A particle dynamics simulation of "S + D" granular systems (where size and density drive segregation simultaneously) in various irregular shaped tumblers in the rolling regime (10(-4) < Fr < 10(-2)) has been performed. A new way of quantifying the state of mixing or segregation has been developed. Using this new measure of segregation (or entropy of mixing) we show that segregation is enhanced in elliptical tumblers as compared to circular ones and in rectangular tumblers as compared to square ones with the extent of enhancement determined by the aspect ratio of the tumbler. A spectral analysis of the oscillating entropy of mixing shows that in addition to the fundamental frequency of rotation of the tumbler, the evolving granular bed may exhibit harmonics corresponding to 2 times and even 3 times the fundamental frequency of rotation. We attribute this harmonic response to the drifting of the core of particles in addition to the stretching and contraction of the interface of the bed. (C) 2015 Elsevier B.V. All rights reserved.