When constrain the search space based on commonly-used scales in Western music the space collapses dramatically. Given that there have been successful copyright claims made on short phrases I think the idea of exhausting the search space for popular western music becomes a lot more plausible.

the actual computation was left as an exercise for the reader, but the issue is not the length of the scales, it is how they can be combined. take 10 notes and combine them in 16 ways. two small numbers, but how long to count to all 10^16 possiblities? or rephrased: how many days in 10 quadrillion seconds?