11/8: Difference between revisions

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~~<h2>IMPORTED REVISION FROM WIKISPACES<~~/~~h2>~~

{{interwiki

~~This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>~~

| de = Alphorn-Fa

~~: This revision was by author [[User:spt3125~~|~~spt3125]] and made on <tt>2014-06-07 15:33:47 UTC</tt>.<br>~~

| en = 11/8

~~: The original revision id was <tt>513194320</tt>.<br>~~

| es =

~~: The revision comment was: <tt></tt><br>~~

| ja =

~~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>~~

{{Infobox Interval

~~<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">**11/8**

| Name = undecimal superfourth, harmonic fourth, undecimal tritone, undecimal major fourth, undecimal semiaugmented fourth, harmonic semiaugmented fourth

|~~-3 0 0 0 1>~~

| Color name = 1o4, ilo 4th

~~551.31794 cents~~

| Sound = jid_11_8_pluck_adu_dr220.mp3

~~[[media type="file" key~~=~~"jid_11_8_pluck_adu_dr220.mp3"]] [[file:xenharmonic/~~jid_11_8_pluck_adu_dr220.mp3|~~sound sample]]~~

}}

In [[11-limit]] [[~~Just Intonation~~]], 11/8 is an undecimal ~~(11-based)~~ [[superfourth]] of about 551.3¢. ~~Falling about halfway~~ between [[~~12edo]]'s [[~~perfect fourth]] and [[~~tritone~~]], ~~it is very xenharmonic. It~~ is the ~~simplest superfourth in JI. As an octave-reduced overtone, it is a basis~~ of ~~consonance in 11-limit JI, alongside~~ the lower odd numbers 9, 7, 5 and 3. It can be found in harmonic series chords such as 4:5:6:7:8:9:10:11:12, sitting somewhere between the much stronger and more familiar consonances of 10 (5) and 12 (3). It is very well-represented in [[~~24edo~~]], ~~making that system especially good for approximations of JI chords involving primes 3 and 11 such as 8:9:11:12~~.

In [[11-limit]] [[just intonation]], '''11/8''' is an '''undecimal [[superfourth|semiaugmented fourth]]''' of about 551.3{{cent}}. This interval is close (~3{{cent}}) to exactly between a [[4/3|perfect fourth]] and [[729/512|augmented fourth]], the latter of which is the ''augmented'' version of the [[Pythagorean tuning|Pythagorean]] [[diatonic]] generator, therefore may be called the '''harmonic semiaugmented fourth'''.

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

This interval is the simplest superfourth in JI, and as it falls about halfway between [[12edo]]'s [[perfect fourth]] and [[tritone]], it is very xenharmonic. As an octave-reduced harmonic, it is a basis of consonance in 11-limit JI, alongside the lower odd numbers 9, 7, 5 and 3. It can be found in harmonic series chords such as 4:5:6:7:8:9:10:11:12, sitting somewhere between the stronger and more familiar consonances of 10 (prime 5) and 12 (prime 3).

~~<h4>Original HTML content:</h4>~~

== Terminology ==

~~|-3 0 0 0 1&gt;<br />~~

The naming pattern from [[11/9|undecimal neutral third]] and [[12/11|undecimal neutral second]] and their octave complements can be rigorously generalized and results in the somewhat unconventional '''harmonic/undecimal neutral fourth'''. This interval has also been termed the '''undecimal major fourth''' since the tempered version found in [[24edo]] was dubbed the "major fourth" by [[Ivan Wyschnegradsky]], although this may be confusing in diatonic contexts.

~~551.31794 cents<br />~~

Because it is right between the diatonic fourth and tritone, it may also be called the '''(lesser) undecimal tritone'''.<ref>Kyle Gann (1998) [https://www.kylegann.com/Octave.html ''Anatomy of an Octave'']</ref>

<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_11_8_pluck_adu_dr220.mp3?file_extension=mp3&autostart=false&repeat=false&showdigits=true&showfsbutton=false&width=240&height=20"></embed> <a href="http://xenharmonic.wikispaces.com/file/view/jid_11_8_pluck_adu_dr220.mp3/513194244/jid_11_8_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_11_8_pluck_adu_dr220.mp3/513194244/jid_11_8_pluck_adu_dr220.mp3');">sound sample</a><br />

More recently, [[Zhea Erose]] has suggested calling it something more simple: the '''harmonic fourth''' – under the idea that it is the simplest [[harmonic]] that is in the general (very) rough range of "fourths" when octave-reduced.

~~<br />~~

Furthermore, as stacks of this interval form a core axis of [[Alpharabian tuning]], it has also been dubbed the '''Axirabian paramajor fourth''' or more simply the '''just paramajor fourth'''.

~~In <a class="wiki_link" href="/11-limit">11-limit</a> <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>, 11/8~~ is ~~an undecimal (11-based) <a class="wiki_link" href="/~~superfourth~~">superfourth</a> of about 551.3¢. Falling~~ about halfway between ~~<a class="wiki_link" href="/~~12edo~~">12edo</a>~~'s ~~<a class="wiki_link" href="/perfect%20fourth">~~perfect fourth~~</a>~~ and ~~<a class="wiki_link" href="/~~tritone~~">tritone</a>~~, it is very xenharmonic. ~~It is the simplest superfourth in JI.~~ As an octave-reduced ~~overtone~~, it is a basis of consonance in 11-limit JI, alongside the lower odd numbers 9, 7, 5 and 3. It can be found in harmonic series chords such as 4:5:6:7:8:9:10:11:12, sitting somewhere between the ~~much~~ stronger and more familiar consonances of 10 (5) and 12 (3). It is very well-represented in ~~<a class="wiki_link" href="/24edo">~~24edo~~</a>~~, making that system especially good for approximations of JI chords involving primes 3 and 11 such as 8:9:11:12.~~<br~~ /~~>~~

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

== Potential usage ==

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

This interval is very well-represented in 24edo, making that system especially good for approximations of JI chords involving primes 3 and 11 such as 8:9:11:12. Not only that, but composers who have experience with 24edo may find it very useful not only as a fantastic addition to major chords, but also as an interesting chord root both for chord progressions within a key, and for modulations to key signatures that are not in the same chain of fifths. Furthermore, these same useful functions can carry over to higher EDOs with good 11-limit representation such as [[159edo]].

In more tonal music, 11/8 relative to the tonic ends up being used as the chord root for what amounts to a voicing variation of a 1/1-9/8-225/176-3/2 chord, which, is preceded by a variation on a 1/1-5/4-3/2-225/128 chord built on [[16/15]] relative to the tonic (basically, a type of [[Wikipedia: Neapolitan chord|Neapolitan chord]]), and, followed up by a variation on the 1/1-5/4-3/2-16/9 dominant seventh chord (or potentially even a 1/1-5/4-3/2-16/9-16/15 dominant ninth chord) built on [[3/2]] relative to the tonic for a special type of half cadence. This is a dramatic musical gesture that [[User:Aura|Aura]] has named the "simul half cadence".

== Approximations by EDOs ==

== See also ==

* [[16/11]] – its [[octave complement]]

* [[12/11]] – its [[fifth complement]]

* [[Gallery of just intervals]]

== References ==

[[Category:Fourth]]

[[Category:Superfourth]]

[[Category:Alpharabian]]

@@ Line 1: / Line 1: @@
-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+{{interwiki
-This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
+| de = Alphorn-Fa
-: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-07 15:33:47 UTC</tt>.<br>
+| en = 11/8
-: The original revision id was <tt>513194320</tt>.<br>
+| es =
-: The revision comment was: <tt></tt><br>
+| ja =
-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>
+{{Infobox Interval
-<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">**11/8**
+| Name = undecimal superfourth, harmonic fourth, undecimal tritone, undecimal major fourth, undecimal semiaugmented fourth, harmonic semiaugmented fourth
-|-3 0 0 0 1&gt;
+| Color name = 1o4, ilo 4th
-.31794 cents
+| Sound = jid_11_8_pluck_adu_dr220.mp3
-[[media type="file" key="jid_11_8_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_11_8_pluck_adu_dr220.mp3|sound sample]]
+}}
+{{Wikipedia|Major fourth and minor fifth}}
-In [[11-limit]] [[Just Intonation]], 11/8 is an undecimal (11-based) [[superfourth]] of about 551.3¢. Falling about halfway between [[12edo]]'s [[perfect fourth]] and [[tritone]], it is very xenharmonic. It is the simplest superfourth in JI. As an octave-reduced overtone, it is a basis of consonance in 11-limit JI, alongside the lower odd numbers 9, 7, 5 and 3. It can be found in harmonic series chords such as 4:5:6:7:8:9:10:11:12, sitting somewhere between the much stronger and more familiar consonances of 10 (5) and 12 (3). It is very well-represented in [[24edo]], making that system especially good for approximations of JI chords involving primes 3 and 11 such as 8:9:11:12.
+In [[11-limit]] [[just intonation]], '''11/8''' is an '''undecimal  [[superfourth|semiaugmented fourth]]''' of about 551.3{{cent}}. This interval is close (~3{{cent}}) to exactly between a [[4/3|perfect fourth]] and [[729/512|augmented fourth]], the latter of which is the ''augmented'' version of the [[Pythagorean tuning|Pythagorean]] [[diatonic]] generator, therefore may be called the '''harmonic semiaugmented fourth'''.
-See: [[Gallery of Just Intervals]]</pre></div>
+This interval is the simplest superfourth in JI, and as it falls about halfway between [[12edo]]'s [[perfect fourth]] and [[tritone]], it is very xenharmonic.  As an octave-reduced harmonic, it is a basis of consonance in 11-limit JI, alongside the lower odd numbers 9, 7, 5 and 3. It can be found in harmonic series chords such as 4:5:6:7:8:9:10:11:12, sitting somewhere between the stronger and more familiar consonances of 10 (prime 5) and 12 (prime 3).
-<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_8&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;11/8&lt;/strong&gt;&lt;br /&gt;
+== Terminology ==
-|-3 0 0 0 1&amp;gt;&lt;br /&gt;
+The naming pattern from [[11/9|undecimal neutral third]] and [[12/11|undecimal neutral second]] and their octave complements can be rigorously generalized and results in the somewhat unconventional '''harmonic/undecimal neutral fourth'''. This interval has also been termed the '''undecimal major fourth''' since the tempered version found in [[24edo]] was dubbed the "major fourth" by [[Ivan Wyschnegradsky]], although this may be confusing in diatonic contexts.
-.31794 cents&lt;br /&gt;
+Because it is right between the diatonic fourth and tritone, it may also be called the '''(lesser) undecimal tritone'''.<ref>Kyle Gann (1998) [https://www.kylegann.com/Octave.html ''Anatomy of an Octave'']</ref>
-&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_11_8_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_11_8_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_11_8_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_11_8_pluck_adu_dr220.mp3/513194244/jid_11_8_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_11_8_pluck_adu_dr220.mp3/513194244/jid_11_8_pluck_adu_dr220.mp3');"&gt;sound sample&lt;/a&gt;&lt;br /&gt;
+More recently, [[Zhea Erose]] has suggested calling it something more simple: the '''harmonic fourth''' – under the idea that it is the simplest [[harmonic]] that is in the general (very) rough range of "fourths" when octave-reduced.
-&lt;br /&gt;
+Furthermore, as stacks of this interval form a core axis of [[Alpharabian tuning]], it has also been dubbed the '''Axirabian paramajor fourth''' or more simply the '''just paramajor fourth'''.
-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;, 11/8 is an undecimal (11-based) &lt;a class="wiki_link" href="/superfourth"&gt;superfourth&lt;/a&gt; of about 551.3¢. Falling about halfway between &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;'s &lt;a class="wiki_link" href="/perfect%20fourth"&gt;perfect fourth&lt;/a&gt; and &lt;a class="wiki_link" href="/tritone"&gt;tritone&lt;/a&gt;, it is very xenharmonic. It is the simplest superfourth in JI. As an octave-reduced overtone, it is a basis of consonance in 11-limit JI, alongside the lower odd numbers 9, 7, 5 and 3. It can be found in harmonic series chords such as 4:5:6:7:8:9:10:11:12, sitting somewhere between the much stronger and more familiar consonances of 10 (5) and 12 (3). It is very well-represented in &lt;a class="wiki_link" href="/24edo"&gt;24edo&lt;/a&gt;, making that system especially good for approximations of JI chords involving primes 3 and 11 such as 8:9:11:12.&lt;br /&gt;
-&lt;br /&gt;
+== Potential usage ==
-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>
+This interval is very well-represented in 24edo, making that system especially good for approximations of JI chords involving primes 3 and 11 such as 8:9:11:12.  Not only that, but composers who have experience with 24edo may find it very useful not only as a fantastic addition to major chords, but also as an interesting chord root both for chord progressions within a key, and for modulations to key signatures that are not in the same chain of fifths.  Furthermore, these same useful functions can carry over to higher EDOs with good 11-limit representation such as [[159edo]].
+In more tonal music, 11/8 relative to the tonic ends up being used as the chord root for what amounts to a voicing variation of a 1/1-9/8-225/176-3/2 chord, which, is preceded by a variation on a 1/1-5/4-3/2-225/128 chord built on [[16/15]] relative to the tonic (basically, a type of [[Wikipedia: Neapolitan chord|Neapolitan chord]]), and, followed up by a variation on the 1/1-5/4-3/2-16/9 dominant seventh chord (or potentially even a 1/1-5/4-3/2-16/9-16/15 dominant ninth chord) built on [[3/2]] relative to the tonic for a special type of half cadence.  This is a dramatic musical gesture that [[User:Aura|Aura]] has named the "simul half cadence".
+== Approximations by EDOs ==
+{{Interval edo approximation|11/8}}
+<references group="note" />
+== See also ==
+* [[16/11]] – its [[octave complement]]
+* [[12/11]] – its [[fifth complement]]
+* [[Gallery of just intervals]]
+== References ==
+<references />
+[[Category:Fourth]]
+[[Category:Superfourth]]
+[[Category:Alpharabian]]