| What makes a good piano performance? An expressive piano performance owes its emotive power to the performer's skills in shaping the music with nuances. For the purpose of performance analysis, nuance can be defined as any subtle manipulation of sound parameters including attack, timing, pitch, loudness and timbre. A major obstacle to a systematic computational analysis of musical nuances is that it is often difficult to uncover relevant sound parameters from the complex audio signal of a piano music performance. A piano piece invariably involves simultaneous striking of multiple keys, and it is not obvious how one may extract the parameters of individual keys from the combined mixed signal. This problem of parameter extraction can be formulated as a source separation problem. Our research goal is to extract individual tones (frequencies, amplitudes and phases) from a mixture of piano tones.;We propose a Bayesian monaural source separation system to extract each individual tone from mixture signals of piano music performance. Specifically, tone extractions can be facilitated by model-based inference. Two signal models based on summation of sinusoidal waves were employed to represent piano tones. The first model is the traditional General Model, which is a variant of sinusoidal modeling, for representing a tone for high modeling quality; but this model often fails for mixtures of tones. The second model is an instrument-specific model tailored for the piano sound; its modeling quality is not as high as the traditional General Model, but its structure makes source separation easier. To exploit the benefits offered by both the traditional General Model and our proposed Piano Model, we used the hierarchical Bayesian framework to combine both models in the source separation process. These procedures allowed us to recover suitable parameters (frequencies, amplitudes, phases, intensities and fine-tuned onsets) for thorough analyses and characterizations of musical nuances. Isolated tones from a target recording were used to train the Piano Model, and the timing and pitch of individual music notes in the target recording were supplied to our proposed system for different experiments. Our results show that our proposed system gives robust and accurate separation of signal mixtures, and yields a separation quality significantly better than those reported in previous works. |
