I'm not clear whether your intention is to write a "perfect music shuffler" or some sort of general purpose "pattern destroying" shuffler;

in the latter case, note that if we pick a random permutation of n numbers in [0,n-1] ( or equivalently and more correctly, if we sample a uniformly distributed random variable in the group of permutations of order n ) then the permutation "0 1 2 3 4 5 6 7 8 9" has the same probability of "4 7 9 5 0 6 4 1 8 2".
Therefore, "patterness" and "probability evenness" are two unrelated concepts.

Now, in physics ( and with a slightly different sense in information theory ) there is a measure of some basic notion of "patterness": the entropy. Hence, one option is to find a permutation that maximze a properly defined entropy. This might or might not solve your problem depending on what you exactly mean by "patterness". Indeed, we simply have recasted the problem into finding a suitable entropy definition for the system that satisfy your "patterness" condition.

This is a simpler problem in physics because there is (often) a physically natural notion of entropy. This is a simpler problem in information theory because there are natural notions of entropies in information systems ( Shannon entropy , Fisher entropy, and so on ... each with their own interpretations and relations ).

You need to make clear what you mean by "patterness" first, because there's no such universal concept.

Conversely, if your intent is to write a "perfect XXX shuffler", where XXX is some human related to-be-shuffled-thing, then "patterness" becomes a psychophysical property: you measure what makes a sequence of XXX's perceived as "patterned" by a prescribed population of humans in a prescribed environment, then you use those measurements to design random variables over sets of integer sequences that minimize the probability that a unifomly sampled human utters "hey, there's an annoying pattern there !".