/7-9/7-11/7-11/10 || swetismic || 22.049934 ||
|| 63 || 0-9-14-17-22 || 1-11/6-9/7-11/7-11/10 || swetismic || 22.050019 ||
|| 64 || 0-3-15-17-22 || 1-11/9-11/8-11/7-11/10 || utonal || 22.055285 ||
|| 65 || 0-8-15-17-22 || 1-12/7-11/8-11/7-11/10 || unimarvel || 22.055368 ||
|| 66 || 0-9-15-17-22 || 1-11/6-11/8-11/7-11/10 || utonal || 22.055452 ||
|| 67 || 0-5-7-19-22 || 1-7/5-8/5-9/5-11/10 || otonal || 22.169974 ||
|| 68 || 0-5-13-19-22 || 1-7/5-6/5-9/5-11/10 || otonal || 22.172438 ||
|| 69 || 0-7-13-19-22 || 1-8/5-6/5-9/5-11/10 || otonal || 22.172467 ||
|| 70 || 0-5-14-19-22 || 1-7/5-9/7-9/5-11/10 || swetismic || 22.174936 ||
|| 71 || 0-7-14-19-22 || 1-8/5-9/7-9/5-11/10 || unimarvel || 22.174965 ||
|| 72 || 0-5-17-19-22 || 1-7/5-11/7-9/5-11/10 || werckismic || 22.209463 ||
|| 73 || 0-14-17-19-22 || 1-9/7-11/7-9/5-11/10 || jove || 22.214319 ||

=Hexads= 
|| Number || Chord || Transversal || Type || Hash ||
|| 1 || 0-3-6-9-12-15 || 1-11/9-3/2-11/6-9/8-11/8 || rastmic || 15.192640 ||
|| 2 || 0-2-5-8-14-17 || 1-8/7-7/5-12/7-9/7-11/7 || jove || 17.172789 ||
|| 3 || 0-3-9-12-15-17 || 1-11/9-11/6-9/8-11/8-11/7 || jove || 17.362021 ||
|| 4 || 0-2-5-7-14-19 || 1-8/7-7/5-8/5-9/7-9/5 || miracle || 19.044834 ||
|| 5 || 0-5-7-12-14-19 || 1-7/5-8/5-9/8-9/7-9/5 || unimarvel || 19.055709 ||
|| 6 || 0-2-5-14-17-19 || 1-8/7-7/5-9/7-11/7-9/5 || jove || 19.357631 ||
|| 7 || 0-5-12-14-17-19 || 1-7/5-9/8-9/7-11/7-9/5 || miracle || 19.366393 ||
|| 8 || 0-3-5-8-17-22 || 1-11/9-7/5-12/7-11/7-11/10 || jove || 22.044493 ||
|| 9 || 0-5-8-14-17-22 || 1-7/5-12/7-9/7-11/7-11/10 || jove || 22.049945 ||
|| 10 || 0-3-8-15-17-22 || 1-11/9-12/7-11/8-11/7-11/10 || unimarvel || 22.055370 ||
|| 11 || 0-3-9-15-17-22 || 1-11/9-11/6-11/8-11/7-11/10 || utonal || 22.055455 ||
|| 12 || 0-5-7-13-19-22 || 1-7/5-8/5-6/5-9/5-11/10 || otonal || 22.172477 ||
|| 13 || 0-5-7-14-19-22 || 1-7/5-8/5-9/7-9/5-11/10 || unimarvel || 22.174975 ||
|| 14 || 0-5-14-17-19-22 || 1-7/5-9/7-11/7-9/5-11/10 || jove || 22.214329 ||

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<html><head><title>Chords of miracle</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="/Gamelismic%20clan#Miracle">miracle temperament</a>. They are listed in order of increasing <a class="wiki_link" href="/Graham%20complexity">Graham complexity</a>, with hash complexity used to break ties. For any linear temperament, if we chose a generator, we may put any octave-equivalent chord of the temperament in a canonical form by representing it as a set of nonnegative integers, starting with 0, which are the number of generator steps giving an octave-equivalent note class in the chord. If S is such a set, the sum Σ 2^s for all s∊S provides a unique odd number encoding the chord, and the logarithm base two of this number is the hash complexity, listed under the heading &quot;Hash&quot; below. The floor of hash complexity, that is, the greatest integer less than the hash complexity, is equal to the Graham complexity. The heading &quot;transversal&quot; shows a JI chord whose intervals temper to the marvel chord. Under &quot;type&quot; it says otonal if it is an essentially just chord best understood in terms of the overtone series, utonal if it is the inversion of an otonal chord, and ambitonal if it can equally well be seen as otonal or utonal. The other names denote types of essentially tempered chord, giving the least amount of tempering needed to define the chord, so that if for example it says &quot;werckismic&quot; only 441/440 needs to be tempered out. Also, &quot;marvel&quot; denotes 9 odd limit (7-limit) marvel, whereas &quot;unimarvel&quot; means 11-limit marvel. The generator used below is the standard choice for miracle temperament, the secor. 16/15~15/14. However, it should be noted that the choice of generator does not effect the list of chords, only how those chords are interpreted. Does 0-7-13 denote the major triad or the minor triad? It's on the list of chords either way, but with a secor generator it's the major triad.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Triads"></a><!-- ws:end:WikiTextHeadingRule:0 -->Triads</h1>
 Each of the triads below has three inversions. All three inversions for all 63 chords are notated in this <a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads.pdf" rel="nofollow" target="_blank">PDF</a> (uses 41 EDO sagittal notation) and can be heard using <a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads-piano.mp3" rel="nofollow">piano</a>, <a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads-oud.mp3" rel="nofollow">oud</a>, or <a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads-sine-waves.mp3" rel="nofollow">sine wave</a> timbres (all links in MP3 format). Finally, here is a <a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/wp-content/uploads/2014/11/41-EDO-Miracle-scale-and-triads.mid" rel="nofollow">tuned MIDI file</a>.<br />


<table class="wiki_table">
    <tr>
        <td>Number<br />
</td>
        <td>Chord<br />
</td>
        <td>Transversal<br />
</td>
        <td>Type<br />
</td>
        <td>Hash<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>0-2-5<br />
</td>
        <td>1-8/7-7/5<br />
</td>
        <td>werckismic<br />
</td>
        <td>5.209453<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>0-3-5<br />
</td>
        <td>1-11/9-7/5<br />
</td>
        <td>werckismic<br />
</td>
        <td>5.357552<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>0-3-6<br />
</td>
        <td>1-11/9-3/2<br />
</td>
        <td>rastmic<br />
</td>
        <td>6.189825<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>0-2-7<br />
</td>
        <td>1-8/7-8/5<br />
</td>
        <td>utonal<br />
</td>
        <td>7.055282<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>0-5-7<br />
</td>
        <td>1-7/5-8/5<br />
</td>
        <td>otonal<br />
</td>
        <td>7.330917<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>0-2-8<br />
</td>
        <td>1-8/7-12/7<br />
</td>
        <td>otonal<br />
</td>
        <td>8.027906<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>0-3-8<br />
</td>
        <td>1-11/9-12/7<br />
</td>
        <td>swetismic<br />
</td>
        <td>8.049849<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>0-5-8<br />
</td>
        <td>1-7/5-12/7<br />
</td>
        <td>swetismic<br />
</td>
        <td>8.174926<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>0-6-8<br />
</td>
        <td>1-3/2-12/7<br />
</td>
        <td>utonal<br />
</td>
        <td>8.326429<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>0-2-9<br />
</td>
        <td>1-8/7-11/6<br />
</td>
        <td>keenanismic<br />
</td>
        <td>9.014020<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>0-3-9<br />
</td>
        <td>1-11/9-11/6<br />
</td>
        <td>utonal<br />
</td>
        <td>9.025140<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>0-6-9<br />
</td>
        <td>1-3/2-11/6<br />
</td>
        <td>otonal<br />
</td>
        <td>9.172428<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>0-7-9<br />
</td>
        <td>1-8/5-11/6<br />
</td>
        <td>keenanismic<br />
</td>
        <td>9.324181<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>0-3-12<br />
</td>
        <td>1-11/9-9/8<br />
</td>
        <td>rastmic<br />
</td>
        <td>12.003167<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>0-5-12<br />
</td>
        <td>1-7/5-9/8<br />
</td>
        <td>marvel<br />
</td>
        <td>12.011577<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>0-6-12<br />
</td>
        <td>1-3/2-9/8<br />
</td>
        <td>ambitonal<br />
</td>
        <td>12.022715<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>0-7-12<br />
</td>
        <td>1-8/5-9/8<br />
</td>
        <td>marvel<br />
</td>
        <td>12.044736<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>0-9-12<br />
</td>
        <td>1-11/6-9/8<br />
</td>
        <td>rastmic<br />
</td>
        <td>12.170238<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>0-5-13<br />
</td>
        <td>1-7/5-6/5<br />
</td>
        <td>otonal<br />
</td>
        <td>13.005800<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>0-6-13<br />
</td>
        <td>1-3/2-6/5<br />
</td>
        <td>utonal<br />
</td>
        <td>13.011402<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>0-7-13<br />
</td>
        <td>1-8/5-6/5<br />
</td>
        <td>otonal<br />
</td>
        <td>13.022541<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>0-8-13<br />
</td>
        <td>1-12/7-6/5<br />
</td>
        <td>utonal<br />
</td>
        <td>13.044565<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>0-2-14<br />
</td>
        <td>1-8/7-9/7<br />
</td>
        <td>otonal<br />
</td>
        <td>14.000440<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>0-5-14<br />
</td>
        <td>1-7/5-9/7<br />
</td>
        <td>swetismic<br />
</td>
        <td>14.002903<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>0-6-14<br />
</td>
        <td>1-3/2-9/7<br />
</td>
        <td>utonal<br />
</td>
        <td>14.005712<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>0-7-14<br />
</td>
        <td>1-8/5-9/7<br />
</td>
        <td>marvel<br />
</td>
        <td>14.011315<br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>0-8-14<br />
</td>
        <td>1-12/7-9/7<br />
</td>
        <td>otonal<br />
</td>
        <td>14.022455<br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>0-9-14<br />
</td>
        <td>1-11/6-9/7<br />
</td>
        <td>swetismic<br />
</td>
        <td>14.04448<br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>0-12-14<br />
</td>
        <td>1-9/8-9/7<br />
</td>
        <td>utonal<br />
</td>
        <td>14.321999<br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td>0-2-15<br />
</td>
        <td>1-8/7-11/8<br />
</td>
        <td>keenanismic<br />
</td>
        <td>15.000220<br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>0-3-15<br />
</td>
        <td>1-11/9-11/8<br />
</td>
        <td>utonal<br />
</td>
        <td>15.000396<br />
</td>
    </tr>
    <tr>
        <td>32<br />
</td>
        <td>0-6-15<br />
</td>
        <td>1-3/2-11/8<br />
</td>
        <td>otonal<br />
</td>
        <td>15.002859<br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>0-7-15<br />
</td>
        <td>1-8/5-11/8<br />
</td>
        <td>keenanismic<br />
</td>
        <td>15.005660<br />
</td>
    </tr>
    <tr>
        <td>34<br />
</td>
        <td>0-8-15<br />
</td>
        <td>1-12/7-11/8<br />
</td>
        <td>keenanismic<br />
</td>
        <td>15.011271<br />
</td>
    </tr>
    <tr>
        <td>35<br />
</td>
        <td>0-9-15<br />
</td>
        <td>1-11/6-11/8<br />
</td>
        <td>utonal<br />
</td>
        <td>15.022411<br />
</td>
    </tr>
    <tr>
        <td>36<br />
</td>
        <td>0-12-15<br />
</td>
        <td>1-9/8-11/8<br />
</td>
        <td>otonal<br />
</td>
        <td>15.169964<br />
</td>
    </tr>
    <tr>
        <td>37<br />
</td>
        <td>0-13-15<br />
</td>
        <td>1-6/5-11/8<br />
</td>
        <td>keenanismic<br />
</td>
        <td>15.321963<br />
</td>
    </tr>
    <tr>
        <td>38<br />
</td>
        <td>0-2-17<br />
</td>
        <td>1-8/7-11/7<br />
</td>
        <td>otonal<br />
</td>
        <td>17.000055<br />
</td>
    </tr>
    <tr>
        <td>39<br />
</td>
        <td>0-3-17<br />
</td>
        <td>1-11/9-11/7<br />
</td>
        <td>utonal<br />
</td>
        <td>17.000099<br />
</td>
    </tr>
    <tr>
        <td>40<br />
</td>
        <td>0-5-17<br />
</td>
        <td>1-7/5-11/7<br />
</td>
        <td>werckismic<br />
</td>
        <td>17.000363<br />
</td>
    </tr>
    <tr>
        <td>41<br />
</td>
        <td>0-8-17<br />
</td>
        <td>1-12/7-11/7<br />
</td>
        <td>otonal<br />
</td>
        <td>17.002826<br />
</td>
    </tr>
    <tr>
        <td>42<br />
</td>
        <td>0-9-17<br />
</td>
        <td>1-11/6-11/7<br />
</td>
        <td>utonal<br />
</td>
        <td>17.005636<br />
</td>
    </tr>
    <tr>
        <td>43<br />
</td>
        <td>0-12-17<br />
</td>
        <td>1-9/8-11/7<br />
</td>
        <td>werckismic<br />
</td>
        <td>17.0444<br />
</td>
    </tr>
    <tr>
        <td>44<br />
</td>
        <td>0-14-17<br />
</td>
        <td>1-9/7-11/7<br />
</td>
        <td>otonal<br />
</td>
        <td>17.169935<br />
</td>
    </tr>
    <tr>
        <td>45<br />
</td>
        <td>0-15-17<br />
</td>
        <td>1-11/8-11/7<br />
</td>
        <td>utonal<br />
</td>
        <td>17.321937<br />
</td>
    </tr>
    <tr>
        <td>46<br />
</td>
        <td>0-2-19<br />
</td>
        <td>1-8/7-9/5<br />
</td>
        <td>werckismic<br />
</td>
        <td>19.000014<br />
</td>
    </tr>
    <tr>
        <td>47<br />
</td>
        <td>0-5-19<br />
</td>
        <td>1-7/5-9/5<br />
</td>
        <td>otonal<br />
</td>
        <td>19.000091<br />
</td>
    </tr>
    <tr>
        <td>48<br />
</td>
        <td>0-6-19<br />
</td>
        <td>1-3/2-9/5<br />
</td>
        <td>utonal<br />
</td>
        <td>19.000179<br />
</td>
    </tr>
    <tr>
        <td>49<br />
</td>
        <td>0-7-19<br />
</td>
        <td>1-8/5-9/5<br />
</td>
        <td>otonal<br />
</td>
        <td>19.000355<br />
</td>
    </tr>
    <tr>
        <td>50<br />
</td>
        <td>0-12-19<br />
</td>
        <td>1-9/8-9/5<br />
</td>
        <td>utonal<br />
</td>
        <td>19.011230<br />
</td>
    </tr>
    <tr>
        <td>51<br />
</td>
        <td>0-13-19<br />
</td>
        <td>1-6/5-9/5<br />
</td>
        <td>otonal<br />
</td>
        <td>19.022371<br />
</td>
    </tr>
    <tr>
        <td>52<br />
</td>
        <td>0-14-19<br />
</td>
        <td>1-9/7-9/5<br />
</td>
        <td>utonal<br />
</td>
        <td>19.044397<br />
</td>
    </tr>
    <tr>
        <td>53<br />
</td>
        <td>0-17-19<br />
</td>
        <td>1-11/7-9/5<br />
</td>
        <td>werckismic<br />
</td>
        <td>19.321930<br />
</td>
    </tr>
    <tr>
        <td>54<br />
</td>
        <td>0-3-22<br />
</td>
        <td>1-11/9-11/10<br />
</td>
        <td>utonal<br />
</td>
        <td>22.000003<br />
</td>
    </tr>
    <tr>
        <td>55<br />
</td>
        <td>0-5-22<br />
</td>
        <td>1-7/5-11/10<br />
</td>
        <td>otonal<br />
</td>
        <td>22.000011<br />
</td>
    </tr>
    <tr>
        <td>56<br />
</td>
        <td>0-7-22<br />
</td>
        <td>1-8/5-11/10<br />
</td>
        <td>otonal<br />
</td>
        <td>22.000044<br />
</td>
    </tr>
    <tr>
        <td>57<br />
</td>
        <td>0-8-22<br />
</td>
        <td>1-12/7-11/10<br />
</td>
        <td>swetismic<br />
</td>
        <td>22.000088<br />
</td>
    </tr>
    <tr>
        <td>58<br />
</td>
        <td>0-9-22<br />
</td>
        <td>1-11/6-11/10<br />
</td>
        <td>utonal<br />
</td>
        <td>22.000176<br />
</td>
    </tr>
    <tr>
        <td>59<br />
</td>
        <td>0-13-22<br />
</td>
        <td>1-6/5-11/10<br />
</td>
        <td>otonal<br />
</td>
        <td>22.002815<br />
</td>
    </tr>
    <tr>
        <td>60<br />
</td>
        <td>0-14-22<br />
</td>
        <td>1-9/7-11/10<br />
</td>
        <td>swetismic<br />
</td>
        <td>22.005625<br />
</td>
    </tr>
    <tr>
        <td>61<br />
</td>
        <td>0-15-22<br />
</td>
        <td>1-11/8-11/10<br />
</td>
        <td>utonal<br />
</td>
        <td>22.011228<br />
</td>
    </tr>
    <tr>
        <td>62<br />
</td>
        <td>0-17-22<br />
</td>
        <td>1-11/7-11/10<br />
</td>
        <td>utonal<br />
</td>
        <td>22.044394<br />
</td>
    </tr>
    <tr>
        <td>63<br />
</td>
        <td>0-19-22<br />
</td>
        <td>1-9/5-11/10<br />
</td>
        <td>otonal<br />
</td>
        <td>22.169925<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>
        <td>Hash<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>0-2-5-7<br />
</td>
        <td>1-8/7-7/5-8/5<br />
</td>
        <td>werckismic<br />
</td>
        <td>7.366322<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>0-2-5-8<br />
</td>
        <td>1-8/7-7/5-12/7<br />
</td>
        <td>jove<br />
</td>
        <td>8.194757<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>0-3-5-8<br />
</td>
        <td>1-11/9-7/5-12/7<br />
</td>
        <td>jove<br />
</td>
        <td>8.214319<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>0-3-6-8<br />
</td>
        <td>1-11/9-3/2-12/7<br />
</td>
        <td>jove<br />
</td>
        <td>8.361944<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>0-3-6-9<br />
</td>
        <td>1-11/9-3/2-11/6<br />
</td>
        <td>rastmic<br />
</td>
        <td>9.192293<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>0-2-7-9<br />
</td>
        <td>1-8/7-8/5-11/6<br />
</td>
        <td>keenanismic<br />
</td>
        <td>9.333155<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>0-3-5-12<br />
</td>
        <td>1-11/9-7/5-9/8<br />
</td>
        <td>miracle<br />
</td>
        <td>12.014369<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>0-3-6-12<br />
</td>
        <td>1-11/9-3/2-9/8<br />
</td>
        <td>rastmic<br />
</td>
        <td>12.025486<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>0-5-7-12<br />
</td>
        <td>1-7/5-8/5-9/8<br />
</td>
        <td>marvel<br />
</td>
        <td>12.055621<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>0-3-9-12<br />
</td>
        <td>1-11/9-11/6-9/8<br />
</td>
        <td>rastmic<br />
</td>
        <td>12.172740<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>0-6-9-12<br />
</td>
        <td>1-3/2-11/6-9/8<br />
</td>
        <td>rastmic<br />
</td>
        <td>12.190133<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>0-7-9-12<br />
</td>
        <td>1-8/5-11/6-9/8<br />
</td>
        <td>miracle<br />
</td>
        <td>12.209758<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>0-5-7-13<br />
</td>
        <td>1-7/5-8/5-6/5<br />
</td>
        <td>otonal<br />
</td>
        <td>13.028079<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>0-5-8-13<br />
</td>
        <td>1-7/5-12/7-6/5<br />
</td>
        <td>swetismic<br />
</td>
        <td>13.050019<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>0-6-8-13<br />
</td>
        <td>1-3/2-12/7-6/5<br />
</td>
        <td>utonal<br />
</td>
        <td>13.055452<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>0-2-5-14<br />
</td>
        <td>1-8/7-7/5-9/7<br />
</td>
        <td>jove<br />
</td>
        <td>14.003254<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>0-2-7-14<br />
</td>
        <td>1-8/7-8/5-9/7<br />
</td>
        <td>marvel<br />
</td>
        <td>14.011664<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>0-5-7-14<br />
</td>
        <td>1-7/5-8/5-9/7<br />
</td>
        <td>unimarvel<br />
</td>
        <td>14.014108<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>0-2-8-14<br />
</td>
        <td>1-8/7-12/7-9/7<br />
</td>
        <td>otonal<br />
</td>
        <td>14.022801<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>0-5-8-14<br />
</td>
        <td>1-7/5-12/7-9/7<br />
</td>
        <td>swetismic<br />
</td>
        <td>14.025226<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>0-6-8-14<br />
</td>
        <td>1-3/2-12/7-9/7<br />
</td>
        <td>ambitonal<br />
</td>
        <td>14.027992<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>0-2-9-14<br />
</td>
        <td>1-8/7-11/6-9/7<br />
</td>
        <td>unimarvel<br />
</td>
        <td>14.044821<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>0-6-9-14<br />
</td>
        <td>1-3/2-11/6-9/7<br />
</td>
        <td>swetismic<br />
</td>
        <td>14.049934<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>0-7-9-14<br />
</td>
        <td>1-8/5-11/6-9/7<br />
</td>
        <td>unimarvel<br />
</td>
        <td>14.055367<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>0-5-12-14<br />
</td>
        <td>1-7/5-9/8-9/7<br />
</td>
        <td>unimarvel<br />
</td>
        <td>14.324251<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>0-6-12-14<br />
</td>
        <td>1-3/2-9/8-9/7<br />
</td>
        <td>utonal<br />
</td>
        <td>14.326500<br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>0-7-12-14<br />
</td>
        <td>1-8/5-9/8-9/7<br />
</td>
        <td>marvel<br />
</td>
        <td>14.330987<br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>0-9-12-14<br />
</td>
        <td>1-11/6-9/8-9/7<br />
</td>
        <td>jove<br />
</td>
        <td>14.357621<br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>0-3-6-15<br />
</td>
        <td>1-11/9-3/2-11/8<br />
</td>
        <td>rastmic<br />
</td>
        <td>15.003210<br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td>0-2-7-15<br />
</td>
        <td>1-8/7-8/5-11/8<br />
</td>
        <td>keenanismic<br />
</td>
        <td>15.005844<br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>0-2-8-15<br />
</td>
        <td>1-8/7-12/7-11/8<br />
</td>
        <td>keenanismic<br />
</td>
        <td>15.011446<br />
</td>
    </tr>
    <tr>
        <td>32<br />
</td>
        <td>0-3-8-15<br />
</td>
        <td>1-11/9-12/7-11/8<br />
</td>
        <td>unimarvel<br />
</td>
        <td>15.011620<br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>0-6-8-15<br />
</td>
        <td>1-3/2-12/7-11/8<br />
</td>
        <td>keenanismic<br />
</td>
        <td>15.014064<br />
</td>
    </tr>
    <tr>
        <td>34<br />
</td>
        <td>0-2-9-15<br />
</td>
        <td>1-8/7-11/6-11/8<br />
</td>
        <td>keenanismic<br />
</td>
        <td>15.022585<br />
</td>
    </tr>
    <tr>
        <td>35<br />
</td>
        <td>0-3-9-15<br />
</td>
        <td>1-11/9-11/6-11/8<br />
</td>
        <td>utonal<br />
</td>
        <td>15.022758<br />
</td>
    </tr>
    <tr>
        <td>36<br />
</td>
        <td>0-6-9-15<br />
</td>
        <td>1-3/2-11/6-11/8<br />
</td>
        <td>ambitonal<br />
</td>
        <td>15.025183<br />
</td>
    </tr>
    <tr>
        <td>37<br />
</td>
        <td>0-7-9-15<br />
</td>
        <td>1-8/5-11/6-11/8<br />
</td>
        <td>keenanismic<br />
</td>
        <td>15.027949<br />
</td>
    </tr>
    <tr>
        <td>38<br />
</td>
        <td>0-3-12-15<br />
</td>
        <td>1-11/9-9/8-11/8<br />
</td>
        <td>rastmic<br />
</td>
        <td>15.170277<br />
</td>
    </tr>
    <tr>
        <td>39<br />
</td>
        <td>0-6-12-15<br />
</td>
        <td>1-3/2-9/8-11/8<br />
</td>
        <td>otonal<br />
</td>
        <td>15.172467<br />
</td>
    </tr>
    <tr>
        <td>40<br />
</td>
        <td>0-7-12-15<br />
</td>
        <td>1-8/5-9/8-11/8<br />
</td>
        <td>unimarvel<br />
</td>
        <td>15.174965<br />
</td>
    </tr>
    <tr>
        <td>41<br />
</td>
        <td>0-9-12-15<br />
</td>
        <td>1-11/6-9/8-11/8<br />
</td>
        <td>rastmic<br />
</td>
        <td>15.189863<br />
</td>
    </tr>
    <tr>
        <td>42<br />
</td>
        <td>0-6-13-15<br />
</td>
        <td>1-3/2-6/5-11/8<br />
</td>
        <td>keenanismic<br />
</td>
        <td>15.324216<br />
</td>
    </tr>
    <tr>
        <td>43<br />
</td>
        <td>0-7-13-15<br />
</td>
        <td>1-8/5-6/5-11/8<br />
</td>
        <td>keenanismic<br />
</td>
        <td>15.326465<br />
</td>
    </tr>
    <tr>
        <td>44<br />
</td>
        <td>0-8-13-15<br />
</td>
        <td>1-12/7-6/5-11/8<br />
</td>
        <td>keenanismic<br />
</td>
        <td>15.330952<br />
</td>
    </tr>
    <tr>
        <td>45<br />
</td>
        <td>0-2-5-17<br />
</td>
        <td>1-8/7-7/5-11/7<br />
</td>
        <td>werckismic<br />
</td>
        <td>17.000407<br />
</td>
    </tr>
    <tr>
        <td>46<br />
</td>
        <td>0-3-5-17<br />
</td>
        <td>1-11/9-7/5-11/7<br />
</td>
        <td>werckismic<br />
</td>
        <td>17.000451<br />
</td>
    </tr>
    <tr>
        <td>47<br />
</td>
        <td>0-2-8-17<br />
</td>
        <td>1-8/7-12/7-11/7<br />
</td>
        <td>otonal<br />
</td>
        <td>17.002870<br />
</td>
    </tr>
    <tr>
        <td>48<br />
</td>
        <td>0-3-8-17<br />
</td>
        <td>1-11/9-12/7-11/7<br />
</td>
        <td>swetismic<br />
</td>
        <td>17.002914<br />
</td>
    </tr>
    <tr>
        <td>49<br />
</td>
        <td>0-5-8-17<br />
</td>
        <td>1-7/5-12/7-11/7<br />
</td>
        <td>jove<br />
</td>
        <td>17.003177<br />
</td>
    </tr>
    <tr>
        <td>50<br />
</td>
        <td>0-2-9-17<br />
</td>
        <td>1-8/7-11/6-11/7<br />
</td>
        <td>keenanismic<br />
</td>
        <td>17.005679<br />
</td>
    </tr>
    <tr>
        <td>51<br />
</td>
        <td>0-3-9-17<br />
</td>
        <td>1-11/9-11/6-11/7<br />
</td>
        <td>utonal<br />
</td>
        <td>17.005723<br />
</td>
    </tr>
    <tr>
        <td>52<br />
</td>
        <td>0-3-12-17<br />
</td>
        <td>1-11/9-9/8-11/7<br />
</td>
        <td>jove<br />
</td>
        <td>17.044490<br />
</td>
    </tr>
    <tr>
        <td>53<br />
</td>
        <td>0-5-12-17<br />
</td>
        <td>1-7/5-9/8-11/7<br />
</td>
        <td>prodigy<br />
</td>
        <td>17.044746<br />
</td>
    </tr>
    <tr>
        <td>54<br />
</td>
        <td>0-9-12-17<br />
</td>
        <td>1-11/6-9/8-11/7<br />
</td>
        <td>jove<br />
</td>
        <td>17.049859<br />
</td>
    </tr>
    <tr>
        <td>55<br />
</td>
        <td>0-2-14-17<br />
</td>
        <td>1-8/7-9/7-11/7<br />
</td>
        <td>otonal<br />
</td>
        <td>17.169974<br />
</td>
    </tr>
    <tr>
        <td>56<br />
</td>
        <td>0-5-14-17<br />
</td>
        <td>1-7/5-9/7-11/7<br />
</td>
        <td>jove<br />
</td>
        <td>17.170248<br />
</td>
    </tr>
    <tr>
        <td>57<br />
</td>
        <td>0-8-14-17<br />
</td>
        <td>1-12/7-9/7-11/7<br />
</td>
        <td>otonal<br />
</td>
        <td>17.172437<br />
</td>
    </tr>
    <tr>
        <td>58<br />
</td>
        <td>0-9-14-17<br />
</td>
        <td>1-11/6-9/7-11/7<br />
</td>
        <td>swetismic<br />
</td>
        <td>17.174935<br />
</td>
    </tr>
    <tr>
        <td>59<br />
</td>
        <td>0-12-14-17<br />
</td>
        <td>1-9/8-9/7-11/7<br />
</td>
        <td>werckismic<br />
</td>
        <td>17.209463<br />
</td>
    </tr>
    <tr>
        <td>60<br />
</td>
        <td>0-2-15-17<br />
</td>
        <td>1-8/7-11/8-11/7<br />
</td>
        <td>keenanismic<br />
</td>
        <td>17.321972<br />
</td>
    </tr>
    <tr>
        <td>61<br />
</td>
        <td>0-3-15-17<br />
</td>
        <td>1-11/9-11/8-11/7<br />
</td>
        <td>utonal<br />
</td>
        <td>17.322007<br />
</td>
    </tr>
    <tr>
        <td>62<br />
</td>
        <td>0-8-15-17<br />
</td>
        <td>1-12/7-11/8-11/7<br />
</td>
        <td>keenanismic<br />
</td>
        <td>17.324189<br />
</td>
    </tr>
    <tr>
        <td>63<br />
</td>
        <td>0-9-15-17<br />
</td>
        <td>1-11/6-11/8-11/7<br />
</td>
        <td>utonal<br />
</td>
        <td>17.326438<br />
</td>
    </tr>
    <tr>
        <td>64<br />
</td>
        <td>0-12-15-17<br />
</td>
        <td>1-9/8-11/8-11/7<br />
</td>
        <td>werckismic<br />
</td>
        <td>17.357561<br />
</td>
    </tr>
    <tr>
        <td>65<br />
</td>
        <td>0-2-5-19<br />
</td>
        <td>1-8/7-7/5-9/5<br />
</td>
        <td>werckismic<br />
</td>
        <td>19.000102<br />
</td>
    </tr>
    <tr>
        <td>66<br />
</td>
        <td>0-2-7-19<br />
</td>
        <td>1-8/7-8/5-9/5<br />
</td>
        <td>werckismic<br />
</td>
        <td>19.000366<br />
</td>
    </tr>
    <tr>
        <td>67<br />
</td>
        <td>0-5-7-19<br />
</td>
        <td>1-7/5-8/5-9/5<br />
</td>
        <td>otonal<br />
</td>
        <td>19.000443<br />
</td>
    </tr>
    <tr>
        <td>68<br />
</td>
        <td>0-5-12-19<br />
</td>
        <td>1-7/5-9/8-9/5<br />
</td>
        <td>marvel<br />
</td>
        <td>19.011317<br />
</td>
    </tr>
    <tr>
        <td>69<br />
</td>
        <td>0-6-12-19<br />
</td>
        <td>1-3/2-9/8-9/5<br />
</td>
        <td>utonal<br />
</td>
        <td>19.011405<br />
</td>
    </tr>
    <tr>
        <td>70<br />
</td>
        <td>0-7-12-19<br />
</td>
        <td>1-8/5-9/8-9/5<br />
</td>
        <td>marvel<br />
</td>
        <td>19.011579<br />
</td>
    </tr>
    <tr>
        <td>71<br />
</td>
        <td>0-5-13-19<br />
</td>
        <td>1-7/5-6/5-9/5<br />
</td>
        <td>otonal<br />
</td>
        <td>19.022457<br />
</td>
    </tr>
    <tr>
        <td>72<br />
</td>
        <td>0-6-13-19<br />
</td>
        <td>1-3/2-6/5-9/5<br />
</td>
        <td>ambitonal<br />
</td>
        <td>19.022544<br />
</td>
    </tr>
    <tr>
        <td>73<br />
</td>
        <td>0-7-13-19<br />
</td>
        <td>1-8/5-6/5-9/5<br />
</td>
        <td>otonal<br />
</td>
        <td>19.022717<br />
</td>
    </tr>
    <tr>
        <td>74<br />
</td>
        <td>0-2-14-19<br />
</td>
        <td>1-8/7-9/7-9/5<br />
</td>
        <td>werckismic<br />
</td>
        <td>19.044407<br />
</td>
    </tr>
    <tr>
        <td>75<br />
</td>
        <td>0-5-14-19<br />
</td>
        <td>1-7/5-9/7-9/5<br />
</td>
        <td>swetismic<br />
</td>
        <td>19.044482<br />
</td>
    </tr>
    <tr>
        <td>76<br />
</td>
        <td>0-6-14-19<br />
</td>
        <td>1-3/2-9/7-9/5<br />
</td>
        <td>utonal<br />
</td>
        <td>19.044568<br />
</td>
    </tr>
    <tr>
        <td>77<br />
</td>
        <td>0-7-14-19<br />
</td>
        <td>1-8/5-9/7-9/5<br />
</td>
        <td>marvel<br />
</td>
        <td>19.044738<br />
</td>
    </tr>
    <tr>
        <td>78<br />
</td>
        <td>0-12-14-19<br />
</td>
        <td>1-9/8-9/7-9/5<br />
</td>
        <td>utonal<br />
</td>
        <td>19.055285<br />
</td>
    </tr>
    <tr>
        <td>79<br />
</td>
        <td>0-2-17-19<br />
</td>
        <td>1-8/7-11/7-9/5<br />
</td>
        <td>werckismic<br />
</td>
        <td>19.321939<br />
</td>
    </tr>
    <tr>
        <td>80<br />
</td>
        <td>0-5-17-19<br />
</td>
        <td>1-7/5-11/7-9/5<br />
</td>
        <td>werckismic<br />
</td>
        <td>19.322001<br />
</td>
    </tr>
    <tr>
        <td>81<br />
</td>
        <td>0-12-17-19<br />
</td>
        <td>1-9/8-11/7-9/5<br />
</td>
        <td>werckismic<br />
</td>
        <td>19.330919<br />
</td>
    </tr>
    <tr>
        <td>82<br />
</td>
        <td>0-14-17-19<br />
</td>
        <td>1-9/7-11/7-9/5<br />
</td>
        <td>werckismic<br />
</td>
        <td>19.357554<br />
</td>
    </tr>
    <tr>
        <td>83<br />
</td>
        <td>0-3-5-22<br />
</td>
        <td>1-11/9-7/5-11/10<br />
</td>
        <td>werckismic<br />
</td>
        <td>22.000014<br />
</td>
    </tr>
    <tr>
        <td>84<br />
</td>
        <td>0-5-7-22<br />
</td>
        <td>1-7/5-8/5-11/10<br />
</td>
        <td>otonal<br />
</td>
        <td>22.000055<br />
</td>
    </tr>
    <tr>
        <td>85<br />
</td>
        <td>0-3-8-22<br />
</td>
        <td>1-11/9-12/7-11/10<br />
</td>
        <td>swetismic<br />
</td>
        <td>22.000091<br />
</td>
    </tr>
    <tr>
        <td>86<br />
</td>
        <td>0-5-8-22<br />
</td>
        <td>1-7/5-12/7-11/10<br />
</td>
        <td>swetismic<br />
</td>
        <td>22.000099<br />
</td>
    </tr>
    <tr>
        <td>87<br />
</td>
        <td>0-3-9-22<br />
</td>
        <td>1-11/9-11/6-11/10<br />
</td>
        <td>utonal<br />
</td>
        <td>22.000179<br />
</td>
    </tr>
    <tr>
        <td>88<br />
</td>
        <td>0-7-9-22<br />
</td>
        <td>1-8/5-11/6-11/10<br />
</td>
        <td>keenanismic<br />
</td>
        <td>22.000220<br />
</td>
    </tr>
    <tr>
        <td>89<br />
</td>
        <td>0-5-13-22<br />
</td>
        <td>1-7/5-6/5-11/10<br />
</td>
        <td>otonal<br />
</td>
        <td>22.002826<br />
</td>
    </tr>
    <tr>
        <td>90<br />
</td>
        <td>0-7-13-22<br />
</td>
        <td>1-8/5-6/5-11/10<br />
</td>
        <td>otonal<br />
</td>
        <td>22.002859<br />
</td>
    </tr>
    <tr>
        <td>91<br />
</td>
        <td>0-8-13-22<br />
</td>
        <td>1-12/7-6/5-11/10<br />
</td>
        <td>swetismic<br />
</td>
        <td>22.002903<br />
</td>
    </tr>
    <tr>
        <td>92<br />
</td>
        <td>0-5-14-22<br />
</td>
        <td>1-7/5-9/7-11/10<br />
</td>
        <td>swetismic<br />
</td>
        <td>22.005636<br />
</td>
    </tr>
    <tr>
        <td>93<br />
</td>
        <td>0-7-14-22<br />
</td>
        <td>1-8/5-9/7-11/10<br />
</td>
        <td>unimarvel<br />
</td>
        <td>22.005669<br />
</td>
    </tr>
    <tr>
        <td>94<br />
</td>
        <td>0-8-14-22<br />
</td>
        <td>1-12/7-9/7-11/10<br />
</td>
        <td>swetismic<br />
</td>
        <td>22.005713<br />
</td>
    </tr>
    <tr>
        <td>95<br />
</td>
        <td>0-9-14-22<br />
</td>
        <td>1-11/6-9/7-11/10<br />
</td>
        <td>swetismic<br />
</td>
        <td>22.005800<br />
</td>
    </tr>
    <tr>
        <td>96<br />
</td>
        <td>0-3-15-22<br />
</td>
        <td>1-11/9-11/8-11/10<br />
</td>
        <td>utonal<br />
</td>
        <td>22.011230<br />
</td>
    </tr>
    <tr>
        <td>97<br />
</td>
        <td>0-7-15-22<br />
</td>
        <td>1-8/5-11/8-11/10<br />
</td>
        <td>keenanismic<br />
</td>
        <td>22.011271<br />
</td>
    </tr>
    <tr>
        <td>98<br />
</td>
        <td>0-8-15-22<br />
</td>
        <td>1-12/7-11/8-11/10<br />
</td>
        <td>unimarvel<br />
</td>
        <td>22.011315<br />
</td>
    </tr>
    <tr>
        <td>99<br />
</td>
        <td>0-9-15-22<br />
</td>
        <td>1-11/6-11/8-11/10<br />
</td>
        <td>utonal<br />
</td>
        <td>22.011402<br />
</td>
    </tr>
    <tr>
        <td>100<br />
</td>
        <td>0-13-15-22<br />
</td>
        <td>1-6/5-11/8-11/10<br />
</td>
        <td>keenanismic<br />
</td>
        <td>22.014021<br />
</td>
    </tr>
    <tr>
        <td>101<br />
</td>
        <td>0-3-17-22<br />
</td>
        <td>1-11/9-11/7-11/10<br />
</td>
        <td>utonal<br />
</td>
        <td>22.044397<br />
</td>
    </tr>
    <tr>
        <td>102<br />
</td>
        <td>0-5-17-22<br />
</td>
        <td>1-7/5-11/7-11/10<br />
</td>
        <td>werckismic<br />
</td>
        <td>22.044405<br />
</td>
    </tr>
    <tr>
        <td>103<br />
</td>
        <td>0-8-17-22<br />
</td>
        <td>1-12/7-11/7-11/10<br />
</td>
        <td>swetismic<br />
</td>
        <td>22.044480<br />
</td>
    </tr>
    <tr>
        <td>104<br />
</td>
        <td>0-9-17-22<br />
</td>
        <td>1-11/6-11/7-11/10<br />
</td>
        <td>utonal<br />
</td>
        <td>22.044565<br />
</td>
    </tr>
    <tr>
        <td>105<br />
</td>
        <td>0-14-17-22<br />
</td>
        <td>1-9/7-11/7-11/10<br />
</td>
        <td>swetismic<br />
</td>
        <td>22.049849<br />
</td>
    </tr>
    <tr>
        <td>106<br />
</td>
        <td>0-15-17-22<br />
</td>
        <td>1-11/8-11/7-11/10<br />
</td>
        <td>utonal<br />
</td>
        <td>22.055283<br />
</td>
    </tr>
    <tr>
        <td>107<br />
</td>
        <td>0-5-19-22<br />
</td>
        <td>1-7/5-9/5-11/10<br />
</td>
        <td>otonal<br />
</td>
        <td>22.169935<br />
</td>
    </tr>
    <tr>
        <td>108<br />
</td>
        <td>0-7-19-22<br />
</td>
        <td>1-8/5-9/5-11/10<br />
</td>
        <td>otonal<br />
</td>
        <td>22.169964<br />
</td>
    </tr>
    <tr>
        <td>109<br />
</td>
        <td>0-13-19-22<br />
</td>
        <td>1-6/5-9/5-11/10<br />
</td>
        <td>otonal<br />
</td>
        <td>22.172428<br />
</td>
    </tr>
    <tr>
        <td>110<br />
</td>
        <td>0-14-19-22<br />
</td>
        <td>1-9/7-9/5-11/10<br />
</td>
        <td>swetismic<br />
</td>
        <td>22.174926<br />
</td>
    </tr>
    <tr>
        <td>111<br />
</td>
        <td>0-17-19-22<br />
</td>
        <td>1-11/7-9/5-11/10<br />
</td>
        <td>werckismic<br />
</td>
        <td>22.209454<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>
        <td>Hash<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>0-3-6-9-12<br />
</td>
        <td>1-11/9-3/2-11/6-9/8<br />
</td>
        <td>rastmic<br />
</td>
        <td>12.192601<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>0-2-5-7-14<br />
</td>
        <td>1-8/7-7/5-8/5-9/7<br />
</td>
        <td>miracle<br />
</td>
        <td>14.014456<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>0-2-5-8-14<br />
</td>
        <td>1-8/7-7/5-12/7-9/7<br />
</td>
        <td>jove<br />
</td>
        <td>14.025572<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>0-2-7-9-14<br />
</td>
        <td>1-8/7-8/5-11/6-9/7<br />
</td>
        <td>unimarvel<br />
</td>
        <td>14.055706<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>0-5-7-12-14<br />
</td>
        <td>1-7/5-8/5-9/8-9/7<br />
</td>
        <td>unimarvel<br />
</td>
        <td>14.333225<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>0-6-9-12-14<br />
</td>
        <td>1-3/2-11/6-9/8-9/7<br />
</td>
        <td>jove<br />
</td>
        <td>14.362012<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>0-7-9-12-14<br />
</td>
        <td>1-8/5-11/6-9/8-9/7<br />
</td>
        <td>miracle<br />
</td>
        <td>14.366391<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>0-3-6-8-15<br />
</td>
        <td>1-11/9-3/2-12/7-11/8<br />
</td>
        <td>miracle<br />
</td>
        <td>15.014413<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>0-3-6-9-15<br />
</td>
        <td>1-11/9-3/2-11/6-11/8<br />
</td>
        <td>rastmic<br />
</td>
        <td>15.025529<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>0-2-7-9-15<br />
</td>
        <td>1-8/7-8/5-11/6-11/8<br />
</td>
        <td>keenanismic<br />
</td>
        <td>15.028122<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>0-3-6-12-15<br />
</td>
        <td>1-11/9-3/2-9/8-11/8<br />
</td>
        <td>rastmic<br />
</td>
        <td>15.172779<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>0-3-9-12-15<br />
</td>
        <td>1-11/9-11/6-9/8-11/8<br />
</td>
        <td>rastmic<br />
</td>
        <td>15.190172<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>0-6-9-12-15<br />
</td>
        <td>1-3/2-11/6-9/8-11/8<br />
</td>
        <td>rastmic<br />
</td>
        <td>15.192331<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>0-7-9-12-15<br />
</td>
        <td>1-8/5-11/6-9/8-11/8<br />
</td>
        <td>miracle<br />
</td>
        <td>15.194795<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>0-6-8-13-15<br />
</td>
        <td>1-3/2-12/7-6/5-11/8<br />
</td>
        <td>keenanismic<br />
</td>
        <td>15.333190<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>0-2-5-8-17<br />
</td>
        <td>1-8/7-7/5-12/7-11/7<br />
</td>
        <td>jove<br />
</td>
        <td>17.003221<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>0-3-5-8-17<br />
</td>
        <td>1-11/9-7/5-12/7-11/7<br />
</td>
        <td>jove<br />
</td>
        <td>17.003265<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>0-3-5-12-17<br />
</td>
        <td>1-11/9-7/5-9/8-11/7<br />
</td>
        <td>miracle<br />
</td>
        <td>17.044832<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>0-3-9-12-17<br />
</td>
        <td>1-11/9-11/6-9/8-11/7<br />
</td>
        <td>jove<br />
</td>
        <td>17.049944<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>0-2-5-14-17<br />
</td>
        <td>1-8/7-7/5-9/7-11/7<br />
</td>
        <td>jove<br />
</td>
        <td>17.170287<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>0-2-8-14-17<br />
</td>
        <td>1-8/7-12/7-9/7-11/7<br />
</td>
        <td>otonal<br />
</td>
        <td>17.172476<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>0-5-8-14-17<br />
</td>
        <td>1-7/5-12/7-9/7-11/7<br />
</td>
        <td>jove<br />
</td>
        <td>17.172750<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>0-2-9-14-17<br />
</td>
        <td>1-8/7-11/6-9/7-11/7<br />
</td>
        <td>unimarvel<br />
</td>
        <td>17.174974<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>0-5-12-14-17<br />
</td>
        <td>1-7/5-9/8-9/7-11/7<br />
</td>
        <td>miracle<br />
</td>
        <td>17.209767<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>0-9-12-14-17<br />
</td>
        <td>1-11/6-9/8-9/7-11/7<br />
</td>
        <td>jove<br />
</td>
        <td>17.214329<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>0-2-8-15-17<br />
</td>
        <td>1-8/7-12/7-11/8-11/7<br />
</td>
        <td>keenanismic<br />
</td>
        <td>17.324225<br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>0-3-8-15-17<br />
</td>
        <td>1-11/9-12/7-11/8-11/7<br />
</td>
        <td>unimarvel<br />
</td>
        <td>17.324260<br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>0-2-9-15-17<br />
</td>
        <td>1-8/7-11/6-11/8-11/7<br />
</td>
        <td>keenanismic<br />
</td>
        <td>17.326473<br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>0-3-9-15-17<br />
</td>
        <td>1-11/9-11/6-11/8-11/7<br />
</td>
        <td>utonal<br />
</td>
        <td>17.326508<br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td>0-3-12-15-17<br />
</td>
        <td>1-11/9-9/8-11/8-11/7<br />
</td>
        <td>jove<br />
</td>
        <td>17.357629<br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>0-9-12-15-17<br />
</td>
        <td>1-11/6-9/8-11/8-11/7<br />
</td>
        <td>jove<br />
</td>
        <td>17.361952<br />
</td>
    </tr>
    <tr>
        <td>32<br />
</td>
        <td>0-2-5-7-19<br />
</td>
        <td>1-8/7-7/5-8/5-9/5<br />
</td>
        <td>werckismic<br />
</td>
        <td>19.000454<br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>0-5-7-12-19<br />
</td>
        <td>1-7/5-8/5-9/8-9/5<br />
</td>
        <td>marvel<br />
</td>
        <td>19.011667<br />
</td>
    </tr>
    <tr>
        <td>34<br />
</td>
        <td>0-5-7-13-19<br />
</td>
        <td>1-7/5-8/5-6/5-9/5<br />
</td>
        <td>otonal<br />
</td>
        <td>19.022804<br />
</td>
    </tr>
    <tr>
        <td>35<br />
</td>
        <td>0-2-5-14-19<br />
</td>
        <td>1-8/7-7/5-9/7-9/5<br />
</td>
        <td>jove<br />
</td>
        <td>19.044493<br />
</td>
    </tr>
    <tr>
        <td>36<br />
</td>
        <td>0-2-7-14-19<br />
</td>
        <td>1-8/7-8/5-9/7-9/5<br />
</td>
        <td>prodigy<br />
</td>
        <td>19.044749<br />
</td>
    </tr>
    <tr>
        <td>37<br />
</td>
        <td>0-5-7-14-19<br />
</td>
        <td>1-7/5-8/5-9/7-9/5<br />
</td>
        <td>unimarvel<br />
</td>
        <td>19.044824<br />
</td>
    </tr>
    <tr>
        <td>38<br />
</td>
        <td>0-5-12-14-19<br />
</td>
        <td>1-7/5-9/8-9/7-9/5<br />
</td>
        <td>unimarvel<br />
</td>
        <td>19.055370<br />
</td>
    </tr>
    <tr>
        <td>39<br />
</td>
        <td>0-6-12-14-19<br />
</td>
        <td>1-3/2-9/8-9/7-9/5<br />
</td>
        <td>utonal<br />
</td>
        <td>19.055455<br />
</td>
    </tr>
    <tr>
        <td>40<br />
</td>
        <td>0-7-12-14-19<br />
</td>
        <td>1-8/5-9/8-9/7-9/5<br />
</td>
        <td>marvel<br />
</td>
        <td>19.055624<br />
</td>
    </tr>
    <tr>
        <td>41<br />
</td>
        <td>0-2-5-17-19<br />
</td>
        <td>1-8/7-7/5-11/7-9/5<br />
</td>
        <td>werckismic<br />
</td>
        <td>19.322010<br />
</td>
    </tr>
    <tr>
        <td>42<br />
</td>
        <td>0-5-12-17-19<br />
</td>
        <td>1-7/5-9/8-11/7-9/5<br />
</td>
        <td>prodigy<br />
</td>
        <td>19.330989<br />
</td>
    </tr>
    <tr>
        <td>43<br />
</td>
        <td>0-2-14-17-19<br />
</td>
        <td>1-8/7-9/7-11/7-9/5<br />
</td>
        <td>werckismic<br />
</td>
        <td>19.357563<br />
</td>
    </tr>
    <tr>
        <td>44<br />
</td>
        <td>0-5-14-17-19<br />
</td>
        <td>1-7/5-9/7-11/7-9/5<br />
</td>
        <td>jove<br />
</td>
        <td>19.357623<br />
</td>
    </tr>
    <tr>
        <td>45<br />
</td>
        <td>0-12-14-17-19<br />
</td>
        <td>1-9/8-9/7-11/7-9/5<br />
</td>
        <td>werckismic<br />
</td>
        <td>19.366324<br />
</td>
    </tr>
    <tr>
        <td>46<br />
</td>
        <td>0-3-5-8-22<br />
</td>
        <td>1-11/9-7/5-12/7-11/10<br />
</td>
        <td>jove<br />
</td>
        <td>22.000102<br />
</td>
    </tr>
    <tr>
        <td>47<br />
</td>
        <td>0-5-7-13-22<br />
</td>
        <td>1-7/5-8/5-6/5-11/10<br />
</td>
        <td>otonal<br />
</td>
        <td>22.002870<br />
</td>
    </tr>
    <tr>
        <td>48<br />
</td>
        <td>0-5-8-13-22<br />
</td>
        <td>1-7/5-12/7-6/5-11/10<br />
</td>
        <td>swetismic<br />
</td>
        <td>22.002914<br />
</td>
    </tr>
    <tr>
        <td>49<br />
</td>
        <td>0-5-7-14-22<br />
</td>
        <td>1-7/5-8/5-9/7-11/10<br />
</td>
        <td>unimarvel<br />
</td>
        <td>22.005680<br />
</td>
    </tr>
    <tr>
        <td>50<br />
</td>
        <td>0-5-8-14-22<br />
</td>
        <td>1-7/5-12/7-9/7-11/10<br />
</td>
        <td>swetismic<br />
</td>
        <td>22.005724<br />
</td>
    </tr>
    <tr>
        <td>51<br />
</td>
        <td>0-7-9-14-22<br />
</td>
        <td>1-8/5-11/6-9/7-11/10<br />
</td>
        <td>unimarvel<br />
</td>
        <td>22.005844<br />
</td>
    </tr>
    <tr>
        <td>52<br />
</td>
        <td>0-3-8-15-22<br />
</td>
        <td>1-11/9-12/7-11/8-11/10<br />
</td>
        <td>unimarvel<br />
</td>
        <td>22.011318<br />
</td>
    </tr>
    <tr>
        <td>53<br />
</td>
        <td>0-3-9-15-22<br />
</td>
        <td>1-11/9-11/6-11/8-11/10<br />
</td>
        <td>utonal<br />
</td>
        <td>22.011405<br />
</td>
    </tr>
    <tr>
        <td>54<br />
</td>
        <td>0-7-9-15-22<br />
</td>
        <td>1-8/5-11/6-11/8-11/10<br />
</td>
        <td>keenanismic<br />
</td>
        <td>22.011446<br />
</td>
    </tr>
    <tr>
        <td>55<br />
</td>
        <td>0-7-13-15-22<br />
</td>
        <td>1-8/5-6/5-11/8-11/10<br />
</td>
        <td>keenanismic<br />
</td>
        <td>22.014064<br />
</td>
    </tr>
    <tr>
        <td>56<br />
</td>
        <td>0-8-13-15-22<br />
</td>
        <td>1-12/7-6/5-11/8-11/10<br />
</td>
        <td>unimarvel<br />
</td>
        <td>22.014108<br />
</td>
    </tr>
    <tr>
        <td>57<br />
</td>
        <td>0-3-5-17-22<br />
</td>
        <td>1-11/9-7/5-11/7-11/10<br />
</td>
        <td>werckismic<br />
</td>
        <td>22.044408<br />
</td>
    </tr>
    <tr>
        <td>58<br />
</td>
        <td>0-3-8-17-22<br />
</td>
        <td>1-11/9-12/7-11/7-11/10<br />
</td>
        <td>swetismic<br />
</td>
        <td>22.044483<br />
</td>
    </tr>
    <tr>
        <td>59<br />
</td>
        <td>0-5-8-17-22<br />
</td>
        <td>1-7/5-12/7-11/7-11/10<br />
</td>
        <td>jove<br />
</td>
        <td>22.044491<br />
</td>
    </tr>
    <tr>
        <td>60<br />
</td>
        <td>0-3-9-17-22<br />
</td>
        <td>1-11/9-11/6-11/7-11/10<br />
</td>
        <td>utonal<br />
</td>
        <td>22.044568<br />
</td>
    </tr>
    <tr>
        <td>61<br />
</td>
        <td>0-5-14-17-22<br />
</td>
        <td>1-7/5-9/7-11/7-11/10<br />
</td>
        <td>jove<br />
</td>
        <td>22.049860<br />
</td>
    </tr>
    <tr>
        <td>62<br />
</td>
        <td>0-8-14-17-22<br />
</td>
        <td>1-12/7-9/7-11/7-11/10<br />
</td>
        <td>swetismic<br />
</td>
        <td>22.049934<br />
</td>
    </tr>
    <tr>
        <td>63<br />
</td>
        <td>0-9-14-17-22<br />
</td>
        <td>1-11/6-9/7-11/7-11/10<br />
</td>
        <td>swetismic<br />
</td>
        <td>22.050019<br />
</td>
    </tr>
    <tr>
        <td>64<br />
</td>
        <td>0-3-15-17-22<br />
</td>
        <td>1-11/9-11/8-11/7-11/10<br />
</td>
        <td>utonal<br />
</td>
        <td>22.055285<br />
</td>
    </tr>
    <tr>
        <td>65<br />
</td>
        <td>0-8-15-17-22<br />
</td>
        <td>1-12/7-11/8-11/7-11/10<br />
</td>
        <td>unimarvel<br />
</td>
        <td>22.055368<br />
</td>
    </tr>
    <tr>
        <td>66<br />
</td>
        <td>0-9-15-17-22<br />
</td>
        <td>1-11/6-11/8-11/7-11/10<br />
</td>
        <td>utonal<br />
</td>
        <td>22.055452<br />
</td>
    </tr>
    <tr>
        <td>67<br />
</td>
        <td>0-5-7-19-22<br />
</td>
        <td>1-7/5-8/5-9/5-11/10<br />
</td>
        <td>otonal<br />
</td>
        <td>22.169974<br />
</td>
    </tr>
    <tr>
        <td>68<br />
</td>
        <td>0-5-13-19-22<br />
</td>
        <td>1-7/5-6/5-9/5-11/10<br />
</td>
        <td>otonal<br />
</td>
        <td>22.172438<br />
</td>
    </tr>
    <tr>
        <td>69<br />
</td>
        <td>0-7-13-19-22<br />
</td>
        <td>1-8/5-6/5-9/5-11/10<br />
</td>
        <td>otonal<br />
</td>
        <td>22.172467<br />
</td>
    </tr>
    <tr>
        <td>70<br />
</td>
        <td>0-5-14-19-22<br />
</td>
        <td>1-7/5-9/7-9/5-11/10<br />
</td>
        <td>swetismic<br />
</td>
        <td>22.174936<br />
</td>
    </tr>
    <tr>
        <td>71<br />
</td>
        <td>0-7-14-19-22<br />
</td>
        <td>1-8/5-9/7-9/5-11/10<br />
</td>
        <td>unimarvel<br />
</td>
        <td>22.174965<br />
</td>
    </tr>
    <tr>
        <td>72<br />
</td>
        <td>0-5-17-19-22<br />
</td>
        <td>1-7/5-11/7-9/5-11/10<br />
</td>
        <td>werckismic<br />
</td>
        <td>22.209463<br />
</td>
    </tr>
    <tr>
        <td>73<br />
</td>
        <td>0-14-17-19-22<br />
</td>
        <td>1-9/7-11/7-9/5-11/10<br />
</td>
        <td>jove<br />
</td>
        <td>22.214319<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>
        <td>Hash<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>0-3-6-9-12-15<br />
</td>
        <td>1-11/9-3/2-11/6-9/8-11/8<br />
</td>
        <td>rastmic<br />
</td>
        <td>15.192640<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>0-2-5-8-14-17<br />
</td>
        <td>1-8/7-7/5-12/7-9/7-11/7<br />
</td>
        <td>jove<br />
</td>
        <td>17.172789<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>0-3-9-12-15-17<br />
</td>
        <td>1-11/9-11/6-9/8-11/8-11/7<br />
</td>
        <td>jove<br />
</td>
        <td>17.362021<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>0-2-5-7-14-19<br />
</td>
        <td>1-8/7-7/5-8/5-9/7-9/5<br />
</td>
        <td>miracle<br />
</td>
        <td>19.044834<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>0-5-7-12-14-19<br />
</td>
        <td>1-7/5-8/5-9/8-9/7-9/5<br />
</td>
        <td>unimarvel<br />
</td>
        <td>19.055709<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>0-2-5-14-17-19<br />
</td>
        <td>1-8/7-7/5-9/7-11/7-9/5<br />
</td>
        <td>jove<br />
</td>
        <td>19.357631<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>0-5-12-14-17-19<br />
</td>
        <td>1-7/5-9/8-9/7-11/7-9/5<br />
</td>
        <td>miracle<br />
</td>
        <td>19.366393<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>0-3-5-8-17-22<br />
</td>
        <td>1-11/9-7/5-12/7-11/7-11/10<br />
</td>
        <td>jove<br />
</td>
        <td>22.044493<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>0-5-8-14-17-22<br />
</td>
        <td>1-7/5-12/7-9/7-11/7-11/10<br />
</td>
        <td>jove<br />
</td>
        <td>22.049945<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>0-3-8-15-17-22<br />
</td>
        <td>1-11/9-12/7-11/8-11/7-11/10<br />
</td>
        <td>unimarvel<br />
</td>
        <td>22.055370<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>0-3-9-15-17-22<br />
</td>
        <td>1-11/9-11/6-11/8-11/7-11/10<br />
</td>
        <td>utonal<br />
</td>
        <td>22.055455<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>0-5-7-13-19-22<br />
</td>
        <td>1-7/5-8/5-6/5-9/5-11/10<br />
</td>
        <td>otonal<br />
</td>
        <td>22.172477<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>0-5-7-14-19-22<br />
</td>
        <td>1-7/5-8/5-9/7-9/5-11/10<br />
</td>
        <td>unimarvel<br />
</td>
        <td>22.174975<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>0-5-14-17-19-22<br />
</td>
        <td>1-7/5-9/7-11/7-9/5-11/10<br />
</td>
        <td>jove<br />
</td>
        <td>22.214329<br />
</td>
    </tr>
</table>

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