Diapason

In harmony, diapason is the ratio of 2:1 between a pair of frequencies or, equivalently, of 1:2 between a pair of wavelengths. It is the simplest ratio other than unison. It is the basis of the base 2 logarithm (lg x) system used in music (the mind naturally perceives pitches in terms of the logarithm of their frequency).

When constructing scales, a pair of notes related by diapason are considered to be equivalent. This relation is called octave equivalency, they are the same note, but on a different octave. This allows thinking of frequencies as wrapping around in a circle. The circle starts at unison and ends at diapason, except that unison and diapason are joined together to form the circle. Any frequency f which is smaller than 1 (unison) or larger than 2 (diapason) has an equivalent frequency within this circle:

where

.

Diapason is 10 in binary, and it is the sum of all the reciprocals of triangular numbers:

.

See also: unison, diapente.