11/9
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- This revision was by author Chartrekhan and made on 2016-09-25 08:49:13 UTC.
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**11/9** |0 -2 0 0 1> 347.40794 cents [[media type="file" key="jid_11_9_pluck_adu_dr220.mp3" width="240" height="20"]] [[file:xenharmonic/jid_11_9_pluck_adu_dr220.mp3|sound sample]] 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 persony (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 theyxad 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. Persony temperaments, including [[17edo]], [[24edo]], [[31edo]], [[41edo]], [[58edo]], [[72edo]], [[130edo]], [[202edo]], [[Gamelismic clan#Miracle|miracle]], [[Breedsmic temperaments#Harry|harry]], and [[Schismatic family#Sesquiquartififths|sesquart]], 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,%20aka%20Wonder|jove]]. By coincidence, the ratio between the common tuning frequency 440hz and the most common AC power frequency of 60hz is exactly 11/9 (but 6 octaves up) See: [[Gallery of Just Intervals]]
Original HTML content:
<html><head><title>11_9</title></head><body><strong>11/9</strong><br />
|0 -2 0 0 1><br />
347.40794 cents<br />
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In <a class="wiki_link" href="/11-limit">11-limit</a> <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>, <strong>11/9</strong> 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 persony (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 theyxad 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. Persony temperaments, including <a class="wiki_link" href="/17edo">17edo</a>, <a class="wiki_link" href="/24edo">24edo</a>, <a class="wiki_link" href="/31edo">31edo</a>, <a class="wiki_link" href="/41edo">41edo</a>, <a class="wiki_link" href="/58edo">58edo</a>, <a class="wiki_link" href="/72edo">72edo</a>, <a class="wiki_link" href="/130edo">130edo</a>, <a class="wiki_link" href="/202edo">202edo</a>, <a class="wiki_link" href="/Gamelismic%20clan#Miracle">miracle</a>, <a class="wiki_link" href="/Breedsmic%20temperaments#Harry">harry</a>, and <a class="wiki_link" href="/Schismatic%20family#Sesquiquartififths">sesquart</a>, 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,%20aka%20Wonder">jove</a>.<br />
<br />
By coincidence, the ratio between the common tuning frequency 440hz and the most common AC power frequency of 60hz is exactly 11/9 (but 6 octaves up)<br />
<br />
See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></body></html>