Frequency temperament

Arithmetic interval chains are interval chains similar to regular temperaments. Whereas regular temperaments are created by reducing integer powers of a generator, an arithmetic interval chain is created by reducing integer multiples of a generator. The n-th interval in an arithmetic interval chain prior to octave-reduction is given by n*g + 1, where g is the generator.

For example, this is an arithmetic interval chain with a generator of 0.29 and period 2/1:

1+0.29 = 1.29
1+2*0.29 = 1.58
1+3*0.29 = 1.87
1+4*0.29 = 2.16 -> 1.08
1+5*0.29 = 2.45 -> 1.225
1+6*0.29 = 2.74 -> 1.37
...

List of arithmetic interval chains

• Sqrttwo
• Neutrino