Neutral third scales
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author genewardsmith and made on 2011-08-18 13:57:29 UTC.
- The original revision id was 246753671.
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Original Wikitext content:
Mohajira is characterized by the division of the 3/2 "perfect fifth" into two equal "neutral thirds", which are 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"]]. Alternatively, 64/63 could be tempered out, leading to 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.
==Interval chains==
===Basic 2.3.11 mohajira===
|| 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 meantone-like mohajira ("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 beatles===
|| 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 ||Original HTML content:
<html><head><title>Neutral third scales</title></head><body>Mohajira is characterized by the division of the 3/2 "perfect fifth" into two equal "neutral thirds", which are 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">"mohaha"</a>. Alternatively, 64/63 could be tempered out, leading to 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 "neutral thirds" scale.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:<h2> --><h2 id="toc0"><a name="x-Interval chains"></a><!-- ws:end:WikiTextHeadingRule:0 -->Interval chains</h2>
<!-- ws:start:WikiTextHeadingRule:2:<h3> --><h3 id="toc1"><a name="x-Interval chains-Basic 2.3.11 mohajira"></a><!-- ws:end:WikiTextHeadingRule:2 -->Basic 2.3.11 mohajira</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:<h3> --><h3 id="toc2"><a name="x-Interval chains-2.3.5.11 meantone-like mohajira ("mohaha")"></a><!-- ws:end:WikiTextHeadingRule:4 -->2.3.5.11 meantone-like mohajira ("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:<h3> --><h3 id="toc3"><a name="x-Interval chains-2.3.7.11 beatles"></a><!-- ws:end:WikiTextHeadingRule:6 -->2.3.7.11 beatles</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>
</body></html>