20/11: 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 = small undecimal neutral seventh, undecimal supraminor seventh
: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-10 21:41:23 UTC</tt>.<br>
| Color name = 1uy7, luyo 7th
: The original revision id was <tt>513546266</tt>.<br>
| Sound = jid_20_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>
'''20/11''' the '''small undecimal neutral seventh''' or '''undecimal supraminor seventh''' is an [[11-limit]] [[interval]] measuring about 1035{{cent}} in size. It can be used as a seventh in chords like [[11:14:16:20]] and [[44:55:66:80]]. Three intervals of 20/11 exceed [[6/1]] by [[4000/3993]], a comma about 3{{c}} in size.
<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">**20/11**
 
|2 0 1 0 -1&gt;
== Approximation ==
1034.9958 cents
20/11 is approximated extremely precisely by [[80edo]] and its multiples, with a chain of eighty 20/11's failing to close at the octave by a mere third of a cent, close enough that you could theoretically tune an instrument to 80edo by ear using it if you had the patience.
[[media type="file" key="jid_20_11_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_20_11_pluck_adu_dr220.mp3|sound sample]]
{{Interval edo approximation|20/11}}
</pre></div>
 
<h4>Original HTML content:</h4>
== See also ==
<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;20_11&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;20/11&lt;/strong&gt;&lt;br /&gt;
* [[11/10]] – its [[octave complement]]
|2 0 1 0 -1&amp;gt;&lt;br /&gt;
* [[Gallery of just intervals]]
1034.9958 cents&lt;br /&gt;
 
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[[Category:Seventh]]
[[Category:Neutral seventh]]
[[Category:Supraminor seventh]]
[[Category:Over-11 intervals]]
[[Category:Equable heptatonic]]

Latest revision as of 13:26, 30 April 2026

Interval information
Ratio 20/11
Factorization 22 × 5 × 11-1
Monzo [2 0 1 0 -1⟩
Size in cents 1034.996¢
Names small undecimal neutral seventh,
undecimal supraminor seventh
Color name 1uy7, luyo 7th
FJS name [math]\displaystyle{ \text{M7}^{5}_{11} }[/math]
Special properties reduced
Tenney norm (log2 nd) 7.78136
Weil norm (log2 max(n, d)) 8.64386
Wilson norm (sopfr(nd)) 20

[sound info]
Open this interval in xen-calc

20/11 the small undecimal neutral seventh or undecimal supraminor seventh is an 11-limit interval measuring about 1035 ¢ in size. It can be used as a seventh in chords like 11:14:16:20 and 44:55:66:80. Three intervals of 20/11 exceed 6/1 by 4000/3993, a comma about 3 ¢ in size.

Approximation

20/11 is approximated extremely precisely by 80edo and its multiples, with a chain of eighty 20/11's failing to close at the octave by a mere third of a cent, close enough that you could theoretically tune an instrument to 80edo by ear using it if you had the patience.

Edo approximations for 20/11 (1035.00 ¢)
≤ 80edo, relative error ≤ 10%
Edo Step size Cents (¢) Absolute error (¢) Relative error (%)
7 6\7 1028.57 -6.42 -3.75
14 12\14 1028.57 -6.42 -7.50
15 13\15 1040.00 +5.00 +6.26
22 19\22 1036.36 +1.37 +2.51
29 25\29 1034.48 -0.51 -1.24
36 31\36 1033.33 -1.66 -4.99
37 32\37 1037.84 +2.84 +8.76
43 37\43 1032.56 -2.44 -8.73
44 38\44 1036.36 +1.37 +5.02
51 44\51 1035.29 +0.30 +1.27
58 50\58 1034.48 -0.51 -2.48
65 56\65 1033.85 -1.15 -6.23
66 57\66 1036.36 +1.37 +7.52
72 62\72 1033.33 -1.66 -9.97
73 63\73 1035.62 +0.62 +3.78
80 69\80 1035.00 +0.00 +0.03

See also

Retrieved from "https://en.xen.wiki/index.php?title=20/11&oldid=229090"