26/25: 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 = large tridecimal third tone
: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-09-29 18:45:38 UTC</tt>.<br>
| Color name = 3ogg2, thogugu 2nd
: The original revision id was <tt>259804936</tt>.<br>
| Sound = jid_26_25_pluck_adu_dr220.mp3
: The revision comment was: <tt></tt><br>
| Comma = yes
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>
In [[13-limit]] [[just intonation]], '''26/25''', the '''large tridecimal third tone''' appears as the difference between the 26th and 25th [[harmonic]]s. Thus it makes the difference between [[13/8]] and [[25/16]] (a stack of two [[5/4]]'s). If it is treated as a comma, then [[5/4]] and [[13/10]] both collapse to a Neogothic-flavored major third in between them representing half of 13/8. It measures about 67.9¢.  
<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">In [[13-limit]] [[Just Intonation]], 26/25 appears as the difference between the 26th harmonic and the 25th. Thus it makes the difference between [[13_8|13/8]] and [[25_16|25/16]] (a stack of two [[5_4|5/4]]'s). It measures about 67.9¢.


See: [[Gallery of Just Intervals]], [[List of Superparticular Intervals]]</pre></div>
== Approximation ==
<h4>Original HTML content:</h4>
26/25 is very well approximated in [[53edo]] as 3\53 (+0.024{{cent}}), and in [[28edt]] as 1\28edt (+0.027{{cent}}). Its equal multiplication - 1ed26/25 - is effectively the same thing as 28edt.
<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_25&lt;/title&gt;&lt;/head&gt;&lt;body&gt;In &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt; &lt;a class="wiki_link" href="/Just%20Intonation"&gt;Just Intonation&lt;/a&gt;, 26/25 appears as the difference between the 26th harmonic and the 25th. Thus it makes the difference between &lt;a class="wiki_link" href="/13_8"&gt;13/8&lt;/a&gt; and &lt;a class="wiki_link" href="/25_16"&gt;25/16&lt;/a&gt; (a stack of two &lt;a class="wiki_link" href="/5_4"&gt;5/4&lt;/a&gt;'s). It measures about 67.9¢.&lt;br /&gt;
{{interval edo approximation}}
&lt;br /&gt;
== See also ==
See: &lt;a class="wiki_link" href="/Gallery%20of%20Just%20Intervals"&gt;Gallery of Just Intervals&lt;/a&gt;, &lt;a class="wiki_link" href="/List%20of%20Superparticular%20Intervals"&gt;List of Superparticular Intervals&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
* [[25/13]] - its [[octave complement]]
* [[27/26]] - the small tridecimal third tone
* [[Gallery of just intervals]]
* [[List of superparticular intervals]]
 
[[Category:Third tone]]
[[Category:Commas named after their interval size]]

Latest revision as of 01:46, 27 November 2025

Interval information
Ratio 26/25
Factorization 2 × 5-2 × 13
Monzo [1 0 -2 0 0 1⟩
Size in cents 67.90023¢
Name large tridecimal third tone
Color name 3ogg2, thogugu 2nd
FJS name [math]\displaystyle{ \text{d2}^{13}_{5,5} }[/math]
Special properties superparticular,
reduced
Tenney norm (log2 nd) 9.3443
Weil norm (log2 max(n, d)) 9.40088
Wilson norm (sopfr(nd)) 25
Comma size medium

[sound info]
Open this interval in xen-calc

In 13-limit just intonation, 26/25, the large tridecimal third tone appears as the difference between the 26th and 25th harmonics. Thus it makes the difference between 13/8 and 25/16 (a stack of two 5/4's). If it is treated as a comma, then 5/4 and 13/10 both collapse to a Neogothic-flavored major third in between them representing half of 13/8. It measures about 67.9¢.

Approximation

26/25 is very well approximated in 53edo as 3\53 (+0.024 ¢), and in 28edt as 1\28edt (+0.027 ¢). Its equal multiplication - 1ed26/25 - is effectively the same thing as 28edt.

Edo approximations for 26/25 (67.90 ¢)
≤ 80edo, relative error ≤ 10%
Edo Step size Cents (¢) Absolute error (¢) Relative error (%)
16 1\16 75.00 +7.10 +9.47
17 1\17 70.59 +2.69 +3.81
18 1\18 66.67 -1.23 -1.85
19 1\19 63.16 -4.74 -7.51
34 2\34 70.59 +2.69 +7.62
35 2\35 68.57 +0.67 +1.96
36 2\36 66.67 -1.23 -3.70
37 2\37 64.86 -3.04 -9.36
52 3\52 69.23 +1.33 +5.77
53 3\53 67.92 +0.02 +0.11
54 3\54 66.67 -1.23 -5.55
69 4\69 69.57 +1.66 +9.57
70 4\70 68.57 +0.67 +3.92
71 4\71 67.61 -0.29 -1.74
72 4\72 66.67 -1.23 -7.40

See also

Retrieved from "https://en.xen.wiki/index.php?title=26/25&oldid=217797"