25/24: Difference between revisions

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The '''classic 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]] comma, it can be used for a complete system of [[5-limit]] notation. If it is treated as a comma to be tempered out, you remove the distinction between major & minor thirds and get only a single neutral interval in their place as in [[dicot family]], and edos like [[10edo]] or [[17edo]].

The '''classic 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]] comma, it can be used for a complete system of [[5-limit]] notation.

It is very accurately approximated by 17edo's 1\17 (70.588¢). In fact, the interval that results from stacking seventeen 25/24 chromatic semitones is only 1.428¢ ~~flat of~~ the ~~octave~~.

It 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 it 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]]

* [[Dicot family]], ~~which tempers~~ it out

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

* [[Gallery of just intervals]]

* [[Medium comma]]

* [[List of superparticular intervals]]

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

* [[2187/2048|Pythagorean chromatic semitone]]

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

[[Category:5-limit]]

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-The '''classic 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]] comma, it can be used for a complete system of [[5-limit]] notation. If it is treated as a comma to be tempered out, you remove the distinction between major & minor thirds and get only a single neutral interval in their place as in [[dicot family]], and edos like [[10edo]] or [[17edo]].
+The '''classic 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]] comma, it can be used for a complete system of [[5-limit]] notation.
-It is very accurately approximated by 17edo's 1\17 (70.588¢). In fact, the interval that results from stacking seventeen 25/24 chromatic semitones is only 1.428¢ flat of the octave.
+It 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 it 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]]
-* [[Dicot family]], which tempers it out
+* [[Dicot family]], where it is tempered out
 * [[Gallery of just intervals]]
 * [[Medium comma]]
 * [[List of superparticular intervals]]
 * [[Chroma]] – a generalising concept for [[MOS]] scales
-* [[2187/2048|Pythagorean chromatic semitone]]
+* [[2187/2048]] – the Pythagorean chromatic semitone
 [[Category:5-limit]]