In contemporary practice, both music theory and musical practice are interpreted in terms of physical laws, which are formulated through mathematical relations. Within acoustics, the branch of physics concerned with sound and its properties, a musical interval is defined as the ratio of two frequencies. In cases where this ratio is simple, such as the perfect fifth (3/2), the perfect fourth (4/3), or the octave (2/1), interval comparison is straightforward. In contrast, when the ratio involves large integers due to the absence of a greatest common divisor, as in the case of the diesis (2048/2025), direct comparison becomes impractical.

A significant simplification in the representation and comparison of musical intervals is obtained through the use of a logarithmic formula:

size of a musical interval = k * log(f2 / f1) / log(2)

In this formula, f1 and f2 denote the frequencies of the pitches forming the interval, with f2 > f1. The constant k specifies the unit system adopted for interval measurement.

Mathematics and Music