We present a music information retrieval approach based on power laws. Research in cognitive science and neuroscience reveals connections between power laws, human cognition, and human physiology. Empirical studies also demonstrate connections between power laws and human aesthetics. We utilize 250+ power-law metrics to extract statistical proportions of music-theoretic and other attributes of music pieces. We discuss an experiment where artificial neural networks classify 2,000 music pieces, based on aesthetic preferences of human listeners, with 90.70% accuracy. Also, we present audio results from a music information retrieval experiment, in which a music search engine prototype retrieves music based on "aesthetic" similarity from a corpus of 15,200+ pieces. These results suggest that power-law metrics are a promising model of music aesthetics, as they may be capturing statistical properties of the human hearing apparatus.