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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 = tridecimal supraminor sixth |
| : This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-12-28 14:19:37 UTC</tt>.<br>
| | | Color name = thuzo 6th, 3uz6 |
| : The original revision id was <tt>602877076</tt>.<br>
| | | Sound = ji-21-13-csound-foscil-220hz.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">**21/13**
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| | 0 1 0 1 0 -1> | |
| 830.25325 cents
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| [[media type="file" key="ji-21-13-csound-foscil-220hz.mp3"]] [[file:xenharmonic/ji-21-13-csound-foscil-220hz.mp3|sound sample]]
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| The **tredecimal minor sixth**. Its inverse is the tredecimal major third [[26_21|26/21]].
| | '''21/13''', the '''tridecimal supraminor sixth''', is ''ca''. 830 [[cent]]s in size. It has a very good approximation in [[13edo]], and notably, 5 of these intervals differ from [[11/1]] by 4084223/4084101, a comma of a mere 0.052{{cent}}. |
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| See [[Gallery of Just Intervals]]</pre></div>
| | This interval is a ratio of two consecutive {{w|Fibonacci numbers}} and thus a convergent to [[acoustic phi]] (the interval of a [[golden ratio]]). In this case, 21/13 is ~2.8{{cent}} flat of acoustic phi. It differs from [[13/8]], the previous such convergent, by [[169/168]], and from the following convergent [[34/21]] by [[442/441]]. |
| <h4>Original HTML content:</h4>
| | == Approximation == |
| <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>21_13</title></head><body><strong>21/13</strong><br />
| | {{Interval edo approximation|21/13}} |
| | 0 1 0 1 0 -1&gt;<br />
| | == See also == |
| 830.25325 cents<br />
| | * [[26/21]] – its [[octave complement]] |
| <!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/ji-21-13-csound-foscil-220hz.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;ji-21-13-csound-foscil-220hz.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%252Fji-21-13-csound-foscil-220hz.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/ji-21-13-csound-foscil-220hz.mp3/602876480/ji-21-13-csound-foscil-220hz.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/ji-21-13-csound-foscil-220hz.mp3/602876480/ji-21-13-csound-foscil-220hz.mp3');">sound sample</a><br />
| | * [[Gallery of just intervals]] |
| <br />
| | |
| The <strong>tredecimal minor sixth</strong>. Its inverse is the tredecimal major third <a class="wiki_link" href="/26_21">26/21</a>.<br />
| | [[Category:Sixth]] |
| <br />
| | [[Category:Supraminor sixth]] |
| See <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></body></html></pre></div>
| | [[Category:Golden ratio approximations]] |
21/13, the tridecimal supraminor sixth, is ca. 830 cents in size. It has a very good approximation in 13edo, and notably, 5 of these intervals differ from 11/1 by 4084223/4084101, a comma of a mere 0.052 ¢.
This interval is a ratio of two consecutive Fibonacci numbers and thus a convergent to acoustic phi (the interval of a golden ratio). In this case, 21/13 is ~2.8 ¢ flat of acoustic phi. It differs from 13/8, the previous such convergent, by 169/168, and from the following convergent 34/21 by 442/441.
Approximation
Edo approximations for 21/13 (830.25 ¢)
≤ 80edo, relative error ≤ 10%
| Edo |
Step size |
Cents (¢) |
Absolute error (¢) |
Relative error (%)
|
| 3 |
2\3 |
800.00 |
-30.25 |
-7.56
|
| 10 |
7\10 |
840.00 |
+9.75 |
+8.12
|
| 13 |
9\13 |
830.77 |
+0.52 |
+0.56
|
| 16 |
11\16 |
825.00 |
-5.25 |
-7.00
|
| 23 |
16\23 |
834.78 |
+4.53 |
+8.68
|
| 26 |
18\26 |
830.77 |
+0.52 |
+1.12
|
| 29 |
20\29 |
827.59 |
-2.67 |
-6.45
|
| 36 |
25\36 |
833.33 |
+3.08 |
+9.24
|
| 39 |
27\39 |
830.77 |
+0.52 |
+1.68
|
| 42 |
29\42 |
828.57 |
-1.68 |
-5.89
|
| 49 |
34\49 |
832.65 |
+2.40 |
+9.80
|
| 52 |
36\52 |
830.77 |
+0.52 |
+2.24
|
| 55 |
38\55 |
829.09 |
-1.16 |
-5.33
|
| 65 |
45\65 |
830.77 |
+0.52 |
+2.79
|
| 68 |
47\68 |
829.41 |
-0.84 |
-4.77
|
| 78 |
54\78 |
830.77 |
+0.52 |
+3.35
|
See also