11/6: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
VisualWikitext
Wikispaces>genewardsmith
**Imported revision 300960620 - Original comment: **
 
m 11/6 2 octaves up is 22/3
 
(19 intermediate revisions by 13 users not shown)
Line 1: Line 1:
<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 neutral seventh
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-12 14:09:52 UTC</tt>.<br>
| Color name = 1o7, ilo 7th
: The original revision id was <tt>300960620</tt>.<br>
| Sound = jid_11_6_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>
'''11/6''' is the '''undecimal neutral seventh''' of about 1049.4 [[cent]]s. It can be treated as a consonance in [[11-limit]] harmony, forming a part of such chords as 6:7:9:11 (1-[[7/6]]-[[3/2]]-11/6) and the [[neutral tetrad]] 18:22:27:33 (1-[[11/9]]-[[3/2]]-11/6).
<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">11/9, the undecimal neutral seventh, can be treated as a consonance in 11-limit harmony, forming a part of such chords as 1-7/6-3/2-11/6 and 1-11/9-3/2-11/6 (the JI [[neutral tetrad]].)</pre></div>
 
<h4>Original HTML content:</h4>
Coincidentally, the ratio between the most common musical tuning frequency (A440) and the most common electrical AC frequency in the Americas (60hz) is like 11/6, but two octaves up (thus, [[22/3]]).
<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;11_6&lt;/title&gt;&lt;/head&gt;&lt;body&gt;11/9, the undecimal neutral seventh, can be treated as a consonance in 11-limit harmony, forming a part of such chords as 1-7/6-3/2-11/6 and 1-11/9-3/2-11/6 (the JI &lt;a class="wiki_link" href="/neutral%20tetrad"&gt;neutral tetrad&lt;/a&gt;.)&lt;/body&gt;&lt;/html&gt;</pre></div>
 
== Approximation ==
{{Interval edo approximation|11/6}}
 
== See also ==
* [[12/11]] – its [[octave complement]]
* [[Iceface tuning]]
* [[Gallery of just intervals]]
 
[[Category:Seventh]]
[[Category:Neutral seventh]]

Latest revision as of 10:50, 17 March 2026

Interval information
Ratio 11/6
Factorization 2-1 × 3-1 × 11
Monzo [-1 -1 0 0 1⟩
Size in cents 1049.363¢
Name undecimal neutral seventh
Color name 1o7, ilo 7th
FJS name [math]\displaystyle{ \text{m7}^{11} }[/math]
Special properties reduced
Tenney norm (log2 nd) 6.04439
Weil norm (log2 max(n, d)) 6.91886
Wilson norm (sopfr(nd)) 16

[sound info]
Open this interval in xen-calc

11/6 is the undecimal neutral seventh of about 1049.4 cents. It can be treated as a consonance in 11-limit harmony, forming a part of such chords as 6:7:9:11 (1-7/6-3/2-11/6) and the neutral tetrad 18:22:27:33 (1-11/9-3/2-11/6).

Coincidentally, the ratio between the most common musical tuning frequency (A440) and the most common electrical AC frequency in the Americas (60hz) is like 11/6, but two octaves up (thus, 22/3).

Approximation

Edo approximations for 11/6 (1049.36 ¢)
≤ 80edo, relative error ≤ 10%
Edo Step size Cents (¢) Absolute error (¢) Relative error (%)
8 7\8 1050.00 +0.64 +0.42
16 14\16 1050.00 +0.64 +0.85
24 21\24 1050.00 +0.64 +1.27
32 28\32 1050.00 +0.64 +1.70
40 35\40 1050.00 +0.64 +2.12
48 42\48 1050.00 +0.64 +2.55
55 48\55 1047.27 -2.09 -9.58
56 49\56 1050.00 +0.64 +2.97
63 55\63 1047.62 -1.74 -9.16
64 56\64 1050.00 +0.64 +3.40
71 62\71 1047.89 -1.48 -8.73
72 63\72 1050.00 +0.64 +3.82
79 69\79 1048.10 -1.26 -8.31
80 70\80 1050.00 +0.64 +4.25

See also

Retrieved from "https://en.xen.wiki/index.php?title=11/6&oldid=226234"