25/24

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

• 36/25 – its fifth complement
• 48/25 – its octave complement
• 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 – the Pythagorean chromatic semitone
• Sqrt(25/24) – its exact half