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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 = diatismic minor third |
| : This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-02-22 17:02:41 UTC</tt>.<br>
| | | Sound = jid_20_17_pluck_adu_dr220.mp3 |
| : The original revision id was <tt>575539647</tt>.<br>
| | | Color name = 17uy2, suyo 2nd |
| : 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">**20/17**
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| |2 0 1 0 0 0 -1> | |
| 281.3583 cents
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| [[media type="file" key="jid_20_17_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_20_17_pluck_adu_dr220.mp3|sound sample]]
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| In [[17-limit]] [[Just Intonation]], 20/17 is the "septendecimal minor third", measuring about 281.4¢. It is the [[mediant]] between [[7_6|7/6]] and [[13_11|13/11]], as it is (7+13)/(6+11). It is found in the [[OverToneSeries|harmonic series]] between the 17th and 20th harmonics. | | In [[17-limit]] [[just intonation]], '''20/17''' is the '''diatismic minor third''', measuring about 281.4{{cent}}. It falls short of the [[32/27|Pythagorean minor third (32/27)]] by a [[136/135|diatisma (136/135)]], hence the name. It is the [[mediant]] of [[7/6]] and [[13/11]], as it is (7 + 13)/(6 + 11). It is found in the [[harmonic series]] between the 17th and 20th [[harmonic]]s. |
| | == Approximation == |
| | {{Interval edo approximation|20/17}} |
| | == See also == |
| | * [[17/10]] – its [[octave complement]] |
| | * [[51/40]] – its [[fifth complement]] |
| | * [[17/15]] – its [[fourth complement]] |
| | * [[17edo|4\17]] (282.353 cents) |
| | * [[Gallery of just intervals]] |
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| See:
| | [[Category:Third]] |
| * [[17edo|4\17]] (282.358 cents)
| | [[Category:Minor third]] |
| * [[Gallery of Just Intervals]]</pre></div>
| | [[Category:Diatismic]] |
| <h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>20_17</title></head><body><strong>20/17</strong><br />
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| |2 0 1 0 0 0 -1&gt;<br />
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| 281.3583 cents<br />
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| <!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_20_17_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_20_17_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_20_17_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_20_17_pluck_adu_dr220.mp3/513250052/jid_20_17_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_20_17_pluck_adu_dr220.mp3/513250052/jid_20_17_pluck_adu_dr220.mp3');">sound sample</a><br />
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| <br />
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| In <a class="wiki_link" href="/17-limit">17-limit</a> <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>, 20/17 is the &quot;septendecimal minor third&quot;, measuring about 281.4¢. It is the <a class="wiki_link" href="/mediant">mediant</a> between <a class="wiki_link" href="/7_6">7/6</a> and <a class="wiki_link" href="/13_11">13/11</a>, as it is (7+13)/(6+11). It is found in the <a class="wiki_link" href="/OverToneSeries">harmonic series</a> between the 17th and 20th harmonics.<br />
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| See:<br />
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| <ul><li><a class="wiki_link" href="/17edo">4\17</a> (282.358 cents)</li><li><a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></li></ul></body></html></pre></div>
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In 17-limit just intonation, 20/17 is the diatismic minor third, measuring about 281.4 ¢. It falls short of the Pythagorean minor third (32/27) by a diatisma (136/135), hence the name. It is the mediant of 7/6 and 13/11, as it is (7 + 13)/(6 + 11). It is found in the harmonic series between the 17th and 20th harmonics.
Approximation
Edo approximations for 20/17 (281.36 ¢)
≤ 80edo, relative error ≤ 10%
| Edo |
Step size |
Cents (¢) |
Absolute error (¢) |
Relative error (%)
|
| 4 |
1\4 |
300.00 |
+18.64 |
+6.21
|
| 13 |
3\13 |
276.92 |
-4.44 |
-4.80
|
| 17 |
4\17 |
282.35 |
+0.99 |
+1.41
|
| 21 |
5\21 |
285.71 |
+4.36 |
+7.62
|
| 26 |
6\26 |
276.92 |
-4.44 |
-9.61
|
| 30 |
7\30 |
280.00 |
-1.36 |
-3.40
|
| 34 |
8\34 |
282.35 |
+0.99 |
+2.82
|
| 38 |
9\38 |
284.21 |
+2.85 |
+9.03
|
| 43 |
10\43 |
279.07 |
-2.29 |
-8.20
|
| 47 |
11\47 |
280.85 |
-0.51 |
-1.99
|
| 51 |
12\51 |
282.35 |
+0.99 |
+4.23
|
| 60 |
14\60 |
280.00 |
-1.36 |
-6.79
|
| 64 |
15\64 |
281.25 |
-0.11 |
-0.58
|
| 68 |
16\68 |
282.35 |
+0.99 |
+5.64
|
| 77 |
18\77 |
280.52 |
-0.84 |
-5.38
|
See also