11/9
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author genewardsmith and made on 2011-09-21 17:09:28 UTC.
- The original revision id was 256747890.
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Original Wikitext content:
In [[11-limit]] [[Just Intonation]], 11/9 is a neutral third of about 347.4¢, falling in between "major third" and "minor third" territory. It is the simplest neutral third in just intonation, but of course, only one of many (others include [[16_13|16/13]], [[27_22|27/22]], [[49_40|49/40]] and [[60_49|60/49]]). It is nearly halfway between two intervals of [[12edo]], implying that it is both very xenharmonic and well-represented in [[24edo]]. In the 11-limit hexad 4:5:6:7:9:11, 11/9 appears between the harmonic 11th and the harmonic 9th. A triad can also be built with a 3/2 fifth and 11/9 third: this would be 18:22:27. This introduces a second neutral third, 27/22, which together make a perfect fifth. Many temperaments, including [[17edo]], [[24edo]] and [[31edo]], to name a few, conflate these two neutral thirds, allowing one neutral third interval to be stacked to generate a perfect fifth. 11/9 differs from 27/22 by 243/242, but also from 49/40 by 441/440 and 60/49 by 540/539, with varied consequences when one or more of them are tempered out. Tempering out all of them leads to the 11-limit rank three temperament [[Breed family#Jove, aka Wonder|jove]]. See: [[Gallery of Just Intervals]]
Original HTML content:
<html><head><title>11_9</title></head><body>In <a class="wiki_link" href="/11-limit">11-limit</a> <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>, 11/9 is a neutral third of about 347.4¢, falling in between "major third" and "minor third" territory. It is the simplest neutral third in just intonation, but of course, only one of many (others include <a class="wiki_link" href="/16_13">16/13</a>, <a class="wiki_link" href="/27_22">27/22</a>, <a class="wiki_link" href="/49_40">49/40</a> and <a class="wiki_link" href="/60_49">60/49</a>). It is nearly halfway between two intervals of <a class="wiki_link" href="/12edo">12edo</a>, implying that it is both very xenharmonic and well-represented in <a class="wiki_link" href="/24edo">24edo</a>.<br /> <br /> In the 11-limit hexad 4:5:6:7:9:11, 11/9 appears between the harmonic 11th and the harmonic 9th. A triad can also be built with a 3/2 fifth and 11/9 third: this would be 18:22:27. This introduces a second neutral third, 27/22, which together make a perfect fifth. Many temperaments, including <a class="wiki_link" href="/17edo">17edo</a>, <a class="wiki_link" href="/24edo">24edo</a> and <a class="wiki_link" href="/31edo">31edo</a>, to name a few, conflate these two neutral thirds, allowing one neutral third interval to be stacked to generate a perfect fifth. 11/9 differs from 27/22 by 243/242, but also from 49/40 by 441/440 and 60/49 by 540/539, with varied consequences when one or more of them are tempered out. Tempering out all of them leads to the 11-limit rank three temperament <a class="wiki_link" href="/Breed%20family#Jove, aka Wonder">jove</a>.<br /> <br /> See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></body></html>