This paper deals with the computational analysis of musical audio from recorded audio waveforms. This general problem includes, as sub-tasks, music transcription, extraction of musical pitch, dynamics, timbre, instrument identity, and source separation. Analysis of real musical signals is a highly ill-posed task which is made complicated by the presence of transient sounds, background interference or the complex structure of musical pitches in the time-frequency domain. This paper focuses on models and algorithms for computer transcription of multiple musical pitches in audio, elaborated from previous work by two of the authors. The audio data are supposedly pre-segmented into fixed pitch regimes such as individual chords. The models presented apply to pitched (tonal) music and are formulated via a Gabor representation of non-stationary signals. A Bayesian probabilistic structure is employed for representation of prior information about the parameters of the notes. This paper introduces a numerical Bayesian inference strategy for estimation of the pitches and other parameters of the waveform. The improved algorithm is much quicker, and makes the approach feasible in realistic sitautions. Results are presented for estimation of a known number of notes present in randomly generated note clusters from a real musical instrument database.