Catakleismic/13-limit chords: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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>2012-02-21 00:59:13 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-21 08:54:20 UTC</tt>.<br>

: The original revision id was <tt>~~303551468~~</tt>.<br>

: The original revision id was <tt>303617526</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>

<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 15-limit [[Dyadic chord|dyadic chords]] of [[Kleismic family#Catakleismic-13-limit|tridecimal catakleismic 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 225/224 are labeled marvel, by 385/384 keenanismic, by 540/539 swetismic, by 169/168 dhanvantarismic, by 325/324 marveltwin, by 351/350 ratwolfsmic, by 676/675 island, by 729/728 squbemic, by 1001/1000 sinbadmic and by 1287/1280 catadictmic. [[Rank and codimension|Codimension]] two temperaments are labeled marveltwin-island, ratwolfsmic-island, marvel-marveltwin, dhanvantarismic-marveltwin, dhanvantarismic-marvel, keenanismic-ratwolfsmic, swetismic-ratwolfsmic, and marvel-catadictmic. Rank three temperaments are labeled [[Ragisma family#Beyla-13-limit|beyla]], [[Marvel family#Hestia|hestia]], [[Swetismic temperaments#Hypnos-13-limit|hypnos]], [[Marvel family#Catakleismoid|catakleismoid]], [[Kleismic rank three family#Isimud|isimud]], [[Marvel family#Marvel|unimarvel]] and [[Marvel family#Marvel|tridecimal marvel]]. Finally, if the full tridecimal catakleismic temperament is required, the chord is labeled catakleismic.

Tridecimal catakleismic is more richly endowed with chords, and in particular chords of lower complexity, than 7- or 11-limit catakleismic, with harmonies including but not limited to those of marvel temperament and [[the Archipelago]]. It has MOS of size 7, 11, 15, 19, 34 and 53. Triads and tetrads abound even in the 7-note MOS, and with the 11-note MOS pentads appear.

=Triads=

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|| 28 || 0-16-21-26-33-43 || 1-7/6-16/11-20/11-18/11-14/11 || unimarvel ||

|| 29 || 0-17-26-27-33-43 || 1-7/5-20/11-12/11-18/11-14/11 || swetismic-ratwolfsmic ||

|| 30 || 0-21-26-27-33-43 || 1-16/11-20/11-12/11-18/11-14/11 || otonal ||

|| 30 || 0-21-26-27-33-43 || 1-16/11-20/11-12/11-18/11-14/11 || otonal ||</pre></div>

</pre></div>

<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"><html><head><title>Chords of tridecimal catakleismic</title></head><body><br />

<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"><html><head><title>Chords of tridecimal catakleismic</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#Catakleismic-13-limit">tridecimal catakleismic 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 225/224 are labeled marvel, by 385/384 keenanismic, by 540/539 swetismic, by 169/168 dhanvantarismic, by 325/324 marveltwin, by 351/350 ratwolfsmic, by 676/675 island, by 729/728 squbemic, by 1001/1000 sinbadmic and by 1287/1280 catadictmic. <a class="wiki_link" href="/Rank%20and%20codimension">Codimension</a> two temperaments are labeled marveltwin-island, ratwolfsmic-island, marvel-marveltwin, dhanvantarismic-marveltwin, dhanvantarismic-marvel, keenanismic-ratwolfsmic, swetismic-ratwolfsmic, and marvel-catadictmic. Rank three temperaments are labeled <a class="wiki_link" href="/Ragisma%20family#Beyla-13-limit">beyla</a>, <a class="wiki_link" href="/Marvel%20family#Hestia">hestia</a>, <a class="wiki_link" href="/Swetismic%20temperaments#Hypnos-13-limit">hypnos</a>, <a class="wiki_link" href="/Marvel%20family#Catakleismoid">catakleismoid</a>, <a class="wiki_link" href="/Kleismic%20rank%20three%20family#Isimud">isimud</a>, <a class="wiki_link" href="/Marvel%20family#Marvel">unimarvel</a> and <a class="wiki_link" href="/Marvel%20family#Marvel">tridecimal marvel</a>. Finally, if the full tridecimal catakleismic temperament is required, the chord is labeled catakleismic. <br />

<br />

Tridecimal catakleismic is more richly endowed with chords, and in particular chords of lower complexity, than 7- or 11-limit catakleismic, with harmonies including but not limited to those of marvel temperament and <a class="wiki_link" href="/the%20Archipelago">the Archipelago</a>. It has MOS of size 7, 11, 15, 19, 34 and 53. Triads and tetrads abound even in the 7-note MOS, and with the 11-note MOS pentads appear.<br />

<br />

<h1 id="toc0"><a name="Triads"></a>Triads</h1>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2012-02-21 00:59:13 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-21 08:54:20 UTC</tt>.<br>
-: The original revision id was <tt>303551468</tt>.<br>
+: The original revision id was <tt>303617526</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>
 <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#Catakleismic-13-limit|tridecimal catakleismic 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 225/224 are labeled marvel, by 385/384 keenanismic, by 540/539 swetismic, by 169/168 dhanvantarismic, by 325/324 marveltwin, by 351/350 ratwolfsmic, by 676/675 island, by 729/728 squbemic, by 1001/1000 sinbadmic and by 1287/1280 catadictmic. [[Rank and codimension|Codimension]] two temperaments are labeled marveltwin-island, ratwolfsmic-island, marvel-marveltwin, dhanvantarismic-marveltwin, dhanvantarismic-marvel, keenanismic-ratwolfsmic, swetismic-ratwolfsmic, and marvel-catadictmic. Rank three temperaments are labeled [[Ragisma family#Beyla-13-limit|beyla]], [[Marvel family#Hestia|hestia]], [[Swetismic temperaments#Hypnos-13-limit|hypnos]], [[Marvel family#Catakleismoid|catakleismoid]], [[Kleismic rank three family#Isimud|isimud]], [[Marvel family#Marvel|unimarvel]] and [[Marvel family#Marvel|tridecimal marvel]]. Finally, if the full tridecimal catakleismic temperament is required, the chord is labeled catakleismic.
+Tridecimal catakleismic is more richly endowed with chords, and in particular chords of lower complexity, than 7- or 11-limit catakleismic, with harmonies including but not limited to those of marvel temperament and [[the Archipelago]]. It has MOS of size 7, 11, 15, 19, 34 and 53. Triads and tetrads abound even in the 7-note MOS, and with the 11-note MOS pentads appear.
 =Triads=
@@ Line 533: / Line 534: @@
 || 28 || 0-16-21-26-33-43 || 1-7/6-16/11-20/11-18/11-14/11 || unimarvel ||
 || 29 || 0-17-26-27-33-43 || 1-7/5-20/11-12/11-18/11-14/11 || swetismic-ratwolfsmic ||
-|| 30 || 0-21-26-27-33-43 || 1-16/11-20/11-12/11-18/11-14/11 || otonal ||
+|| 30 || 0-21-26-27-33-43 || 1-16/11-20/11-12/11-18/11-14/11 || otonal ||</pre></div>
-</pre></div>
 <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 tridecimal catakleismic&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 tridecimal catakleismic&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#Catakleismic-13-limit"&gt;tridecimal catakleismic 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 225/224 are labeled marvel, by 385/384 keenanismic, by 540/539 swetismic, by 169/168 dhanvantarismic, by 325/324 marveltwin, by 351/350 ratwolfsmic, by 676/675 island, by 729/728 squbemic, by 1001/1000 sinbadmic and by 1287/1280 catadictmic. &lt;a class="wiki_link" href="/Rank%20and%20codimension"&gt;Codimension&lt;/a&gt; two temperaments are labeled marveltwin-island, ratwolfsmic-island, marvel-marveltwin, dhanvantarismic-marveltwin, dhanvantarismic-marvel, keenanismic-ratwolfsmic, swetismic-ratwolfsmic, and marvel-catadictmic. Rank three temperaments are labeled &lt;a class="wiki_link" href="/Ragisma%20family#Beyla-13-limit"&gt;beyla&lt;/a&gt;, &lt;a class="wiki_link" href="/Marvel%20family#Hestia"&gt;hestia&lt;/a&gt;, &lt;a class="wiki_link" href="/Swetismic%20temperaments#Hypnos-13-limit"&gt;hypnos&lt;/a&gt;, &lt;a class="wiki_link" href="/Marvel%20family#Catakleismoid"&gt;catakleismoid&lt;/a&gt;, &lt;a class="wiki_link" href="/Kleismic%20rank%20three%20family#Isimud"&gt;isimud&lt;/a&gt;, &lt;a class="wiki_link" href="/Marvel%20family#Marvel"&gt;unimarvel&lt;/a&gt; and &lt;a class="wiki_link" href="/Marvel%20family#Marvel"&gt;tridecimal marvel&lt;/a&gt;. Finally, if the full tridecimal catakleismic temperament is required, the chord is labeled catakleismic. &lt;br /&gt;
 &lt;br /&gt;
+Tridecimal catakleismic is more richly endowed with chords, and in particular chords of lower complexity, than 7- or 11-limit catakleismic, with harmonies including but not limited to those of marvel temperament and &lt;a class="wiki_link" href="/the%20Archipelago"&gt;the Archipelago&lt;/a&gt;. It has MOS of size 7, 11, 15, 19, 34 and 53. Triads and tetrads abound even in the 7-note MOS, and with the 11-note MOS pentads appear.&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;