Existing systems for automatic genre classification follows a supervised framework that extracts genre-specific information from manually-labeled music data and then identifies unknown music data. However, such systems may not be suitable for personal music management, because manually labeling music based on individually-defined genres can be labor intensive and subject to inconsistence from time to time. In this paper, we study an unsupervised paradigm for music genre classification. It is aimed to partition a collection of unknown music recordings into several clusters such that each cluster contains recordings in only one genre, and different clusters represent different genres. This enables users to organize their personal music database without needing specific knowledge about genre. This study investigates how to measure the genre similarities between music recordings and estimate the number of genres in a music collection. Our experiment results show the feasibility of clustering music recordings by genre.