88/63: Difference between revisions

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**Imported revision 515324324 - Original comment: **
 
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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 = pentacircle diminished fifth
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-06-30 23:07:55 UTC</tt>.<br>
| Color name = 1or4, loru 4th
: The original revision id was <tt>515324324</tt>.<br>
}}
: 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">**88/63**
|3 -2 0 -1 1&gt;
578.582034 cents


**88/63**, the werckismic diminished fourth, is 441/440 (3.9 cents) below [[7_5|7/5]]. It is 0.01 cent sharp of the [[56edo]] diminished fourth of 27\56. It can arise in 11-limit scales as the interval from 9/8 to 11/7, or 14/11 to 16/9.</pre></div>
'''88/63''', the '''pentacircle diminished fifth''', is [[896/891]] below [[1024/729]], the Pythagorean diminished fifth. It is also 441/440 (3.9 cents) below [[7/5]]. It is 0.01 cent sharp of the [[56edo]] augmented fourth of 27\56. It arises in 11-limit scales as the interval from [[9/8]] to [[11/7]], or [[14/11]] to [[16/9]].
<h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;88_63&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;88/63&lt;/strong&gt;&lt;br /&gt;
== Terminology ==
|3 -2 0 -1 1&amp;gt;&lt;br /&gt;
It could also be called ''werckismic augmented fourth'' if viewed as [[fudging]] from [[7/5]] instead.  
578.582034 cents&lt;br /&gt;
 
&lt;br /&gt;
== See also ==
&lt;strong&gt;88/63&lt;/strong&gt;, the werckismic diminished fourth, is 441/440 (3.9 cents) below &lt;a class="wiki_link" href="/7_5"&gt;7/5&lt;/a&gt;. It is 0.01 cent sharp of the &lt;a class="wiki_link" href="/56edo"&gt;56edo&lt;/a&gt; diminished fourth of 27\56. It can arise in 11-limit scales as the interval from 9/8 to 11/7, or 14/11 to 16/9.&lt;/body&gt;&lt;/html&gt;</pre></div>
* [[Gallery of just intervals]]
 
[[Category:Pentacircle]]
[[Category:Tritone]]

Latest revision as of 01:38, 29 December 2022

Interval information
Ratio 88/63
Factorization 23 × 3-2 × 7-1 × 11
Monzo [3 -2 0 -1 1
Size in cents 578.582¢
Name pentacircle diminished fifth
Color name 1or4, loru 4th
FJS name [math]\displaystyle{ \text{P4}^{11}_{7} }[/math]
Special properties reduced
Tenney norm (log2 nd) 12.4367
Weil norm (log2 max(n, d)) 12.9189
Wilson norm (sopfr(nd)) 30
Open this interval in xen-calc

88/63, the pentacircle diminished fifth, is 896/891 below 1024/729, the Pythagorean diminished fifth. It is also 441/440 (3.9 cents) below 7/5. It is 0.01 cent sharp of the 56edo augmented fourth of 27\56. It arises in 11-limit scales as the interval from 9/8 to 11/7, or 14/11 to 16/9.

Terminology

It could also be called werckismic augmented fourth if viewed as fudging from 7/5 instead.

See also