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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Infobox Interval |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | | Name = undecimal neutral third, Alpharabian artoneutral third |
| : This revision was by author [[User:Chartrekhan|Chartrekhan]] and made on <tt>2016-09-25 08:49:13 UTC</tt>.<br>
| | | Color name = 1o3, ilo 3rd |
| : The original revision id was <tt>593234990</tt>.<br>
| | | Sound = jid_11_9_pluck_adu_dr220.mp3 |
| : 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>
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| <h4>Original Wikitext content:</h4>
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| <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">**11/9**
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| 347.40794 cents
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| [[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]]
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| 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 [[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 it is only one of many, of which others include [[16/13]], [[27/22]], [[39/32]], [[49/40]] and [[60/49]]. As this is the smaller of the two [[11-limit]] neutral thirds obtained by modifying Pythagorean intervals by [[33/32]], it is dubbed the '''Alpharabian artoneutral third''' in [[Alpharabian tuning]]. Since it is nearly halfway between two intervals of [[12edo]], it implies that it is both very xenharmonic and well-represented in [[24edo]]. It is approximated even more closely in [[31edo]] and [[38edo]], where the slight flatness of the fifth creates two near perfect 11/9's when divided in half, making the neutral triad particularly stable sounding in these tunings. |
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| 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]]. | | In the 11-limit hexad 4:5:6:7:9:11, 11/9 appears between the 11th harmonic and the 9th harmonic. A triad can also be built with 3/2 and 11/9, and the chord formed is 18:22:27. This introduces a second neutral third, 27/22, which is the difference between 3/2 and 11/9. Many temperaments, including [[7edo]], [[10edo]], [[17edo]], [[24edo]], [[31edo]], [[41edo]], [[58edo]], [[Gamelismic clan#Miracle|miracle]], [[Breedsmic temperaments #Harry|harry]], and [[Schismatic family #Sesquiquartififths|sesquart]], conflate these two neutral thirds. The interval which represents both neutral thirds can then be stacked twice 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 these commas leads to the 11-limit rank three temperament [[Breed family #Jove, aka Wonder|jove]]. |
| | == Approximation == |
| | {{Interval edo approximation|11/9}} |
| | == See also == |
| | * [[7edo]] |
| | * [[24edo]] |
| | * [[18/11]] – its [[octave complement]] |
| | * [[27/22]] – its [[fifth complement]] |
| | * [[12/11]] – its [[fourth complement]] |
| | * [[Gallery of just intervals]] |
| | * [[Iceface tuning]] |
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| 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)
| | [[Category:Third]] |
| | | [[Category:Neutral third]] |
| See: [[Gallery of Just Intervals]]</pre></div>
| | [[Category:Alpharabian]] |
| <h4>Original HTML content:</h4>
| | [[Category:Tritave-reduced harmonics]] |
| <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"><html><head><title>11_9</title></head><body><strong>11/9</strong><br />
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| |0 -2 0 0 1&gt;<br />
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| 347.40794 cents<br />
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| <!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_11_9_pluck_adu_dr220.mp3?h=20&amp;w=240&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;jid_11_9_pluck_adu_dr220.mp3&amp;quot; width=&amp;quot;240&amp;quot; height=&amp;quot;20&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;20&quot; width=&quot;240&quot;/&gt; --><embed src="/s/mediaplayer.swf" pluginspage="http://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" quality="high" width="240" height="20" wmode="transparent" flashvars="file=http%253A%252F%252Fxenharmonic.wikispaces.com%252Ffile%252Fview%252Fjid_11_9_pluck_adu_dr220.mp3?file_extension=mp3&autostart=false&repeat=false&showdigits=true&showfsbutton=false&width=240&height=20"></embed><!-- ws:end:WikiTextMediaRule:0 --> <a href="http://xenharmonic.wikispaces.com/file/view/jid_11_9_pluck_adu_dr220.mp3/513194394/jid_11_9_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_11_9_pluck_adu_dr220.mp3/513194394/jid_11_9_pluck_adu_dr220.mp3');">sound sample</a><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 &quot;major third&quot; and &quot;minor third&quot; 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 />
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| 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 />
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| 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 />
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| See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></body></html></pre></div>
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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 it is only one of many, of which others include 16/13, 27/22, 39/32, 49/40 and 60/49. As this is the smaller of the two 11-limit neutral thirds obtained by modifying Pythagorean intervals by 33/32, it is dubbed the Alpharabian artoneutral third in Alpharabian tuning. Since it is nearly halfway between two intervals of 12edo, it implies that it is both very xenharmonic and well-represented in 24edo. It is approximated even more closely in 31edo and 38edo, where the slight flatness of the fifth creates two near perfect 11/9's when divided in half, making the neutral triad particularly stable sounding in these tunings.
In the 11-limit hexad 4:5:6:7:9:11, 11/9 appears between the 11th harmonic and the 9th harmonic. A triad can also be built with 3/2 and 11/9, and the chord formed is 18:22:27. This introduces a second neutral third, 27/22, which is the difference between 3/2 and 11/9. Many temperaments, including 7edo, 10edo, 17edo, 24edo, 31edo, 41edo, 58edo, miracle, harry, and sesquart, conflate these two neutral thirds. The interval which represents both neutral thirds can then be stacked twice 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 these commas leads to the 11-limit rank three temperament jove.
Approximation
Edo approximations for 11/9 (347.41 ¢)
≤ 80edo, relative error ≤ 10%
| Edo |
Step size |
Cents (¢) |
Absolute error (¢) |
Relative error (%)
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| 7 |
2\7 |
342.86 |
-4.55 |
-2.65
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| 14 |
4\14 |
342.86 |
-4.55 |
-5.31
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| 17 |
5\17 |
352.94 |
+5.53 |
+7.84
|
| 21 |
6\21 |
342.86 |
-4.55 |
-7.96
|
| 24 |
7\24 |
350.00 |
+2.59 |
+5.18
|
| 31 |
9\31 |
348.39 |
+0.98 |
+2.53
|
| 38 |
11\38 |
347.37 |
-0.04 |
-0.13
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| 45 |
13\45 |
346.67 |
-0.74 |
-2.78
|
| 52 |
15\52 |
346.15 |
-1.25 |
-5.43
|
| 55 |
16\55 |
349.09 |
+1.68 |
+7.71
|
| 59 |
17\59 |
345.76 |
-1.65 |
-8.09
|
| 62 |
18\62 |
348.39 |
+0.98 |
+5.06
|
| 69 |
20\69 |
347.83 |
+0.42 |
+2.40
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| 76 |
22\76 |
347.37 |
-0.04 |
-0.25
|
See also