17/9: Difference between revisions

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**Imported revision 283166100 - 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 = large septendecimal major seventh
: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-12-07 02:36:08 UTC</tt>.<br>
| Color name = 17o8, iso octave
: The original revision id was <tt>283166100</tt>.<br>
| Sound = jid_17_9_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]], 17/9 is the "large septendecimal major seventh," measuring about 1101.045¢. It is the [[mediant]] between [[15_8|15/8]] and [[2_1|2/1]]. Its inversion is [[18_17|18/17]], the "small septendecimal semitone".


See: [[Gallery of Just Intervals]]</pre></div>
In [[17-limit]] [[just intonation]], '''17/9''' is the '''septendecimal diminished octave''' or the '''septendecimal major seventh''', depending on how one views it. It measures about 1101¢. It is the [[mediant]] between [[15/8]] and [[2/1]]. Its inversion is [[18/17]], the "small septendecimal semitone".
<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;17_9&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;, 17/9 is the &amp;quot;large septendecimal major seventh,&amp;quot; measuring about 1101.045¢. It is the &lt;a class="wiki_link" href="/mediant"&gt;mediant&lt;/a&gt; between &lt;a class="wiki_link" href="/15_8"&gt;15/8&lt;/a&gt; and &lt;a class="wiki_link" href="/2_1"&gt;2/1&lt;/a&gt;. Its inversion is &lt;a class="wiki_link" href="/18_17"&gt;18/17&lt;/a&gt;, the &amp;quot;small septendecimal semitone&amp;quot;.&lt;br /&gt;
== Terminology and notation ==
&lt;br /&gt;
There exists a disagreement in different conceptualization systems on whether 17/9 should be a major seventh or a diminished octave. The diminished octave view corresponds to [[Functional Just System]], with the formal comma [[4131/4096]] separating it from [[4096/2187]], the Pythagorean diminished octave. The major seventh view corresponds to [[Helmholtz-Ellis notation]], with the formal comma [[2187/2176]] separating it from [[243/128]], the Pythagorean major seventh.
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>
 
In practice, the interval category may, arguably, vary by context. One solution for the JI user who uses expanded [[circle-of-fifths notation]] is to prepare a [[Pythagorean comma]] accidental so that the interval can be notated in either category. 
 
== See also ==
* [[18/17]] – its [[octave complement]]
* [[Gallery of Just Intervals]]
 
[[Category:Seventh]]
[[Category:Major seventh]]
[[Category:Octave]]
[[Category:Diminished octave]]

Latest revision as of 09:38, 12 January 2023

Interval information
Ratio 17/9
Subgroup monzo 3.17 [-2 1⟩
Size in cents 1101.045¢
Name large septendecimal major seventh
Color name 17o8, iso octave
FJS name [math]\displaystyle{ \text{d8}^{17} }[/math]
Special properties reduced
Tenney height (log2 nd) 7.25739
Weil height (log2 max(n, d)) 8.17493
Wilson height (sopfr(nd)) 23

[sound info]
Open this interval in xen-calc

In 17-limit just intonation, 17/9 is the septendecimal diminished octave or the septendecimal major seventh, depending on how one views it. It measures about 1101¢. It is the mediant between 15/8 and 2/1. Its inversion is 18/17, the "small septendecimal semitone".

Terminology and notation

There exists a disagreement in different conceptualization systems on whether 17/9 should be a major seventh or a diminished octave. The diminished octave view corresponds to Functional Just System, with the formal comma 4131/4096 separating it from 4096/2187, the Pythagorean diminished octave. The major seventh view corresponds to Helmholtz-Ellis notation, with the formal comma 2187/2176 separating it from 243/128, the Pythagorean major seventh.

In practice, the interval category may, arguably, vary by context. One solution for the JI user who uses expanded circle-of-fifths notation is to prepare a Pythagorean comma accidental so that the interval can be notated in either category.

See also

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