Analysis and Modeling of Piano Sustain-Pedal Effects

Title
Analysis and Modeling of Piano Sustain-Pedal Effects
Authors
Heidi-Maria Lehtonen, Henri Penttinen, Jukka Rauhala, and Vesa Välimäki
Laboratory of Acoustics and Audio Signal Processing
Helsinki University of Technology
Espoo, Finland
Abstract
This paper describes the main features of the sustain-pedal effect in the piano through signal analysis and presents an algorithm for simulating the effect. The sustain pedal is found to increase the decay time of partials in the middle range of the keyboard, but this effect is not observed in the case of the bass and treble tones. The amplitude beating characteristics of piano tones are measured with and without the sustain pedal engaged, and amplitude envelopes of partial overtone decay are estimated and displayed. It is found that the usage of the sustain pedal introduces interesting distortions of the two-stage decay. The string register response was investigated by removing partials from recorded tones; it was observed that as the string register is free to vibrate, the amount of sympathetic vibrations is increased. The synthesis algorithm, which simulates the string register, is based on 12 string models that correspond to the lowest tones of the piano. The algorithm has been tested with recorded piano tones without the sustain pedal. The objective and subjective results show that the algorithm is able to approximately reproduce the main features of the sustain-pedal effect.
PACS numbers
43.75.Mn, 43.75.Zz, 43.75.Wx
Sound samples
    Recorded Tones with Synthetic and Real Sustain Pedal

    The example tones are played first without the sustain pedal and then with the synthetic and real sustain pedals, respectively. The tones are separated by 1 second of silence:

    [ (1) no sustain pedal --- (2) synthetic sustain pedal --- (3) real sustain pedal ]

  • C2
  • C3
  • Gb3
  • C4
  • A4
  • D5
  • Ab5
  • C6
  • A6

  • Examples of String Register Responses

    The residual signals are presented first without the sustain pedal engaged and then with the synthetic and real sustain pedals engaged, respectively. The signals are separated by 1 second of silence:

    [ (1) no sustain pedal --- (2) synthetic sustain pedal --- (3) real sustain pedal ]

  • C2res
  • C3res
  • Gb3res
  • C4res
  • A4res
  • D5res
  • Ab5res
  • C6res
  • A6res

  • Example tone without the dispersion filters

    The first sound example illustrates the effect of the dispersion filters. The sound example consists of two tones: the tone A4 (key index 49) is first processed with the sustain-pedal algorithm without the dispersion filters, and then the same tone is processed with the proposed algorithm, which contains the dispersion filters. The difference is best audible in the late decay; in the first tone it is more regular compared to the late decay of the second tone.

    The second sound example presents the residual signals of the same tones.

    Organization of tones in the sound example:

    [ (1) synthetic sustain pedal without the dispersion filters --- (2) synthetic sustain pedal with the dispersion filters ]

  • A4
  • A4res

 

http://www.acoustics.hut.fi/go/piano-pedal/
Author: Heidi-Maria Lehtonen
Modified: September 6, 2007 by Heidi-Maria Lehtonen

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