17/12: 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 = larger septendecimal tritone

~~: This revision was by author [[User:Andrew_Heathwaite~~|~~Andrew_Heathwaite]] and made on <tt>2011-12-07 02:04:55 UTC</tt>.<br>~~

| Color name = 17o5, iso 5th

~~: The original revision id was <tt>283162882</tt>.<br>~~

| Sound = jid_17_12_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]], 17/12 is the "second~~ septendecimal tritone~~," measuring very nearly 603¢. Its inversion is the "first septendecimal tritone," [[24_17~~|~~24/17]]~~, ~~and the interval that separates them is the small [[comma]] [[299_298~~|299/298]], about 6¢. This difference is usually negligible, and tempering out this comma allows the 600¢ half-octave to function as both septendecimal tritones. Thus, every even-numbered [[EDO]] system contains a close approximation to these intervals.

17/12 is the [[~~mediant~~]] ~~between~~ the ~~two septimal tritones~~ [[~~7_5|7~~/5]] and [[~~10_7|10/7~~]].

In [[17-limit]] [[just intonation]], '''17/12''' is the '''large septendecimal tritone''', measuring very nearly 603¢. Its inversion is the smaller septendecimal tritone, [[24/17]], and the interval that separates them is the small [[comma]] [[289/288]], about 6¢. This difference is usually negligible, and tempering out this comma allows the 600¢ half-octave to function as both septendecimal tritones. Thus, every even-numbered [[edo]] system contains a close approximation to these intervals.

~~See:~~ [[~~Gallery of Just Intervals~~]]</~~pre><~~/~~div>~~

17/12 is the [[mediant]] between the two septimal tritones [[7/5]] and [[10/7]].

~~<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"><html><head><title>17_12<~~/~~title></head><body>In <~~a class~~="wiki_link" href="/~~17-limit~~">17-limit</~~a~~> <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>,~~ 17/12 ~~is the &quot;second septendecimal tritone~~,~~&quot; measuring very nearly 603¢. Its inversion~~ is ~~the &quot;first septendecimal tritone~~,~~&quot; <a class="wiki_link" href="~~/~~24_17">24~~/~~17<~~/~~a>~~, ~~and the interval that separates them~~ is the ~~small <a class="wiki_link" href="~~/~~comma">comma<~~/~~a> <a class="wiki_link" href="/299_298">299/298</a>, about 6¢~~. ~~This difference is usually negligible,~~ and ~~tempering out this comma allows~~ the ~~600¢ half-octave~~ to ~~function as both~~ septendecimal ~~tritones. Thus, every even-numbered <a class="wiki_link" href="~~/~~EDO">EDO</a> system contains a close approximation to these intervals~~.~~<br />~~

== Terminology and notation ==

~~<br />~~

Conceptualization systems disagree on whether [[17/16]] should be a [[diatonic semitone]] or a [[chromatic semitone]], and as a result the disagreement propagates to all intervals of [[harmonic class|HC17]]. See [[17-limit]] for a detailed discussion.

~~17/12 is the <a class~~=~~"wiki_link" href~~=~~"/mediant">mediant</a> between the two septimal tritones <a class~~=~~"wiki_link" href~~="/~~7_5">7/5</a> and <a class="wiki_link" href="/10_7">10/7</a>.<br />~~

~~<br~~ /~~>~~

For 17/12 specifically:

~~See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">~~Gallery of ~~Just Intervals</a></body></html></pre></div>~~

* In [[Functional Just System]], it is a diminished fifth, separated by [[4131/4096]] from the [[1024/729|Pythagorean diminished fifth (1024/729)]].

* In [[Helmholtz-Ellis notation]], it is an augmented fourth, separated by [[2187/2176]] from the [[729/512|Pythagorean augmented fourth (729/512)]].

The term ''large septendecimal tritone'' omits the distinction and only describes its melodic property i.e. the size. It is said in contrast to the small septendecimal tritone of 24/17.

== See also ==

* [[24/17]] – its [[octave complement]]

* [[18/17]] – its [[fifth complement]]

* [[Gallery of just intervals]]

[[Category:Tritone]]

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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 = larger septendecimal tritone
-: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-12-07 02:04:55 UTC</tt>.<br>
+| Color name = 17o5, iso 5th
-: The original revision id was <tt>283162882</tt>.<br>
+| Sound = jid_17_12_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]], 17/12 is the "second septendecimal tritone," measuring very nearly 603¢. Its inversion is the "first septendecimal tritone," [[24_17|24/17]], and the interval that separates them is the small [[comma]] [[299_298|299/298]], about 6¢. This difference is usually negligible, and tempering out this comma allows the 600¢ half-octave to function as both septendecimal tritones. Thus, every even-numbered [[EDO]] system contains a close approximation to these intervals.
-/12 is the [[mediant]] between the two septimal tritones [[7_5|7/5]] and [[10_7|10/7]].
+In [[17-limit]] [[just intonation]], '''17/12''' is the '''large septendecimal tritone''', measuring very nearly 603¢. Its inversion is the smaller septendecimal tritone, [[24/17]], and the interval that separates them is the small [[comma]] [[289/288]], about 6¢. This difference is usually negligible, and tempering out this comma allows the 600¢ half-octave to function as both septendecimal tritones. Thus, every even-numbered [[edo]] system contains a close approximation to these intervals.
-See: [[Gallery of Just Intervals]]</pre></div>
+/12 is the [[mediant]] between the two septimal tritones [[7/5]] and [[10/7]].
-<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_12&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;, 17/12 is the &amp;quot;second septendecimal tritone,&amp;quot; measuring very nearly 603¢. Its inversion is the &amp;quot;first septendecimal tritone,&amp;quot; &lt;a class="wiki_link" href="/24_17"&gt;24/17&lt;/a&gt;, and the interval that separates them is the small &lt;a class="wiki_link" href="/comma"&gt;comma&lt;/a&gt; &lt;a class="wiki_link" href="/299_298"&gt;299/298&lt;/a&gt;, about 6¢. This difference is usually negligible, and tempering out this comma allows the 600¢ half-octave to function as both septendecimal tritones. Thus, every even-numbered &lt;a class="wiki_link" href="/EDO"&gt;EDO&lt;/a&gt; system contains a close approximation to these intervals.&lt;br /&gt;
+== Terminology and notation ==
-&lt;br /&gt;
+Conceptualization systems disagree on whether [[17/16]] should be a [[diatonic semitone]] or a [[chromatic semitone]], and as a result the disagreement propagates to all intervals of [[harmonic class|HC17]]. See [[17-limit]] for a detailed discussion.
-/12 is the &lt;a class="wiki_link" href="/mediant"&gt;mediant&lt;/a&gt; between the two septimal tritones &lt;a class="wiki_link" href="/7_5"&gt;7/5&lt;/a&gt; and &lt;a class="wiki_link" href="/10_7"&gt;10/7&lt;/a&gt;.&lt;br /&gt;
-&lt;br /&gt;
+For 17/12 specifically:
-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 [[Functional Just System]], it is a diminished fifth, separated by [[4131/4096]] from the [[1024/729|Pythagorean diminished fifth (1024/729)]].
+* In [[Helmholtz-Ellis notation]], it is an augmented fourth, separated by [[2187/2176]] from the [[729/512|Pythagorean augmented fourth (729/512)]].
+The term ''large septendecimal tritone'' omits the distinction and only describes its melodic property i.e. the size. It is said in contrast to the small septendecimal tritone of 24/17.
+== See also ==
+* [[24/17]] – its [[octave complement]]
+* [[18/17]] – its [[fifth complement]]
+* [[Gallery of just intervals]]
+[[Category:Tritone]]