8/3: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Wikispaces>spt3125
**Imported revision 513248370 - Original comment: **
 
Aura (talk | contribs)
Found this out a few weeks ago
 
(11 intermediate revisions by 10 users not shown)
Line 1: Line 1:
<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 = perfect eleventh
: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-08 13:51:14 UTC</tt>.<br>
| Color name = w11, wa 11th
: The original revision id was <tt>513248370</tt>.<br>
| Sound = jid_8_3_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>
<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">**8/3**
|3 -1&gt;
1698.0450 cents
[[media type="file" key="jid_8_3_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_8_3_pluck_adu_dr220.mp3|sound sample]]


The ratio between the 3rd and 8th harmonics; one octave above [[4_3|4/3]].
'''8/3''', the '''perfect eleventh''', is the ratio between the 3rd and 8th [[harmonic]]s; one octave above [[4/3]]. See also [[ed8/3]].
</pre></div>
 
<h4>Original HTML content:</h4>
== Chord construction ==
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;8_3&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;8/3&lt;/strong&gt;&lt;br /&gt;
Notably, 8/3 can be used as a framework for chords, but the usage of 8/3 as a framework for chords is intimately connected with the use of [[perfect fifth]]s in the same capacity- at least in [[Octave #Octave equivalence|octave-equivalent]] systems- due to the same pitch classes being involved in both 4:5:6 and 3:5:8 where 5 is kept as the same note, thus rendering the two chords as different voicings of the same underlying harmonic unit.
|3 -1&amp;gt;&lt;br /&gt;
 
1698.0450 cents&lt;br /&gt;
[[Category:Tritave-reduced harmonics]]
&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_8_3_pluck_adu_dr220.mp3?h=20&amp;amp;w=240&amp;quot; class=&amp;quot;WikiMedia WikiMediaFile&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;file&amp;amp;quot; key=&amp;amp;quot;jid_8_3_pluck_adu_dr220.mp3&amp;amp;quot;&amp;quot; title=&amp;quot;Local Media File&amp;quot;height=&amp;quot;20&amp;quot; width=&amp;quot;240&amp;quot;/&amp;gt; --&gt;&lt;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_8_3_pluck_adu_dr220.mp3?file_extension=mp3&amp;autostart=false&amp;repeat=false&amp;showdigits=true&amp;showfsbutton=false&amp;width=240&amp;height=20"&gt;&lt;/embed&gt;&lt;!-- ws:end:WikiTextMediaRule:0 --&gt; &lt;a href="http://xenharmonic.wikispaces.com/file/view/jid_8_3_pluck_adu_dr220.mp3/513246216/jid_8_3_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_8_3_pluck_adu_dr220.mp3/513246216/jid_8_3_pluck_adu_dr220.mp3');"&gt;sound sample&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
The ratio between the 3rd and 8th harmonics; one octave above &lt;a class="wiki_link" href="/4_3"&gt;4/3&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>

Latest revision as of 16:28, 29 November 2025

Interval information
Ratio 8/3
Factorization 23 × 3-1
Monzo [3 -1
Size in cents 1698.045¢
Name perfect eleventh
Color name w11, wa 11th
FJS name [math]\displaystyle{ \text{P11} }[/math]
Tenney norm (log2 nd) 4.58496
Weil norm (log2 max(n, d)) 6
Wilson norm (sopfr(nd)) 9

[sound info]
Open this interval in xen-calc

8/3, the perfect eleventh, is the ratio between the 3rd and 8th harmonics; one octave above 4/3. See also ed8/3.

Chord construction

Notably, 8/3 can be used as a framework for chords, but the usage of 8/3 as a framework for chords is intimately connected with the use of perfect fifths in the same capacity- at least in octave-equivalent systems- due to the same pitch classes being involved in both 4:5:6 and 3:5:8 where 5 is kept as the same note, thus rendering the two chords as different voicings of the same underlying harmonic unit.