21/11: Difference between revisions

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**Imported revision 513546296 - Original comment: **
 
Rework; +"pentacircle major seventh" and reasons
 
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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 undecimal diminished octave, undecimal major seventh, pentacircle major seventh
: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-10 21:41:54 UTC</tt>.<br>
| Color name = 1uz8, luzo 8ve
: The original revision id was <tt>513546296</tt>.<br>
| Sound = jid_21_11_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>
'''21/11''', commonly known as the '''large undecimal diminished octave''', is an [[11-limit]] interval, and the octave complement of [[22/21]].
<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">**21/11**
In many notation systems (e.g. [[FJS]], [[HEJI]]), it is an imperfect octave, as it is the octave minus 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]]. However, it is only sharp of the [[243/128|Pythagorean major seventh (243/128)]] by a [[896/891|pentacircle comma (896/891)]]. For this reason it could be called the '''pentacircle major seventh'''.  
|0 1 0 1 -1&gt;
 
1119.463 cents
Of note is that the Huygens-Fokker Foundation dubs this interval the '''undecimal major seventh''', which also makes sense, resulting in this interval being perhaps best classified as a "sevtave" – a type of cross between a seventh and an octave.  
[[media type="file" key="jid_21_11_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_21_11_pluck_adu_dr220.mp3|sound sample]]
 
</pre></div>
== See also ==
<h4>Original HTML content:</h4>
* [[22/21]] – its [[octave 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;21_11&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;21/11&lt;/strong&gt;&lt;br /&gt;
 
|0 1 0 1 -1&amp;gt;&lt;br /&gt;
[[Category:Octave]]
1119.463 cents&lt;br /&gt;
[[Category:Diminished octave]]
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[[Category:Seventh]]
[[Category:Major seventh]]
[[Category:Over-11 intervals]]

Latest revision as of 08:41, 25 October 2024

Interval information
Ratio 21/11
Factorization 3 × 7 × 11-1
Monzo [0 1 0 1 -1⟩
Size in cents 1119.463¢
Names large undecimal diminished octave,
undecimal major seventh,
pentacircle major seventh
Color name 1uz8, luzo 8ve
FJS name [math]\displaystyle{ \text{P8}^{7}_{11} }[/math]
Special properties reduced
Tenney height (log2 nd) 7.85175
Weil height (log2 max(n, d)) 8.78463
Wilson height (sopfr(nd)) 21

[sound info]
Open this interval in xen-calc

21/11, commonly known as the large undecimal diminished octave, is an 11-limit interval, and the octave complement of 22/21.

In many notation systems (e.g. FJS, HEJI), it is an imperfect octave, as it is the octave minus a stack consisting of an undecimal quartertone (33/32) and a septimal comma (64/63), neither of which changes the scale degree or quality. However, it is only sharp of the Pythagorean major seventh (243/128) by a pentacircle comma (896/891). For this reason it could be called the pentacircle major seventh.

Of note is that the Huygens-Fokker Foundation dubs this interval the undecimal major seventh, which also makes sense, resulting in this interval being perhaps best classified as a "sevtave" – a type of cross between a seventh and an octave.

See also

Retrieved from "https://en.xen.wiki/index.php?title=21/11&oldid=162121"