25/24: Difference between revisions

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'''25/24''', the '''classic''' or '''just chromatic semitone''' (short: '''chroma'''), 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]] comma, it can be used for a complete system of [[5-limit]] notation.

'''25/24''', the '''classic''' or '''just chromatic semitone''' (short: '''chroma'''), 70.672 cents, is the [[superparticular]] ratio which marks the difference between the 5-limit seconds, [[16/15]] and [[10/9]], [[27/25]] and [[9/8]], thirds, [[6/5]] and [[5/4]], sixths, [[8/5]] and [[5/3]], and sevenths, [[16/9]] and [[50/27]], and [[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.

== Approximation ==

==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 ==

==Temperaments==

If 25/24 is treated as a comma to be tempered out, you remove the distinction between major and minor thirds and get only a single neutral interval in their place as in [[dicot family]], and edos like [[10edo]] or [[17edo]].

== See also ==

==See also==

* [[36/25]] – its [[fifth complement]]

* [[48/25]] – its [[octave complement]]

*[[48/25]] – its [[octave complement]]

* [[Dicot family]], where it is tempered out

*[[Dicot family]], where it is tempered out

* [[Gallery of just intervals]]

*[[Gallery of just intervals]]

* [[Medium comma]]

*[[Medium comma]]

* [[List of superparticular intervals]]

*[[List of superparticular intervals]]

* [[Chroma]] – a generalising concept for [[MOS]] scales

*[[Chroma]] – a generalising concept for [[MOS]] scales

* [[2187/2048]] – the Pythagorean chromatic semitone

*[[2187/2048]] – the Pythagorean chromatic semitone

[[Category:5-limit]]

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 }}
-'''25/24''', the '''classic''' or '''just chromatic semitone''' (short: '''chroma'''), 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]] comma, it can be used for a complete system of [[5-limit]] notation.
+'''25/24''', the '''classic''' or '''just chromatic semitone''' (short: '''chroma'''), 70.672 cents, is the [[superparticular]] ratio which marks the difference between the 5-limit seconds, [[16/15]] and [[10/9]], [[27/25]] and [[9/8]], thirds, [[6/5]] and [[5/4]], sixths, [[8/5]] and [[5/3]], and sevenths, [[16/9]] and [[50/27]], and [[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.
-== Approximation ==
+==Approximation==
 /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 ==
+==Temperaments==
 If 25/24 is treated as a comma to be tempered out, you remove the distinction between major and minor thirds and get only a single neutral interval in their place as in [[dicot family]], and edos like [[10edo]] or [[17edo]].
-== See also ==
+==See also==
 * [[36/25]] – its [[fifth complement]]
-* [[48/25]] – its [[octave complement]]
+*[[48/25]] – its [[octave complement]]
-* [[Dicot family]], where it is tempered out
+*[[Dicot family]], where it is tempered out
-* [[Gallery of just intervals]]
+*[[Gallery of just intervals]]
-* [[Medium comma]]
+*[[Medium comma]]
-* [[List of superparticular intervals]]
+*[[List of superparticular intervals]]
-* [[Chroma]] – a generalising concept for [[MOS]] scales
+*[[Chroma]] – a generalising concept for [[MOS]] scales
-* [[2187/2048]] – the Pythagorean chromatic semitone
+*[[2187/2048]] – the Pythagorean chromatic semitone
 [[Category:5-limit]]