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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 = large septendecimal major seventh |
| : This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-08 22:10:01 UTC</tt>.<br>
| | | Color name = 17o8, iso octave |
| : The original revision id was <tt>513282064</tt>.<br>
| | | Sound = jid_17_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>
| |
| <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">**17/9**
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| |0 -2 0 0 0 0 1> | |
| 1101.0454 cents
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| [[media type="file" key="jid_17_9_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_17_9_pluck_adu_dr220.mp3|sound sample]]
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| In [[17-limit]] [[Just Intonation]], 17/9 is the "large septendecimal major seventh," measuring about 1101¢. It is the [[mediant]] between [[15_8|15/8]] and [[2_1|2/1]]. Its inversion is [[18_17|18/17]], the "small septendecimal semitone". | | In [[17-limit]] [[just intonation]], '''17/9''' is the '''septendecimal diminished octave''' or the '''septendecimal major seventh''', depending on how one views it. It measures about 1101¢. It is the [[mediant]] between [[15/8]] and [[2/1]]. Its inversion is [[18/17]], the "small septendecimal semitone". |
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| See: [[Gallery of Just Intervals]]</pre></div>
| | == Terminology and notation == |
| <h4>Original HTML content:</h4>
| | There exists a disagreement in different conceptualization systems on whether 17/9 should be a major seventh or a diminished octave. The diminished octave view corresponds to [[Functional Just System]], with the formal comma [[4131/4096]] separating it from [[4096/2187]], the Pythagorean diminished octave. The major seventh view corresponds to [[Helmholtz-Ellis notation]], with the formal comma [[2187/2176]] separating it from [[243/128]], the Pythagorean major seventh. |
| <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>17_9</title></head><body><strong>17/9</strong><br />
| | |
| |0 -2 0 0 0 0 1&gt;<br />
| | In practice, the interval category may, arguably, vary by context. One solution for the JI user who uses expanded [[circle-of-fifths notation]] is to prepare a [[Pythagorean comma]] accidental so that the interval can be notated in either category. |
| 1101.0454 cents<br />
| | == Approximation == |
| <!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_17_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_17_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_17_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_17_9_pluck_adu_dr220.mp3/513249810/jid_17_9_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_17_9_pluck_adu_dr220.mp3/513249810/jid_17_9_pluck_adu_dr220.mp3');">sound sample</a><br />
| | {{Interval edo approximation|17/9}} |
| <br />
| | |
| In <a class="wiki_link" href="/17-limit">17-limit</a> <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>, 17/9 is the &quot;large septendecimal major seventh,&quot; measuring about 1101¢. It is the <a class="wiki_link" href="/mediant">mediant</a> between <a class="wiki_link" href="/15_8">15/8</a> and <a class="wiki_link" href="/2_1">2/1</a>. Its inversion is <a class="wiki_link" href="/18_17">18/17</a>, the &quot;small septendecimal semitone&quot;.<br /> | | == See also == |
| <br />
| | * [[18/17]] – its [[octave complement]] |
| See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></body></html></pre></div>
| | * [[Gallery of Just Intervals]] |
| | |
| | [[Category:Seventh]] |
| | [[Category:Major seventh]] |
| | [[Category:Octave]] |
| | [[Category:Diminished octave]] |
In 17-limit just intonation, 17/9 is the septendecimal diminished octave or the septendecimal major seventh, depending on how one views it. It measures about 1101¢. It is the mediant between 15/8 and 2/1. Its inversion is 18/17, the "small septendecimal semitone".
Terminology and notation
There exists a disagreement in different conceptualization systems on whether 17/9 should be a major seventh or a diminished octave. The diminished octave view corresponds to Functional Just System, with the formal comma 4131/4096 separating it from 4096/2187, the Pythagorean diminished octave. The major seventh view corresponds to Helmholtz-Ellis notation, with the formal comma 2187/2176 separating it from 243/128, the Pythagorean major seventh.
In practice, the interval category may, arguably, vary by context. One solution for the JI user who uses expanded circle-of-fifths notation is to prepare a Pythagorean comma accidental so that the interval can be notated in either category.
Approximation
Edo approximations for 17/9 (1101.05 ¢)
≤ 80edo, relative error ≤ 10%
| Edo |
Step size |
Cents (¢) |
Absolute error (¢) |
Relative error (%)
|
| 11 |
10\11 |
1090.91 |
-10.14 |
-9.29
|
| 12 |
11\12 |
1100.00 |
-1.05 |
-1.05
|
| 13 |
12\13 |
1107.69 |
+6.65 |
+7.20
|
| 24 |
22\24 |
1100.00 |
-1.05 |
-2.09
|
| 25 |
23\25 |
1104.00 |
+2.95 |
+6.16
|
| 36 |
33\36 |
1100.00 |
-1.05 |
-3.14
|
| 37 |
34\37 |
1102.70 |
+1.66 |
+5.11
|
| 48 |
44\48 |
1100.00 |
-1.05 |
-4.18
|
| 49 |
45\49 |
1102.04 |
+1.00 |
+4.06
|
| 60 |
55\60 |
1100.00 |
-1.05 |
-5.23
|
| 61 |
56\61 |
1101.64 |
+0.59 |
+3.02
|
| 72 |
66\72 |
1100.00 |
-1.05 |
-6.27
|
| 73 |
67\73 |
1101.37 |
+0.32 |
+1.97
|
See also