25/24: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

| Name = just chromatic semitone, classic(al) chromatic semitone, diptolemaic chromatic semitone, dicot comma

~~| Ratio = 25/24~~

| Color name = yy1, yoyo unison

~~| Monzo = -3 -1 2~~

~~| Cents = 70.67243~~

| Name = classic chromatic semitone, ~~<br>chroma~~

| Color name =

~~| FJS name = A1<sup>25</sup>~~

| Sound = jid_25_24_pluck_adu_dr220.mp3

| Comma = yes

}}

'''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.

~~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]]~~.

== Approximation ==

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.

It is ~~very accurately approximated by 17edo~~'~~s 1\17 (70~~.~~588¢). In fact~~, ~~a chain of seventeen 25/24 chromatic semitones~~ is only 1.~~428¢ flat of~~ the ~~octave~~.

== 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]]

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

* [[Sqrt(25/24)]] – its exact half

* [[Gallery of just intervals]]

* [[Medium comma]]

* [[List of superparticular intervals]]

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

* [[Chromatic semitone]] – a generalising concept for the [[5L 2s|diatonic]] scale

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

* [[Chroma]] – a generalising concept for all [[mos]] scales

~~[[Category:5-limit]]~~

[[Category:Chroma]]

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

[[Category:Semitone]]

[[Category:Third tone]]

[[Category:~~Listen~~]]

[[Category:Dicot]]

[[Category:~~Superparticular~~]]

[[Category:Commas named for how they divide the fifth]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
+| Name = just chromatic semitone, classic(al) chromatic semitone, diptolemaic chromatic semitone, dicot comma
-| Ratio = 25/24
+| Color name = yy1, yoyo unison
-| Monzo = -3 -1 2
-| Cents = 70.67243
-| Name = classic chromatic semitone, <br>chroma
-| Color name =
-| FJS name = A1<sup>25</sup>
 | Sound = jid_25_24_pluck_adu_dr220.mp3
+| Comma = yes
 }}
+'''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.
-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]].
+== 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.
-It is very accurately approximated by 17edo's 1\17 (70.588¢). In fact, a chain of seventeen 25/24 chromatic semitones is only 1.428¢ flat of the octave.
+== 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]]
-* [[Dicot family]], which tempers it out
+* [[Sqrt(25/24)]] – its exact half
 * [[Gallery of just intervals]]
 * [[Medium comma]]
 * [[List of superparticular intervals]]
-* [[Chroma]] – a generalising concept for [[MOS]] scales
+* [[Chromatic semitone]] – a generalising concept for the [[5L 2s|diatonic]] scale
-* [[2187/2048|Pythagorean chromatic semitone]]
+* [[Chroma]] – a generalising concept for all [[mos]] scales
-[[Category:5-limit]]
 [[Category:Chroma]]
-[[Category:Interval ratio]]
 [[Category:Semitone]]
 [[Category:Third tone]]
-[[Category:Listen]]
+[[Category:Dicot]]
-[[Category:Superparticular]]
+[[Category:Commas named for how they divide the fifth]]