11/6: Difference between revisions

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
	https://en.xen.wiki/w/File:Jid_11_6_pluck_adu_dr220.mp3; [sound info]
	Open this interval in xen-calc

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VisualWikitext

Latest revision as of 10:50, 17 March 2026

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

@@ 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:xenwolf|xenwolf]] and made on <tt>2012-02-24 15:07:31 UTC</tt>.<br>
+| Color name = 1o7, ilo 7th
-: The original revision id was <tt>304895624</tt>.<br>
+| Sound = jid_11_6_pluck_adu_dr220.mp3
-: The revision comment was: <tt>cent size and links added</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">**11/6**, the undecimal neutral seventh o about 1049.36 [[cent]]. It can be treated as a consonance in [[11-limit]] harmony, forming a part of such chords as 1-[[7_6|7/6]]-[[3_2|3/2]]-**11_6|11/6** and 1-[[11_9|11/9]]-[[3_2|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;&lt;strong&gt;11/6&lt;/strong&gt;, the undecimal neutral seventh o about 1049.36 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;. It can be treated as a consonance in &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt; harmony, forming a part of such chords as 1-&lt;a class="wiki_link" href="/7_6"&gt;7/6&lt;/a&gt;-&lt;a class="wiki_link" href="/3_2"&gt;3/2&lt;/a&gt;-&lt;strong&gt;11_6|11/6&lt;/strong&gt; and 1-&lt;a class="wiki_link" href="/11_9"&gt;11/9&lt;/a&gt;-&lt;a class="wiki_link" href="/3_2"&gt;3/2&lt;/a&gt;-&lt;strong&gt;11/6&lt;/strong&gt; (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]]

11/6: Difference between revisions

Latest revision as of 10:50, 17 March 2026

Approximation

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