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 reducing integer powers of a [[generator]], an arithmetic temperament is created by reducing integer multiples of a generator. The n-th interval in an arithmetic temperament is given by ng mod (p - 1) + 1, where g is the generator and p is the period. | '''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 n-th interval in an arithmetic temperament is given by ng mod (p - 1) + 1, where g is the generator and p is the period. | ||
For example, | For example, this is the interval chain of an arithmetic temperament with a generator of 1.29 (440 cents) and period [[2/1]]: | ||
<pre> | <pre> | ||
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5*1.29 - 5 = 1.45 ≈ 643¢ | 5*1.29 - 5 = 1.45 ≈ 643¢ | ||
6*1.29 - 6 = 1.74 ≈ 960¢ | 6*1.29 - 6 = 1.74 ≈ 960¢ | ||
7*1.29 - 8 = 1.74 ≈ 51¢ | |||
... | ... | ||
</pre> | </pre> | ||