25/24: Difference between revisions

25/24, the just chromatic semitone, classic(al) chromatic semitone or diptolemaic chromatic semitone, 70.672 ¢, is the superparticular ratio which marks the difference between the 5-limit seconds, 16/15 and 10/9, thirds, 6/5 and 5/4, sixths, 8/5 and 5/3, and sevenths, 9/5 and 15/8. It is therefore the amount which sharpens or flattens a 5-limit second, third, sixth, or seventh, and when notating 5-limit just intonation it can be associated with the sharp or flat symbol, and along with an additional symbol for the 81/80 comma, it can be used for a complete system of 5-limit notation as an extension of diatonic.

Approximation

25/24 is very accurately approximated by 17edo's 1\17 (70.588 ¢). In fact, the interval that results from stacking seventeen 25/24 chromatic semitones reduced by an octave is the septendecima, only 1.428 ¢ in size.

Temperaments

If 25/24 is treated as a comma to be tempered out, it may be called the dicot comma. Doing so leads to the dicot temperament, where the distinction between 5-limit major and minor thirds are removed and there is only a single neutral interval functioning as both, as in 7edo, 10edo, and 17edo. See dicot family for the rank-2 family where it is tempered out.

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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 = just chromatic semitone, classic(al) chromatic semitone, diptolemaic chromatic semitone, dicot comma
-: This revision was by author [[User:PiotrGrochowski|PiotrGrochowski]] and made on <tt>2016-08-11 04:02:38 UTC</tt>.<br>
+| Color name = yy1, yoyo unison
-: The original revision id was <tt>589204050</tt>.<br>
+| Sound = jid_25_24_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>
+'''25/24''', the '''just chromatic semitone''', '''classic(al) chromatic semitone''' or '''diptolemaic chromatic semitone''', 70.672{{cent}}, is the [[superparticular]] ratio which marks the difference between the [[5-limit]] seconds, [[16/15]] and [[10/9]], thirds, [[6/5]] and [[5/4]], sixths, [[8/5]] and [[5/3]], and sevenths, [[9/5]] and [[15/8]]. It is therefore the amount which sharpens or flattens a 5-limit second, third, sixth, or seventh, and when notating 5-limit just intonation it can be associated with the sharp or flat symbol, and along with an additional symbol for the [[81/80]] comma, it can be used for a complete system of [[5-limit]] notation as an extension of diatonic.
-<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">**25/24**
-|-3 -1 2&gt;
-.6724 cents
-[[media type="file" key="jid_25_24_pluck_adu_dr220.mp3" width="240" height="20"]] [[file:xenharmonic/jid_25_24_pluck_adu_dr220.mp3|sound sample]]
-The **5-limit chromatic semitone** (short: **chroma**), 25/24, 70.672 cents, is the [[superparticular]] ratio which marks the difference between the 5-limit thirds, 6/5 and 5/4, and sixths, 8/5 and 5/3. It is therefore the amount which sharpens or flattens a 5-limit third or sixth, and when notating 5-limit just intonation it can be associated with the sharp or flat symbol, and along with an additional symbol for the [[81_80|81/80]] comma, it can be used for a complete system of [[5-limit]] notation.
+== Approximation ==
+/24 is very accurately approximated by [[17edo]]'s 1\17 (70.588{{cent}}). In fact, the interval that results from stacking seventeen 25/24 chromatic semitones reduced by an octave is the [[septendecima]], only 1.428{{cent}} in size.
-----
+== Temperaments ==
-See also:
+If 25/24 is treated as a comma to be tempered out, it may be called the '''dicot comma'''. Doing so leads to the [[dicot]] temperament, where the distinction between 5-limit major and minor thirds are removed and there is only a single neutral interval functioning as both, as in [[7edo]], [[10edo]], and [[17edo]]. See [[dicot family]] for the rank-2 family where it is tempered out.
-* [[Chroma]] -- a generalising concept for MOS scales
-* [[Gallery of Just Intervals]]
+== See also ==
-* [[comma]]</pre></div>
+* [[36/25]] – its [[fifth complement]]
-<h4>Original HTML content:</h4>
+* [[48/25]] – 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;25_24&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;25/24&lt;/strong&gt;&lt;br /&gt;
+* [[Sqrt(25/24)]] – its exact half
-|-3 -1 2&amp;gt;&lt;br /&gt;
+* [[Gallery of just intervals]]
-.6724 cents&lt;br /&gt;
+* [[Medium comma]]
-&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_25_24_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_25_24_pluck_adu_dr220.mp3&amp;amp;quot; width=&amp;amp;quot;240&amp;amp;quot; height=&amp;amp;quot;20&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_25_24_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_25_24_pluck_adu_dr220.mp3/515315630/jid_25_24_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_25_24_pluck_adu_dr220.mp3/515315630/jid_25_24_pluck_adu_dr220.mp3');"&gt;sound sample&lt;/a&gt;&lt;br /&gt;
+* [[List of superparticular intervals]]
-&lt;br /&gt;
+* [[Chromatic semitone]] – a generalising concept for the [[5L 2s|diatonic]] scale
-The &lt;strong&gt;5-limit chromatic semitone&lt;/strong&gt; (short: &lt;strong&gt;chroma&lt;/strong&gt;), 25/24, 70.672 cents, is the &lt;a class="wiki_link" href="/superparticular"&gt;superparticular&lt;/a&gt; ratio which marks the difference between the 5-limit thirds, 6/5 and 5/4, and sixths, 8/5 and 5/3. It is therefore the amount which sharpens or flattens a 5-limit third or sixth, and when notating 5-limit just intonation it can be associated with the sharp or flat symbol, and along with an additional symbol for the &lt;a class="wiki_link" href="/81_80"&gt;81/80&lt;/a&gt; comma, it can be used for a complete system of &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; notation.&lt;br /&gt;
+* [[Chroma]] – a generalising concept for all [[mos]] scales
-&lt;br /&gt;
-&lt;hr /&gt;
+[[Category:Chroma]]
-See also:&lt;br /&gt;
+[[Category:Semitone]]
-&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Chroma"&gt;Chroma&lt;/a&gt; -- a generalising concept for MOS scales&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Gallery%20of%20Just%20Intervals"&gt;Gallery of Just Intervals&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/comma"&gt;comma&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
+[[Category:Third tone]]
+[[Category:Dicot]]
+[[Category:Commas named for how they divide the fifth]]

25/24: Difference between revisions

Latest revision as of 06:00, 4 August 2025

Approximation

Temperaments

See also

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