Frequency temperament: Difference between revisions
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'''Arithmetic temperaments''' are the arithmetic counterpart to [[regular temperament]]s. Whereas regular temperaments are created by | '''Arithmetic temperaments''' are the arithmetic counterpart to [[regular temperament]]s. Whereas regular temperaments are created by reducing integer powers of a [[generator]], an arithmetic temperament is created by reducing integer multiples of a generator. The nth step of an arithmetic temperament is given by x<sub>n</sub> = ng mod 1 + 1, where g is the generator andpn is the period. | ||
== Example == | |||
Cconsider an arithmetic temperament with a generator of 1.29 (440 cents) and period [[2/1]]. | |||
== List of arithmetic temperaments == | == List of arithmetic temperaments == | ||
Revision as of 05:12, 2 March 2023
Arithmetic temperaments are the arithmetic counterpart to regular temperaments. Whereas regular temperaments are created by reducing integer powers of a generator, an arithmetic temperament is created by reducing integer multiples of a generator. The nth step of an arithmetic temperament is given by xn = ng mod 1 + 1, where g is the generator andpn is the period.
Example
Cconsider an arithmetic temperament with a generator of 1.29 (440 cents) and period 2/1.