Neutral third scales: Difference between revisions

<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 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==  

===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===  

==Munits==

Though they differ in the specifics of their temperaments, all neutral third scales have certain [[munit]]s in common.

* 4/3 Lss, 4/3 sLs: Rather than being divided into two large steps and one small step as in the diatonic scale, 4/3 can always be divided into one large step and two small steps. The large step is 9/8, and the two small steps are "neutral seconds" representing the sub-munit "32/27 ss".

* 11/8 LsL: In contrast, two large steps and a small step make a much less consonant and more colorful interval, 11/8.</pre></div>

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

&lt;table class="wiki_table"&gt;

        &lt;td&gt;296.85&lt;br /&gt;

        &lt;td&gt;647.37&lt;br /&gt;

        &lt;td&gt;997.90&lt;br /&gt;

        &lt;td&gt;16/11&lt;br /&gt;

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

&lt;table class="wiki_table"&gt;

        &lt;td&gt;696.19&lt;br /&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;

&lt;table class="wiki_table"&gt;

        &lt;td&gt;630.21&lt;br /&gt;

&lt;ul&gt;&lt;li&gt;4/3 Lss, 4/3 sLs: Rather than being divided into two large steps and one small step as in the diatonic scale, 4/3 can always be divided into one large step and two small steps. The large step is 9/8, and the two small steps are &amp;quot;neutral seconds&amp;quot; representing the sub-munit &amp;quot;32/27 ss&amp;quot;.&lt;/li&gt;&lt;li&gt;11/8 LsL: In contrast, two large steps and a small step make a much less consonant and more colorful interval, 11/8.&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>