21/20: 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 = septimal minor semitone, septimal chromatic semitone, large septimal chroma

~~: This revision was by author [[User:spt3125~~|~~spt3125]] and made on <tt>2014-06-30 20:58:37 UTC</tt>.<br>~~

| Color name = zg2, zogu 2nd

~~: The original revision id was <tt>515317334</tt>.<br>~~

| Sound = jid_21_20_pluck_adu_dr220.mp3

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

| Comma = yes

~~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">**21/20**

|~~-2 1 -1 1>~~

~~84.4672 cents~~

~~[[media type~~=~~"file" key="jid_21_20_pluck_adu_dr220.mp3"]] [[file:xenharmonic/~~jid_21_20_pluck_adu_dr220.mp3|~~sound sample]]~~

A small semitone of about 84.~~5 cents, 21/20~~ may be found in 7-limit just intonation as, for example, the difference between 8/7 and 6/5, or ~~between~~ 5/3 and 7/4.

'''21/20''' is a small semitone of about 85 cents. It may be found in [[7-limit]] [[just intonation]] as, for example, the difference between [[4/3]] and [[7/5]], [[8/7]] and [[6/5]], or [[5/3]] and [[7/4]].

[[~~http:~~/~~/en~~.~~wikipedia.org~~/~~wiki~~/~~Septimal_chromatic_semitone~~]]</~~pre>~~<~~/div~~>

== Terminology ==

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

21/20 is traditionally called a ''chroma'', perhaps for its proximity (and conflation in systems like septimal [[meantone]]) with the major chroma [[135/128]]. However, it is a ''diatonic semitone'' in both [[Helmholtz–Ellis notation]] and [[Functional Just System]], viewed as the Pythagorean minor second [[256/243]] altered by [[5120/5103]]. [[Marc Sabat]] has taken to call it the ''minor diatonic semitone'' in the same material where [[15/14]] is also named as the major chromatic semitone<ref>Marc Sabat. [https://masa.plainsound.org/pdfs/crystal-growth.pdf ''Three Crystal Growth Algorithms in 23-limit constrained Harmonic Space'']. Plainsound Music Edition, 2008.</ref>.

~~|-2 1 -1 1&gt;<br />~~

== Interval chain ==

84.~~4672 cents<br />~~

An [[interval chain]] of 21/20s stacked on top of one another comes close to approximating some important [[JI]] intervals. The error between the approximation and the target JI interval may be tempered out in some [[regular temperaments]].

~~ <a href="http://xenharmonic~~.~~wikispaces~~.~~com~~/~~file~~/~~view~~/~~jid_21_20_pluck_adu_dr220.mp3~~/~~515315588~~/~~jid_21_20_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http:~~//~~xenharmonic.wikispaces.com~~/~~file~~/~~view~~/~~jid_21_20_pluck_adu_dr220.mp3~~/~~515315588~~/~~jid_21_20_pluck_adu_dr220.mp3');">sound sample</a><br />~~

~~<br />~~

Some examples include:

A ~~small semitone~~ of ~~about 84.5 cents,~~ 21/20 ~~may be found in~~ 7~~-limit just intonation~~ as, ~~for example,~~ the ~~difference between 8~~/~~7 and 6~~/5, or ~~between 5~~/~~3 and 7/4~~.~~<br />~~

* A stack of two 21/20 upwards is ~4¢ from [[11/10]]

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

* A stack of seven 21/20 upwards is ~9¢ from [[7/5]]

~~<~~a ~~class="wiki_link_ext" href="http://en~~.~~wikipedia~~.~~org~~/~~wiki/Septimal_chromatic_semitone" rel="nofollow">http://en~~.~~wikipedia~~.~~org~~/~~wiki~~/~~Septimal_chromatic_semitone</a></body></html>~~</~~pre></div~~>

* A stack of ten 21/20 upwards is ~4¢ from [[13/8]]

* A stack of twelve 21/20 upwards is ~4¢ from [[9/5]]

and

* A stack of six 21/20 downwards is ~10¢ from [[3/2]]

* A stack of nine 21/20 downwards is ~5¢ from [[9/7]]

* A stack of eleven 21/20 downwards is ~4¢ from [[7/6]]

When treated as a scale, this interval chain can be called the '''[[ambitonal sequence]] of 21/20''' ('''AS21/20''' or '''1ed21/20''').

1ed21/20 is equal to approximately 14.2067 EDO, and as a result of tethering between compressed 14 and heavily stretched 15 it is quite xenharmonic in its sound. It is related to the [[nautilus]], [[sextilifourths]] and [[floral]] temperaments.

1ed21/20 offers a possible approximation of the no-3s [[11-limit]]. It might alternatively be used as a [[dual-fifth tuning]].

== See also ==

* [[40/21]] – its [[octave complement]]

* [[10/7]] – its [[fifth complement]]

* [[List of superparticular intervals]]

* [[Gallery of just intervals]]

* [[Septisemi temperaments]], where it is tempered out

== References ==

[[Category:Second]]

[[Category:Semitone]]

[[Category:Chroma]]

[[Category:Septisemi]]

[[Category:Commas named after their interval size]]

@@ 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 = septimal minor semitone, septimal chromatic semitone, large septimal chroma
-: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-30 20:58:37 UTC</tt>.<br>
+| Color name = zg2, zogu 2nd
-: The original revision id was <tt>515317334</tt>.<br>
+| Sound = jid_21_20_pluck_adu_dr220.mp3
-: The revision comment was: <tt></tt><br>
+| Comma = yes
-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>
+{{Wikipedia|Septimal chromatic semitone}}
-<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">**21/20**
-|-2 1 -1 1&gt;
-.4672 cents
-[[media type="file" key="jid_21_20_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_21_20_pluck_adu_dr220.mp3|sound sample]]
-A small semitone of about 84.5 cents, 21/20 may be found in 7-limit just intonation as, for example, the difference between 8/7 and 6/5, or between 5/3 and 7/4.
+'''21/20''' is a small semitone of about 85 cents. It may be found in [[7-limit]] [[just intonation]] as, for example, the difference between [[4/3]] and [[7/5]], [[8/7]] and [[6/5]], or [[5/3]] and [[7/4]].
-[[http://en.wikipedia.org/wiki/Septimal_chromatic_semitone]]</pre></div>
+== Terminology ==
-<h4>Original HTML content:</h4>
+/20 is traditionally called a ''chroma'', perhaps for its proximity (and conflation in systems like septimal [[meantone]]) with the major chroma [[135/128]]. However, it is a ''diatonic semitone'' in both [[Helmholtz–Ellis notation]] and [[Functional Just System]], viewed as the Pythagorean minor second [[256/243]] altered by [[5120/5103]]. [[Marc Sabat]] has taken to call it the ''minor diatonic semitone'' in the same material where [[15/14]] is also named as the major chromatic semitone<ref>Marc Sabat. [https://masa.plainsound.org/pdfs/crystal-growth.pdf ''Three Crystal Growth Algorithms in 23-limit constrained Harmonic Space'']. Plainsound Music Edition, 2008.</ref>.
-<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_20&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;21/20&lt;/strong&gt;&lt;br /&gt;
-|-2 1 -1 1&amp;gt;&lt;br /&gt;
+== Interval chain ==
-.4672 cents&lt;br /&gt;
+An [[interval chain]] of 21/20s stacked on top of one another comes close to approximating some important [[JI]] intervals. The error between the approximation and the target JI interval may be tempered out in some [[regular temperaments]].
-&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_21_20_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_21_20_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_21_20_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_21_20_pluck_adu_dr220.mp3/515315588/jid_21_20_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_21_20_pluck_adu_dr220.mp3/515315588/jid_21_20_pluck_adu_dr220.mp3');"&gt;sound sample&lt;/a&gt;&lt;br /&gt;
-&lt;br /&gt;
+Some examples include:
-A small semitone of about 84.5 cents, 21/20 may be found in 7-limit just intonation as, for example, the difference between 8/7 and 6/5, or between 5/3 and 7/4.&lt;br /&gt;
+* A stack of two 21/20 upwards is ~4¢ from [[11/10]]
-&lt;br /&gt;
+* A stack of seven 21/20 upwards is ~9¢ from [[7/5]]
-&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_chromatic_semitone" rel="nofollow"&gt;http://en.wikipedia.org/wiki/Septimal_chromatic_semitone&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
+* A stack of ten 21/20 upwards is ~4¢ from [[13/8]]
+* A stack of twelve 21/20 upwards is ~4¢ from [[9/5]]
+and
+* A stack of six 21/20 downwards is ~10¢ from [[3/2]]
+* A stack of nine 21/20 downwards is ~5¢ from [[9/7]]
+* A stack of eleven 21/20 downwards is ~4¢ from [[7/6]]
+When treated as a scale, this interval chain can be called the '''[[ambitonal sequence]] of 21/20''' ('''AS21/20''' or '''1ed21/20''').
+ed21/20 is equal to approximately 14.2067 EDO, and as a result of tethering between compressed 14 and heavily stretched 15 it is quite xenharmonic in its sound. It is related to the [[nautilus]], [[sextilifourths]] and [[floral]] temperaments.
+ed21/20 offers a possible approximation of the no-3s [[11-limit]]. It might alternatively be used as a [[dual-fifth tuning]].
+{{Harmonics in equal|1|21|20|intervals=prime}}
+== See also ==
+* [[40/21]] – its [[octave complement]]
+* [[10/7]] – its [[fifth complement]]
+* [[List of superparticular intervals]]
+* [[Gallery of just intervals]]
+* [[Septisemi temperaments]], where it is tempered out
+== References ==
+<references/>
+[[Category:Second]]
+[[Category:Semitone]]
+[[Category:Chroma]]
+[[Category:Septisemi]]
+[[Category:Commas named after their interval size]]
+{{todo|improve synopsis}}