intervallratio

Intervallratio is a concept in music theory describing the frequency ratio between two pitches, and thus the size of a musical interval. If two notes have frequencies f1 and f2 (with f2 > f1), the interval is described by the ratio R = f2 / f1. This ratio is a dimensionless measure that determines the pitch relationship: an octave corresponds to R = 2:1, a perfect fifth to 3:2, a major third to 5:4, and a minor third to 6:5, among many others found in various tuning systems.

The size of an interval can be expressed in cents: cents = 1200 * log2(R). For example, 3:2 equals about 702 cents, 5:4 about 386 cents, and 6:5 about 316 cents. While just intonation uses exact small-integer ratios, equal temperament often approximates these ratios because the octave is divided into equal steps (for 12-TET, each semitone is a ratio of 2^(1/12)).

Intervallratio is central to tuning, intonation, and musical analysis. It underpins the construction of scales, the tuning of instruments, and the perception of harmony. In practice, performers and theorists may refer to interval sizes by their ratios or by their cent values, depending on context.

See also: interval, just intonation, equal temperament, frequency, pitch.