This paper describes our attempt to make the Hidden Markov Model (HMM) score following system developed at Ircam sensible to past experiences in order to obtain better audio to score real-time alignment for musical applications. A new observation modeling based on Gaussian Mixture Models is developed which is trainable using a learning algorithm we call automatic discriminative training. The novelty of this system lies in the fact that this method, unlike classical methods for HMM training, is not concerned with modeling the music signal but with correctly choosing the sequence of music events that was performed. Besides obtaining better alignment, new system's parameters are controllable in a physical manner and the training algorithm learns different styles of music performance as discussed. Experience with the piece "...explosante-fixe..." by Boulez, and with an advanced karaoke system that allows to sing ballads in free tempo with automatic accompaniment are given.