17/14: Difference between revisions

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**Imported revision 283158240 - 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 = septendecimal supraminor third
: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-12-07 01:26:35 UTC</tt>.<br>
| Color name = 17or3, soru 3rd
: The original revision id was <tt>283158240</tt>.<br>
| Sound = jid_17_14_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">In [[17-limit]] [[Just Intonation]], 17/14 is the "septendecimal supraminor third," measuring about 336.130¢. It is the [[mediant]] between [[6_5|6/5]] and [[11_9|11/9]], as it is (6+11)/(5+9). A 14:17:21 [[List of root-3rd-P5 triads in JI|root-3rd-P5]] triad can be built with 17/14 as the bottom third and [[21_17|21/17]] as the top third. This may thus represent a septendecimal "shading" of a minor triad.


See: [[Gallery of Just Intervals]]</pre></div>
In [[17-limit]] [[just intonation]], '''17/14''' is the '''septendecimal supraminor third''' measuring about 336.. It is the [[mediant]] between [[6/5]] and [[11/9]], as it is (6+11)/(5+9). A 14:17:21 [[List of root-3rd-P5 triads in_JI|root-3rd-P5]] triad can be built with 17/14 as the bottom third and [[21/17]] as the top third. This may thus represent a septendecimal "shading" of a minor triad.
<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_14&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;, 17/14 is the &amp;quot;septendecimal supraminor third,&amp;quot; measuring about 336.130¢. It is the &lt;a class="wiki_link" href="/mediant"&gt;mediant&lt;/a&gt; between &lt;a class="wiki_link" href="/6_5"&gt;6/5&lt;/a&gt; and &lt;a class="wiki_link" href="/11_9"&gt;11/9&lt;/a&gt;, as it is (6+11)/(5+9). A 14:17:21 &lt;a class="wiki_link" href="/List%20of%20root-3rd-P5%20triads%20in%20JI"&gt;root-3rd-P5&lt;/a&gt; triad can be built with 17/14 as the bottom third and &lt;a class="wiki_link" href="/21_17"&gt;21/17&lt;/a&gt; as the top third. This may thus represent a septendecimal &amp;quot;shading&amp;quot; of a minor triad.&lt;br /&gt;
{{Interval edo approximation|17/14}}
&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>
* [[28/17]] – its [[octave complement]]
* [[21/17]] – its [[fifth complement]]
* [[Gallery of just intervals]]
 
[[Category:Third]]
[[Category:Supraminor third]]

Latest revision as of 13:17, 3 November 2025

Interval information
Ratio 17/14
Factorization 2-1 × 7-1 × 17
Monzo [-1 0 0 -1 0 0 1
Size in cents 336.1295¢
Name septendecimal supraminor third
Color name 17or3, soru 3rd
FJS name [math]\displaystyle{ \text{m3}^{17}_{7} }[/math]
Special properties reduced
Tenney norm (log2 nd) 7.89482
Weil norm (log2 max(n, d)) 8.17493
Wilson norm (sopfr(nd)) 26

[sound info]
Open this interval in xen-calc

In 17-limit just intonation, 17/14 is the septendecimal supraminor third measuring about 336.1¢. It is the mediant between 6/5 and 11/9, as it is (6+11)/(5+9). A 14:17:21 root-3rd-P5 triad can be built with 17/14 as the bottom third and 21/17 as the top third. This may thus represent a septendecimal "shading" of a minor triad.

Approximation

Edo approximations for 17/14 (336.13 ¢)
≤ 80edo, relative error ≤ 10%
Edo Step size Cents (¢) Absolute error (¢) Relative error (%)
7 2\7 342.86 +6.73 +3.92
11 3\11 327.27 -8.86 -8.12
14 4\14 342.86 +6.73 +7.85
18 5\18 333.33 -2.80 -4.19
25 7\25 336.00 -0.13 -0.27
32 9\32 337.50 +1.37 +3.65
36 10\36 333.33 -2.80 -8.39
39 11\39 338.46 +2.33 +7.58
43 12\43 334.88 -1.25 -4.46
50 14\50 336.00 -0.13 -0.54
57 16\57 336.84 +0.71 +3.38
61 17\61 334.43 -1.70 -8.66
64 18\64 337.50 +1.37 +7.31
68 19\68 335.29 -0.84 -4.73
75 21\75 336.00 -0.13 -0.81

See also