22/13: Difference between revisions

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**Imported revision 513546504 - Original comment: **
 
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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 = tridecimal major sixth, major minthmic major sixth
: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-10 21:44:31 UTC</tt>.<br>
| Color name = 3u1o6, thulo 6th
: The original revision id was <tt>513546504</tt>.<br>
| Sound = jid_22_13_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>
'''22/13''', the '''tridecimal major sixth''' or '''major minthmic major sixth''', is a [[13-limit]] [[just intonation]] interval measuring about 910.8 [[cent]]s. It is the inverse of [[13/11]], the tridecimal minor third. It is sharp of the [[27/16|Pythagorean major sixth (27/16)]] by a [[352/351|major minthma (352/351)]].
<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">**22/13**
 
|1 0 0 0 1 -1&gt;
== Approximation ==
910.7903 cents
This interval is well approximated by [[17edo|13\17]] (917.647 cents), and even better, by [[29edo|22\29]] (910.345 cents).
[[media type="file" key="jid_22_13_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_22_13_pluck_adu_dr220.mp3|sound sample]]
{{Interval edo approximation|22/13}}
</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;22_13&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;22/13&lt;/strong&gt;&lt;br /&gt;
* [[13/11]] – its [[octave complement]]
|1 0 0 0 1 -1&amp;gt;&lt;br /&gt;
* [[Gallery of just intervals]]
910.7903 cents&lt;br /&gt;
 
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[[Category:Sixth]]
[[Category:Major sixth]]
[[Category:Major minthmic]]

Latest revision as of 13:13, 3 November 2025

Interval information
Ratio 22/13
Factorization 2 × 11 × 13-1
Monzo [1 0 0 0 1 -1
Size in cents 910.7903¢
Names tridecimal major sixth,
major minthmic major sixth
Color name 3u1o6, thulo 6th
FJS name [math]\displaystyle{ \text{M6}^{11}_{13} }[/math]
Special properties reduced
Tenney norm (log2 nd) 8.15987
Weil norm (log2 max(n, d)) 8.91886
Wilson norm (sopfr(nd)) 26

[sound info]
Open this interval in xen-calc

22/13, the tridecimal major sixth or major minthmic major sixth, is a 13-limit just intonation interval measuring about 910.8 cents. It is the inverse of 13/11, the tridecimal minor third. It is sharp of the Pythagorean major sixth (27/16) by a major minthma (352/351).

Approximation

This interval is well approximated by 13\17 (917.647 cents), and even better, by 22\29 (910.345 cents).

Edo approximations for 22/13 (910.79 ¢)
≤ 80edo, relative error ≤ 10%
Edo Step size Cents (¢) Absolute error (¢) Relative error (%)
4 3\4 900.00 -10.79 -3.60
8 6\8 900.00 -10.79 -7.19
17 13\17 917.65 +6.86 +9.71
21 16\21 914.29 +3.50 +6.12
25 19\25 912.00 +1.21 +2.52
29 22\29 910.34 -0.45 -1.08
33 25\33 909.09 -1.70 -4.67
37 28\37 908.11 -2.68 -8.27
46 35\46 913.04 +2.25 +8.64
50 38\50 912.00 +1.21 +5.04
54 41\54 911.11 +0.32 +1.44
58 44\58 910.34 -0.45 -2.15
62 47\62 909.68 -1.11 -5.75
66 50\66 909.09 -1.70 -9.35
75 57\75 912.00 +1.21 +7.56
79 60\79 911.39 +0.60 +3.96

See also