Analysis, perception, and synthesis of the piano sound

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Aalto-yliopiston teknillinen korkeakoulu | Doctoral thesis (article-based)
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Report / Helsinki University of Technology, Department of Signal Processing and Acoustics, 21
This thesis deals with the signal analysis, auditory perception, and physics-based synthesis of the piano sound. Contributions of this thesis can be grouped into four main categories: Analysis and modeling of the sustain pedal effect, analysis of harmonic and inharmonic musical tones by means of an inverse comb filter, loss filter design for waveguide piano synthesis, and perception of longitudinal vibrations in piano tones. The sustain pedal effect is studied through signal analysis of recorded tones, and the results show that the use of the sustain pedal increases the decay times of middle range tones, increases beating, and makes the sounds more reverberant. Based on the results, an algorithm is designed for simulating the sustain pedal effect. Objective and subjective studies show that the algorithm is capable of producing the main effects of the sustain pedal. The signal analysis of tones played with a partial sustain pedal reveals that the tone decay can be divided into three distinct time intervals, namely the initial decay, the damper-string interaction, and the final free vibration. Additionally, the nonlinear amplitude limitation during the damper-string interaction can excite missing modes in the lowest piano tones. Decomposition of harmonic and inharmonic musical instrument tones to tonal and noise components and selecting single partials with an inverse comb filter structure is discussed. The filters are designed based on the fundamental frequency and the inharmonicity coefficient, and they are found to provide a simple and efficient analysis tool for musical signals. A multi-stage ripple filter structure for modeling the complicated decay process of the piano tones is presented. The filter is capable of accurately matching a desired number of partial decay times or, alternatively, modeling the overall decay characteristics of a piano tone. Finally, the threshold of audibility is sought for perception of longitudinal components in fortissimo piano tones through formal listening tests. The results suggest that the longitudinal components are audible up to note C5 (fundamental frequency 523 Hz), but based on the listeners' opinions modeling the longitudinal components in a piano synthesizer up to note A3 (fundamental frequency 220 Hz) only is sufficient.
Supervising professor
Välimäki, Vesa, Prof.
Thesis advisor
Välimäki, Vesa, Prof.
acoustics, digital signal processing, music, sound synthesis
Other note
  • [Publication 1]: Heidi-Maria Lehtonen, Henri Penttinen, Jukka Rauhala, and Vesa Välimäki. 2007. Analysis and modeling of piano sustain-pedal effects. The Journal of the Acoustical Society of America, volume 122, number 3, pages 1787-1797. © 2007 Acoustical Society of America. By permission.
  • [Publication 2]: Heidi-Maria Lehtonen, Anders Askenfelt, and Vesa Välimäki. 2009. Analysis of the part-pedaling effect in the piano. The Journal of the Acoustical Society of America Express Letters, volume 126, number 2, pages EL49-EL54. © 2009 Acoustical Society of America. By permission.
  • [Publication 3]: Heidi-Maria Lehtonen, Vesa Välimäki, and Timo I. Laakso. 2008. Canceling and selecting partials from musical tones using fractional-delay filters. Computer Music Journal, volume 32, number 2, pages 43-56. © 2008 Massachusetts Institute of Technology (MIT). By permission.
  • [Publication 4]: Heidi-Maria Lehtonen. 2008. Analysis of piano tones using an inharmonic inverse comb filter. In: Jyri Pakarinen, Cumhur Erkut, Henri Penttinen, and Vesa Välimäki (editors). Proceedings of the 11th International Conference on Digital Audio Effects (DAFx 2008). Espoo, Finland. 1-4 September 2008. Pages 333-340. ISBN 978-951-22-9516-6. © 2008 by author.
  • [Publication 5]: Heidi-Maria Lehtonen, Jukka Rauhala, and Vesa Välimäki. 2005. Sparse multi-stage loss filter design for waveguide piano synthesis. In: Proceedings of the 2005 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA 2005). New Paltz, NY, USA. 16-19 October 2005. Pages 331-334. ISBN 0-7803-9154-3. © 2005 Institute of Electrical and Electronics Engineers (IEEE). By permission.
  • [Publication 6]: Balázs Bank and Heidi-Maria Lehtonen. 2010. Perception of longitudinal components in piano string vibrations. The Journal of the Acoustical Society of America Express Letters, volume 128, number 3, pages EL117-EL123. © 2010 Acoustical Society of America. By permission.