Sound SamplesHere are some results from our piano modeling project. These are calculated piano tones, computed using only Newton's laws (i.e., F=ma). In addition, ALL of the parameters of the calculation have been determined from separates studies of hammers, strings, soundboards, etc. None of the parameters have been adjusted so as to make the tones sound good. C4 is middle C, so these scales begin two octaves below middle C, and go up to the note two octaves above.
These sound files are in AIFF format, so if your brouser cannot play them directly, it will probably give you the choice of downloading the files.
A full discussion of our modeling calculations will be given in a paper
which we are now in the process of writing. We'll post it here soon.
First we will calibrate your ear. Here are some recorded sounds from
my grand piano (a Steinway model M).
Next are calculated sounds in which only the motion of the strings is
computed. The soundboard and the room are basically ignored.
The results are suprisingly good (in our opinion).
Next are calculated sounds in which the strings,
soundboard, and room are all included. The hammers are assumed
to have reversible, power law force-compression characteristics.
The results are not bad, but sound a bit "plucked" in the
We are now working on experiments to investigate the hysteretic behavior of piano hammers. It turns out that the simple power law force equation used above does not describe real hammers very well, at least when they are hitting piano strings. Our plan is to then use the measured hysteretic behavior in our simulations. We'll put results here as soon as we have them.
Copyright © 2003 Piano Physics at Purdue Team