A Model of Consonance for N-TET

 Simply, given a root note R and a harmony note H, let s equal the absolute value of the difference in semitones between the notes R and H, and N be the number of tone classes in the temperament. Then the consonance between R and H, C(R,H), is the square root of the ratio between the octaves per cycle of the interval and its steps to octave.

We compute the octaves per cycle, OPC, as s divided by the greatest common divisor between s and N, and the steps to octave STO as N divided by s. Then

N = 12,
s = |d(R,H)|,
OPC = s/GCD(s,N),
STO = N/s.

C(R,H) = sqrt(OPC/STO).

The way we interpret this model is as follows. The greater the resulting number, the greater the consonance between the given notes. Hence, the most consonant interval is the unison. So, its consonance is defined as infinite.

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