The doctoral dissertations of the former Helsinki University of Technology (TKK) and Aalto University Schools of Technology (CHEM, ELEC, ENG, SCI) published in electronic format are available in the electronic publications archive of Aalto University - Aaltodoc.

Physics-Based Parametric Synthesis of Inharmonic Piano Tones

Jukka Rauhala

Dissertation for the degree of Doctor of Science in Technology to be presented with due permission of the Department of Electrical and Communications Engineering for public examination and debate in Auditorium S4 at Helsinki University of Technology (Espoo, Finland) on the 14th of December, 2007, at 12 o'clock noon.

Overview in PDF format (ISBN 978-951-22-9066-6)   [981 KB]
Dissertation is also available in print (ISBN 978-951-22-9065-9)


This dissertation studies methods for developing a parametric piano synthesis model using the physics-based approach. The goal is to develop a model that can be controlled with physically meaningful parameters. Moreover, the model is required to be computationally efficient for real-time implementation. The basis of this work is to use the digital waveguide technique for implementing a piano string model. The excitation signal, simulation of dispersion, the beating effect, and simulation of sympathetic resonances are considered. Novel and improved simulation methods are developed for each of these aspects by applying signal processing techniques and knowledge of the human auditory system. The new simulation methods include a novel excitation model with parametric control and the first closed-form design method for dispersion filter design. In addition, two new beating effect simulation methods suitable for parametric real-time synthesis are created. One of the developed methods can be also used for modifying the partial envelopes in recorded tones. Furthermore, an efficient and improved method for simulation of sympathetic resonances has been suggested. Additionally, a novel analysis method for estimating inharmonicity coefficient values from recorded tones, which is needed for high-quality synthesis, is developed giving good results. Finally, a real-time piano synthesis model without any sampled sounds is implemented using the developed simulation methods in collaboration with the Sibelius Academy. The model can be controlled in real-time using physical parameters, such as the fundamental frequency and the inharmonicity coefficient value. The implementation suggests that the goals set for this thesis work are met. The results can be applied to physics-based piano synthesis. The methods can be used to implement a synthesis model for restricted environments, and they can be used to produce test tones for evaluating properties of the human auditory system and testing signal analysis algorithms.

Sympathetic resonance simulation demonstration samples

These are sample files to demonstrate the sympathetic resonance simulation technique. This example simulates the so-called "silent chord" case, where two notes are first played silently (E4 and G4), and then a loud staccato note is played (C2). If the sympathetic resonances are simulated correctly, the loud staccato note should transfer energy to the other strings as well. All samples are in PCM WAV 44.1 kHz 16-bit format.

Synthetic piano tone without/with sympathetic resonances:

This thesis consists of an overview and of the following 7 publications:

  1. J. Rauhala and V. Välimäki, Tunable dispersion filter design for piano synthesis, IEEE Signal Processing Letters, vol. 13, no. 5, pp. 253-256, 2006. © 2006 IEEE. By permission.
  2. J. Rauhala and V. Välimäki, Dispersion modeling in waveguide piano synthesis using tunable allpass filters, in Proceedings of the 9th International Conference on Digital Audio Effects, Montreal, Canada, 2006, pp. 71-76. © 2006 by authors.
  3. J. Rauhala and V. Välimäki, Parametric excitation model for waveguide piano synthesis, in Proceedings of the 2006 IEEE International Conference on Acoustics, Speech, and Signal Processing, Toulouse, France, 2006, pp. 157-160. © 2006 IEEE. By permission.
  4. J. Rauhala, H.-M. Lehtonen, and V. Välimäki, Toward next-generation digital keyboard instruments, IEEE Signal Processing Magazine, vol. 24, no. 2, pp. 12-20, 2007. © 2007 IEEE. By permission.
  5. J. Rauhala, H.-M. Lehtonen, and V. Välimäki, Fast automatic inharmonicity estimation algorithm, Journal of the Acoustical Society of America, vol. 121, no. 5, pp. EL184-EL189, 2007. © 2007 Acoustical Society of America. By permission.
  6. J. Rauhala, The beating equalizer and its application to the synthesis and modification of piano tones, in Proceedings of the 10th International Conference on Digital Audio Effects, Bordeaux, France, 2007, pp. 181-187. © 2007 by author.
  7. J. Rauhala, M. Laurson, V. Välimäki, H.-M. Lehtonen, and V. Norilo, Physics-based piano synthesizer, Helsinki University of Technology, Laboratory of Acoustics and Audio Signal Processing, Report 84, 2007. Computer Music Journal, submitted for publication on June 29th, 2007.

Keywords: acoustic signal processing, digital signal processing, music

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© 2007 Helsinki University of Technology

Last update 2011-05-26