Sqrtphi/Chords: Difference between revisions

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**Imported revision 305328792 - Original comment: **
 
Wikispaces>genewardsmith
**Imported revision 305348348 - 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>2012-02-26 21:38:58 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-26 23:01:42 UTC</tt>.<br>
: The original revision id was <tt>305328792</tt>.<br>
: The original revision id was <tt>305348348</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">
<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 15-limit [[Dyadic chord|dyadic chords]] of [[Kleismic family#Sqrtphi|sqrtphi temperament]], subject to the condition that no interval smaller than [[12_11|12/11]], at 150 cents, appears. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 325/324 are labeled marveltwin, by 364/363 gentle, by 540/539 swetismic, by 676/675 island, and by 1575/1573 nicolic. [[Rank and codimension|Codimension]] two temperaments are labeled swetismic-gentle, island-gentle and kleismic-marveltwin according to two commas which define it.


Sqrtphi has MOS of size 5, 8, 11, 14, 17, 20, 23, 26, 49 and 72. The largest chords on these lists have complexity 70, and so would require the 72 note MOS, but there are many chords of much lower complexity. Sqrtphi has a generator very close to √φ, which can be chosen to be exactly √φ. Either way, aside from the dyadic chords, chords with stacks of φ are interesting since φ² - φ = 1, resulting in a relationship between difference tones. Though it isn't the "official" 13/8 of sqrtphi, φ is 7.44 cents flat of 13/8 which is close enough for government work. Chords such as 0-1-2-9-10 or 0-1-8-9-10 work a stack of φs into chords which composers might find of interest.


=Triads=
=Triads=
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=Pentads=
=Pentads=
|| Number || Chord || Transversal || Type ||
|| Number || Chord || Transversal || Type ||
|| 1 || 0-1-9-14-22 || 1-11/7-11/6-11/10-9/7 || swetismic ||
|| 2 || 0-8-13-21-22 || 1-7/6-7/5-18/11-9/7 || swetismic ||
|| 3 || 0-5-14-15-30 || 1-6/5-11/10-26/15-3/2 || island-gentle ||
|| 4 || 0-8-16-21-30 || 1-7/6-15/11-18/11-3/2 || swetismic ||
|| 5 || 0-8-9-22-30 || 1-7/6-11/6-9/7-3/2 || swetismic ||
|| 6 || 0-9-14-22-30 || 1-11/6-11/10-9/7-3/2 || swetismic ||
|| 7 || 0-8-21-22-30 || 1-7/6-18/11-9/7-3/2 || swetismic ||
|| 8 || 0-15-16-25-30 || 1-26/15-15/11-5/4-3/2 || island-gentle ||
|| 9 || 0-1-9-10-31 || 1-11/7-11/6-13/9-13/11 || gentle ||
|| 10 || 0-1-10-15-31 || 1-11/7-13/9-26/15-13/11 || gentle ||
|| 11 || 0-1-15-16-31 || 1-11/7-26/15-15/11-13/11 || island-gentle ||
|| 12 || 0-1-9-22-31 || 1-11/7-11/6-9/7-13/11 || swetismic-gentle ||
|| 13 || 0-15-16-30-31 || 1-26/15-15/11-3/2-13/11 || island-gentle ||
|| 14 || 0-16-21-30-31 || 1-15/11-18/11-3/2-13/11 || gentle ||
|| 15 || 0-9-22-30-31 || 1-11/6-9/7-3/2-13/11 || swetismic-gentle ||
|| 16 || 0-21-22-30-31 || 1-18/11-9/7-3/2-13/11 || gentle ||
|| 17 || 0-5-13-14-35 || 1-6/5-7/5-11/10-9/5 || otonal ||
|| 18 || 0-5-13-21-35 || 1-6/5-7/5-18/11-9/5 || swetismic ||
|| 19 || 0-13-14-22-35 || 1-7/5-11/10-9/7-9/5 || swetismic ||
|| 20 || 0-13-21-22-35 || 1-7/5-18/11-9/7-9/5 || swetismic ||
|| 21 || 0-5-14-30-35 || 1-6/5-11/10-3/2-9/5 || otonal ||
|| 22 || 0-5-21-30-35 || 1-6/5-18/11-3/2-9/5 || utonal ||
|| 23 || 0-14-22-30-35 || 1-11/10-9/7-3/2-9/5 || swetismic ||
|| 24 || 0-21-22-30-35 || 1-18/11-9/7-3/2-9/5 || utonal ||
|| 25 || 0-8-13-22-38 || 1-7/6-7/5-9/7-7/4 || swetismic ||
|| 26 || 0-8-16-30-38 || 1-7/6-15/11-3/2-7/4 || swetismic ||
|| 27 || 0-8-22-30-38 || 1-7/6-9/7-3/2-7/4 || swetismic ||
|| 28 || 0-16-25-30-38 || 1-15/11-5/4-3/2-7/4 || swetismic ||
|| 29 || 0-1-9-14-39 || 1-11/7-11/6-11/10-11/8 || utonal ||
|| 30 || 0-8-9-30-39 || 1-7/6-11/6-3/2-11/8 || gentle ||
|| 31 || 0-9-14-30-39 || 1-11/6-11/10-3/2-11/8 || utonal ||
|| 32 || 0-9-25-30-39 || 1-11/6-5/4-3/2-11/8 || otonal ||
|| 33 || 0-1-9-31-39 || 1-11/7-11/6-13/11-11/8 || gentle ||
|| 34 || 0-9-30-31-39 || 1-11/6-3/2-13/11-11/8 || gentle ||
|| 35 || 0-8-30-38-39 || 1-7/6-3/2-7/4-11/8 || gentle ||
|| 36 || 0-25-30-38-39 || 1-5/4-3/2-7/4-11/8 || otonal ||
|| 37 || 0-14-15-30-45 || 1-11/10-26/15-3/2-13/10 || island-gentle ||
|| 38 || 0-10-15-31-45 || 1-13/9-26/15-13/11-13/10 || utonal ||
|| 39 || 0-15-30-31-45 || 1-26/15-3/2-13/11-13/10 || island-gentle ||
|| 40 || 0-14-30-35-45 || 1-11/10-3/2-9/5-13/10 || otonal ||
|| 41 || 0-21-22-30-60 || 1-18/11-9/7-3/2-9/8 || utonal ||
|| 42 || 0-15-25-30-60 || 1-26/15-5/4-3/2-9/8 || island ||
|| 43 || 0-21-22-35-60 || 1-18/11-9/7-9/5-9/8 || utonal ||
|| 44 || 0-21-30-35-60 || 1-18/11-3/2-9/5-9/8 || utonal ||
|| 45 || 0-22-30-35-60 || 1-9/7-3/2-9/5-9/8 || utonal ||
|| 46 || 0-25-30-35-60 || 1-5/4-3/2-9/5-9/8 || marveltwin ||
|| 47 || 0-22-30-38-60 || 1-9/7-3/2-7/4-9/8 || swetismic ||
|| 48 || 0-25-30-38-60 || 1-5/4-3/2-7/4-9/8 || otonal ||
|| 49 || 0-25-30-39-60 || 1-5/4-3/2-11/8-9/8 || otonal ||
|| 50 || 0-25-38-39-60 || 1-5/4-7/4-11/8-9/8 || otonal ||
|| 51 || 0-30-38-39-60 || 1-3/2-7/4-11/8-9/8 || otonal ||
|| 52 || 0-15-30-45-60 || 1-26/15-3/2-13/10-9/8 || island ||
|| 53 || 0-30-35-45-60 || 1-3/2-9/5-13/10-9/8 || island ||
|| 54 || 0-10-25-35-70 || 1-13/9-5/4-9/5-13/8 || kleismic-marveltwin ||
|| 55 || 0-10-31-45-70 || 1-13/9-13/11-13/10-13/8 || utonal ||
|| 56 || 0-10-35-45-70 || 1-13/9-9/5-13/10-13/8 || marveltwin ||
|| 57 || 0-25-35-60-70 || 1-5/4-9/5-9/8-13/8 || marveltwin ||
|| 58 || 0-25-39-60-70 || 1-5/4-11/8-9/8-13/8 || otonal ||
|| 59 || 0-35-45-60-70 || 1-9/5-13/10-9/8-13/8 || kleismic-marveltwin ||


=Hexads=
=Hexads=
|| Number || Chord || Transversal || Type ||</pre></div>
|| Number || Chord || Transversal || Type ||
|| 1 || 0-21-22-30-35-60 || 1-18/11-9/7-3/2-9/5-9/8 ||utonal ||
|| 2 || 0-25-30-38-39-60 || 1-5/4-3/2-7/4-11/8-9/8 || otonal ||
</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 sqrtphi&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&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 sqrtphi&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Below are listed the 15-limit &lt;a class="wiki_link" href="/Dyadic%20chord"&gt;dyadic chords&lt;/a&gt; of &lt;a class="wiki_link" href="/Kleismic%20family#Sqrtphi"&gt;sqrtphi temperament&lt;/a&gt;, subject to the condition that no interval smaller than &lt;a class="wiki_link" href="/12_11"&gt;12/11&lt;/a&gt;, at 150 cents, appears. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 325/324 are labeled marveltwin, by 364/363 gentle, by 540/539 swetismic, by 676/675 island, and by 1575/1573 nicolic. &lt;a class="wiki_link" href="/Rank%20and%20codimension"&gt;Codimension&lt;/a&gt; two temperaments are labeled swetismic-gentle, island-gentle and kleismic-marveltwin according to two commas which define it. &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Sqrtphi has MOS of size 5, 8, 11, 14, 17, 20, 23, 26, 49 and 72. The largest chords on these lists have complexity 70, and so would require the 72 note MOS, but there are many chords of much lower complexity. Sqrtphi has a generator very close to √φ, which can be chosen to be exactly √φ. Either way, aside from the dyadic chords, chords with stacks of φ are interesting since φ² - φ = 1, resulting in a relationship between difference tones. Though it isn't the &amp;quot;official&amp;quot; 13/8 of sqrtphi, φ is 7.44 cents flat of 13/8 which is close enough for government work. Chords such as 0-1-2-9-10 or 0-1-8-9-10 work a stack of φs into chords which composers might find of interest.&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;
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&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
&lt;/table&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;table class="wiki_table"&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;Number&lt;br /&gt;
         &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-1-9-14-22&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/7-11/6-11/10-9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-8-13-21-22&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/6-7/5-18/11-9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-5-14-15-30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-6/5-11/10-26/15-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;island-gentle&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;Chord&lt;br /&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
         &lt;td&gt;4&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;Transversal&lt;br /&gt;
        &lt;td&gt;0-8-16-21-30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/6-15/11-18/11-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-8-9-22-30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/6-11/6-9/7-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-9-14-22-30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/6-11/10-9/7-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-8-21-22-30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/6-18/11-9/7-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-15-16-25-30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-26/15-15/11-5/4-3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;island-gentle&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-1-9-10-31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/7-11/6-13/9-13/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;gentle&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-1-10-15-31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/7-13/9-26/15-13/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;gentle&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-1-15-16-31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/7-26/15-15/11-13/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;island-gentle&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-1-9-22-31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/7-11/6-9/7-13/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic-gentle&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-15-16-30-31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-26/15-15/11-3/2-13/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;island-gentle&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-16-21-30-31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-15/11-18/11-3/2-13/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;gentle&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-9-22-30-31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/6-9/7-3/2-13/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic-gentle&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-21-22-30-31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-18/11-9/7-3/2-13/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;gentle&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-5-13-14-35&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-6/5-7/5-11/10-9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;18&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-5-13-21-35&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-6/5-7/5-18/11-9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-13-14-22-35&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/5-11/10-9/7-9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;20&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-13-21-22-35&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/5-18/11-9/7-9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-5-14-30-35&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-6/5-11/10-3/2-9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;22&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-5-21-30-35&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-6/5-18/11-3/2-9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-14-22-30-35&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/10-9/7-3/2-9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;24&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-21-22-30-35&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-18/11-9/7-3/2-9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-8-13-22-38&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/6-7/5-9/7-7/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;26&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-8-16-30-38&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/6-15/11-3/2-7/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-8-22-30-38&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/6-9/7-3/2-7/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-16-25-30-38&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-15/11-5/4-3/2-7/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;29&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-1-9-14-39&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/7-11/6-11/10-11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-8-9-30-39&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/6-11/6-3/2-11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;gentle&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-9-14-30-39&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/6-11/10-3/2-11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-9-25-30-39&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/6-5/4-3/2-11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;33&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-1-9-31-39&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/7-11/6-13/11-11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;gentle&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;34&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-9-30-31-39&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/6-3/2-13/11-11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;gentle&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;35&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-8-30-38-39&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-7/6-3/2-7/4-11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;gentle&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;36&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-25-30-38-39&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-3/2-7/4-11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;37&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-14-15-30-45&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/10-26/15-3/2-13/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;island-gentle&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;38&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-10-15-31-45&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-13/9-26/15-13/11-13/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;39&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-15-30-31-45&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-26/15-3/2-13/11-13/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;island-gentle&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;40&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-14-30-35-45&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-11/10-3/2-9/5-13/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;41&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-21-22-30-60&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-18/11-9/7-3/2-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;42&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-15-25-30-60&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-26/15-5/4-3/2-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;island&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;43&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-21-22-35-60&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-18/11-9/7-9/5-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;44&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-21-30-35-60&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-18/11-3/2-9/5-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;45&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-22-30-35-60&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-9/7-3/2-9/5-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;46&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-25-30-35-60&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-3/2-9/5-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;marveltwin&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;47&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-22-30-38-60&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-9/7-3/2-7/4-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;swetismic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;48&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-25-30-38-60&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-3/2-7/4-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;49&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-25-30-39-60&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-3/2-11/8-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;50&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-25-38-39-60&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-7/4-11/8-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;51&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-30-38-39-60&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-3/2-7/4-11/8-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;52&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-15-30-45-60&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-26/15-3/2-13/10-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;island&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;53&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-30-35-45-60&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-3/2-9/5-13/10-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;island&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;54&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-10-25-35-70&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-13/9-5/4-9/5-13/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;kleismic-marveltwin&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;55&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-10-31-45-70&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-13/9-13/11-13/10-13/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;56&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-10-35-45-70&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-13/9-9/5-13/10-13/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;marveltwin&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;57&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-25-35-60-70&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-9/5-9/8-13/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;marveltwin&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;58&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-25-39-60-70&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-11/8-9/8-13/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;59&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-35-45-60-70&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-9/5-13/10-9/8-13/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;kleismic-marveltwin&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&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;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;Number&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Chord&lt;br /&gt;
&lt;/td&gt;
         &lt;td&gt;Transversal&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;Type&lt;br /&gt;
         &lt;td&gt;Type&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-21-22-30-35-60&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-18/11-9/7-3/2-9/5-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;utonal&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0-25-30-38-39-60&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1-5/4-3/2-7/4-11/8-9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;otonal&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;

Revision as of 23:01, 26 February 2012

IMPORTED REVISION FROM WIKISPACES

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This revision was by author genewardsmith and made on 2012-02-26 23:01:42 UTC.
The original revision id was 305348348.
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Original Wikitext content:

Below are listed the 15-limit [[Dyadic chord|dyadic chords]] of [[Kleismic family#Sqrtphi|sqrtphi temperament]], subject to the condition that no interval smaller than [[12_11|12/11]], at 150 cents, appears. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 325/324 are labeled marveltwin, by 364/363 gentle, by 540/539 swetismic, by 676/675 island, and by 1575/1573 nicolic. [[Rank and codimension|Codimension]] two temperaments are labeled swetismic-gentle, island-gentle and kleismic-marveltwin according to two commas which define it. 

Sqrtphi has MOS of size 5, 8, 11, 14, 17, 20, 23, 26, 49 and 72. The largest chords on these lists have complexity 70, and so would require the 72 note MOS, but there are many chords of much lower complexity. Sqrtphi has a generator very close to √φ, which can be chosen to be exactly √φ. Either way, aside from the dyadic chords, chords with stacks of φ are interesting since φ² - φ = 1, resulting in a relationship between difference tones. Though it isn't the "official" 13/8 of sqrtphi, φ is 7.44 cents flat of 13/8 which is close enough for government work. Chords such as 0-1-2-9-10 or 0-1-8-9-10 work a stack of φs into chords which composers might find of interest.

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

=Tetrads=
|| Number || Chord || Transversal || Type ||
|| 1 || 0-1-9-10 || 1-11/7-11/6-13/9 || gentle ||
|| 2 || 0-1-9-14 || 1-11/7-11/6-11/10 || utonal ||
|| 3 || 0-5-13-14 || 1-6/5-7/5-11/10 || otonal ||
|| 4 || 0-1-10-15 || 1-11/7-13/9-26/15 || gentle ||
|| 5 || 0-5-10-15 || 1-6/5-13/9-26/15 || marveltwin ||
|| 6 || 0-1-14-15 || 1-11/7-11/10-26/15 || gentle ||
|| 7 || 0-5-14-15 || 1-6/5-11/10-26/15 || gentle ||
|| 8 || 0-1-15-16 || 1-11/7-26/15-15/11 || island-gentle ||
|| 9 || 0-5-13-21 || 1-6/5-7/5-18/11 || swetismic ||
|| 10 || 0-8-13-21 || 1-7/6-7/5-18/11 || swetismic ||
|| 11 || 0-8-16-21 || 1-7/6-15/11-18/11 || swetismic ||
|| 12 || 0-1-9-22 || 1-11/7-11/6-9/7 || swetismic ||
|| 13 || 0-8-9-22 || 1-7/6-11/6-9/7 || swetismic ||
|| 14 || 0-8-13-22 || 1-7/6-7/5-9/7 || swetismic ||
|| 15 || 0-1-14-22 || 1-11/7-11/10-9/7 || swetismic ||
|| 16 || 0-9-14-22 || 1-11/6-11/10-9/7 || swetismic ||
|| 17 || 0-13-14-22 || 1-7/5-11/10-9/7 || swetismic ||
|| 18 || 0-8-21-22 || 1-7/6-18/11-9/7 || swetismic ||
|| 19 || 0-13-21-22 || 1-7/5-18/11-9/7 || swetismic ||
|| 20 || 0-9-10-25 || 1-11/6-13/9-5/4 || island-gentle ||
|| 21 || 0-10-15-25 || 1-13/9-26/15-5/4 || island ||
|| 22 || 0-15-16-25 || 1-26/15-15/11-5/4 || island-gentle ||
|| 23 || 0-8-9-30 || 1-7/6-11/6-3/2 || otonal ||
|| 24 || 0-5-14-30 || 1-6/5-11/10-3/2 || otonal ||
|| 25 || 0-9-14-30 || 1-11/6-11/10-3/2 || utonal ||
|| 26 || 0-5-15-30 || 1-6/5-26/15-3/2 || island ||
|| 27 || 0-14-15-30 || 1-11/10-26/15-3/2 || island-gentle ||
|| 28 || 0-8-16-30 || 1-7/6-15/11-3/2 || swetismic ||
|| 29 || 0-15-16-30 || 1-26/15-15/11-3/2 || island-gentle ||
|| 30 || 0-5-21-30 || 1-6/5-18/11-3/2 || utonal ||
|| 31 || 0-8-21-30 || 1-7/6-18/11-3/2 || swetismic ||
|| 32 || 0-16-21-30 || 1-15/11-18/11-3/2 || otonal ||
|| 33 || 0-8-22-30 || 1-7/6-9/7-3/2 || swetismic ||
|| 34 || 0-9-22-30 || 1-11/6-9/7-3/2 || swetismic ||
|| 35 || 0-14-22-30 || 1-11/10-9/7-3/2 || swetismic ||
|| 36 || 0-21-22-30 || 1-18/11-9/7-3/2 || utonal ||
|| 37 || 0-9-25-30 || 1-11/6-5/4-3/2 || otonal ||
|| 38 || 0-15-25-30 || 1-26/15-5/4-3/2 || island ||
|| 39 || 0-16-25-30 || 1-15/11-5/4-3/2 || utonal ||
|| 40 || 0-1-9-31 || 1-11/7-11/6-13/11 || gentle ||
|| 41 || 0-1-10-31 || 1-11/7-13/9-13/11 || gentle ||
|| 42 || 0-9-10-31 || 1-11/6-13/9-13/11 || gentle ||
|| 43 || 0-1-15-31 || 1-11/7-26/15-13/11 || gentle ||
|| 44 || 0-10-15-31 || 1-13/9-26/15-13/11 || utonal ||
|| 45 || 0-1-16-31 || 1-11/7-15/11-13/11 || island-gentle ||
|| 46 || 0-15-16-31 || 1-26/15-15/11-13/11 || nicolic ||
|| 47 || 0-16-21-31 || 1-15/11-18/11-13/11 || otonal ||
|| 48 || 0-1-22-31 || 1-11/7-9/7-13/11 || gentle ||
|| 49 || 0-9-22-31 || 1-11/6-9/7-13/11 || swetismic-gentle ||
|| 50 || 0-21-22-31 || 1-18/11-9/7-13/11 || gentle ||
|| 51 || 0-9-30-31 || 1-11/6-3/2-13/11 || gentle ||
|| 52 || 0-15-30-31 || 1-26/15-3/2-13/11 || island-gentle ||
|| 53 || 0-16-30-31 || 1-15/11-3/2-13/11 || gentle ||
|| 54 || 0-21-30-31 || 1-18/11-3/2-13/11 || gentle ||
|| 55 || 0-22-30-31 || 1-9/7-3/2-13/11 || gentle ||
|| 56 || 0-5-10-35 || 1-6/5-13/9-9/5 || marveltwin ||
|| 57 || 0-5-13-35 || 1-6/5-7/5-9/5 || otonal ||
|| 58 || 0-5-14-35 || 1-6/5-11/10-9/5 || otonal ||
|| 59 || 0-13-14-35 || 1-7/5-11/10-9/5 || otonal ||
|| 60 || 0-5-21-35 || 1-6/5-18/11-9/5 || utonal ||
|| 61 || 0-13-21-35 || 1-7/5-18/11-9/5 || swetismic ||
|| 62 || 0-13-22-35 || 1-7/5-9/7-9/5 || swetismic ||
|| 63 || 0-14-22-35 || 1-11/10-9/7-9/5 || swetismic ||
|| 64 || 0-21-22-35 || 1-18/11-9/7-9/5 || utonal ||
|| 65 || 0-10-25-35 || 1-13/9-5/4-9/5 || kleismic-marveltwin ||
|| 66 || 0-5-30-35 || 1-6/5-3/2-9/5 || ambitonal ||
|| 67 || 0-14-30-35 || 1-11/10-3/2-9/5 || otonal ||
|| 68 || 0-21-30-35 || 1-18/11-3/2-9/5 || utonal ||
|| 69 || 0-22-30-35 || 1-9/7-3/2-9/5 || utonal ||
|| 70 || 0-25-30-35 || 1-5/4-3/2-9/5 || marveltwin ||
|| 71 || 0-8-13-38 || 1-7/6-7/5-7/4 || utonal ||
|| 72 || 0-8-16-38 || 1-7/6-15/11-7/4 || swetismic ||
|| 73 || 0-8-22-38 || 1-7/6-9/7-7/4 || swetismic ||
|| 74 || 0-13-22-38 || 1-7/5-9/7-7/4 || swetismic ||
|| 75 || 0-16-25-38 || 1-15/11-5/4-7/4 || swetismic ||
|| 76 || 0-8-30-38 || 1-7/6-3/2-7/4 || ambitonal ||
|| 77 || 0-16-30-38 || 1-15/11-3/2-7/4 || swetismic ||
|| 78 || 0-22-30-38 || 1-9/7-3/2-7/4 || swetismic ||
|| 79 || 0-25-30-38 || 1-5/4-3/2-7/4 || otonal ||
|| 80 || 0-1-9-39 || 1-11/7-11/6-11/8 || utonal ||
|| 81 || 0-8-9-39 || 1-7/6-11/6-11/8 || gentle ||
|| 82 || 0-1-14-39 || 1-11/7-11/10-11/8 || utonal ||
|| 83 || 0-9-14-39 || 1-11/6-11/10-11/8 || utonal ||
|| 84 || 0-9-25-39 || 1-11/6-5/4-11/8 || otonal ||
|| 85 || 0-8-30-39 || 1-7/6-3/2-11/8 || gentle ||
|| 86 || 0-9-30-39 || 1-11/6-3/2-11/8 || ambitonal ||
|| 87 || 0-14-30-39 || 1-11/10-3/2-11/8 || utonal ||
|| 88 || 0-25-30-39 || 1-5/4-3/2-11/8 || otonal ||
|| 89 || 0-1-31-39 || 1-11/7-13/11-11/8 || gentle ||
|| 90 || 0-9-31-39 || 1-11/6-13/11-11/8 || gentle ||
|| 91 || 0-30-31-39 || 1-3/2-13/11-11/8 || gentle ||
|| 92 || 0-8-38-39 || 1-7/6-7/4-11/8 || gentle ||
|| 93 || 0-25-38-39 || 1-5/4-7/4-11/8 || otonal ||
|| 94 || 0-30-38-39 || 1-3/2-7/4-11/8 || otonal ||
|| 95 || 0-10-15-45 || 1-13/9-26/15-13/10 || utonal ||
|| 96 || 0-14-15-45 || 1-11/10-26/15-13/10 || gentle ||
|| 97 || 0-14-30-45 || 1-11/10-3/2-13/10 || otonal ||
|| 98 || 0-15-30-45 || 1-26/15-3/2-13/10 || island ||
|| 99 || 0-10-31-45 || 1-13/9-13/11-13/10 || utonal ||
|| 100 || 0-15-31-45 || 1-26/15-13/11-13/10 || utonal ||
|| 101 || 0-30-31-45 || 1-3/2-13/11-13/10 || gentle ||
|| 102 || 0-10-35-45 || 1-13/9-9/5-13/10 || marveltwin ||
|| 103 || 0-14-35-45 || 1-11/10-9/5-13/10 || otonal ||
|| 104 || 0-30-35-45 || 1-3/2-9/5-13/10 || otonal ||
|| 105 || 0-21-22-60 || 1-18/11-9/7-9/8 || utonal ||
|| 106 || 0-15-25-60 || 1-26/15-5/4-9/8 || island ||
|| 107 || 0-15-30-60 || 1-26/15-3/2-9/8 || island ||
|| 108 || 0-21-30-60 || 1-18/11-3/2-9/8 || utonal ||
|| 109 || 0-22-30-60 || 1-9/7-3/2-9/8 || utonal ||
|| 110 || 0-25-30-60 || 1-5/4-3/2-9/8 || otonal ||
|| 111 || 0-21-35-60 || 1-18/11-9/5-9/8 || utonal ||
|| 112 || 0-22-35-60 || 1-9/7-9/5-9/8 || utonal ||
|| 113 || 0-25-35-60 || 1-5/4-9/5-9/8 || marveltwin ||
|| 114 || 0-30-35-60 || 1-3/2-9/5-9/8 || utonal ||
|| 115 || 0-22-38-60 || 1-9/7-7/4-9/8 || swetismic ||
|| 116 || 0-25-38-60 || 1-5/4-7/4-9/8 || otonal ||
|| 117 || 0-30-38-60 || 1-3/2-7/4-9/8 || otonal ||
|| 118 || 0-25-39-60 || 1-5/4-11/8-9/8 || otonal ||
|| 119 || 0-30-39-60 || 1-3/2-11/8-9/8 || otonal ||
|| 120 || 0-38-39-60 || 1-7/4-11/8-9/8 || otonal ||
|| 121 || 0-15-45-60 || 1-26/15-13/10-9/8 || island ||
|| 122 || 0-30-45-60 || 1-3/2-13/10-9/8 || island ||
|| 123 || 0-35-45-60 || 1-9/5-13/10-9/8 || island ||
|| 124 || 0-10-25-70 || 1-13/9-5/4-13/8 || island ||
|| 125 || 0-10-31-70 || 1-13/9-13/11-13/8 || utonal ||
|| 126 || 0-10-35-70 || 1-13/9-9/5-13/8 || marveltwin ||
|| 127 || 0-25-35-70 || 1-5/4-9/5-13/8 || marveltwin ||
|| 128 || 0-25-39-70 || 1-5/4-11/8-13/8 || otonal ||
|| 129 || 0-31-39-70 || 1-13/11-11/8-13/8 || gentle ||
|| 130 || 0-10-45-70 || 1-13/9-13/10-13/8 || utonal ||
|| 131 || 0-31-45-70 || 1-13/11-13/10-13/8 || utonal ||
|| 132 || 0-35-45-70 || 1-9/5-13/10-13/8 || marveltwin ||
|| 133 || 0-25-60-70 || 1-5/4-9/8-13/8 || otonal ||
|| 134 || 0-35-60-70 || 1-9/5-9/8-13/8 || marveltwin ||
|| 135 || 0-39-60-70 || 1-11/8-9/8-13/8 || otonal ||
|| 136 || 0-45-60-70 || 1-13/10-9/8-13/8 || island ||

=Pentads=
|| Number || Chord || Transversal || Type ||
|| 1 || 0-1-9-14-22 || 1-11/7-11/6-11/10-9/7 || swetismic ||
|| 2 || 0-8-13-21-22 || 1-7/6-7/5-18/11-9/7 || swetismic ||
|| 3 || 0-5-14-15-30 || 1-6/5-11/10-26/15-3/2 || island-gentle ||
|| 4 || 0-8-16-21-30 || 1-7/6-15/11-18/11-3/2 || swetismic ||
|| 5 || 0-8-9-22-30 || 1-7/6-11/6-9/7-3/2 || swetismic ||
|| 6 || 0-9-14-22-30 || 1-11/6-11/10-9/7-3/2 || swetismic ||
|| 7 || 0-8-21-22-30 || 1-7/6-18/11-9/7-3/2 || swetismic ||
|| 8 || 0-15-16-25-30 || 1-26/15-15/11-5/4-3/2 || island-gentle ||
|| 9 || 0-1-9-10-31 || 1-11/7-11/6-13/9-13/11 || gentle ||
|| 10 || 0-1-10-15-31 || 1-11/7-13/9-26/15-13/11 || gentle ||
|| 11 || 0-1-15-16-31 || 1-11/7-26/15-15/11-13/11 || island-gentle ||
|| 12 || 0-1-9-22-31 || 1-11/7-11/6-9/7-13/11 || swetismic-gentle ||
|| 13 || 0-15-16-30-31 || 1-26/15-15/11-3/2-13/11 || island-gentle ||
|| 14 || 0-16-21-30-31 || 1-15/11-18/11-3/2-13/11 || gentle ||
|| 15 || 0-9-22-30-31 || 1-11/6-9/7-3/2-13/11 || swetismic-gentle ||
|| 16 || 0-21-22-30-31 || 1-18/11-9/7-3/2-13/11 || gentle ||
|| 17 || 0-5-13-14-35 || 1-6/5-7/5-11/10-9/5 || otonal ||
|| 18 || 0-5-13-21-35 || 1-6/5-7/5-18/11-9/5 || swetismic ||
|| 19 || 0-13-14-22-35 || 1-7/5-11/10-9/7-9/5 || swetismic ||
|| 20 || 0-13-21-22-35 || 1-7/5-18/11-9/7-9/5 || swetismic ||
|| 21 || 0-5-14-30-35 || 1-6/5-11/10-3/2-9/5 || otonal ||
|| 22 || 0-5-21-30-35 || 1-6/5-18/11-3/2-9/5 || utonal ||
|| 23 || 0-14-22-30-35 || 1-11/10-9/7-3/2-9/5 || swetismic ||
|| 24 || 0-21-22-30-35 || 1-18/11-9/7-3/2-9/5 || utonal ||
|| 25 || 0-8-13-22-38 || 1-7/6-7/5-9/7-7/4 || swetismic ||
|| 26 || 0-8-16-30-38 || 1-7/6-15/11-3/2-7/4 || swetismic ||
|| 27 || 0-8-22-30-38 || 1-7/6-9/7-3/2-7/4 || swetismic ||
|| 28 || 0-16-25-30-38 || 1-15/11-5/4-3/2-7/4 || swetismic ||
|| 29 || 0-1-9-14-39 || 1-11/7-11/6-11/10-11/8 || utonal ||
|| 30 || 0-8-9-30-39 || 1-7/6-11/6-3/2-11/8 || gentle ||
|| 31 || 0-9-14-30-39 || 1-11/6-11/10-3/2-11/8 || utonal ||
|| 32 || 0-9-25-30-39 || 1-11/6-5/4-3/2-11/8 || otonal ||
|| 33 || 0-1-9-31-39 || 1-11/7-11/6-13/11-11/8 || gentle ||
|| 34 || 0-9-30-31-39 || 1-11/6-3/2-13/11-11/8 || gentle ||
|| 35 || 0-8-30-38-39 || 1-7/6-3/2-7/4-11/8 || gentle ||
|| 36 || 0-25-30-38-39 || 1-5/4-3/2-7/4-11/8 || otonal ||
|| 37 || 0-14-15-30-45 || 1-11/10-26/15-3/2-13/10 || island-gentle ||
|| 38 || 0-10-15-31-45 || 1-13/9-26/15-13/11-13/10 || utonal ||
|| 39 || 0-15-30-31-45 || 1-26/15-3/2-13/11-13/10 || island-gentle ||
|| 40 || 0-14-30-35-45 || 1-11/10-3/2-9/5-13/10 || otonal ||
|| 41 || 0-21-22-30-60 || 1-18/11-9/7-3/2-9/8 || utonal ||
|| 42 || 0-15-25-30-60 || 1-26/15-5/4-3/2-9/8 || island ||
|| 43 || 0-21-22-35-60 || 1-18/11-9/7-9/5-9/8 || utonal ||
|| 44 || 0-21-30-35-60 || 1-18/11-3/2-9/5-9/8 || utonal ||
|| 45 || 0-22-30-35-60 || 1-9/7-3/2-9/5-9/8 || utonal ||
|| 46 || 0-25-30-35-60 || 1-5/4-3/2-9/5-9/8 || marveltwin ||
|| 47 || 0-22-30-38-60 || 1-9/7-3/2-7/4-9/8 || swetismic ||
|| 48 || 0-25-30-38-60 || 1-5/4-3/2-7/4-9/8 || otonal ||
|| 49 || 0-25-30-39-60 || 1-5/4-3/2-11/8-9/8 || otonal ||
|| 50 || 0-25-38-39-60 || 1-5/4-7/4-11/8-9/8 || otonal ||
|| 51 || 0-30-38-39-60 || 1-3/2-7/4-11/8-9/8 || otonal ||
|| 52 || 0-15-30-45-60 || 1-26/15-3/2-13/10-9/8 || island ||
|| 53 || 0-30-35-45-60 || 1-3/2-9/5-13/10-9/8 || island ||
|| 54 || 0-10-25-35-70 || 1-13/9-5/4-9/5-13/8 || kleismic-marveltwin ||
|| 55 || 0-10-31-45-70 || 1-13/9-13/11-13/10-13/8 || utonal ||
|| 56 || 0-10-35-45-70 || 1-13/9-9/5-13/10-13/8 || marveltwin ||
|| 57 || 0-25-35-60-70 || 1-5/4-9/5-9/8-13/8 || marveltwin ||
|| 58 || 0-25-39-60-70 || 1-5/4-11/8-9/8-13/8 || otonal ||
|| 59 || 0-35-45-60-70 || 1-9/5-13/10-9/8-13/8 || kleismic-marveltwin ||

=Hexads=
|| Number || Chord || Transversal || Type ||
|| 1 || 0-21-22-30-35-60 || 1-18/11-9/7-3/2-9/5-9/8 ||utonal ||
|| 2 || 0-25-30-38-39-60 || 1-5/4-3/2-7/4-11/8-9/8 || otonal ||

Original HTML content:

<html><head><title>Chords of sqrtphi</title></head><body>Below are listed the 15-limit <a class="wiki_link" href="/Dyadic%20chord">dyadic chords</a> of <a class="wiki_link" href="/Kleismic%20family#Sqrtphi">sqrtphi temperament</a>, subject to the condition that no interval smaller than <a class="wiki_link" href="/12_11">12/11</a>, at 150 cents, appears. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 325/324 are labeled marveltwin, by 364/363 gentle, by 540/539 swetismic, by 676/675 island, and by 1575/1573 nicolic. <a class="wiki_link" href="/Rank%20and%20codimension">Codimension</a> two temperaments are labeled swetismic-gentle, island-gentle and kleismic-marveltwin according to two commas which define it. <br />
<br />
Sqrtphi has MOS of size 5, 8, 11, 14, 17, 20, 23, 26, 49 and 72. The largest chords on these lists have complexity 70, and so would require the 72 note MOS, but there are many chords of much lower complexity. Sqrtphi has a generator very close to √φ, which can be chosen to be exactly √φ. Either way, aside from the dyadic chords, chords with stacks of φ are interesting since φ² - φ = 1, resulting in a relationship between difference tones. Though it isn't the &quot;official&quot; 13/8 of sqrtphi, φ is 7.44 cents flat of 13/8 which is close enough for government work. Chords such as 0-1-2-9-10 or 0-1-8-9-10 work a stack of φs into chords which composers might find of interest.<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>0-1-9<br />
</td>
        <td>1-11/7-11/6<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>0-8-9<br />
</td>
        <td>1-7/6-11/6<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>0-1-10<br />
</td>
        <td>1-11/7-13/9<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>0-5-10<br />
</td>
        <td>1-6/5-13/9<br />
</td>
        <td>marveltwin<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>0-9-10<br />
</td>
        <td>1-11/6-13/9<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>0-5-13<br />
</td>
        <td>1-6/5-7/5<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>0-8-13<br />
</td>
        <td>1-7/6-7/5<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>0-1-14<br />
</td>
        <td>1-11/7-11/10<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>0-5-14<br />
</td>
        <td>1-6/5-11/10<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>0-9-14<br />
</td>
        <td>1-11/6-11/10<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>0-13-14<br />
</td>
        <td>1-7/5-11/10<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>0-1-15<br />
</td>
        <td>1-11/7-26/15<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>0-5-15<br />
</td>
        <td>1-6/5-26/15<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>0-10-15<br />
</td>
        <td>1-13/9-26/15<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>0-14-15<br />
</td>
        <td>1-11/10-26/15<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>0-1-16<br />
</td>
        <td>1-11/7-15/11<br />
</td>
        <td>nicolic<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>0-8-16<br />
</td>
        <td>1-7/6-15/11<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>0-15-16<br />
</td>
        <td>1-26/15-15/11<br />
</td>
        <td>nicolic<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>0-5-21<br />
</td>
        <td>1-6/5-18/11<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>0-8-21<br />
</td>
        <td>1-7/6-18/11<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>0-13-21<br />
</td>
        <td>1-7/5-18/11<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>0-16-21<br />
</td>
        <td>1-15/11-18/11<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>0-1-22<br />
</td>
        <td>1-11/7-9/7<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>0-8-22<br />
</td>
        <td>1-7/6-9/7<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>0-9-22<br />
</td>
        <td>1-11/6-9/7<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>0-13-22<br />
</td>
        <td>1-7/5-9/7<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>0-14-22<br />
</td>
        <td>1-11/10-9/7<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>0-21-22<br />
</td>
        <td>1-18/11-9/7<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>0-9-25<br />
</td>
        <td>1-11/6-5/4<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td>0-10-25<br />
</td>
        <td>1-13/9-5/4<br />
</td>
        <td>island<br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>0-15-25<br />
</td>
        <td>1-26/15-5/4<br />
</td>
        <td>island<br />
</td>
    </tr>
    <tr>
        <td>32<br />
</td>
        <td>0-16-25<br />
</td>
        <td>1-15/11-5/4<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>0-5-30<br />
</td>
        <td>1-6/5-3/2<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>34<br />
</td>
        <td>0-8-30<br />
</td>
        <td>1-7/6-3/2<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>35<br />
</td>
        <td>0-9-30<br />
</td>
        <td>1-11/6-3/2<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>36<br />
</td>
        <td>0-14-30<br />
</td>
        <td>1-11/10-3/2<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>37<br />
</td>
        <td>0-15-30<br />
</td>
        <td>1-26/15-3/2<br />
</td>
        <td>island<br />
</td>
    </tr>
    <tr>
        <td>38<br />
</td>
        <td>0-16-30<br />
</td>
        <td>1-15/11-3/2<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>39<br />
</td>
        <td>0-21-30<br />
</td>
        <td>1-18/11-3/2<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>40<br />
</td>
        <td>0-22-30<br />
</td>
        <td>1-9/7-3/2<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>41<br />
</td>
        <td>0-25-30<br />
</td>
        <td>1-5/4-3/2<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>42<br />
</td>
        <td>0-1-31<br />
</td>
        <td>1-11/7-13/11<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>43<br />
</td>
        <td>0-9-31<br />
</td>
        <td>1-11/6-13/11<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>44<br />
</td>
        <td>0-10-31<br />
</td>
        <td>1-13/9-13/11<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>45<br />
</td>
        <td>0-15-31<br />
</td>
        <td>1-26/15-13/11<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>46<br />
</td>
        <td>0-16-31<br />
</td>
        <td>1-15/11-13/11<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>47<br />
</td>
        <td>0-21-31<br />
</td>
        <td>1-18/11-13/11<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>48<br />
</td>
        <td>0-22-31<br />
</td>
        <td>1-9/7-13/11<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>49<br />
</td>
        <td>0-30-31<br />
</td>
        <td>1-3/2-13/11<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>50<br />
</td>
        <td>0-5-35<br />
</td>
        <td>1-6/5-9/5<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>51<br />
</td>
        <td>0-10-35<br />
</td>
        <td>1-13/9-9/5<br />
</td>
        <td>marveltwin<br />
</td>
    </tr>
    <tr>
        <td>52<br />
</td>
        <td>0-13-35<br />
</td>
        <td>1-7/5-9/5<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>53<br />
</td>
        <td>0-14-35<br />
</td>
        <td>1-11/10-9/5<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>54<br />
</td>
        <td>0-21-35<br />
</td>
        <td>1-18/11-9/5<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>55<br />
</td>
        <td>0-22-35<br />
</td>
        <td>1-9/7-9/5<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>56<br />
</td>
        <td>0-25-35<br />
</td>
        <td>1-5/4-9/5<br />
</td>
        <td>marveltwin<br />
</td>
    </tr>
    <tr>
        <td>57<br />
</td>
        <td>0-30-35<br />
</td>
        <td>1-3/2-9/5<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>58<br />
</td>
        <td>0-8-38<br />
</td>
        <td>1-7/6-7/4<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>59<br />
</td>
        <td>0-13-38<br />
</td>
        <td>1-7/5-7/4<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>60<br />
</td>
        <td>0-16-38<br />
</td>
        <td>1-15/11-7/4<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>61<br />
</td>
        <td>0-22-38<br />
</td>
        <td>1-9/7-7/4<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>62<br />
</td>
        <td>0-25-38<br />
</td>
        <td>1-5/4-7/4<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>63<br />
</td>
        <td>0-30-38<br />
</td>
        <td>1-3/2-7/4<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>64<br />
</td>
        <td>0-1-39<br />
</td>
        <td>1-11/7-11/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>65<br />
</td>
        <td>0-8-39<br />
</td>
        <td>1-7/6-11/8<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>66<br />
</td>
        <td>0-9-39<br />
</td>
        <td>1-11/6-11/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>67<br />
</td>
        <td>0-14-39<br />
</td>
        <td>1-11/10-11/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>68<br />
</td>
        <td>0-25-39<br />
</td>
        <td>1-5/4-11/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>69<br />
</td>
        <td>0-30-39<br />
</td>
        <td>1-3/2-11/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>70<br />
</td>
        <td>0-31-39<br />
</td>
        <td>1-13/11-11/8<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>71<br />
</td>
        <td>0-38-39<br />
</td>
        <td>1-7/4-11/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>72<br />
</td>
        <td>0-10-45<br />
</td>
        <td>1-13/9-13/10<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>73<br />
</td>
        <td>0-14-45<br />
</td>
        <td>1-11/10-13/10<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>74<br />
</td>
        <td>0-15-45<br />
</td>
        <td>1-26/15-13/10<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>75<br />
</td>
        <td>0-30-45<br />
</td>
        <td>1-3/2-13/10<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>76<br />
</td>
        <td>0-31-45<br />
</td>
        <td>1-13/11-13/10<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>77<br />
</td>
        <td>0-35-45<br />
</td>
        <td>1-9/5-13/10<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>78<br />
</td>
        <td>0-15-60<br />
</td>
        <td>1-26/15-9/8<br />
</td>
        <td>island<br />
</td>
    </tr>
    <tr>
        <td>79<br />
</td>
        <td>0-21-60<br />
</td>
        <td>1-18/11-9/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>80<br />
</td>
        <td>0-22-60<br />
</td>
        <td>1-9/7-9/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>81<br />
</td>
        <td>0-25-60<br />
</td>
        <td>1-5/4-9/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>82<br />
</td>
        <td>0-30-60<br />
</td>
        <td>1-3/2-9/8<br />
</td>
        <td>ambitonal<br />
</td>
    </tr>
    <tr>
        <td>83<br />
</td>
        <td>0-35-60<br />
</td>
        <td>1-9/5-9/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>84<br />
</td>
        <td>0-38-60<br />
</td>
        <td>1-7/4-9/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>85<br />
</td>
        <td>0-39-60<br />
</td>
        <td>1-11/8-9/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>86<br />
</td>
        <td>0-45-60<br />
</td>
        <td>1-13/10-9/8<br />
</td>
        <td>island<br />
</td>
    </tr>
    <tr>
        <td>87<br />
</td>
        <td>0-10-70<br />
</td>
        <td>1-13/9-13/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>88<br />
</td>
        <td>0-25-70<br />
</td>
        <td>1-5/4-13/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>89<br />
</td>
        <td>0-31-70<br />
</td>
        <td>1-13/11-13/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>90<br />
</td>
        <td>0-35-70<br />
</td>
        <td>1-9/5-13/8<br />
</td>
        <td>marveltwin<br />
</td>
    </tr>
    <tr>
        <td>91<br />
</td>
        <td>0-39-70<br />
</td>
        <td>1-11/8-13/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>92<br />
</td>
        <td>0-45-70<br />
</td>
        <td>1-13/10-13/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>93<br />
</td>
        <td>0-60-70<br />
</td>
        <td>1-9/8-13/8<br />
</td>
        <td>otonal<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>0-1-9-10<br />
</td>
        <td>1-11/7-11/6-13/9<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>0-1-9-14<br />
</td>
        <td>1-11/7-11/6-11/10<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>0-5-13-14<br />
</td>
        <td>1-6/5-7/5-11/10<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>0-1-10-15<br />
</td>
        <td>1-11/7-13/9-26/15<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>0-5-10-15<br />
</td>
        <td>1-6/5-13/9-26/15<br />
</td>
        <td>marveltwin<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>0-1-14-15<br />
</td>
        <td>1-11/7-11/10-26/15<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>0-5-14-15<br />
</td>
        <td>1-6/5-11/10-26/15<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>0-1-15-16<br />
</td>
        <td>1-11/7-26/15-15/11<br />
</td>
        <td>island-gentle<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>0-5-13-21<br />
</td>
        <td>1-6/5-7/5-18/11<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>0-8-13-21<br />
</td>
        <td>1-7/6-7/5-18/11<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>0-8-16-21<br />
</td>
        <td>1-7/6-15/11-18/11<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>0-1-9-22<br />
</td>
        <td>1-11/7-11/6-9/7<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>0-8-9-22<br />
</td>
        <td>1-7/6-11/6-9/7<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>0-8-13-22<br />
</td>
        <td>1-7/6-7/5-9/7<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>0-1-14-22<br />
</td>
        <td>1-11/7-11/10-9/7<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>0-9-14-22<br />
</td>
        <td>1-11/6-11/10-9/7<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>0-13-14-22<br />
</td>
        <td>1-7/5-11/10-9/7<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>0-8-21-22<br />
</td>
        <td>1-7/6-18/11-9/7<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>0-13-21-22<br />
</td>
        <td>1-7/5-18/11-9/7<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>0-9-10-25<br />
</td>
        <td>1-11/6-13/9-5/4<br />
</td>
        <td>island-gentle<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>0-10-15-25<br />
</td>
        <td>1-13/9-26/15-5/4<br />
</td>
        <td>island<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>0-15-16-25<br />
</td>
        <td>1-26/15-15/11-5/4<br />
</td>
        <td>island-gentle<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>0-8-9-30<br />
</td>
        <td>1-7/6-11/6-3/2<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>0-5-14-30<br />
</td>
        <td>1-6/5-11/10-3/2<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>0-9-14-30<br />
</td>
        <td>1-11/6-11/10-3/2<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>0-5-15-30<br />
</td>
        <td>1-6/5-26/15-3/2<br />
</td>
        <td>island<br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>0-14-15-30<br />
</td>
        <td>1-11/10-26/15-3/2<br />
</td>
        <td>island-gentle<br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>0-8-16-30<br />
</td>
        <td>1-7/6-15/11-3/2<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>0-15-16-30<br />
</td>
        <td>1-26/15-15/11-3/2<br />
</td>
        <td>island-gentle<br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td>0-5-21-30<br />
</td>
        <td>1-6/5-18/11-3/2<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>0-8-21-30<br />
</td>
        <td>1-7/6-18/11-3/2<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>32<br />
</td>
        <td>0-16-21-30<br />
</td>
        <td>1-15/11-18/11-3/2<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>0-8-22-30<br />
</td>
        <td>1-7/6-9/7-3/2<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>34<br />
</td>
        <td>0-9-22-30<br />
</td>
        <td>1-11/6-9/7-3/2<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>35<br />
</td>
        <td>0-14-22-30<br />
</td>
        <td>1-11/10-9/7-3/2<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>36<br />
</td>
        <td>0-21-22-30<br />
</td>
        <td>1-18/11-9/7-3/2<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>37<br />
</td>
        <td>0-9-25-30<br />
</td>
        <td>1-11/6-5/4-3/2<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>38<br />
</td>
        <td>0-15-25-30<br />
</td>
        <td>1-26/15-5/4-3/2<br />
</td>
        <td>island<br />
</td>
    </tr>
    <tr>
        <td>39<br />
</td>
        <td>0-16-25-30<br />
</td>
        <td>1-15/11-5/4-3/2<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>40<br />
</td>
        <td>0-1-9-31<br />
</td>
        <td>1-11/7-11/6-13/11<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>41<br />
</td>
        <td>0-1-10-31<br />
</td>
        <td>1-11/7-13/9-13/11<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>42<br />
</td>
        <td>0-9-10-31<br />
</td>
        <td>1-11/6-13/9-13/11<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>43<br />
</td>
        <td>0-1-15-31<br />
</td>
        <td>1-11/7-26/15-13/11<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>44<br />
</td>
        <td>0-10-15-31<br />
</td>
        <td>1-13/9-26/15-13/11<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>45<br />
</td>
        <td>0-1-16-31<br />
</td>
        <td>1-11/7-15/11-13/11<br />
</td>
        <td>island-gentle<br />
</td>
    </tr>
    <tr>
        <td>46<br />
</td>
        <td>0-15-16-31<br />
</td>
        <td>1-26/15-15/11-13/11<br />
</td>
        <td>nicolic<br />
</td>
    </tr>
    <tr>
        <td>47<br />
</td>
        <td>0-16-21-31<br />
</td>
        <td>1-15/11-18/11-13/11<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>48<br />
</td>
        <td>0-1-22-31<br />
</td>
        <td>1-11/7-9/7-13/11<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>49<br />
</td>
        <td>0-9-22-31<br />
</td>
        <td>1-11/6-9/7-13/11<br />
</td>
        <td>swetismic-gentle<br />
</td>
    </tr>
    <tr>
        <td>50<br />
</td>
        <td>0-21-22-31<br />
</td>
        <td>1-18/11-9/7-13/11<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>51<br />
</td>
        <td>0-9-30-31<br />
</td>
        <td>1-11/6-3/2-13/11<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>52<br />
</td>
        <td>0-15-30-31<br />
</td>
        <td>1-26/15-3/2-13/11<br />
</td>
        <td>island-gentle<br />
</td>
    </tr>
    <tr>
        <td>53<br />
</td>
        <td>0-16-30-31<br />
</td>
        <td>1-15/11-3/2-13/11<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>54<br />
</td>
        <td>0-21-30-31<br />
</td>
        <td>1-18/11-3/2-13/11<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>55<br />
</td>
        <td>0-22-30-31<br />
</td>
        <td>1-9/7-3/2-13/11<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>56<br />
</td>
        <td>0-5-10-35<br />
</td>
        <td>1-6/5-13/9-9/5<br />
</td>
        <td>marveltwin<br />
</td>
    </tr>
    <tr>
        <td>57<br />
</td>
        <td>0-5-13-35<br />
</td>
        <td>1-6/5-7/5-9/5<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>58<br />
</td>
        <td>0-5-14-35<br />
</td>
        <td>1-6/5-11/10-9/5<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>59<br />
</td>
        <td>0-13-14-35<br />
</td>
        <td>1-7/5-11/10-9/5<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>60<br />
</td>
        <td>0-5-21-35<br />
</td>
        <td>1-6/5-18/11-9/5<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>61<br />
</td>
        <td>0-13-21-35<br />
</td>
        <td>1-7/5-18/11-9/5<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>62<br />
</td>
        <td>0-13-22-35<br />
</td>
        <td>1-7/5-9/7-9/5<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>63<br />
</td>
        <td>0-14-22-35<br />
</td>
        <td>1-11/10-9/7-9/5<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>64<br />
</td>
        <td>0-21-22-35<br />
</td>
        <td>1-18/11-9/7-9/5<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>65<br />
</td>
        <td>0-10-25-35<br />
</td>
        <td>1-13/9-5/4-9/5<br />
</td>
        <td>kleismic-marveltwin<br />
</td>
    </tr>
    <tr>
        <td>66<br />
</td>
        <td>0-5-30-35<br />
</td>
        <td>1-6/5-3/2-9/5<br />
</td>
        <td>ambitonal<br />
</td>
    </tr>
    <tr>
        <td>67<br />
</td>
        <td>0-14-30-35<br />
</td>
        <td>1-11/10-3/2-9/5<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>68<br />
</td>
        <td>0-21-30-35<br />
</td>
        <td>1-18/11-3/2-9/5<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>69<br />
</td>
        <td>0-22-30-35<br />
</td>
        <td>1-9/7-3/2-9/5<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>70<br />
</td>
        <td>0-25-30-35<br />
</td>
        <td>1-5/4-3/2-9/5<br />
</td>
        <td>marveltwin<br />
</td>
    </tr>
    <tr>
        <td>71<br />
</td>
        <td>0-8-13-38<br />
</td>
        <td>1-7/6-7/5-7/4<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>72<br />
</td>
        <td>0-8-16-38<br />
</td>
        <td>1-7/6-15/11-7/4<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>73<br />
</td>
        <td>0-8-22-38<br />
</td>
        <td>1-7/6-9/7-7/4<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>74<br />
</td>
        <td>0-13-22-38<br />
</td>
        <td>1-7/5-9/7-7/4<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>75<br />
</td>
        <td>0-16-25-38<br />
</td>
        <td>1-15/11-5/4-7/4<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>76<br />
</td>
        <td>0-8-30-38<br />
</td>
        <td>1-7/6-3/2-7/4<br />
</td>
        <td>ambitonal<br />
</td>
    </tr>
    <tr>
        <td>77<br />
</td>
        <td>0-16-30-38<br />
</td>
        <td>1-15/11-3/2-7/4<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>78<br />
</td>
        <td>0-22-30-38<br />
</td>
        <td>1-9/7-3/2-7/4<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>79<br />
</td>
        <td>0-25-30-38<br />
</td>
        <td>1-5/4-3/2-7/4<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>80<br />
</td>
        <td>0-1-9-39<br />
</td>
        <td>1-11/7-11/6-11/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>81<br />
</td>
        <td>0-8-9-39<br />
</td>
        <td>1-7/6-11/6-11/8<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>82<br />
</td>
        <td>0-1-14-39<br />
</td>
        <td>1-11/7-11/10-11/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>83<br />
</td>
        <td>0-9-14-39<br />
</td>
        <td>1-11/6-11/10-11/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>84<br />
</td>
        <td>0-9-25-39<br />
</td>
        <td>1-11/6-5/4-11/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>85<br />
</td>
        <td>0-8-30-39<br />
</td>
        <td>1-7/6-3/2-11/8<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>86<br />
</td>
        <td>0-9-30-39<br />
</td>
        <td>1-11/6-3/2-11/8<br />
</td>
        <td>ambitonal<br />
</td>
    </tr>
    <tr>
        <td>87<br />
</td>
        <td>0-14-30-39<br />
</td>
        <td>1-11/10-3/2-11/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>88<br />
</td>
        <td>0-25-30-39<br />
</td>
        <td>1-5/4-3/2-11/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>89<br />
</td>
        <td>0-1-31-39<br />
</td>
        <td>1-11/7-13/11-11/8<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>90<br />
</td>
        <td>0-9-31-39<br />
</td>
        <td>1-11/6-13/11-11/8<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>91<br />
</td>
        <td>0-30-31-39<br />
</td>
        <td>1-3/2-13/11-11/8<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>92<br />
</td>
        <td>0-8-38-39<br />
</td>
        <td>1-7/6-7/4-11/8<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>93<br />
</td>
        <td>0-25-38-39<br />
</td>
        <td>1-5/4-7/4-11/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>94<br />
</td>
        <td>0-30-38-39<br />
</td>
        <td>1-3/2-7/4-11/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>95<br />
</td>
        <td>0-10-15-45<br />
</td>
        <td>1-13/9-26/15-13/10<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>96<br />
</td>
        <td>0-14-15-45<br />
</td>
        <td>1-11/10-26/15-13/10<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>97<br />
</td>
        <td>0-14-30-45<br />
</td>
        <td>1-11/10-3/2-13/10<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>98<br />
</td>
        <td>0-15-30-45<br />
</td>
        <td>1-26/15-3/2-13/10<br />
</td>
        <td>island<br />
</td>
    </tr>
    <tr>
        <td>99<br />
</td>
        <td>0-10-31-45<br />
</td>
        <td>1-13/9-13/11-13/10<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>100<br />
</td>
        <td>0-15-31-45<br />
</td>
        <td>1-26/15-13/11-13/10<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>101<br />
</td>
        <td>0-30-31-45<br />
</td>
        <td>1-3/2-13/11-13/10<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>102<br />
</td>
        <td>0-10-35-45<br />
</td>
        <td>1-13/9-9/5-13/10<br />
</td>
        <td>marveltwin<br />
</td>
    </tr>
    <tr>
        <td>103<br />
</td>
        <td>0-14-35-45<br />
</td>
        <td>1-11/10-9/5-13/10<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>104<br />
</td>
        <td>0-30-35-45<br />
</td>
        <td>1-3/2-9/5-13/10<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>105<br />
</td>
        <td>0-21-22-60<br />
</td>
        <td>1-18/11-9/7-9/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>106<br />
</td>
        <td>0-15-25-60<br />
</td>
        <td>1-26/15-5/4-9/8<br />
</td>
        <td>island<br />
</td>
    </tr>
    <tr>
        <td>107<br />
</td>
        <td>0-15-30-60<br />
</td>
        <td>1-26/15-3/2-9/8<br />
</td>
        <td>island<br />
</td>
    </tr>
    <tr>
        <td>108<br />
</td>
        <td>0-21-30-60<br />
</td>
        <td>1-18/11-3/2-9/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>109<br />
</td>
        <td>0-22-30-60<br />
</td>
        <td>1-9/7-3/2-9/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>110<br />
</td>
        <td>0-25-30-60<br />
</td>
        <td>1-5/4-3/2-9/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>111<br />
</td>
        <td>0-21-35-60<br />
</td>
        <td>1-18/11-9/5-9/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>112<br />
</td>
        <td>0-22-35-60<br />
</td>
        <td>1-9/7-9/5-9/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>113<br />
</td>
        <td>0-25-35-60<br />
</td>
        <td>1-5/4-9/5-9/8<br />
</td>
        <td>marveltwin<br />
</td>
    </tr>
    <tr>
        <td>114<br />
</td>
        <td>0-30-35-60<br />
</td>
        <td>1-3/2-9/5-9/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>115<br />
</td>
        <td>0-22-38-60<br />
</td>
        <td>1-9/7-7/4-9/8<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>116<br />
</td>
        <td>0-25-38-60<br />
</td>
        <td>1-5/4-7/4-9/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>117<br />
</td>
        <td>0-30-38-60<br />
</td>
        <td>1-3/2-7/4-9/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>118<br />
</td>
        <td>0-25-39-60<br />
</td>
        <td>1-5/4-11/8-9/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>119<br />
</td>
        <td>0-30-39-60<br />
</td>
        <td>1-3/2-11/8-9/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>120<br />
</td>
        <td>0-38-39-60<br />
</td>
        <td>1-7/4-11/8-9/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>121<br />
</td>
        <td>0-15-45-60<br />
</td>
        <td>1-26/15-13/10-9/8<br />
</td>
        <td>island<br />
</td>
    </tr>
    <tr>
        <td>122<br />
</td>
        <td>0-30-45-60<br />
</td>
        <td>1-3/2-13/10-9/8<br />
</td>
        <td>island<br />
</td>
    </tr>
    <tr>
        <td>123<br />
</td>
        <td>0-35-45-60<br />
</td>
        <td>1-9/5-13/10-9/8<br />
</td>
        <td>island<br />
</td>
    </tr>
    <tr>
        <td>124<br />
</td>
        <td>0-10-25-70<br />
</td>
        <td>1-13/9-5/4-13/8<br />
</td>
        <td>island<br />
</td>
    </tr>
    <tr>
        <td>125<br />
</td>
        <td>0-10-31-70<br />
</td>
        <td>1-13/9-13/11-13/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>126<br />
</td>
        <td>0-10-35-70<br />
</td>
        <td>1-13/9-9/5-13/8<br />
</td>
        <td>marveltwin<br />
</td>
    </tr>
    <tr>
        <td>127<br />
</td>
        <td>0-25-35-70<br />
</td>
        <td>1-5/4-9/5-13/8<br />
</td>
        <td>marveltwin<br />
</td>
    </tr>
    <tr>
        <td>128<br />
</td>
        <td>0-25-39-70<br />
</td>
        <td>1-5/4-11/8-13/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>129<br />
</td>
        <td>0-31-39-70<br />
</td>
        <td>1-13/11-11/8-13/8<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>130<br />
</td>
        <td>0-10-45-70<br />
</td>
        <td>1-13/9-13/10-13/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>131<br />
</td>
        <td>0-31-45-70<br />
</td>
        <td>1-13/11-13/10-13/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>132<br />
</td>
        <td>0-35-45-70<br />
</td>
        <td>1-9/5-13/10-13/8<br />
</td>
        <td>marveltwin<br />
</td>
    </tr>
    <tr>
        <td>133<br />
</td>
        <td>0-25-60-70<br />
</td>
        <td>1-5/4-9/8-13/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>134<br />
</td>
        <td>0-35-60-70<br />
</td>
        <td>1-9/5-9/8-13/8<br />
</td>
        <td>marveltwin<br />
</td>
    </tr>
    <tr>
        <td>135<br />
</td>
        <td>0-39-60-70<br />
</td>
        <td>1-11/8-9/8-13/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>136<br />
</td>
        <td>0-45-60-70<br />
</td>
        <td>1-13/10-9/8-13/8<br />
</td>
        <td>island<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>0-1-9-14-22<br />
</td>
        <td>1-11/7-11/6-11/10-9/7<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>0-8-13-21-22<br />
</td>
        <td>1-7/6-7/5-18/11-9/7<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>0-5-14-15-30<br />
</td>
        <td>1-6/5-11/10-26/15-3/2<br />
</td>
        <td>island-gentle<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>0-8-16-21-30<br />
</td>
        <td>1-7/6-15/11-18/11-3/2<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>0-8-9-22-30<br />
</td>
        <td>1-7/6-11/6-9/7-3/2<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>0-9-14-22-30<br />
</td>
        <td>1-11/6-11/10-9/7-3/2<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>0-8-21-22-30<br />
</td>
        <td>1-7/6-18/11-9/7-3/2<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>0-15-16-25-30<br />
</td>
        <td>1-26/15-15/11-5/4-3/2<br />
</td>
        <td>island-gentle<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>0-1-9-10-31<br />
</td>
        <td>1-11/7-11/6-13/9-13/11<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>0-1-10-15-31<br />
</td>
        <td>1-11/7-13/9-26/15-13/11<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>0-1-15-16-31<br />
</td>
        <td>1-11/7-26/15-15/11-13/11<br />
</td>
        <td>island-gentle<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>0-1-9-22-31<br />
</td>
        <td>1-11/7-11/6-9/7-13/11<br />
</td>
        <td>swetismic-gentle<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>0-15-16-30-31<br />
</td>
        <td>1-26/15-15/11-3/2-13/11<br />
</td>
        <td>island-gentle<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>0-16-21-30-31<br />
</td>
        <td>1-15/11-18/11-3/2-13/11<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>0-9-22-30-31<br />
</td>
        <td>1-11/6-9/7-3/2-13/11<br />
</td>
        <td>swetismic-gentle<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>0-21-22-30-31<br />
</td>
        <td>1-18/11-9/7-3/2-13/11<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>0-5-13-14-35<br />
</td>
        <td>1-6/5-7/5-11/10-9/5<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>0-5-13-21-35<br />
</td>
        <td>1-6/5-7/5-18/11-9/5<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>0-13-14-22-35<br />
</td>
        <td>1-7/5-11/10-9/7-9/5<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>0-13-21-22-35<br />
</td>
        <td>1-7/5-18/11-9/7-9/5<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>0-5-14-30-35<br />
</td>
        <td>1-6/5-11/10-3/2-9/5<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>0-5-21-30-35<br />
</td>
        <td>1-6/5-18/11-3/2-9/5<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>0-14-22-30-35<br />
</td>
        <td>1-11/10-9/7-3/2-9/5<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>0-21-22-30-35<br />
</td>
        <td>1-18/11-9/7-3/2-9/5<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>0-8-13-22-38<br />
</td>
        <td>1-7/6-7/5-9/7-7/4<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>0-8-16-30-38<br />
</td>
        <td>1-7/6-15/11-3/2-7/4<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>0-8-22-30-38<br />
</td>
        <td>1-7/6-9/7-3/2-7/4<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>0-16-25-30-38<br />
</td>
        <td>1-15/11-5/4-3/2-7/4<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>0-1-9-14-39<br />
</td>
        <td>1-11/7-11/6-11/10-11/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td>0-8-9-30-39<br />
</td>
        <td>1-7/6-11/6-3/2-11/8<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>0-9-14-30-39<br />
</td>
        <td>1-11/6-11/10-3/2-11/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>32<br />
</td>
        <td>0-9-25-30-39<br />
</td>
        <td>1-11/6-5/4-3/2-11/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>0-1-9-31-39<br />
</td>
        <td>1-11/7-11/6-13/11-11/8<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>34<br />
</td>
        <td>0-9-30-31-39<br />
</td>
        <td>1-11/6-3/2-13/11-11/8<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>35<br />
</td>
        <td>0-8-30-38-39<br />
</td>
        <td>1-7/6-3/2-7/4-11/8<br />
</td>
        <td>gentle<br />
</td>
    </tr>
    <tr>
        <td>36<br />
</td>
        <td>0-25-30-38-39<br />
</td>
        <td>1-5/4-3/2-7/4-11/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>37<br />
</td>
        <td>0-14-15-30-45<br />
</td>
        <td>1-11/10-26/15-3/2-13/10<br />
</td>
        <td>island-gentle<br />
</td>
    </tr>
    <tr>
        <td>38<br />
</td>
        <td>0-10-15-31-45<br />
</td>
        <td>1-13/9-26/15-13/11-13/10<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>39<br />
</td>
        <td>0-15-30-31-45<br />
</td>
        <td>1-26/15-3/2-13/11-13/10<br />
</td>
        <td>island-gentle<br />
</td>
    </tr>
    <tr>
        <td>40<br />
</td>
        <td>0-14-30-35-45<br />
</td>
        <td>1-11/10-3/2-9/5-13/10<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>41<br />
</td>
        <td>0-21-22-30-60<br />
</td>
        <td>1-18/11-9/7-3/2-9/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>42<br />
</td>
        <td>0-15-25-30-60<br />
</td>
        <td>1-26/15-5/4-3/2-9/8<br />
</td>
        <td>island<br />
</td>
    </tr>
    <tr>
        <td>43<br />
</td>
        <td>0-21-22-35-60<br />
</td>
        <td>1-18/11-9/7-9/5-9/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>44<br />
</td>
        <td>0-21-30-35-60<br />
</td>
        <td>1-18/11-3/2-9/5-9/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>45<br />
</td>
        <td>0-22-30-35-60<br />
</td>
        <td>1-9/7-3/2-9/5-9/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>46<br />
</td>
        <td>0-25-30-35-60<br />
</td>
        <td>1-5/4-3/2-9/5-9/8<br />
</td>
        <td>marveltwin<br />
</td>
    </tr>
    <tr>
        <td>47<br />
</td>
        <td>0-22-30-38-60<br />
</td>
        <td>1-9/7-3/2-7/4-9/8<br />
</td>
        <td>swetismic<br />
</td>
    </tr>
    <tr>
        <td>48<br />
</td>
        <td>0-25-30-38-60<br />
</td>
        <td>1-5/4-3/2-7/4-9/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>49<br />
</td>
        <td>0-25-30-39-60<br />
</td>
        <td>1-5/4-3/2-11/8-9/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>50<br />
</td>
        <td>0-25-38-39-60<br />
</td>
        <td>1-5/4-7/4-11/8-9/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>51<br />
</td>
        <td>0-30-38-39-60<br />
</td>
        <td>1-3/2-7/4-11/8-9/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>52<br />
</td>
        <td>0-15-30-45-60<br />
</td>
        <td>1-26/15-3/2-13/10-9/8<br />
</td>
        <td>island<br />
</td>
    </tr>
    <tr>
        <td>53<br />
</td>
        <td>0-30-35-45-60<br />
</td>
        <td>1-3/2-9/5-13/10-9/8<br />
</td>
        <td>island<br />
</td>
    </tr>
    <tr>
        <td>54<br />
</td>
        <td>0-10-25-35-70<br />
</td>
        <td>1-13/9-5/4-9/5-13/8<br />
</td>
        <td>kleismic-marveltwin<br />
</td>
    </tr>
    <tr>
        <td>55<br />
</td>
        <td>0-10-31-45-70<br />
</td>
        <td>1-13/9-13/11-13/10-13/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>56<br />
</td>
        <td>0-10-35-45-70<br />
</td>
        <td>1-13/9-9/5-13/10-13/8<br />
</td>
        <td>marveltwin<br />
</td>
    </tr>
    <tr>
        <td>57<br />
</td>
        <td>0-25-35-60-70<br />
</td>
        <td>1-5/4-9/5-9/8-13/8<br />
</td>
        <td>marveltwin<br />
</td>
    </tr>
    <tr>
        <td>58<br />
</td>
        <td>0-25-39-60-70<br />
</td>
        <td>1-5/4-11/8-9/8-13/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
    <tr>
        <td>59<br />
</td>
        <td>0-35-45-60-70<br />
</td>
        <td>1-9/5-13/10-9/8-13/8<br />
</td>
        <td>kleismic-marveltwin<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>0-21-22-30-35-60<br />
</td>
        <td>1-18/11-9/7-3/2-9/5-9/8<br />
</td>
        <td>utonal<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>0-25-30-38-39-60<br />
</td>
        <td>1-5/4-3/2-7/4-11/8-9/8<br />
</td>
        <td>otonal<br />
</td>
    </tr>
</table>

</body></html>
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