11/7: 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 = undecimal minor sixth, pentacircle minor sixth

~~: This revision was by author [[User:Andrew_Heathwaite~~|~~Andrew_Heathwaite]] and made on <tt>2011-10-07 21:27:13 UTC</tt>.<br>~~

| Color name = 1or5, loru 5th

~~: The original revision id was <tt>262753184</tt>.<br>~~

| Sound = jid_11_7_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 [[11-limit]] [[Just Intonation]], 11/7 is an~~ undecimal ~~(11-based) subminor~~ sixth, ~~measuring about 782.5¢ It is the inversion of [[14_11|14/11]], the undecimal supermajor third. Another subminor~~ sixth ~~is [[14_9~~|~~14/9]]~~, ~~at about 764.9¢; the interval between these is [[99_98~~|~~99/98]], about 17.6¢~~.

11/7 is [[~~22_21|22/21~~]] ~~(about 80~~.~~5¢) above~~ the [[~~3_2|3~~/2]] ~~perfect fifth~~, ~~allowing~~ the ~~possibility~~ of ~~a resolution down by a step from 11/7 to 3/2~~.

In [[11-limit]] [[just intonation]], '''11/7''' is an '''undecimal minor sixth''', specifically the '''pentacircle minor sixth''', measuring about 782.5 [[cent]]s. It is the inversion of [[14/11]], the pentacircle major third, and represents the difference between the 7th and 11th harmonics of the [[harmonic series]].

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

In many notation systems (e.g. [[FJS]], [[HEJI]]), it is an imperfect fifth, as it is a [[3/2|perfect fifth (3/2)]] plus an instance of [[22/21]], which is a stack consisting of an [[33/32|undecimal quartertone (33/32)]] and a [[64/63|septimal comma (64/63)]], neither of which changes the [[scale|scale degree]] or [[interval quality|quality]]. It functions as such in voicings of the harmonic eleventh chord, [[4:5:6:7:9:11]].

~~<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>11_7</title></head><body>In <a class="wiki_link" href="/11~~-limit">11-limit<~~/a~~> <a class="wiki_link" href="~~/~~Just%20Intonation">Just Intonation<~~/a~~>~~, 11/~~7 is an undecimal~~ (~~11-based~~) ~~subminor sixth~~, ~~measuring about 782~~.5¢ It is the ~~inversion~~ of ~~<a class="wiki_link" href="~~/~~14_11">14~~/~~11</a>,~~ the ~~undecimal supermajor third. Another~~ subminor sixth ~~is <a class="wiki_link" href="/14_9">~~14/9~~</a>, at~~ about 764.~~9¢; the interval between these is <~~a ~~class="wiki_link" href="/99_98">~~99/98~~<~~/a~~>~~, ~~about 17~~.~~6¢.<br />~~

However, it is only flat of the [[128/81|Pythagorean minor sixth]] (about 792.2{{c}}) by a [[896/891|pentacircle comma (896/891)]], which makes it function sometimes as a minor sixth, hence the names. For one thing, as it is 22/21 (about 80.5{{c}}) above the perfect fifth, it can be resolved down by a step to the perfect fifth.

~~<br />~~

11/7 ~~is <a class~~=~~"wiki_link" href~~=~~"/22_21">~~22/~~21</~~a~~> (about 80~~.~~5¢) above~~ the ~~<a class~~=~~"wiki_link" href~~="/~~3_2">3~~/~~2<~~/~~a> perfect fifth, allowing the possibility~~ of ~~a resolution down by a step from~~ 11/7 ~~to 3/2~~.~~<br />~~

It is flat of the 5-limit minor sixth of [[8/5]] (about 813.7{{c}}) by [[56/55]]. It is sharp of the 7-limit subminor sixth of [[14/9]] (about 764.9{{c}}) by a mothwellsma, [[99/98]]. And finally, it is sharp of the classic augmented fifth of [[25/16]] (about 772.6{{c}}) by a valinorsma, [[176/175]].

~~<br />~~

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

== Approximation ==

== Proximity with acoustic pi ==

[[22/7]], one octave higher, is a fraction convergent to the continued fraction of acoustic pi. Such is the exactness, that 22/7π is an [[unnoticeable comma]] of only 0.7 cents.

== See also ==

* [[14/11]] – its [[octave complement]]

* [[21/11]] – its [[twelfth complement]]

* [[Ed11/7]]

* [[Gallery of just intervals]]

* [[:File:Ji-11-7-csound-foscil-220hz.mp3]] – another sound example

[[Category:Over-7 intervals]]

[[Category:Sixth]]

[[Category:Minor sixth]]

[[Category:Subminor sixth]]

[[Category:Pentacircle]]

[[Category:Taxicab-2 intervals]]

@@ Line 1: / Line 1: @@
-<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 = undecimal minor sixth, pentacircle minor sixth
-: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-10-07 21:27:13 UTC</tt>.<br>
+| Color name = 1or5, loru 5th
-: The original revision id was <tt>262753184</tt>.<br>
+| Sound = jid_11_7_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 [[11-limit]] [[Just Intonation]], 11/7 is an undecimal (11-based) subminor sixth, measuring about 782.5¢ It is the inversion of [[14_11|14/11]], the undecimal supermajor third. Another subminor sixth is [[14_9|14/9]], at about 764.9¢; the interval between these is [[99_98|99/98]], about 17.6¢.
-/7 is [[22_21|22/21]] (about 80.5¢) above the [[3_2|3/2]] perfect fifth, allowing the possibility of a resolution down by a step from 11/7 to 3/2.
+In [[11-limit]] [[just intonation]], '''11/7''' is an '''undecimal minor sixth''', specifically the '''pentacircle minor sixth''', measuring about 782.5 [[cent]]s. It is the inversion of [[14/11]], the pentacircle major third, and represents the difference between the 7th and 11th harmonics of the [[harmonic series]].
-See: [[Gallery of Just Intervals]]</pre></div>
+In many notation systems (e.g. [[FJS]], [[HEJI]]), it is an imperfect fifth, as it is a [[3/2|perfect fifth (3/2)]] plus an instance of [[22/21]], which is a stack consisting of an [[33/32|undecimal quartertone (33/32)]] and a [[64/63|septimal comma (64/63)]], neither of which changes the [[scale|scale degree]] or [[interval quality|quality]]. It functions as such in voicings of the harmonic eleventh chord, [[4:5:6:7:9:11]].
-<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;11_7&lt;/title&gt;&lt;/head&gt;&lt;body&gt;In &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt; &lt;a class="wiki_link" href="/Just%20Intonation"&gt;Just Intonation&lt;/a&gt;, 11/7 is an undecimal (11-based) subminor sixth, measuring about 782.5¢ It is the inversion of &lt;a class="wiki_link" href="/14_11"&gt;14/11&lt;/a&gt;, the undecimal supermajor third. Another subminor sixth is &lt;a class="wiki_link" href="/14_9"&gt;14/9&lt;/a&gt;, at about 764.9¢; the interval between these is &lt;a class="wiki_link" href="/99_98"&gt;99/98&lt;/a&gt;, about 17.6¢.&lt;br /&gt;
+However, it is only flat of the [[128/81|Pythagorean minor sixth]] (about 792.2{{c}}) by a [[896/891|pentacircle comma (896/891)]], which makes it function sometimes as a minor sixth, hence the names. For one thing, as it is 22/21 (about 80.5{{c}}) above the perfect fifth, it can be resolved down by a step to the perfect fifth.
-&lt;br /&gt;
-/7 is &lt;a class="wiki_link" href="/22_21"&gt;22/21&lt;/a&gt; (about 80.5¢) above the &lt;a class="wiki_link" href="/3_2"&gt;3/2&lt;/a&gt; perfect fifth, allowing the possibility of a resolution down by a step from 11/7 to 3/2.&lt;br /&gt;
+It is flat of the 5-limit minor sixth of [[8/5]] (about 813.7{{c}}) by [[56/55]]. It is sharp of the 7-limit subminor sixth of [[14/9]] (about 764.9{{c}}) by a mothwellsma, [[99/98]]. And finally, it is sharp of the classic augmented fifth of [[25/16]] (about 772.6{{c}}) by a valinorsma, [[176/175]].
-&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>
+== Approximation ==
+{{Interval edo approximation|11/7}}
+== Proximity with acoustic pi ==
+[[22/7]], one octave higher, is a fraction convergent to the continued fraction of acoustic pi. Such is the exactness, that 22/7π is an [[unnoticeable comma]] of only 0.7 cents.
+== See also ==
+* [[14/11]] – its [[octave complement]]
+* [[21/11]] – its [[twelfth complement]]
+* [[Ed11/7]]
+* [[Gallery of just intervals]]
+* [[:File:Ji-11-7-csound-foscil-220hz.mp3]] – another sound example
+[[Category:Over-7 intervals]]
+[[Category:Sixth]]
+[[Category:Minor sixth]]
+[[Category:Subminor sixth]]
+[[Category:Pentacircle]]
+[[Category:Taxicab-2 intervals]]