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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 = vicesimononal supraminor seventh, octave-reduced 29th harmonic |
| : This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-10 22:09:04 UTC</tt>.<br>
| | | Color name = 29o7, tweno 7th |
| : The original revision id was <tt>513548470</tt>.<br>
| | | Sound = jid_29_16_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>
| | In [[29-limit]] [[just intonation]], '''29/16''' is the '''vicesimononal supraminor seventh''', which is also the [[octave reduction|octave-reduced]] 29th [[harmonic]]. It is sharp of the [[16/9|Pythagorean minor seventh (16/9)]] by [[261/256]] (~33{{cent}}), and sharp of the [[9/5|classic minor seventh (9/5)]] by [[145/144]] (~12{{cent}}). |
| <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">**29/16**
| |
| |-4 0 0 0 0 0 0 0 0 1> | |
| 1029.5772 cents
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| [[media type="file" key="jid_29_16_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_29_16_pluck_adu_dr220.mp3|sound sample]] | |
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| The 29th harmonic, octave-reduced.</pre></div>
| | == Approximation == |
| <h4>Original HTML content:</h4>
| | This interval is very accurately approximated by [[7edo]] (6\7). It is approximately a cent away from it, the difference being 1/7 of the [[jackpot comma]], 17249876309/17179869184. |
| <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>29_16</title></head><body><strong>29/16</strong><br />
| | {{Interval edo approximation|29/16}} |
| |-4 0 0 0 0 0 0 0 0 1&gt;<br />
| | |
| 1029.5772 cents<br />
| | == See also == |
| <!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_29_16_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_29_16_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_29_16_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_29_16_pluck_adu_dr220.mp3/513545524/jid_29_16_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_29_16_pluck_adu_dr220.mp3/513545524/jid_29_16_pluck_adu_dr220.mp3');">sound sample</a><br />
| | * [[32/29]] – its [[octave complement]] |
| <br />
| | * [[48/29]] – its [[twelfth complement]] |
| The 29th harmonic, octave-reduced.</body></html></pre></div>
| | |
| | [[Category:Seventh]] |
| | [[Category:Minor seventh]] |
| | [[Category:Equable heptatonic]] |
In 29-limit just intonation, 29/16 is the vicesimononal supraminor seventh, which is also the octave-reduced 29th harmonic. It is sharp of the Pythagorean minor seventh (16/9) by 261/256 (~33 ¢), and sharp of the classic minor seventh (9/5) by 145/144 (~12 ¢).
Approximation
This interval is very accurately approximated by 7edo (6\7). It is approximately a cent away from it, the difference being 1/7 of the jackpot comma, 17249876309/17179869184.
Edo approximations for 29/16 (1029.58 ¢)
≤ 80edo, relative error ≤ 10%
| Edo |
Step size |
Cents (¢) |
Absolute error (¢) |
Relative error (%)
|
| 7 |
6\7 |
1028.57 |
-1.01 |
-0.59
|
| 14 |
12\14 |
1028.57 |
-1.01 |
-1.17
|
| 21 |
18\21 |
1028.57 |
-1.01 |
-1.76
|
| 28 |
24\28 |
1028.57 |
-1.01 |
-2.35
|
| 35 |
30\35 |
1028.57 |
-1.01 |
-2.93
|
| 42 |
36\42 |
1028.57 |
-1.01 |
-3.52
|
| 49 |
42\49 |
1028.57 |
-1.01 |
-4.11
|
| 56 |
48\56 |
1028.57 |
-1.01 |
-4.69
|
| 57 |
49\57 |
1031.58 |
+2.00 |
+9.51
|
| 63 |
54\63 |
1028.57 |
-1.01 |
-5.28
|
| 64 |
55\64 |
1031.25 |
+1.67 |
+8.92
|
| 70 |
60\70 |
1028.57 |
-1.01 |
-5.87
|
| 71 |
61\71 |
1030.99 |
+1.41 |
+8.33
|
| 77 |
66\77 |
1028.57 |
-1.01 |
-6.45
|
| 78 |
67\78 |
1030.77 |
+1.19 |
+7.75
|
See also