Neutral third scales: Difference between revisions

Revision as of 17:08, 31 October 2011

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This revision was by author keenanpepper and made on 2011-10-31 17:08:48 UTC.

The original revision id was 270418178.

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Original Wikitext content:

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 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== 
===Basic 2.3.11 neutral thirds scale=== 
|| 296.85 || 647.37 || 997.90 || 148.42 || 498.95 || 849.47 || 0. || 350.53 || 701.05 || 1051.58 || 202.10 || 552.63 || 903.15 ||
|| 32/27 || 16/11 || 16/9 || 12/11 || 4/3 || 18/11 || 1/1 || 11/9 || 3/2 || 11/6 || 9/8 || 11/8 || 27/16 ||
===2.3.5.11 mohaha=== 
|| 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 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 ||
==MOSes== 
Neutral third scales are associated with the [[MOSScales|MOS patterns]] [[3L 4s]] and [[7L 3s]].
In the 3L4s MOS, the large step is a 9/8 and the small step is a 12/11 neutral second. In the 7L3s MOS, the 12/11 is now the large step and the small step is a 33/32 quarter tone.

Original HTML content:

<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 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 />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Interval chains"></a><!-- ws:end:WikiTextHeadingRule:0 -->Interval chains</h2>
 <!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x-Interval chains-Basic 2.3.11 neutral thirds scale"></a><!-- ws:end:WikiTextHeadingRule:2 -->Basic 2.3.11 neutral thirds scale</h3>
 

<table class="wiki_table">
    <tr>
        <td>296.85<br />
</td>
        <td>647.37<br />
</td>
        <td>997.90<br />
</td>
        <td>148.42<br />
</td>
        <td>498.95<br />
</td>
        <td>849.47<br />
</td>
        <td>0.<br />
</td>
        <td>350.53<br />
</td>
        <td>701.05<br />
</td>
        <td>1051.58<br />
</td>
        <td>202.10<br />
</td>
        <td>552.63<br />
</td>
        <td>903.15<br />
</td>
    </tr>
    <tr>
        <td>32/27<br />
</td>
        <td>16/11<br />
</td>
        <td>16/9<br />
</td>
        <td>12/11<br />
</td>
        <td>4/3<br />
</td>
        <td>18/11<br />
</td>
        <td>1/1<br />
</td>
        <td>11/9<br />
</td>
        <td>3/2<br />
</td>
        <td>11/6<br />
</td>
        <td>9/8<br />
</td>
        <td>11/8<br />
</td>
        <td>27/16<br />
</td>
    </tr>
</table>

<!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x-Interval chains-2.3.5.11 mohaha"></a><!-- ws:end:WikiTextHeadingRule:4 -->2.3.5.11 mohaha</h3>
 

<table class="wiki_table">
    <tr>
        <td>815.25<br />
</td>
        <td>1163.34<br />
</td>
        <td>311.44<br />
</td>
        <td>659.53<br />
</td>
        <td>1007.63<br />
</td>
        <td>155.72<br />
</td>
        <td>503.81<br />
</td>
        <td>851.91<br />
</td>
        <td>0.<br />
</td>
        <td>348.09<br />
</td>
        <td>696.19<br />
</td>
        <td>1044.28<br />
</td>
        <td>192.37<br />
</td>
        <td>540.47<br />
</td>
        <td>888.56<br />
</td>
        <td>36.66<br />
</td>
        <td>384.75<br />
</td>
    </tr>
    <tr>
        <td>8/5<br />
</td>
        <td><br />
</td>
        <td>6/5<br />
</td>
        <td>16/11<br />
</td>
        <td>16/9~9/5<br />
</td>
        <td>12/11~11/10<br />
</td>
        <td>4/3<br />
</td>
        <td>18/11<br />
</td>
        <td>1/1<br />
</td>
        <td>11/9<br />
</td>
        <td>3/2<br />
</td>
        <td>11/6<br />
</td>
        <td>10/9~9/8<br />
</td>
        <td>11/8<br />
</td>
        <td>5/3<br />
</td>
        <td><br />
</td>
        <td>5/4<br />
</td>
    </tr>
</table>

<!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="x-Interval chains-2.3.7.11 maqamic"></a><!-- ws:end:WikiTextHeadingRule:6 -->2.3.7.11 maqamic</h3>
 

<table class="wiki_table">
    <tr>
        <td>414.38<br />
</td>
        <td>768.34<br />
</td>
        <td>1122.29<br />
</td>
        <td>276.25<br />
</td>
        <td>630.21<br />
</td>
        <td>984.17<br />
</td>
        <td>138.13<br />
</td>
        <td>492.08<br />
</td>
        <td>846.04<br />
</td>
        <td>0.<br />
</td>
        <td>353.96<br />
</td>
        <td>707.92<br />
</td>
        <td>1061.87<br />
</td>
        <td>215.83<br />
</td>
        <td>569.79<br />
</td>
        <td>923.75<br />
</td>
        <td>77.71<br />
</td>
        <td>431.66<br />
</td>
        <td>785.62<br />
</td>
    </tr>
    <tr>
        <td>14/11<br />
</td>
        <td>14/9<br />
</td>
        <td><br />
</td>
        <td>7/6<br />
</td>
        <td>16/11<br />
</td>
        <td>7/4~16/9<br />
</td>
        <td>12/11<br />
</td>
        <td>4/3<br />
</td>
        <td>18/11<br />
</td>
        <td>1/1<br />
</td>
        <td>11/9<br />
</td>
        <td>3/2<br />
</td>
        <td>11/6<br />
</td>
        <td>9/8~8/7<br />
</td>
        <td>11/8<br />
</td>
        <td>12/7<br />
</td>
        <td><br />
</td>
        <td>9/7<br />
</td>
        <td>11/7<br />
</td>
    </tr>
</table>

<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="x-MOSes"></a><!-- ws:end:WikiTextHeadingRule:8 -->MOSes</h2>
 Neutral third scales are associated with the <a class="wiki_link" href="/MOSScales">MOS patterns</a> <a class="wiki_link" href="/3L%204s">3L 4s</a> and <a class="wiki_link" href="/7L%203s">7L 3s</a>.<br />
In the 3L4s MOS, the large step is a 9/8 and the small step is a 12/11 neutral second. In the 7L3s MOS, the 12/11 is now the large step and the small step is a 33/32 quarter tone.</body></html>

@@ 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;

Neutral third scales: Difference between revisions

Revision as of 17:08, 31 October 2011

IMPORTED REVISION FROM WIKISPACES

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