25/24: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Name = classic/just chromatic semitone, chroma
| Name = just chromatic semitone, classic(al) chromatic semitone, diptolemaic chromatic semitone, chroma
| Color name = yy1, yoyo unison
| Color name = yy1, yoyo unison
| Sound = jid_25_24_pluck_adu_dr220.mp3
| Sound = jid_25_24_pluck_adu_dr220.mp3
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}}
}}


'''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.
'''25/24''', the '''just chromatic semitone''', '''classic(al) chromatic semitone''' or '''diptolemaic 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 ==

Revision as of 15:38, 25 January 2023

Interval information
Ratio 25/24
Factorization 2-3 × 3-1 × 52
Monzo [-3 -1 2⟩
Size in cents 70.67243¢
Names just chromatic semitone,
classic(al) chromatic semitone,
diptolemaic chromatic semitone,
chroma
Color name yy1, yoyo unison
FJS name [math]\displaystyle{ \text{A1}^{5,5} }[/math]
Special properties square superparticular,
reduced
Tenney norm (log2 nd) 9.22882
Weil norm (log2 max(n, d)) 9.28771
Wilson norm (sopfr(nd)) 19
Comma size medium
S-expression S5

[sound info]
Open this interval in xen-calc

25/24, the just chromatic semitone, classic(al) chromatic semitone or diptolemaic chromatic semitone (short: chroma), 70.672 ¢, 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

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.

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.

See also

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