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.

@@ 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 = just chromatic semitone, classic(al) chromatic semitone, diptolemaic chromatic semitone, dicot comma
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-08-08 19:15:24 UTC</tt>.<br>
+| Color name = yy1, yoyo unison
-: The original revision id was <tt>244922683</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">The chroma or 5-limit chromatic semitone, 25/24, is 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.</pre></div>
-<h4>Original HTML content:</h4>
+== Approximation ==
-<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;The chroma or 5-limit chromatic semitone, 25/24, is 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 5-limit notation.&lt;/body&gt;&lt;/html&gt;</pre></div>
+/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 ==
+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.
+== See also ==
+* [[36/25]] – its [[fifth complement]]
+* [[48/25]] – its [[octave complement]]
+* [[Sqrt(25/24)]] – its exact half
+* [[Gallery of just intervals]]
+* [[Medium comma]]
+* [[List of superparticular intervals]]
+* [[Chromatic semitone]] – a generalising concept for the [[5L 2s|diatonic]] scale
+* [[Chroma]] – a generalising concept for all [[mos]] scales
+[[Category:Chroma]]
+[[Category:Semitone]]
+[[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

Navigation menu

Search