23/16: Difference between revisions

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**Imported revision 513548348 - Original comment: **
 
m Text replacement - " {{Interval_Edo_Approximation | " to "{{Interval edo approximation|"
 
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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 = octave-reduced 23rd harmonic, vicesimotertial wide tritone
: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-10 22:07:41 UTC</tt>.<br>
| Color name = 23o5, twetho 5th
: The original revision id was <tt>513548348</tt>.<br>
| Sound = jid_23_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>
 
<h4>Original Wikitext content:</h4>
'''23/16''' is the [[Octave reduction|octave-reduced]] 23rd [[harmonic]] and is often referred to as a '''vicesimotertial wide tritone'''. It is very close to [[21edo]]'s 628.57143 cent interval.
<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">**23/16**
== Approximation ==
|-4 0 0 0 0 0 0 0 1&gt;
{{Interval edo approximation|23/16}}
628.2743 cents
== See also ==
[[media type="file" key="jid_23_16_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_23_16_pluck_adu_dr220.mp3|sound sample]]
* [[32/23]] – its [[octave complement]]
</pre></div>
* [[24/23]] – its [[fifth complement]]
<h4>Original HTML content:</h4>
* [[Gallery of just intervals]]
<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;23_16&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;23/16&lt;/strong&gt;&lt;br /&gt;
 
|-4 0 0 0 0 0 0 0 1&amp;gt;&lt;br /&gt;
 
628.2743 cents&lt;br /&gt;
{{stub}}
&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_23_16_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_23_16_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_23_16_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_23_16_pluck_adu_dr220.mp3/513545386/jid_23_16_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_23_16_pluck_adu_dr220.mp3/513545386/jid_23_16_pluck_adu_dr220.mp3');"&gt;sound sample&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

Latest revision as of 13:14, 3 November 2025

Interval information
Ratio 23/16
Subgroup monzo 2.23 [-4 1
Size in cents 628.2743¢
Names octave-reduced 23rd harmonic,
vicesimotertial wide tritone
Color name 23o5, twetho 5th
FJS name [math]\displaystyle{ \text{A4}^{23} }[/math]
Special properties reduced,
reduced harmonic
Tenney norm (log2 nd) 8.52356
Weil norm (log2 max(n, d)) 9.04712
Wilson norm (sopfr(nd)) 31

[sound info]
Open this interval in xen-calc

23/16 is the octave-reduced 23rd harmonic and is often referred to as a vicesimotertial wide tritone. It is very close to 21edo's 628.57143 cent interval.

Approximation

Edo approximations for 23/16 (628.27 ¢)
≤ 80edo, relative error ≤ 10%
Edo Step size Cents (¢) Absolute error (¢) Relative error (%)
2 1\2 600.00 -28.27 -4.71
4 2\4 600.00 -28.27 -9.42
17 9\17 635.29 +7.02 +9.94
19 10\19 631.58 +3.30 +5.23
21 11\21 628.57 +0.30 +0.52
23 12\23 626.09 -2.19 -4.19
25 13\25 624.00 -4.27 -8.90
40 21\40 630.00 +1.73 +5.75
42 22\42 628.57 +0.30 +1.04
44 23\44 627.27 -1.00 -3.67
46 24\46 626.09 -2.19 -8.38
61 32\61 629.51 +1.23 +6.27
63 33\63 628.57 +0.30 +1.56
65 34\65 627.69 -0.58 -3.15
67 35\67 626.87 -1.41 -7.87

See also


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