25/24: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

| Ratio = 25/24

| Monzo = -3 -1 2

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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 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.

'''25/24''', the '''classic''' or '''just chromatic semitone''' (short: '''chroma'''), 70.672{{cent}}, 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.

25/24 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==

== 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]].

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==

* [[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]]

[[Category:Chroma]]

~~[[Category:Interval ratio]]~~

[[Category:Semitone]]

[[Category:Third tone]]

[[Category:Superparticular]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
 | Ratio = 25/24
 | Monzo = -3 -1 2
@@ Line 10: / Line 9: @@
 }}
-'''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.
+'''25/24''', the '''classic''' or '''just chromatic semitone''' (short: '''chroma'''), 70.672{{cent}}, 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.
+/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==
+== 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]].
+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==
 * [[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]]
 [[Category:Chroma]]
-[[Category:Interval ratio]]
 [[Category:Semitone]]
 [[Category:Third tone]]
 [[Category:Superparticular]]