Frequency temperament

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 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, this is the interval chain of an arithmetic temperament with a generator of 1.29 (440 cents) and period 2/1:

1.29 ≈ 440¢
2*1.29 - 1 = 1.58 ≈ 791¢
3*1.29 - 2 = 1.87 ≈ 1084¢
4*1.29 - 4 = 1.16 ≈ 257¢
5*1.29 - 5 = 1.45 ≈ 643¢
6*1.29 - 6 = 1.74 ≈ 960¢
7*1.29 - 8 = 1.03 ≈ 51¢
...

List of arithmetic temperaments

• Sqrttwo