Physical Modeling of the Piano
- PDF / 711,274 Bytes
- 8 Pages / 600 x 792 pts Page_size
- 41 Downloads / 190 Views
Physical Modeling of the Piano N. Giordano Department of Physics, Purdue University, 525 Northwestern Avenue, West Lafayette, IN 47907-2036, USA Email: [email protected]
M. Jiang Department of Physics, Purdue University, 525 Northwestern Avenue, West Lafayette, IN 47907-2036, USA Department of Computer Science, Montana State University, Bozeman, MT 59715, USA Email: [email protected] Received 21 June 2003; Revised 27 October 2003 A project aimed at constructing a physical model of the piano is described. Our goal is to calculate the sound produced by the instrument entirely from Newton’s laws. The structure of the model is described along with experiments that augment and test the model calculations. The state of the model and what can be learned from it are discussed. Keywords and phrases: physical modeling, piano.
1.
INTRODUCTION
This paper describes a long term project by our group aimed at physical modeling of the piano. The theme of this volume, model based sound synthesis of musical instruments, is quite broad, so it is useful to begin by discussing precisely what we mean by the term “physical modeling.” The goal of our project is to use Newton’s laws to describe all aspects of the piano. We aim to use F = ma to calculate the motion of the hammers, strings, and soundboard, and ultimately the sound that reaches the listener. Of course, we are not the first group to take such a Newton’s law approach to the modeling of a musical instrument. For the piano, there have been such modeling studies of the hammer-string interaction [1, 2, 3, 4, 5, 6, 7, 8, 9], string vibrations [8, 9, 10], and soundboard motion [11]. (Nice reviews of the physics of the piano are given in [12, 13, 14, 15].) There has been similar modeling of portions of other instruments (such as the guitar [16]), and of several other complete instruments, including the xylophone and the timpani [17, 18, 19]. Our work is inspired by and builds on this previous work. At this point, we should also mention how our work relates to other modeling work, such as the digital waveguide approach, which was recently reviewed in [20]. The digital waveguide method makes extensive use of physics in choosing the structure of the algorithm; that is, in choosing the proper filter(s) and delay lines, connectivity, and so forth, to properly match and mimic the Newton’s law equations of motion of the strings, soundboard, and other components of
the instrument. However, as far as we can tell, certain features of the model, such as hammer-string impulse functions and the transfer function that ultimately relates the sound pressure to the soundboard motion (and other similar transfer functions), are taken from experiments on real instruments. This approach is a powerful way to produce realistic musical tones efficiently, in real time and in a manner that can be played by a human performer. However, this approach cannot address certain questions. For example, it would not be able to predict the sound that would be produced if a radically new type of soundboard was empl
Data Loading...
