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, dicot comma
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
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25/24, the just chromatic semitone, classic(al) chromatic semitone or diptolemaic chromatic semitone, 70.672 ¢, 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.

Approximation

25/24 is very accurately approximated by 17edo's 1\17 (70.588 ¢), 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 ¢ in size.

Edo approximations for 25/24 (70.67 ¢)
≤ 80edo, relative error ≤ 10%

Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
16	1\16	75.00	+4.33	+5.77
17	1\17	70.59	-0.08	-0.12
18	1\18	66.67	-4.01	-6.01
33	2\33	72.73	+2.05	+5.65
34	2\34	70.59	-0.08	-0.24
35	2\35	68.57	-2.10	-6.13
50	3\50	72.00	+1.33	+5.53
51	3\51	70.59	-0.08	-0.36
52	3\52	69.23	-1.44	-6.25
67	4\67	71.64	+0.97	+5.41
68	4\68	70.59	-0.08	-0.48
69	4\69	69.57	-1.11	-6.37

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.

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 diatonic scale
• Chroma – a generalising concept for all mos scales