17/13: Difference between revisions

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**Imported revision 283161260 - 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 = septendecimal subfourth
: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-12-07 01:52:02 UTC</tt>.<br>
| Color name = 17o3u4, sothu 4th
: The original revision id was <tt>283161260</tt>.<br>
| Sound = jid_17_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>
In [[17-limit]] [[just intonation]], '''17/13''' is the '''septendecimal subfourth''', measuring about 464.4¢. It differs from the [[4/3]] perfect fourth by the [[comma]] [[52/51]], about 33.6¢. It is the [[mediant]] between [[13/10]] and [[4/3]] and falls in the categorically-ambiguous zone between supermajor third and perfect fourth that Margo Schulter calls [[interseptimal]]. It appears in the [[harmonic series]] between the 13th and 17th harmonics.
<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">In [[17-limit]] [[Just Intonation]], 17/13 is the "septendecimal sub-fourth," measuring about 464.428¢. It is the [[mediant]] between [[13_10|13/10]] and [[4_3|4/3]] and falls in the categorically-ambiguous zone between supermajor third and perfect fourth that Margo Schulter calls [[interseptimal]]. Is appears in the [[OverToneSeries|harmonic series]] between the 13th and 17th harmonics.


See: [[Gallery of Just Intervals]]</pre></div>
It is less than 0.1 cents flat of [[31edo]]'s subfourth of 464.52¢ (12\31). In fact, a circle of 31 pure 17/13's closes with an error of only 2.74c ([[relative error]] 7.1%).
<h4>Original HTML content:</h4>
== Approximation ==
<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;17_13&lt;/title&gt;&lt;/head&gt;&lt;body&gt;In &lt;a class="wiki_link" href="/17-limit"&gt;17-limit&lt;/a&gt; &lt;a class="wiki_link" href="/Just%20Intonation"&gt;Just Intonation&lt;/a&gt;, 17/13 is the &amp;quot;septendecimal sub-fourth,&amp;quot; measuring about 464.428¢. It is the &lt;a class="wiki_link" href="/mediant"&gt;mediant&lt;/a&gt; between &lt;a class="wiki_link" href="/13_10"&gt;13/10&lt;/a&gt; and &lt;a class="wiki_link" href="/4_3"&gt;4/3&lt;/a&gt; and falls in the categorically-ambiguous zone between supermajor third and perfect fourth that Margo Schulter calls &lt;a class="wiki_link" href="/interseptimal"&gt;interseptimal&lt;/a&gt;. Is appears in the &lt;a class="wiki_link" href="/OverToneSeries"&gt;harmonic series&lt;/a&gt; between the 13th and 17th harmonics.&lt;br /&gt;
{{Interval edo approximation|17/13}}
&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;/body&gt;&lt;/html&gt;</pre></div>
* [[26/17]] – its [[octave complement]]
* [[Gallery of just intervals]]
 
[[Category:Fourth]]
[[Category:Subfourth]]
[[Category:Interseptimal intervals]]
[[Category:Naiadic]]
[[Category:Taxicab-2 intervals]]

Latest revision as of 13:08, 3 November 2025

Interval information
Ratio 17/13
Subgroup monzo 13.17 [-1 1⟩
Size in cents 464.4277¢
Name septendecimal subfourth
Color name 17o3u4, sothu 4th
FJS name [math]\displaystyle{ \text{P4}^{17}_{13} }[/math]
Special properties reduced
Tenney norm (log2 nd) 7.7879
Weil norm (log2 max(n, d)) 8.17493
Wilson norm (sopfr(nd)) 30

[sound info]
Open this interval in xen-calc

In 17-limit just intonation, 17/13 is the septendecimal subfourth, measuring about 464.4¢. It differs from the 4/3 perfect fourth by the comma 52/51, about 33.6¢. It is the mediant between 13/10 and 4/3 and falls in the categorically-ambiguous zone between supermajor third and perfect fourth that Margo Schulter calls interseptimal. It appears in the harmonic series between the 13th and 17th harmonics.

It is less than 0.1 cents flat of 31edo's subfourth of 464.52¢ (12\31). In fact, a circle of 31 pure 17/13's closes with an error of only 2.74c (relative error 7.1%).

Approximation

Edo approximations for 17/13 (464.43 ¢)
≤ 80edo, relative error ≤ 10%
Edo Step size Cents (¢) Absolute error (¢) Relative error (%)
5 2\5 480.00 +15.57 +6.49
8 3\8 450.00 -14.43 -9.62
13 5\13 461.54 -2.89 -3.13
18 7\18 466.67 +2.24 +3.36
23 9\23 469.57 +5.14 +9.85
26 10\26 461.54 -2.89 -6.26
31 12\31 464.52 +0.09 +0.23
36 14\36 466.67 +2.24 +6.72
39 15\39 461.54 -2.89 -9.39
44 17\44 463.64 -0.79 -2.90
49 19\49 465.31 +0.88 +3.59
57 22\57 463.16 -1.27 -6.03
62 24\62 464.52 +0.09 +0.46
67 26\67 465.67 +1.24 +6.95
70 27\70 462.86 -1.57 -9.16
75 29\75 464.00 -0.43 -2.67
80 31\80 465.00 +0.57 +3.82

See also

Retrieved from "https://en.xen.wiki/index.php?title=17/13&oldid=216034"