Neutral third scales: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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: This revision was by author [[User:~~keenanpepper~~|~~keenanpepper~~]] and made on <tt>~~2011~~-12-~~29 22~~:32:49 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-12-04 19:54:27 UTC</tt>.<br>

: The original revision id was <tt>~~288796499~~</tt>.<br>

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If the fifth harmonic is used at all, it makes sense to map it to 8 generators by tempering out 81/80, making it [[Meantone family#Mohajira|a meantone system]], sometimes called [[Chromatic pairs#Mohaha|"mohaha"]]. If 7 is also mapped a particular way it is called [[mohajira]]. Alternatively, 64/63 could be tempered out, leading to a 2.3.7.11 version of [[maqamic|maqamic temperament]]. But neither of these adjustments to the farther-out intervals affects its basic nature as a "neutral thirds" scale, which equally subdivides the 3/2 into two equal parts.

Any temperament tempering out 243/242 lends itself to neutral thirds; this becomes more significant when fifths are of low complexity, such as hemififths or the rank three temperament jove, but also includes miracle, harry and so forth. Nor does a scale need to be a MOS to qualify as a neutral thirds scale; that name could reasonably be given to [[Graph-theoretic properties of scales#Examples-Oktone|Oktone]], for example.

==Interval chains==

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<br />

If the fifth harmonic is used at all, it makes sense to map it to 8 generators by tempering out 81/80, making it <a class="wiki_link" href="/Meantone%20family#Mohajira">a meantone system</a>, sometimes called <a class="wiki_link" href="/Chromatic%20pairs#Mohaha">&quot;mohaha&quot;</a>. If 7 is also mapped a particular way it is called <a class="wiki_link" href="/mohajira">mohajira</a>. Alternatively, 64/63 could be tempered out, leading to a 2.3.7.11 version of <a class="wiki_link" href="/maqamic">maqamic temperament</a>. But neither of these adjustments to the farther-out intervals affects its basic nature as a &quot;neutral thirds&quot; scale, which equally subdivides the 3/2 into two equal parts.<br />

<br />

Any temperament tempering out 243/242 lends itself to neutral thirds; this becomes more significant when fifths are of low complexity, such as hemififths or the rank three temperament jove, but also includes miracle, harry and so forth. Nor does a scale need to be a MOS to qualify as a neutral thirds scale; that name could reasonably be given to <a class="wiki_link" href="/Graph-theoretic%20properties%20of%20scales#Examples-Oktone">Oktone</a>, for example.<br />

<br />

<h2 id="toc0"><a name="x-Interval chains"></a>Interval chains</h2>

@@ 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>2011-12-29 22:32:49 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-12-04 19:54:27 UTC</tt>.<br>
-: The original revision id was <tt>288796499</tt>.<br>
+: The original revision id was <tt>389190314</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 9: / Line 9: @@
 If the fifth harmonic is used at all, it makes sense to map it to 8 generators by tempering out 81/80, making it [[Meantone family#Mohajira|a meantone system]], sometimes called [[Chromatic pairs#Mohaha|"mohaha"]]. If 7 is also mapped a particular way it is called [[mohajira]]. Alternatively, 64/63 could be tempered out, leading to a 2.3.7.11 version of [[maqamic|maqamic temperament]]. But neither of these adjustments to the farther-out intervals affects its basic nature as a "neutral thirds" scale, which equally subdivides the 3/2 into two equal parts.
+Any temperament tempering out 243/242 lends itself to neutral thirds; this becomes more significant when fifths are of low complexity, such as hemififths or the rank three temperament jove, but also includes miracle, harry and so forth. Nor does a scale need to be a MOS to qualify as a neutral thirds scale; that name could reasonably be given to [[Graph-theoretic properties of scales#Examples-Oktone|Oktone]], for example.
 ==Interval chains==
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 &lt;br /&gt;
 If the fifth harmonic is used at all, it makes sense to map it to 8 generators by tempering out 81/80, making it &lt;a class="wiki_link" href="/Meantone%20family#Mohajira"&gt;a meantone system&lt;/a&gt;, sometimes called &lt;a class="wiki_link" href="/Chromatic%20pairs#Mohaha"&gt;&amp;quot;mohaha&amp;quot;&lt;/a&gt;. If 7 is also mapped a particular way it is called &lt;a class="wiki_link" href="/mohajira"&gt;mohajira&lt;/a&gt;. Alternatively, 64/63 could be tempered out, leading to a 2.3.7.11 version of &lt;a class="wiki_link" href="/maqamic"&gt;maqamic temperament&lt;/a&gt;. But neither of these adjustments to the farther-out intervals affects its basic nature as a &amp;quot;neutral thirds&amp;quot; scale, which equally subdivides the 3/2 into two equal parts.&lt;br /&gt;
+&lt;br /&gt;
+Any temperament tempering out 243/242 lends itself to neutral thirds; this becomes more significant when fifths are of low complexity, such as hemififths or the rank three temperament jove, but also includes miracle, harry and so forth. Nor does a scale need to be a MOS to qualify as a neutral thirds scale; that name could reasonably be given to &lt;a class="wiki_link" href="/Graph-theoretic%20properties%20of%20scales#Examples-Oktone"&gt;Oktone&lt;/a&gt;, for example.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Interval chains"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Interval chains&lt;/h2&gt;