25/24: Difference between revisions

(35 intermediate revisions by 17 users not shown)

Line 1:

'''25/24'''

{{interwiki

|-3 -~~1 2>~~

| de = 25/24

| en = 25/24

| es =

| ja =

}}

{{Infobox Interval

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

| Color name = yy1, yoyo unison

| 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.

70.~~6724 cents~~

== Approximation ==

25/24 is very accurately approximated by [[17edo]]'s 1\17 (70.588{{cent}}), though 17edo does not represent it as such, actually [[tempering out]] 25/24 by [[patent val]] (though [[34edo]] represents it as 1\17 consistently). In fact, the interval that results from stacking seventeen 25/24 chromatic semitones reduced by an octave is the [[septendecima]], only 1.431{{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]] [[exotemperament]], 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.

[[~~File:jid_25_24_pluck_adu_dr220.mp3~~]] [[~~:File:jid_25_24_pluck_adu_dr220.mp3~~|~~sound sample~~]]

== 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

~~The '''5-limit chromatic semitone''' (short: '''chroma'''), 25/24, 70.672 cents, is the~~ [[superparticular|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|81/80]] comma, it can be used for a complete system of [[5-limit|5-limit]] notation.

[[Category:Chroma]]

[[Category:Semitone]]

~~-----~~

[[Category:Third tone]]

~~See also~~:

[[Category:Dicot]]

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

~~<ul><li>[[Chroma|~~Chroma]] ~~-- a generalising concept for MOS scales</li><li>~~[[~~Gallery_of_Just_Intervals|Gallery of Just Intervals~~]]~~</li><li>[[Comma|comma]]</li></ul>~~ [[Category:~~5-limit~~]]

[[Category:~~chroma~~]]

[[Category:~~interval~~]]

@@ Line 1: / Line 1: @@
-'''25/24'''
+{{interwiki
-|-3 -1 2&gt;
+| de = 25/24
+| en = 25/24
+| es =
+| ja =
+}}
+{{Infobox Interval
+| Name = just chromatic semitone, classic(al) chromatic semitone, diptolemaic chromatic semitone, dicot comma
+| Color name = yy1, yoyo unison
+| 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.
-.6724 cents
+== Approximation ==
+/24 is very accurately approximated by [[17edo]]'s 1\17 (70.588{{cent}}), though 17edo does not represent it as such, actually [[tempering out]] 25/24 by [[patent val]] (though [[34edo]] represents it as 1\17 consistently). In fact, the interval that results from stacking seventeen 25/24 chromatic semitones reduced by an octave is the [[septendecima]], only 1.431{{cent}} in size.
+{{Interval edo approximation|25/24}}
+== 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]] [[exotemperament]], 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.
-[[File:jid_25_24_pluck_adu_dr220.mp3]] [[:File:jid_25_24_pluck_adu_dr220.mp3|sound sample]]
+== 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
-The '''5-limit chromatic semitone''' (short: '''chroma'''), 25/24, 70.672 cents, is the [[superparticular|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|81/80]] comma, it can be used for a complete system of [[5-limit|5-limit]] notation.
+[[Category:Chroma]]
+[[Category:Semitone]]
------
+[[Category:Third tone]]
-See also:
+[[Category:Dicot]]
+[[Category:Commas named for how they divide the fifth]]
-<ul><li>[[Chroma|Chroma]] -- a generalising concept for MOS scales</li><li>[[Gallery_of_Just_Intervals|Gallery of Just Intervals]]</li><li>[[Comma|comma]]</li></ul>      [[Category:5-limit]]
-[[Category:chroma]]
-[[Category:interval]]