Neutral third scales: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
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.
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<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>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>
<h4>Original Wikitext content:</h4>
<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.
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|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.
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==  
==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 ||
===Basic 2.3.11 neutral thirds scale===
|| 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===  
{| class="wikitable"
|| 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 ||
| | 296.85
===2.3.7.11 maqamic===
| | 647.37
|| 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 ||
| | 997.90
|| 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 ||
| | 148.42
==MOSes==
| | 498.95
Neutral third scales are associated with the [[MOSScales|MOS patterns]] [[3L 4s]] and [[7L 3s]].
| | 849.47
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.
| | 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==
{| class="wikitable"
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".
| | 815.25
* 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>
| | 1163.34
<h4>Original HTML content:</h4>
| | 311.44
<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;
| | 659.53
&lt;br /&gt;
| | 1007.63
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;
| | 155.72
&lt;br /&gt;
| | 503.81
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;
| | 851.91
&lt;br /&gt;
| | 0.
&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;
| | 348.09
&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;
| | 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
|}


&lt;table class="wiki_table"&gt;
===2.3.7.11 maqamic===
    &lt;tr&gt;
        &lt;td&gt;296.85&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;647.37&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;997.90&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;148.42&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;498.95&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;849.47&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0.&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;350.53&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;701.05&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1051.58&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;202.10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;552.63&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;903.15&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;32/27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;18/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;27/16&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&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;
{| class="wikitable"
|-
| | 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
|}


&lt;table class="wiki_table"&gt;
==MOSes==
    &lt;tr&gt;
Neutral third scales are associated with the [[MOSScales|MOS patterns]] [[3L_4s|3L 4s]] and [[7L_3s|7L 3s]].
        &lt;td&gt;815.25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1163.34&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;311.44&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;659.53&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1007.63&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;155.72&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;503.81&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;851.91&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0.&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;348.09&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;696.19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1044.28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;192.37&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;540.47&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;888.56&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;36.66&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;384.75&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;8/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/9~9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12/11~11/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;18/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10/9~9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/4&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&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 maqamic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;2.3.7.11 maqamic&lt;/h3&gt;
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.


&lt;table class="wiki_table"&gt;
==Munits==
    &lt;tr&gt;
Though they differ in the specifics of their temperaments, all neutral third scales have certain [[Munit|munit]]s in common.
        &lt;td&gt;414.38&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;768.34&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1122.29&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;276.25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;630.21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;984.17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;138.13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;492.08&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;846.04&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0.&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;353.96&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;707.92&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1061.87&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;215.83&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;569.79&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;923.75&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;77.71&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;431.66&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;785.62&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;14/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/4~16/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;18/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/8~8/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/7&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="x-MOSes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;MOSes&lt;/h2&gt;
<ul><li>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".</li><li>11/8 LsL: In contrast, two large steps and a small step make a much less consonant and more colorful interval, 11/8.</li></ul>
Neutral third scales are associated with the &lt;a class="wiki_link" href="/MOSScales"&gt;MOS patterns&lt;/a&gt; &lt;a class="wiki_link" href="/3L%204s"&gt;3L 4s&lt;/a&gt; and &lt;a class="wiki_link" href="/7L%203s"&gt;7L 3s&lt;/a&gt;.&lt;br /&gt;
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.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="x-Munits"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Munits&lt;/h2&gt;
Though they differ in the specifics of their temperaments, all neutral third scales have certain &lt;a class="wiki_link" href="/munit"&gt;munit&lt;/a&gt;s in common.&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>

Revision as of 00:00, 17 July 2018

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 a meantone system, sometimes called "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 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 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

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 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.

Munits

Though they differ in the specifics of their temperaments, all neutral third scales have certain munits 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.
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