Analysis, perception, and synthesis of the piano sound

Heidi-Maria Lehtonen

Research output: ThesisDoctoral ThesisCollection of Articles


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.
Translated title of the contributionAnalysis, perception, and synthesis of the piano sound
Original languageEnglish
QualificationDoctor's degree
Awarding Institution
  • Aalto University
  • Välimäki, Vesa, Supervising Professor
  • Välimäki, Vesa, Thesis Advisor
Print ISBNs978-952-60-3412-6
Electronic ISBNs978-952-60-3413-3
Publication statusPublished - 2010
MoE publication typeG5 Doctoral dissertation (article)


  • acoustics
  • digital signal processing
  • music
  • sound synthesis


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