26/17: 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 = septendecimal superfifth
: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-08 21:14:53 UTC</tt>.<br>
| Color name = 17u3o5, sutho 5th
: The original revision id was <tt>513277608</tt>.<br>
| Sound = jid_26_17_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>
<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">**26/17**
|1 0 0 0 0 1 -1&gt;
735.5723 cents
[[media type="file" key="jid_26_17_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_26_17_pluck_adu_dr220.mp3|sound sample]]


In [[17-limit]] [[Just Intonation]], 26/17 is the "septendecimal super-fifth," measuring about 735.6¢. It differs from a [[3_2|3/2]] perfect fifth by the [[comma]] 52/51, about 33.6¢. Although this difference is considerable, 26/17 may be used as a wide perfect fifth, thus allowing septendecimal versions of [[List of root-3rd-P5 triads in JI|root-3rd-P5]] chords -- in particular, 17:20:26, 17:21:26, 17:22:26.
In [[17-limit]] [[just intonation]], '''26/17''' is the '''septendecimal superfifth'''. It differs from the [[3/2]] perfect fifth by the [[comma]] [[52/51]], about 33.6¢. Although this difference is considerable, 26/17 may be used as a wide perfect fifth, thus allowing septendecimal versions of [[List of root-3rd-P5 triads in JI|root-3rd-P5]] chords in particular, 17:20:26, 17:21:26, 17:22:26.


26/17 is the [[mediant]] between 3/2 and 23/15. Its inversion is [[17_13|17/13]], the "septendecimal sub-fourth".
26/17 is the [[mediant]] of 3/2 and [[23/15]].  


See: [[Gallery of Just Intervals]]</pre></div>
It is less than 0.2 cents sharp of [[31edo]]'s superfifth of 735.48¢ (19\31).
<h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;26_17&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;26/17&lt;/strong&gt;&lt;br /&gt;
== See also ==
|1 0 0 0 0 1 -1&amp;gt;&lt;br /&gt;
* [[17/13]] – its [[octave complement]]
735.5723 cents&lt;br /&gt;
* [[Gallery of just intervals]]
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&lt;br /&gt;
[[Category:Fifth]]
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;, 26/17 is the &amp;quot;septendecimal super-fifth,&amp;quot; measuring about 735.6¢. It differs from a &lt;a class="wiki_link" href="/3_2"&gt;3/2&lt;/a&gt; perfect fifth by the &lt;a class="wiki_link" href="/comma"&gt;comma&lt;/a&gt; 52/51, about 33.6¢. Although this difference is considerable, 26/17 may be used as a wide perfect fifth, thus allowing septendecimal versions of &lt;a class="wiki_link" href="/List%20of%20root-3rd-P5%20triads%20in%20JI"&gt;root-3rd-P5&lt;/a&gt; chords -- in particular, 17:20:26, 17:21:26, 17:22:26.&lt;br /&gt;
[[Category:Superfifth]]
&lt;br /&gt;
[[Category:Interseptimal intervals]]
26/17 is the &lt;a class="wiki_link" href="/mediant"&gt;mediant&lt;/a&gt; between 3/2 and 23/15. Its inversion is &lt;a class="wiki_link" href="/17_13"&gt;17/13&lt;/a&gt;, the &amp;quot;septendecimal sub-fourth&amp;quot;.&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 03:27, 28 April 2023

Interval information
Ratio 26/17
Subgroup monzo 2.13.17 [1 1 -1
Size in cents 735.5723¢
Name septendecimal superfifth
Color name 17u3o5, sutho 5th
FJS name [math]\displaystyle{ \text{P5}^{13}_{17} }[/math]
Special properties reduced
Tenney height (log2 nd) 8.7879
Weil height (log2 max(n, d)) 9.40088
Wilson height (sopfr(nd)) 32

[sound info]
Open this interval in xen-calc

In 17-limit just intonation, 26/17 is the septendecimal superfifth. It differs from the 3/2 perfect fifth by the comma 52/51, about 33.6¢. Although this difference is considerable, 26/17 may be used as a wide perfect fifth, thus allowing septendecimal versions of root-3rd-P5 chords – in particular, 17:20:26, 17:21:26, 17:22:26.

26/17 is the mediant of 3/2 and 23/15.

It is less than 0.2 cents sharp of 31edo's superfifth of 735.48¢ (19\31).

See also