We present an approach to music identification based on weighted finite-state transducers and Gaussian mixture models, inspired by techniques used in large-vocabulary speech recognition. Our modeling approach is based on learning a set of elementary music sounds in a fully unsupervised manner. While the space of possible music sound sequences is very large, our method enables the construction of a compact and efficient representation for the song collection using finite-state transducers. This paper gives a novel and substantially faster algorithm for the construction of factor transducers, the key representation of song snippets supporting our music identification technique. The complexity of our algorithm is linear with respect to the size of the suffix automaton constructed. Our experiments further show that it helps speed up the construction of the weighted suffix automaton in our task by a factor of 17 with respect to our previous method using the intermediate steps of determiniza...