Cassandra triads: 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:MasonGreen1|MasonGreen1]] and made on <tt>2015-12-01 17:46:07 UTC</tt>.<br>

: This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2015-12-01 17:47:04 UTC</tt>.<br>

: The original revision id was <tt>~~568514967~~</tt>.<br>

: The original revision id was <tt>568515141</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>

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==Consonance of Cassandra triads==

The 13:11 and 14:11 dyads both reside near local [[harmonic entropy]] maxima. This, as well as the fact that the triadic just approximations are 242:286:364, do not make the Cassandra triads sound appealing as consonances.

The 13:11 and 14:11 dyads both reside near local [[harmonic entropy]] maxima due to falling almost halfway between a septimal and a pental consonance. This, as well as the fact that the triadic just approximations are 242:286:364, do not make the Cassandra triads sound appealing as consonances.

However, appearances can be deceiving. I (Mason Green) find that Cassandra triads sound //great// harmonically, at least as good as 12edo ones if not better, and I have a theory as to why.

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<h2 id="toc0"><a name="x-Consonance of Cassandra triads"></a>Consonance of Cassandra triads</h2>

<br />

The 13:11 and 14:11 dyads both reside near local <a class="wiki_link" href="/harmonic%20entropy">harmonic entropy</a> maxima. This, as well as the fact that the triadic just approximations are 242:286:364, do not make the Cassandra triads sound appealing as consonances.<br />

The 13:11 and 14:11 dyads both reside near local <a class="wiki_link" href="/harmonic%20entropy">harmonic entropy</a> maxima due to falling almost halfway between a septimal and a pental consonance. This, as well as the fact that the triadic just approximations are 242:286:364, do not make the Cassandra triads sound appealing as consonances.<br />

<br />

However, appearances can be deceiving. I (Mason Green) find that Cassandra triads sound <em>great</em> harmonically, at least as good as 12edo ones if not better, and I have a theory as to why.<br />

@@ 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:MasonGreen1|MasonGreen1]] and made on <tt>2015-12-01 17:46:07 UTC</tt>.<br>
+: This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2015-12-01 17:47:04 UTC</tt>.<br>
-: The original revision id was <tt>568514967</tt>.<br>
+: The original revision id was <tt>568515141</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>
@@ Line 12: / Line 12: @@
 ==Consonance of Cassandra triads==
-The 13:11 and 14:11 dyads both reside near local [[harmonic entropy]] maxima. This, as well as the fact that the triadic just approximations are 242:286:364, do not make the Cassandra triads sound appealing as consonances.
+The 13:11 and 14:11 dyads both reside near local [[harmonic entropy]] maxima due to falling almost halfway between a septimal and a pental consonance. This, as well as the fact that the triadic just approximations are 242:286:364, do not make the Cassandra triads sound appealing as consonances.
 However, appearances can be deceiving. I (Mason Green) find that Cassandra triads sound //great// harmonically, at least as good as 12edo ones if not better, and I have a theory as to why.
@@ Line 34: / Line 34: @@
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Consonance of Cassandra triads"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Consonance of Cassandra triads&lt;/h2&gt;
   &lt;br /&gt;
-The 13:11 and 14:11 dyads both reside near local &lt;a class="wiki_link" href="/harmonic%20entropy"&gt;harmonic entropy&lt;/a&gt; maxima. This, as well as the fact that the triadic just approximations are 242:286:364, do not make the Cassandra triads sound appealing as consonances.&lt;br /&gt;
+The 13:11 and 14:11 dyads both reside near local &lt;a class="wiki_link" href="/harmonic%20entropy"&gt;harmonic entropy&lt;/a&gt; maxima due to falling almost halfway between a septimal and a pental consonance. This, as well as the fact that the triadic just approximations are 242:286:364, do not make the Cassandra triads sound appealing as consonances.&lt;br /&gt;
 &lt;br /&gt;
 However, appearances can be deceiving. I (Mason Green) find that Cassandra triads sound &lt;em&gt;great&lt;/em&gt; harmonically, at least as good as 12edo ones if not better, and I have a theory as to why.&lt;br /&gt;