Several musical scales, like the major scale, can be described as finite
arithmetic sequences modulo octave, i.e. chunks of an arithmetic sequence in a
cyclic group. Hence the question of how many different arithmetic sequences in
a cyclic group will give the same support set. We prove that this number is
always a totient number and characterize the different possible cases. In
particular, there exists scales with an arbitrarily large number of different
generators, but none with 14 generators.