17/15: Difference between revisions

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**Imported revision 513253790 - 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 = diatismic whole tone
: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-08 15:09:17 UTC</tt>.<br>
| Color name = 17og3, sogu 3rd
: The original revision id was <tt>513253790</tt>.<br>
| Sound = jid_17_15_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">**17/15**
|0 -1 -1 0 0 0 1&gt;
216.6867 cents
[[media type="file" key="jid_17_15_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_17_15_pluck_adu_dr220.mp3|sound sample]]


In [[17-limit]] [[Just Intonation]], 17/15 is the "septendecimal whole tone" measuring about 216.7¢. It is the [[mediant]] between [[9_8|9/8]] and [[8_7|8/7]], as it is (9+8)/(8+7). It is found in the [[OverToneSeries|harmonic series]] between the 17th and 15th overtones. [[11edo]]'s second degree, measuring approximately 218.2¢, is close in size to 17/15 -- indeed, the 11edo system has excellent approximations of the 15th and 17th harmonics, and so this harmonic function is plausible in 11edo.
In [[17-limit]] [[just intonation]], '''17/15''' is the '''diatismic whole tone''' measuring about 216.7{{cent}}. It exceeds the [[9/8|Pythagorean whole tone (9/8)]] by a [[136/135|diatisma (136/135)]], hence the name. It is the [[mediant]] of 9/8 and [[8/7]], as it is (9 + 8)/(8 + 7). It is found in the [[harmonic series]] between the 17th and 15th [[harmonic]]s. [[11edo]]'s second degree, measuring approximately 218.2¢, is close in size to 17/15 – indeed, the 11edo system has excellent approximations of the 15th and 17th harmonics, and so this harmonic function is plausible in 11edo.


√2/(17/15) is three cents flat of a 5/4 major third, and this or 17/15 itself can be used for a tuning for wizard and its various relatives (lizard, gizzard, etc.).
√2/(17/15) is three cents flat of a 5/4 major third, and this or 17/15 itself can be used for a tuning for [[wizard]] and its various relatives (lizard, gizzard, etc.).
== Approximation ==
{{Interval edo approximation|17/15}}
== See also ==


See: [[Gallery of Just Intervals]]</pre></div>
* [[30/17]] – its [[octave complement]]
<h4>Original HTML content:</h4>
* [[20/17]] – its [[fourth complement]]
<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_15&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;17/15&lt;/strong&gt;&lt;br /&gt;
* [[Gallery of just intervals]]
|0 -1 -1 0 0 0 1&amp;gt;&lt;br /&gt;
 
216.6867 cents&lt;br /&gt;
[[Category:Second]]
&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_17_15_pluck_adu_dr220.mp3?h=20&amp;amp;w=240&amp;quot; class=&amp;quot;WikiMedia WikiMediaFile&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;file&amp;amp;quot; key=&amp;amp;quot;jid_17_15_pluck_adu_dr220.mp3&amp;amp;quot;&amp;quot; title=&amp;quot;Local Media File&amp;quot;height=&amp;quot;20&amp;quot; width=&amp;quot;240&amp;quot;/&amp;gt; --&gt;&lt;embed src="/s/mediaplayer.swf" pluginspage="http://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" quality="high" width="240" height="20" wmode="transparent" flashvars="file=http%253A%252F%252Fxenharmonic.wikispaces.com%252Ffile%252Fview%252Fjid_17_15_pluck_adu_dr220.mp3?file_extension=mp3&amp;autostart=false&amp;repeat=false&amp;showdigits=true&amp;showfsbutton=false&amp;width=240&amp;height=20"&gt;&lt;/embed&gt;&lt;!-- ws:end:WikiTextMediaRule:0 --&gt; &lt;a href="http://xenharmonic.wikispaces.com/file/view/jid_17_15_pluck_adu_dr220.mp3/513250008/jid_17_15_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_17_15_pluck_adu_dr220.mp3/513250008/jid_17_15_pluck_adu_dr220.mp3');"&gt;sound sample&lt;/a&gt;&lt;br /&gt;
[[Category:Whole tone]]
&lt;br /&gt;
[[Category:Diatismic]]
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;, 17/15 is the &amp;quot;septendecimal whole tone&amp;quot; measuring about 216.7¢. It is the &lt;a class="wiki_link" href="/mediant"&gt;mediant&lt;/a&gt; between &lt;a class="wiki_link" href="/9_8"&gt;9/8&lt;/a&gt; and &lt;a class="wiki_link" href="/8_7"&gt;8/7&lt;/a&gt;, as it is (9+8)/(8+7). It is found in the &lt;a class="wiki_link" href="/OverToneSeries"&gt;harmonic series&lt;/a&gt; between the 17th and 15th overtones. &lt;a class="wiki_link" href="/11edo"&gt;11edo&lt;/a&gt;'s second degree, measuring approximately 218.2¢, is close in size to 17/15 -- indeed, the 11edo system has excellent approximations of the 15th and 17th harmonics, and so this harmonic function is plausible in 11edo.&lt;br /&gt;
&lt;br /&gt;
√2/(17/15) is three cents flat of a 5/4 major third, and this or 17/15 itself can be used for a tuning for wizard and its various relatives (lizard, gizzard, etc.).&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 13:02, 3 November 2025

Interval information
Ratio 17/15
Factorization 3-1 × 5-1 × 17
Monzo [0 -1 -1 0 0 0 1⟩
Size in cents 216.6867¢
Name diatismic whole tone
Color name 17og3, sogu 3rd
FJS name [math]\displaystyle{ \text{d3}^{17}_{5} }[/math]
Special properties reduced
Tenney norm (log2 nd) 7.99435
Weil norm (log2 max(n, d)) 8.17493
Wilson norm (sopfr(nd)) 25

[sound info]
Open this interval in xen-calc

In 17-limit just intonation, 17/15 is the diatismic whole tone measuring about 216.7 ¢. It exceeds the Pythagorean whole tone (9/8) by a diatisma (136/135), hence the name. It is the mediant of 9/8 and 8/7, as it is (9 + 8)/(8 + 7). It is found in the harmonic series between the 17th and 15th harmonics. 11edo's second degree, measuring approximately 218.2¢, is close in size to 17/15 – indeed, the 11edo system has excellent approximations of the 15th and 17th harmonics, and so this harmonic function is plausible in 11edo.

√2/(17/15) is three cents flat of a 5/4 major third, and this or 17/15 itself can be used for a tuning for wizard and its various relatives (lizard, gizzard, etc.).

Approximation

Edo approximations for 17/15 (216.69 ¢)
≤ 80edo, relative error ≤ 10%
Edo Step size Cents (¢) Absolute error (¢) Relative error (%)
5 1\5 240.00 +23.31 +9.71
6 1\6 200.00 -16.69 -8.34
11 2\11 218.18 +1.50 +1.37
17 3\17 211.76 -4.92 -6.97
22 4\22 218.18 +1.50 +2.74
28 5\28 214.29 -2.40 -5.60
33 6\33 218.18 +1.50 +4.11
39 7\39 215.38 -1.30 -4.23
44 8\44 218.18 +1.50 +5.48
50 9\50 216.00 -0.69 -2.86
55 10\55 218.18 +1.50 +6.85
61 11\61 216.39 -0.29 -1.49
66 12\66 218.18 +1.50 +8.22
67 12\67 214.93 -1.76 -9.83
72 13\72 216.67 -0.02 -0.12
77 14\77 218.18 +1.50 +9.59
78 14\78 215.38 -1.30 -8.46

See also

Retrieved from "https://en.xen.wiki/index.php?title=17/15&oldid=215971"