Modal distribution analysis and sum of sinusoids synthesis of piano tones.
Rowena Cristina L. Guevara · Deep Blue (University of Michigan) · 1997
The analysis and synthesis of piano tones were the challenges undertaken in this research. In this thesis, it is shown that it is possible to synthesize a piano tone as a sum of sinusoids which is aurally indiscriminable from the real piano tone. This follows from an exhaustive characterization of the piano tone using the modal distribution analysis. Results that are consistent with documented piano features in the literature are presented. The analysis also revealed that the piano tone consists of two partial series, one of which has not been widely reported. This partial series was carefully studied and demonstrated to be important in the synthesis of piano tones. Scales of notes with different articulation, dynamics and initial damper position, recorded from three acoustic pianos were used in the study. These were analyzed using the modal distribution which is a time-frequency distribution with the Pielemeier and Wakefield modal kernel. Amplitude and frequency estimates from the modal distribution together with models of piano tone onsets were used in the synthesis. These models were developed to compensate for estimation inaccuracies around the tone onset, and consequently, to achieve perceptual equivalence between the original and the synthesized piano tone. A pole cluster model which accounts for non-string sounds was used in the synthesis of mid- to high-frequency piano tones. For the low-frequency range, the onset was modeled using back-extended exponential decay. Psychophysical listening experiments were performed to determine the discriminability of the synthesized from real piano tones. The results of both analysis and synthesis suggest that it is possible to create real-sounding piano tones from a sum of sinusoids.