Rank-2 temperaments by mapping of 3: 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:

: This revision was by author [[User:~~keenanpepper~~|~~keenanpepper~~]] and made on <tt>2011-10-~~29 22~~:43:32 UTC</tt>.

: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2011-11-04 02:53:05 UTC</tt>.

: The original revision id was <tt>~~269921376~~</tt>.

: The original revision id was <tt>271813012</tt>.

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

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Temperaments in this category split either 4/3 or 3/2 into two equal parts.

The first splits 4/3 into two ~250 cent intervals. Mandatory MOSes include 4, 5, and 9 ~~(bug/beep always has a 9-note MOS, right?)~~.

The first splits 4/3 into two ~250 cent intervals. Mandatory MOSes include 4, 5, and 9.

[<1 2...], <0 -2...]>

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* Godzilla

* Semiphore

* Superpelog

And the second splits 3/2 into two ~350 cent "neutral thirds". Mandatory MOSes include 3, 4, and 7.

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* Slendric

Finally we have temperaments in which 8/3 is divided into 3 equal parts of ~566 cents (or equivalently 3/1 into 3 parts of ~634 cents). (~~Intersting~~ fact: This also implies that 9/8 is divided into 3 equal parts.) Mandatory MOSes include 5, 7, 9, 11, 13, and 15.

Finally we have temperaments in which 8/3 is divided into 3 equal parts of ~566 cents (or equivalently 3/1 into 3 parts of ~634 cents). (Interesting fact: This also implies that 9/8 is divided into 3 equal parts.) Mandatory MOSes include 5, 7, 9, 11, 13, and 15.

[<1 3...], <0, -3...]>

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Temperaments in this category split either 4/3 or 3/2 into two equal parts.

The first splits 4/3 into two ~250 cent intervals. Mandatory MOSes include 4, 5, and 9 ~~(bug/beep always has a 9-note MOS, right?)~~.

The first splits 4/3 into two ~250 cent intervals. Mandatory MOSes include 4, 5, and 9.

[&lt;1 2...], &lt;0 -2...]&gt;

<ul><li>Barbados</li><li>Beep</li><li>Bridgetown</li><li>Bug</li><li>Godzilla</li><li>Semiphore</li></ul>

<ul><li>Barbados</li><li>Beep</li><li>Bridgetown</li><li>Bug</li><li>Godzilla</li><li>Semiphore</li><li>Superpelog</li></ul>

And the second splits 3/2 into two ~350 cent &quot;neutral thirds&quot;. Mandatory MOSes include 3, 4, and 7.

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[&lt;1 1...], &lt;0, 3...]&gt;

<ul><li>Cynder</li><li>Gorgo</li><li>Mothra</li><li>Radon</li><li>Rodan</li><li>Slendric</li></ul>

Finally we have temperaments in which 8/3 is divided into 3 equal parts of ~566 cents (or equivalently 3/1 into 3 parts of ~634 cents). (~~Intersting~~ fact: This also implies that 9/8 is divided into 3 equal parts.) Mandatory MOSes include 5, 7, 9, 11, 13, and 15.

Finally we have temperaments in which 8/3 is divided into 3 equal parts of ~566 cents (or equivalently 3/1 into 3 parts of ~634 cents). (Interesting fact: This also implies that 9/8 is divided into 3 equal parts.) Mandatory MOSes include 5, 7, 9, 11, 13, and 15.

[&lt;1 3...], &lt;0, -3...]&gt;

@@ 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:keenanpepper|keenanpepper]] and made on <tt>2011-10-29 22:43:32 UTC</tt>.<br>
+: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2011-11-04 02:53:05 UTC</tt>.<br>
-: The original revision id was <tt>269921376</tt>.<br>
+: The original revision id was <tt>271813012</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 65: / Line 65: @@
 Temperaments in this category split either 4/3 or 3/2 into two equal parts.
-The first splits 4/3 into two ~250 cent intervals. Mandatory MOSes include 4, 5, and 9 (bug/beep always has a 9-note MOS, right?).
+The first splits 4/3 into two ~250 cent intervals. Mandatory MOSes include 4, 5, and 9.
 [&lt;1 2...], &lt;0 -2...]&gt;
@@ Line 74: / Line 74: @@
 * Godzilla
 * Semiphore
+* Superpelog
 And the second splits 3/2 into two ~350 cent "neutral thirds". Mandatory MOSes include 3, 4, and 7.
@@ Line 121: / Line 122: @@
 * Slendric
-Finally we have temperaments in which 8/3 is divided into 3 equal parts of ~566 cents (or equivalently 3/1 into 3 parts of ~634 cents). (Intersting fact: This also implies that 9/8 is divided into 3 equal parts.) Mandatory MOSes include 5, 7, 9, 11, 13, and 15.
+Finally we have temperaments in which 8/3 is divided into 3 equal parts of ~566 cents (or equivalently 3/1 into 3 parts of ~634 cents). (Interesting fact: This also implies that 9/8 is divided into 3 equal parts.) Mandatory MOSes include 5, 7, 9, 11, 13, and 15.
 [&lt;1 3...], &lt;0, -3...]&gt;
@@ Line 378: / Line 379: @@
 Temperaments in this category split either 4/3 or 3/2 into two equal parts.&lt;br /&gt;
 &lt;br /&gt;
-The first splits 4/3 into two ~250 cent intervals. Mandatory MOSes include 4, 5, and 9 (bug/beep always has a 9-note MOS, right?).&lt;br /&gt;
+The first splits 4/3 into two ~250 cent intervals. Mandatory MOSes include 4, 5, and 9.&lt;br /&gt;
 &lt;br /&gt;
 [&amp;lt;1 2...], &amp;lt;0 -2...]&amp;gt;&lt;br /&gt;
-&lt;ul&gt;&lt;li&gt;Barbados&lt;/li&gt;&lt;li&gt;Beep&lt;/li&gt;&lt;li&gt;Bridgetown&lt;/li&gt;&lt;li&gt;Bug&lt;/li&gt;&lt;li&gt;Godzilla&lt;/li&gt;&lt;li&gt;Semiphore&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
+&lt;ul&gt;&lt;li&gt;Barbados&lt;/li&gt;&lt;li&gt;Beep&lt;/li&gt;&lt;li&gt;Bridgetown&lt;/li&gt;&lt;li&gt;Bug&lt;/li&gt;&lt;li&gt;Godzilla&lt;/li&gt;&lt;li&gt;Semiphore&lt;/li&gt;&lt;li&gt;Superpelog&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
 And the second splits 3/2 into two ~350 cent &amp;quot;neutral thirds&amp;quot;. Mandatory MOSes include 3, 4, and 7.&lt;br /&gt;
 &lt;br /&gt;
@@ Line 404: / Line 405: @@
 [&amp;lt;1 1...], &amp;lt;0, 3...]&amp;gt;&lt;br /&gt;
 &lt;ul&gt;&lt;li&gt;Cynder&lt;/li&gt;&lt;li&gt;Gorgo&lt;/li&gt;&lt;li&gt;Mothra&lt;/li&gt;&lt;li&gt;Radon&lt;/li&gt;&lt;li&gt;Rodan&lt;/li&gt;&lt;li&gt;Slendric&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
-Finally we have temperaments in which 8/3 is divided into 3 equal parts of ~566 cents (or equivalently 3/1 into 3 parts of ~634 cents). (Intersting fact: This also implies that 9/8 is divided into 3 equal parts.) Mandatory MOSes include 5, 7, 9, 11, 13, and 15.&lt;br /&gt;
+Finally we have temperaments in which 8/3 is divided into 3 equal parts of ~566 cents (or equivalently 3/1 into 3 parts of ~634 cents). (Interesting fact: This also implies that 9/8 is divided into 3 equal parts.) Mandatory MOSes include 5, 7, 9, 11, 13, and 15.&lt;br /&gt;
 &lt;br /&gt;
 [&amp;lt;1 3...], &amp;lt;0, -3...]&amp;gt;&lt;br /&gt;