15/11: Difference between revisions

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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 = undecimal augmented fourth, undecimal grave infra-augmented fourth
: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-10-09 11:00:51 UTC</tt>.<br>
| Color name = 1uy4, luyo 4th
: The original revision id was <tt>262969694</tt>.<br>
| Sound = jid_15_11_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">The undecimal augmented fourth, or 15/11, is the difference between the 11th and 15th partials of the [[OverToneSeries|harmonic series]]. It is 536.95 [[cent|cents]] wide, exactly [[45_44|45/44]] larger than a perfect fourth, and almost exactly a sixth-tone sharper than a [[12edo|12-edo]] fourth. It is narrower than [[11_8|11/8]] by exactly [[121_10|121/120]]. 15/11 can be called a [[superfourth]], as it falls between the [[interval category|interval categories]] of a [[perfect fourth]] and a [[tritone]]. 4 steps of [[9edo|9-edo ]] is an excellent approximation for 15/11.


See: [[Gallery of Just Intervals]]</pre></div>
The interval '''15/11''', known most frequently as the '''undecimal augmented fourth''', is the difference between the 11th and 15th partials of the [[harmonic series]]. It is 536.95 [[cent]]s wide, exactly [[45/44]] larger than a perfect fourth, and almost exactly a sixth-tone sharper than a [[12edo]] fourth. It is narrower than [[11/8]] by exactly [[121/120]], and is wider than [[27/20]] by exactly [[100/99]].  Additionally, it is narrower than [[243/176]] by exactly [[81/80]], which lends to it being called the '''undecimal grave infra-augmented fourth'''. 15/11 can be called a [[superfourth]], as it falls between the [[interval category|interval categories]] of [[perfect fourth]] and [[tritone]]. 4 steps of [[9edo]] is an excellent approximation for 15/11.
<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;15_11&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The undecimal augmented fourth, or 15/11, is the difference between the 11th and 15th partials of the &lt;a class="wiki_link" href="/OverToneSeries"&gt;harmonic series&lt;/a&gt;. It is 536.95 &lt;a class="wiki_link" href="/cent"&gt;cents&lt;/a&gt; wide, exactly &lt;a class="wiki_link" href="/45_44"&gt;45/44&lt;/a&gt; larger than a perfect fourth, and almost exactly a sixth-tone sharper than a &lt;a class="wiki_link" href="/12edo"&gt;12-edo&lt;/a&gt; fourth. It is narrower than &lt;a class="wiki_link" href="/11_8"&gt;11/8&lt;/a&gt; by exactly &lt;a class="wiki_link" href="/121_10"&gt;121/120&lt;/a&gt;. 15/11 can be called a &lt;a class="wiki_link" href="/superfourth"&gt;superfourth&lt;/a&gt;, as it falls between the &lt;a class="wiki_link" href="/interval%20category"&gt;interval categories&lt;/a&gt; of a &lt;a class="wiki_link" href="/perfect%20fourth"&gt;perfect fourth&lt;/a&gt; and a &lt;a class="wiki_link" href="/tritone"&gt;tritone&lt;/a&gt;. 4 steps of &lt;a class="wiki_link" href="/9edo"&gt;9-edo &lt;/a&gt; is an excellent approximation for 15/11.&lt;br /&gt;
== See also ==
&lt;br /&gt;
* [[22/15]] – its [[octave complement]]
See: &lt;a class="wiki_link" href="/Gallery%20of%20Just%20Intervals"&gt;Gallery of Just Intervals&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
* [[11/10]] – its [[fifth complement]]
* [[Gallery of just intervals]]
 
[[Category:Fourth]]
[[Category:Superfourth]]
[[Category:Over-11 intervals]]

Latest revision as of 20:13, 1 January 2025

Interval information
Ratio 15/11
Factorization 3 × 5 × 11-1
Monzo [0 1 1 0 -1
Size in cents 536.9508¢
Names undecimal augmented fourth,
undecimal grave infra-augmented fourth
Color name 1uy4, luyo 4th
FJS name [math]\displaystyle{ \text{A4}^{5}_{11} }[/math]
Special properties reduced
Tenney height (log2 nd) 7.36632
Weil height (log2 max(n, d)) 7.81378
Wilson height (sopfr(nd)) 19

[sound info]
Open this interval in xen-calc

The interval 15/11, known most frequently as the undecimal augmented fourth, is the difference between the 11th and 15th partials of the harmonic series. It is 536.95 cents wide, exactly 45/44 larger than a perfect fourth, and almost exactly a sixth-tone sharper than a 12edo fourth. It is narrower than 11/8 by exactly 121/120, and is wider than 27/20 by exactly 100/99. Additionally, it is narrower than 243/176 by exactly 81/80, which lends to it being called the undecimal grave infra-augmented fourth. 15/11 can be called a superfourth, as it falls between the interval categories of perfect fourth and tritone. 4 steps of 9edo is an excellent approximation for 15/11.

See also