Algorithmic composition, which enables computer to generate music like human composers, has lasting charm because it intends to approximate artistic creation, most mysterious part of human intelligence. To deliver both melodious and refreshing music, this paper proposes the Musicality-Novelty Generative Adversarial Nets for algorithmic composition. With the same generator, two adversarial nets alternately optimize the musicality and novelty of the machine-composed music. A new model called novelty game is presented to maximize the minimal distance between the machine-composed music sample and any human-composed music sample in the novelty space, where all well-known human composed music products are far from each other. We implement the proposed framework using three supervised CNNs with one for generator, one for musicality critic and one for novelty critic on the time-pitch feature space. Specifically, the novelty critic is implemented by Siamese neural networks with temporal alignment using dynamic time warping. We provide empirical validations by generating the music samples under various scenarios.