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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 = rastmic neutral third, Alpharabian tendoneutral third |
| : This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2014-07-03 16:28:25 UTC</tt>.<br>
| | | Color name = 1u3, lu 3rd |
| : The original revision id was <tt>515541412</tt>.<br>
| | | Sound = jid_27_22_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>
| |
| <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">**27/22**
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| |-1 3 0 0 -1> | |
| 354.5471 cents
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| [[media type="file" key="jid_27_22_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_27_22_pluck_adu_dr220.mp3|sound sample]]
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| **27/22** is 243/242 (7.1 cents) sharp of [[11_9|11/9]], and together with 11/9 makes [[3_2|3/2]], so that we obtain the two neutral triads, 1-11/9-3/2 and 1-27/22-3/2, with intervals of 11/9 and 27/22. It is the interval between [[10_9|10/9]] and [[15_11|15/11]] and 11/9 and [[3_2|3/2]] and their inversions.
| | '''27/22''', conventionally called the '''rastmic neutral third''', is [[243/242]] (7.1{{cent}}) sharp of [[11/9]], and together with 11/9 makes [[3/2]], so that we obtain the two neutral triads, 1-11/9-3/2 and 1-27/22-3/2, with intervals of 11/9 and 27/22. It is the interval between [[10/9]] and [[15/11]], and 11/9 and [[3/2]] and their inversions. As this is the larger of two [[11-limit]] neutral thirds obtained by modifying Pythagorean intervals by [[33/32]], it is dubbed the '''Alpharabian tendoneutral third''' in [[Alpharabian tuning]]. It is extremely close to [[44edo]]'s 13\44 neutral third, however the first multiple of 44edo to map it consistently is [[176edo]]. |
| </pre></div>
| | == Approximation == |
| <h4>Original HTML content:</h4>
| | {{Interval edo approximation|27/22}} |
| <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>27_22</title></head><body><strong>27/22</strong><br />
| | == See also == |
| |-1 3 0 0 -1&gt;<br />
| | * [[24edo]] |
| 354.5471 cents<br />
| | * [[44/27]] – its [[octave complement]] |
| <!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_27_22_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_27_22_pluck_adu_dr220.mp3&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_27_22_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_27_22_pluck_adu_dr220.mp3/513545500/jid_27_22_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_27_22_pluck_adu_dr220.mp3/513545500/jid_27_22_pluck_adu_dr220.mp3');">sound sample</a><br />
| | * [[11/9]] – its [[fifth complement]] |
| <br />
| | * [[Gallery of just intervals]] |
| <strong>27/22</strong> is 243/242 (7.1 cents) sharp of <a class="wiki_link" href="/11_9">11/9</a>, and together with 11/9 makes <a class="wiki_link" href="/3_2">3/2</a>, so that we obtain the two neutral triads, 1-11/9-3/2 and 1-27/22-3/2, with intervals of 11/9 and 27/22. It is the interval between <a class="wiki_link" href="/10_9">10/9</a> and <a class="wiki_link" href="/15_11">15/11</a> and 11/9 and <a class="wiki_link" href="/3_2">3/2</a> and their inversions.</body></html></pre></div>
| | * [[Iceface Tuning]] |
| | |
| | [[Category:Third]] |
| | [[Category:Neutral third]] |
| | [[Category:Rastmic]] |
| | [[Category:Alpharabian]] |
27/22, conventionally called the rastmic neutral third, is 243/242 (7.1 ¢) sharp of 11/9, and together with 11/9 makes 3/2, so that we obtain the two neutral triads, 1-11/9-3/2 and 1-27/22-3/2, with intervals of 11/9 and 27/22. It is the interval between 10/9 and 15/11, and 11/9 and 3/2 and their inversions. As this is the larger of two 11-limit neutral thirds obtained by modifying Pythagorean intervals by 33/32, it is dubbed the Alpharabian tendoneutral third in Alpharabian tuning. It is extremely close to 44edo's 13\44 neutral third, however the first multiple of 44edo to map it consistently is 176edo.
Approximation
Edo approximations for 27/22 (354.55 ¢)
≤ 80edo, relative error ≤ 10%
| Edo |
Step size |
Cents (¢) |
Absolute error (¢) |
Relative error (%)
|
| 7 |
2\7 |
342.86 |
-11.69 |
-6.82
|
| 10 |
3\10 |
360.00 |
+5.45 |
+4.54
|
| 17 |
5\17 |
352.94 |
-1.61 |
-2.28
|
| 20 |
6\20 |
360.00 |
+5.45 |
+9.09
|
| 24 |
7\24 |
350.00 |
-4.55 |
-9.09
|
| 27 |
8\27 |
355.56 |
+1.01 |
+2.27
|
| 34 |
10\34 |
352.94 |
-1.61 |
-4.55
|
| 37 |
11\37 |
356.76 |
+2.21 |
+6.81
|
| 44 |
13\44 |
354.55 |
-0.00 |
-0.01
|
| 51 |
15\51 |
352.94 |
-1.61 |
-6.83
|
| 54 |
16\54 |
355.56 |
+1.01 |
+4.54
|
| 61 |
18\61 |
354.10 |
-0.45 |
-2.28
|
| 64 |
19\64 |
356.25 |
+1.70 |
+9.08
|
| 68 |
20\68 |
352.94 |
-1.61 |
-9.10
|
| 71 |
21\71 |
354.93 |
+0.38 |
+2.26
|
| 78 |
23\78 |
353.85 |
-0.70 |
-4.56
|
See also