26/21: Difference between revisions

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**Imported revision 602877086 - Original comment: **
 
m Text replacement - " {{Interval_Edo_Approximation | " to "{{Interval edo approximation|"
 
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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 submajor third
: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-12-28 14:19:45 UTC</tt>.<br>
| Color name = thoru 3rd, 3or3
: The original revision id was <tt>602877086</tt>.<br>
| Sound = ji-26-21-csound-foscil-220hz.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>
<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">**26/21**
| 1 -1 0 -1 0 1&gt;
369.74675 cents
[[media type="file" key="ji-26-21-csound-foscil-220hz.mp3"]] [[file:xenharmonic/ji-26-21-csound-foscil-220hz.mp3|sound sample]]


The **tredecimal major third**. Its inverse is the tredecimal minor sixth [[21_13|21/13]].
'''26/21''', the '''tridecimal submajor third''', approx. 370 [[cent]]s in size, has a very close approximation in [[13edo]]. Its inverse is the tridecimal supraminor sixth ([[21/13]]).
== Approximation ==
{{Interval edo approximation|26/21}}
== See also ==
* [[21/13]] – its [[octave complement]]
* [[63/52]] – its [[fifth complement]]
* [[Gallery of just intervals]]


See [[Gallery of Just Intervals]]</pre></div>
[[Category:Third]]
<h4>Original HTML content:</h4>
[[Category:Submajor third]]
<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;26_21&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;26/21&lt;/strong&gt;&lt;br /&gt;
| 1 -1 0 -1 0 1&amp;gt;&lt;br /&gt;
369.74675 cents&lt;br /&gt;
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&lt;br /&gt;
The &lt;strong&gt;tredecimal major third&lt;/strong&gt;. Its inverse is the tredecimal minor sixth &lt;a class="wiki_link" href="/21_13"&gt;21/13&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
See &lt;a class="wiki_link" href="/Gallery%20of%20Just%20Intervals"&gt;Gallery of Just Intervals&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

Latest revision as of 13:12, 3 November 2025

Interval information
Ratio 26/21
Factorization 2 × 3-1 × 7-1 × 13
Monzo [1 -1 0 -1 0 1⟩
Size in cents 369.7468¢
Name tridecimal submajor third
Color name thoru 3rd, 3or3
FJS name [math]\displaystyle{ \text{m3}^{13}_{7} }[/math]
Special properties reduced
Tenney norm (log2 nd) 9.09276
Weil norm (log2 max(n, d)) 9.40088
Wilson norm (sopfr(nd)) 25

[sound info]
Open this interval in xen-calc

26/21, the tridecimal submajor third, approx. 370 cents in size, has a very close approximation in 13edo. Its inverse is the tridecimal supraminor sixth (21/13).

Approximation

Edo approximations for 26/21 (369.75 ¢)
≤ 80edo, relative error ≤ 10%
Edo Step size Cents (¢) Absolute error (¢) Relative error (%)
3 1\3 400.00 +30.25 +7.56
10 3\10 360.00 -9.75 -8.12
13 4\13 369.23 -0.52 -0.56
16 5\16 375.00 +5.25 +7.00
23 7\23 365.22 -4.53 -8.68
26 8\26 369.23 -0.52 -1.12
29 9\29 372.41 +2.67 +6.45
36 11\36 366.67 -3.08 -9.24
39 12\39 369.23 -0.52 -1.68
42 13\42 371.43 +1.68 +5.89
49 15\49 367.35 -2.40 -9.80
52 16\52 369.23 -0.52 -2.24
55 17\55 370.91 +1.16 +5.33
65 20\65 369.23 -0.52 -2.79
68 21\68 370.59 +0.84 +4.77
78 24\78 369.23 -0.52 -3.35

See also

Retrieved from "https://en.xen.wiki/index.php?title=26/21&oldid=216070"