Just intonation

In music, just intonation or pure intonation is the attempt to tune all musical intervals as whole number ratios (such as 3:2 or 4:3) of frequencies. An interval tuned in this way is said to be pure, and may be called a just interval; when it is sounded, no beating is heard. Just intervals (and chords created by combining them) consist of members of a single harmonic series of an implied fundamental. For example, in the diagram, the notes G3 and C4 (labeled 3 and 4) may be tuned as members of the harmonic series of the lowest C, in which case their frequencies will be 3 and 4 times, respectively, the fundamental frequency and their interval ratio equal to 4:3; they may also be tuned differently.

Harmonic series, partials 1–5 numbered Play .

In Western musical practice, instruments are hardly ever tuned using only pure intervals – the physics of music makes this impracticable. Some instruments of fixed pitch, such as electric pianos, are commonly tuned using equal temperament, in which all intervals other than octaves consist of irrational-number frequency ratios. Acoustic pianos are usually tuned with the octaves slightly widened, and thus with no pure intervals at all.