23/18: 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 = vicesimotertial major third
: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-10 22:08:21 UTC</tt>.<br>
| Color name = 23o4, twetho 4th
: The original revision id was <tt>513548400</tt>.<br>
| Sound = jid_23_18_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>
'''23/18''', the '''vicesimoterial major third''', is a [[23-limit]] interval that is the [[mediant]] between [[9/7]] and [[14/11]], giving it a character that is somewhere between the gentle undecimal thirds and the more strident septimal supermajor ones. It is sharp of the [[81/64|Pythagorean major third]] by a vicesimoterial formal comma, [[736/729]].  
<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">**23/18**
 
|-1 -2 0 0 0 0 0 0 1&gt;
== Approximation ==
424.3643 cents
This interval is decently represented by 6 steps of [[17edo]], and near perfectly by 29 steps of [[82edo]]. If used as a generator, it creates [[squares]] temperament.
[[media type="file" key="jid_23_18_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_23_18_pluck_adu_dr220.mp3|sound sample]]
{{Interval edo approximation}}
</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;23_18&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;23/18&lt;/strong&gt;&lt;br /&gt;
 
|-1 -2 0 0 0 0 0 0 1&amp;gt;&lt;br /&gt;
* [[36/23]] – its [[octave complement]]
424.3643 cents&lt;br /&gt;
* [[27/23]] – its [[fifth complement]]
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* [[Gallery of just intervals]]
 
[[Category:Third]]
[[Category:Supermajor third]]

Latest revision as of 19:25, 1 June 2026

Interval information
Ratio 23/18
Subgroup monzo 2.3.23 [-1 -2 1
Size in cents 424.3643¢
Name vicesimotertial major third
Color name 23o4, twetho 4th
FJS name [math]\displaystyle{ \text{M3}^{23} }[/math]
Special properties reduced
Tenney norm (log2 nd) 8.69349
Weil norm (log2 max(n, d)) 9.04712
Wilson norm (sopfr(nd)) 31

[sound info]
Open this interval in xen-calc

23/18, the vicesimoterial major third, is a 23-limit interval that is the mediant between 9/7 and 14/11, giving it a character that is somewhere between the gentle undecimal thirds and the more strident septimal supermajor ones. It is sharp of the Pythagorean major third by a vicesimoterial formal comma, 736/729.

Approximation

This interval is decently represented by 6 steps of 17edo, and near perfectly by 29 steps of 82edo. If used as a generator, it creates squares temperament.

Edo approximations for 23/18 (424.36 ¢)
≤ 80edo, relative error ≤ 10%
Edo Step size Cents (¢) Absolute error (¢) Relative error (%)
3 1\3 400.00 -24.36 -6.09
14 5\14 428.57 +4.21 +4.91
17 6\17 423.53 -0.83 -1.18
20 7\20 420.00 -4.36 -7.27
28 10\28 428.57 +4.21 +9.82
31 11\31 425.81 +1.44 +3.73
34 12\34 423.53 -0.83 -2.37
37 13\37 421.62 -2.74 -8.46
45 16\45 426.67 +2.30 +8.63
48 17\48 425.00 +0.64 +2.54
51 18\51 423.53 -0.83 -3.55
54 19\54 422.22 -2.14 -9.64
62 22\62 425.81 +1.44 +7.45
65 23\65 424.62 +0.25 +1.36
68 24\68 423.53 -0.83 -4.73
79 28\79 425.32 +0.95 +6.27

See also