hammer/string interaction

[Stephen Birkett]

Larry Fischer wrote:
>
> The hammer that comes off the string really fast, isn't dampening the really
> high harmonics.  As I understand it, the high harmonics start their journey
> down the string to the termination point at the time of attack.  They reach
> the termination point, make a return trip back up the string and if they
> encounter the hammer still on the string, they're dampened.
> If I got this right, the fundamental and the rest of the lower
> harmonics take a bit longer to make the trip since they're moving
> at a wider amplitude. (dude)
>
The amplitude will not affect the speed of propagation. It is true
that the higher harmonics will travel slightly faster (a phenomenon
known as dispersion), which has the effect of altering the waveform
as it moves down the string...this is a consequence of the non-
linearity of the string. The bigger inharmonicity B the more
dispersion. But dispersion will have no effect on the dynamics of
hammer/string interaction.

> A really light hammer won't have the mass to move the string as much,
> therefore, the fundamental will have less amplitude as will all the
> consequental  multiples, although not as noticably, since they don't have
> that much amplitude to loose in the first place. [...]
>
The transfer of energy from hammer to string is actually quite
inefficient (as are most mechanical energy transfers). The heavy
hammer interaction is actually *less* efficient in energy transfer,
since the hammer must be accelerated away by the string...light
hammers require less energy to push them away, thus leaving more in
the vibrating string.

It is true that in some cases the hammer will still be in contact with
the string when the pulse is reflected from the near end of the
string and returns to the hammer contact point. In some cases the
hammer will lose contact and re-contact one or several times in the
overall interaction. These cases are typically in the *heavy*
hammer/bass string region. `Light' hammers will be immediately
accelerated away from the string before the pulse returns.

Come see my talk on this topic in Dearborn. I'll be presenting some
results from a preliminary computer modelling project of the
hammer/string interaction. There are still many unanswered questions
about this topic which has to be analysed in relation to the action
dynamics, soundboard, etc. That is the subject of a new project for
which I've been trying to get support...if I ever get together the
funding to start on it we may see some interesting results!

Stephen Birkett (Fortepianos)
Authentic Reproductions of 18th and 19th Century Pianos
Waterloo, Ontario, Canada
tel: 519-885-2228
fax: 519-763-4686