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Diatessaron (interval)

In harmony, the diatessaron is a ratio of 4:3 (sesquitertium) between a pair of frequencies or, equivalently, a ratio of 3:4 between a pair of wavelengths. It is the harmonic mean of unison and diapason:

{ 2 \over {1 \over 1:1} + {1 \over 2:1}} = {2 \over 1:1 + 1:2} = {2 \over 3:2} = 4:3 \ .

It is equal to diapason divided by diapente:

{2:1 \over 3:2} = {2 \cdot 2 \over 3 \cdot 1} = 4:3,

therefore it is the inversion of diapente.

It is the sum of the first 2 reciprocals of triangular numbers:

{1 \over 1} + {1 \over 3} = {4 \over 3}

and it is 1.01010101... in binary.

It is also called perfect fourth.

See also: unison, diapason, diapente, ditonus, semiditonus, tonus, semitonium.

Last updated: 06-24-2005 09:50:56
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