Neutral third scales: 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:~~guest~~|~~guest~~]] and made on <tt>2011-10-~~14 19~~:47:36 UTC</tt>.<br>

: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-10-31 17:08:48 UTC</tt>.<br>

: The original revision id was <tt>~~264936556~~</tt>.<br>

: The original revision id was <tt>270418178</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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<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">Neutral third scales are characterized by the division of the 3/2 "perfect fifth" into two equal "neutral thirds", which can be taken to represent either 11/9 or 27/22. This means the comma 243/242 is tempered out.

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 ~~either [[maqamic|maqamic temperament]]; if one wishes to ignore 5 this can be viewed as~~ a 2.3.7.11 version of [[~~Archytas clan#Beatles~~|~~beatles~~]]. 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.

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.

==Interval chains==

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|| 815.25 || 1163.34 || 311.44 || 659.53 || 1007.63 || 155.72 || 503.81 || 851.91 || 0. || 348.09 || 696.19 || 1044.28 || 192.37 || 540.47 || 888.56 || 36.66 || 384.75 ||

|| 8/5 || || 6/5 || 16/11 || 16/9~9/5 || 12/11~11/10 || 4/3 || 18/11 || 1/1 || 11/9 || 3/2 || 11/6 || 10/9~9/8 || 11/8 || 5/3 || || 5/4 ||

===2.3.7.11 ~~beatles~~===

===2.3.7.11 maqamic===

|| 414.38 || 768.34 || 1122.29 || 276.25 || 630.21 || 984.17 || 138.13 || 492.08 || 846.04 || 0. || 353.96 || 707.92 || 1061.87 || 215.83 || 569.79 || 923.75 || 77.71 || 431.66 || 785.62 ||

|| 14/11 || 14/9 || || 7/6 || 16/11 || 7/4~16/9 || 12/11 || 4/3 || 18/11 || 1/1 || 11/9 || 3/2 || 11/6 || 9/8~8/7 || 11/8 || 12/7 || || 9/7 || 11/7 ||

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<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>Neutral third scales</title></head><body>Neutral third scales are characterized by the division of the 3/2 &quot;perfect fifth&quot; into two equal &quot;neutral thirds&quot;, which can be taken to represent either 11/9 or 27/22. This means the comma 243/242 is tempered out.<br />

<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 ~~either <a class="wiki_link" href="/maqamic">maqamic temperament</a>; if one wishes to ignore 5 this can be viewed as~~ a 2.3.7.11 version of <a class="wiki_link" href="/~~Archytas%20clan#Beatles~~">~~beatles~~</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 />

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 />

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

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</table>

<h3 id="toc3"><a name="x-Interval chains-2.3.7.11 ~~beatles~~"></a>2.3.7.11 ~~beatles~~</h3>

<h3 id="toc3"><a name="x-Interval chains-2.3.7.11 maqamic"></a>2.3.7.11 maqamic</h3>

@@ 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:guest|guest]] and made on <tt>2011-10-14 19:47:36 UTC</tt>.<br>
+: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-10-31 17:08:48 UTC</tt>.<br>
-: The original revision id was <tt>264936556</tt>.<br>
+: The original revision id was <tt>270418178</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 8: / Line 8: @@
 <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">Neutral third scales are characterized by the division of the 3/2 "perfect fifth" into two equal "neutral thirds", which can be taken to represent either 11/9 or 27/22. This means the comma 243/242 is tempered out.
-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 either [[maqamic|maqamic temperament]]; if one wishes to ignore 5 this can be viewed as a 2.3.7.11 version of [[Archytas clan#Beatles|beatles]]. 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.
+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.
 ==Interval chains==
@@ Line 17: / Line 17: @@
 || 815.25 || 1163.34 || 311.44 || 659.53 || 1007.63 || 155.72 || 503.81 || 851.91 || 0. || 348.09 || 696.19 || 1044.28 || 192.37 || 540.47 || 888.56 || 36.66 || 384.75 ||
 || 8/5 ||   || 6/5 || 16/11 || 16/9~9/5 || 12/11~11/10 || 4/3 || 18/11 || 1/1 || 11/9 || 3/2 || 11/6 || 10/9~9/8 || 11/8 || 5/3 ||   || 5/4 ||
-===2.3.7.11 beatles===
+===2.3.7.11 maqamic===
 || 414.38 || 768.34 || 1122.29 || 276.25 || 630.21 || 984.17 || 138.13 || 492.08 || 846.04 || 0. || 353.96 || 707.92 || 1061.87 || 215.83 || 569.79 || 923.75 || 77.71 || 431.66 || 785.62 ||
 || 14/11 || 14/9 ||   || 7/6 || 16/11 || 7/4~16/9 || 12/11 || 4/3 || 18/11 || 1/1 || 11/9 || 3/2 || 11/6 || 9/8~8/7 || 11/8 || 12/7 ||   || 9/7 || 11/7 ||
@@ Line 26: / Line 26: @@
 <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;Neutral third scales&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Neutral third scales are characterized by the division of the 3/2 &amp;quot;perfect fifth&amp;quot; into two equal &amp;quot;neutral thirds&amp;quot;, which can be taken to represent either 11/9 or 27/22. This means the comma 243/242 is tempered out.&lt;br /&gt;
 &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 either &lt;a class="wiki_link" href="/maqamic"&gt;maqamic temperament&lt;/a&gt;; if one wishes to ignore 5 this can be viewed as a 2.3.7.11 version of &lt;a class="wiki_link" href="/Archytas%20clan#Beatles"&gt;beatles&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;
+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;
 &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;
@@ Line 169: / Line 169: @@
 &lt;/table&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="x-Interval chains-2.3.7.11 beatles"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;2.3.7.11 beatles&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="x-Interval chains-2.3.7.11 maqamic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;2.3.7.11 maqamic&lt;/h3&gt;