15/11: Difference between revisions

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**Imported revision 244976433 - 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 = undecimal augmented fourth, undecimal grave infra-augmented fourth
: This revision was by author [[User:Sarzadoce|Sarzadoce]] and made on <tt>2011-08-09 00:58:24 UTC</tt>.<br>
| Color name = 1uy4, luyo 4th
: The original revision id was <tt>244976433</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>
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.
<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 harmonic series. It is 536.95 [[cent|cents]] wide, exactly 45/44 larger than a perfect fourth, and almost exactly a sixth-tone sharper than a [[12edo|12-edo]] fourth. 4 steps of [[9edo|9-edo ]] is an excellent approximation for 15/11.</pre></div>
== Approximation ==
<h4>Original HTML content:</h4>
{{Interval edo approximation|15/11}}
<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 harmonic series. It is 536.95 &lt;a class="wiki_link" href="/cent"&gt;cents&lt;/a&gt; wide, exactly 45/44 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. 4 steps of &lt;a class="wiki_link" href="/9edo"&gt;9-edo &lt;/a&gt; is an excellent approximation for 15/11.&lt;/body&gt;&lt;/html&gt;</pre></div>
== See also ==
* [[22/15]] – its [[octave complement]]
* [[11/10]] – its [[fifth complement]]
* [[Gallery of just intervals]]
 
[[Category:Fourth]]
[[Category:Superfourth]]
[[Category:Over-11 intervals]]

Latest revision as of 13:07, 3 November 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 norm (log2 nd) 7.36632
Weil norm (log2 max(n, d)) 7.81378
Wilson norm (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.

Approximation

Edo approximations for 15/11 (536.95 ¢)
≤ 80edo, relative error ≤ 10%
Edo Step size Cents (¢) Absolute error (¢) Relative error (%)
9 4\9 533.33 -3.62 -2.71
11 5\11 545.45 +8.50 +7.80
18 8\18 533.33 -3.62 -5.43
20 9\20 540.00 +3.05 +5.08
27 12\27 533.33 -3.62 -8.14
29 13\29 537.93 +0.98 +2.37
38 17\38 536.84 -0.11 -0.34
47 21\47 536.17 -0.78 -3.06
49 22\49 538.78 +1.82 +7.45
56 25\56 535.71 -1.24 -5.77
58 26\58 537.93 +0.98 +4.74
65 29\65 535.38 -1.57 -8.48
67 30\67 537.31 +0.36 +2.02
76 34\76 536.84 -0.11 -0.69
78 35\78 538.46 +1.51 +9.82

See also

Retrieved from "https://en.xen.wiki/index.php?title=15/11&oldid=216022"