25/24: Difference between revisions

'''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.

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.

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.

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