Fifteen limit tetrads: 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>2011-08-05 00:29:45 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-08-05 00:42:12 UTC</tt>.<br>

: The original revision id was <tt>~~244436083~~</tt>.<br>

: The original revision id was <tt>244437687</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">The two //trinidad tetrads// are 15-limit tetrads with no step size smaller than 10/9; ~~they~~ are the otonal trinidad tetrad, 1-13/10-3/2-9/5, with steps 13/10-15/13-6/5-10/9, and the utonal trinidad tetrad, 1-15/13-3/2-5/3, with steps 15/13-13/10-10/9-6/5. These are just intonation tetrads and do not require tempering in [[The Archipelago#Subgroup temperaments|trinidad temperament]] or anything else, but they do belong to the same 2.3.5.13 subgroup on which trinidad is defined and are certainly characteristic of the temperament.</pre></div>

=5-9-13-15=

The two //trinidad tetrads// are 15-limit tetrads with no step size smaller than 10/9 and containing an interval of a fifth; these are the otonal trinidad tetrad, 1-13/10-3/2-9/5, with steps 13/10-15/13-6/5-10/9, and the utonal trinidad tetrad, 1-15/13-3/2-5/3, with steps 15/13-13/10-10/9-6/5. These are just intonation tetrads and do not require tempering in [[The Archipelago#Subgroup temperaments|trinidad temperament]] or anything else, but they do belong to the same 2.3.5.13 subgroup on which trinidad is defined and are certainly characteristic of the temperament.

=9-11-13-15=

These two tetrads are the otonal, 1-15/13-15/11-5/3, with steps of 15/13-13/11-11/9-6/5, and the utonal, 1-11/9-13/9-5/3 with steps of 11/9-13/11-15/13-6/5.</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>fifteen limit tetrads</title></head><body>The two <em>trinidad tetrads</em> are 15-limit tetrads with no step size smaller than 10/9; ~~they~~ are the otonal trinidad tetrad, 1-13/10-3/2-9/5, with steps 13/10-15/13-6/5-10/9, and the utonal trinidad tetrad, 1-15/13-3/2-5/3, with steps 15/13-13/10-10/9-6/5. These are just intonation tetrads and do not require tempering in <a class="wiki_link" href="/The%20Archipelago#Subgroup temperaments">trinidad temperament</a> or anything else, but they do belong to the same 2.3.5.13 subgroup on which trinidad is defined and are certainly characteristic of the temperament.</body></html></pre></div>

<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>fifteen limit tetrads</title></head><body><br />

<h1 id="toc0"><a name="x5-9-13-15"></a>5-9-13-15</h1>

The two <em>trinidad tetrads</em> are 15-limit tetrads with no step size smaller than 10/9 and containing an interval of a fifth; these are the otonal trinidad tetrad, 1-13/10-3/2-9/5, with steps 13/10-15/13-6/5-10/9, and the utonal trinidad tetrad, 1-15/13-3/2-5/3, with steps 15/13-13/10-10/9-6/5. These are just intonation tetrads and do not require tempering in <a class="wiki_link" href="/The%20Archipelago#Subgroup temperaments">trinidad temperament</a> or anything else, but they do belong to the same 2.3.5.13 subgroup on which trinidad is defined and are certainly characteristic of the temperament.<br />

<br />

<h1 id="toc1"><a name="x9-11-13-15"></a>9-11-13-15</h1>

These two tetrads are the otonal, 1-15/13-15/11-5/3, with steps of 15/13-13/11-11/9-6/5, and the utonal, 1-11/9-13/9-5/3 with steps of 11/9-13/11-15/13-6/5.</body></html></pre></div>

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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>2011-08-05 00:29:45 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-08-05 00:42:12 UTC</tt>.<br>
-: The original revision id was <tt>244436083</tt>.<br>
+: The original revision id was <tt>244437687</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">The two //trinidad tetrads// are 15-limit tetrads with no step size smaller than 10/9; they are the otonal trinidad tetrad, 1-13/10-3/2-9/5, with steps 13/10-15/13-6/5-10/9, and the utonal trinidad tetrad, 1-15/13-3/2-5/3, with steps 15/13-13/10-10/9-6/5. These are just intonation tetrads and do not require tempering in [[The Archipelago#Subgroup temperaments|trinidad temperament]] or anything else, but they do belong to the same 2.3.5.13 subgroup on which trinidad is defined and are certainly characteristic of the temperament.</pre></div>
+<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">
+=5-9-13-15=
+The two //trinidad tetrads// are 15-limit tetrads with no step size smaller than 10/9 and containing an interval of a fifth; these are the otonal trinidad tetrad, 1-13/10-3/2-9/5, with steps 13/10-15/13-6/5-10/9, and the utonal trinidad tetrad, 1-15/13-3/2-5/3, with steps 15/13-13/10-10/9-6/5. These are just intonation tetrads and do not require tempering in [[The Archipelago#Subgroup temperaments|trinidad temperament]] or anything else, but they do belong to the same 2.3.5.13 subgroup on which trinidad is defined and are certainly characteristic of the temperament.
+=9-11-13-15=
+These two tetrads are the otonal, 1-15/13-15/11-5/3, with steps of 15/13-13/11-11/9-6/5, and the utonal, 1-11/9-13/9-5/3 with steps of 11/9-13/11-15/13-6/5.</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;fifteen limit tetrads&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The two &lt;em&gt;trinidad tetrads&lt;/em&gt; are 15-limit tetrads with no step size smaller than 10/9; they are the otonal trinidad tetrad, 1-13/10-3/2-9/5, with steps 13/10-15/13-6/5-10/9, and the utonal trinidad tetrad, 1-15/13-3/2-5/3, with steps 15/13-13/10-10/9-6/5. These are just intonation tetrads and do not require tempering in &lt;a class="wiki_link" href="/The%20Archipelago#Subgroup temperaments"&gt;trinidad temperament&lt;/a&gt; or anything else, but they do belong to the same 2.3.5.13 subgroup on which trinidad is defined and are certainly characteristic of the temperament.&lt;/body&gt;&lt;/html&gt;</pre></div>
+<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;fifteen limit tetrads&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x5-9-13-15"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;5-9-13-15&lt;/h1&gt;
+The two &lt;em&gt;trinidad tetrads&lt;/em&gt; are 15-limit tetrads with no step size smaller than 10/9 and containing an interval of a fifth; these are the otonal trinidad tetrad, 1-13/10-3/2-9/5, with steps 13/10-15/13-6/5-10/9, and the utonal trinidad tetrad, 1-15/13-3/2-5/3, with steps 15/13-13/10-10/9-6/5. These are just intonation tetrads and do not require tempering in &lt;a class="wiki_link" href="/The%20Archipelago#Subgroup temperaments"&gt;trinidad temperament&lt;/a&gt; or anything else, but they do belong to the same 2.3.5.13 subgroup on which trinidad is defined and are certainly characteristic of the temperament.&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="x9-11-13-15"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;9-11-13-15&lt;/h1&gt;
+These two tetrads are the otonal, 1-15/13-15/11-5/3, with steps of 15/13-13/11-11/9-6/5, and the utonal, 1-11/9-13/9-5/3 with steps of 11/9-13/11-15/13-6/5.&lt;/body&gt;&lt;/html&gt;</pre></div>