The Diapason reference article from the English Wikipedia on 24-Apr-2004
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Diapason

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The word diapason is used in a number of musical contexts. Generally is can mean the range of a musical instrument or voice. It also has more specific uses:

Table of contents
1 The organ stop
2 In harmony
3 The diapason normal

The organ stop

The diapason is the principal stop of the pipe organ, which has pipes throughout the entire range of the instrument. Diapason pipes give the organ its characteristic sound.

Diapasons come in two varieties: open, where the end of the pipe is clear, producing a bright sound; and stopped where the end of the pipe is blocked, producing a more muffled, sweeter sound. The name diapason is also used on some electric organs for voices which imitate the pipe organ stop.

In harmony

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.

The diapason normal

Diapason normal is the name given to the historical pitch standard (see pitch) where the A above middle C is tuned to 435 Hertz. This standard was set by law in 1859 in France, and the standard became popular throughout Europe. Nowadays, A=440Hz is more normal.