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In this paper, we present a connectionist approach to automatic transcription of polyphonic piano music. We first compare the performance of several neural network models on the task of recognizing tones from time-frequency representation of a musical signal. We then propose a new partial tracking technique, based on a combination of an auditory model and adaptive oscillator networks. We show how synchronization of adaptive oscillators can be exploited to track partials in a musical signal. We also present an extension of our technique for tracking individual partials to a method for tracking groups of partials by joining adaptive oscillators into networks. We show that oscillator networks improve the accuracy of transcription with neural networks. We also provide a short overview of our entire transcription system and present its performance on transcriptions of several synthesized and real piano recordings. Results show that our approach represents a viable alternative to existing transcription systems.