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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 = Pythagorean minor seventh |
| : This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-07 23:43:18 UTC</tt>.<br>
| | | Color name = w7, wa 7th |
| : The original revision id was <tt>513215964</tt>.<br>
| | | Sound = jid_16_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>
| | {{Wikipedia|Minor seventh}} |
| <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">**16/9**
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| |4 -2> | |
| 996.09000 cents
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| [[media type="file" key="jid_16_9_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_16_9_pluck_adu_dr220.mp3|sound sample]]
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| In [[3-limit]] [[Just Intonation]], 16/9 is the [[Pythagorean]] minor seventh, at about 996.1 cents. It is equal to two perfect fourths, or (4/3)*(4/3). It differs from the nearby [[5-limit]] minor seventh [[9_5|9/5]] (~1017.6 cents) by the syntonic comma of [[81_80|81/80]] (~21.5 cents). | | In [[3-limit]] [[just intonation]], '''16/9''' is the '''Pythagorean minor seventh''', at about 996.1 cents. It is equal to two [[4/3|perfect fourth]]s, or (4/3)×(4/3), and is thus the [[octave reduced]] form of the ninth [[subharmonic]]. It differs from the nearby [[5-limit]] minor seventh [[9/5]] (~1017.6 cents) by the syntonic comma of [[81/80]] (~21.5 cents), and the [[7-limit]] minor seventh [[7/4]] (~968.8 cents) by the septimal comma of [[64/63]] (~27.3 cents). |
| | == Approximation == |
| | {{Interval edo approximation|16/9}} |
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| See: [[Gallery of Just Intervals]]</pre></div> | | == See also == |
| <h4>Original HTML content:</h4>
| | * [[9/8]] – its [[octave complement]] |
| <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>16_9</title></head><body><strong>16/9</strong><br />
| | * [[Ed16/9]] |
| |4 -2&gt;<br />
| | * [[Gallery of just intervals]] |
| 996.09000 cents<br />
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| <!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_16_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_16_9_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_16_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_16_9_pluck_adu_dr220.mp3/513215798/jid_16_9_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_16_9_pluck_adu_dr220.mp3/513215798/jid_16_9_pluck_adu_dr220.mp3');">sound sample</a><br />
| | [[Category:Seventh]] |
| <br />
| | [[Category:Minor seventh]] |
| In <a class="wiki_link" href="/3-limit">3-limit</a> <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>, 16/9 is the <a class="wiki_link" href="/Pythagorean">Pythagorean</a> minor seventh, at about 996.1 cents. It is equal to two perfect fourths, or (4/3)*(4/3). It differs from the nearby <a class="wiki_link" href="/5-limit">5-limit</a> minor seventh <a class="wiki_link" href="/9_5">9/5</a> (~1017.6 cents) by the syntonic comma of <a class="wiki_link" href="/81_80">81/80</a> (~21.5 cents).<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 3-limit just intonation, 16/9 is the Pythagorean minor seventh, at about 996.1 cents. It is equal to two perfect fourths, or (4/3)×(4/3), and is thus the octave reduced form of the ninth subharmonic. It differs from the nearby 5-limit minor seventh 9/5 (~1017.6 cents) by the syntonic comma of 81/80 (~21.5 cents), and the 7-limit minor seventh 7/4 (~968.8 cents) by the septimal comma of 64/63 (~27.3 cents).
Approximation
Edo approximations for 16/9 (996.09 ¢)
≤ 80edo, relative error ≤ 10%
| Edo |
Step size |
Cents (¢) |
Absolute error (¢) |
Relative error (%)
|
| 6 |
5\6 |
1000.00 |
+3.91 |
+1.96
|
| 12 |
10\12 |
1000.00 |
+3.91 |
+3.91
|
| 18 |
15\18 |
1000.00 |
+3.91 |
+5.87
|
| 23 |
19\23 |
991.30 |
-4.79 |
-9.17
|
| 24 |
20\24 |
1000.00 |
+3.91 |
+7.82
|
| 29 |
24\29 |
993.10 |
-2.99 |
-7.22
|
| 30 |
25\30 |
1000.00 |
+3.91 |
+9.78
|
| 35 |
29\35 |
994.29 |
-1.80 |
-5.26
|
| 41 |
34\41 |
995.12 |
-0.97 |
-3.31
|
| 47 |
39\47 |
995.74 |
-0.35 |
-1.35
|
| 53 |
44\53 |
996.23 |
+0.14 |
+0.60
|
| 59 |
49\59 |
996.61 |
+0.52 |
+2.56
|
| 65 |
54\65 |
996.92 |
+0.83 |
+4.51
|
| 71 |
59\71 |
997.18 |
+1.09 |
+6.47
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| 76 |
63\76 |
994.74 |
-1.35 |
-8.57
|
| 77 |
64\77 |
997.40 |
+1.31 |
+8.42
|
See also
