25/24
Ratio | 25/24 |
Factorization | 2^{-3} × 3^{-1} × 5^{2} |
Monzo | [-3 -1 2⟩ |
Size in cents | 70.672427¢ |
Names | just chromatic semitone, classic(al) chromatic semitone, diptolemaic chromatic semitone, dicot comma |
Color name | yy1, yoyo unison |
FJS name | [math]\text{A1}^{5,5}[/math] |
Special properties | square superparticular, reduced |
Tenney height (log_{2} nd) | 9.22882 |
Weil height (log_{2} max(n, d)) | 9.28771 |
Wilson height (sopfr (nd)) | 19 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.35172 bits |
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, 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, it may be called the dicot comma. Doing so leads to the dicot temperament, where the distinction between major and minor thirds are removed and there is only a single neutral interval functioning as both, as in 7edo and 10edo. 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
- 1ed25/24 - its equal multiplication
- 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