Leveling of strings

[Michael J. Wathen]

I've been thinking about this problem.  What I think now is that it has
nothing to do with the relative phases of the three strings.  More likely,
the strange sound that occurs when the hammer strikes strings that are not
level, is in fact due to the motion of the hammer. 

Suppose the left string of a unison is slightly higher.  This means that the
hammer will strike the middle and right string first causing a Torque force
to be applied to the hammer head. The hammer would then twist and possibly
slide slightly up to make its contact to the left string of the unison.  The
resulting motion of the hammer head from then until it actually leaves all
of three strings behind would be a kind of quiver effect.

There was the argument on Pianotech a couple of years ago about how the
hammer string contact time effected the dampening of higher partials.  I
remember that the consensus seemed to be the belief that the longer the
hammer remained in contact with the string the more the higher partials were
dampened. I presented what I thought was a more likely scenario that applies
to the leveling question as well. My belief is that the contact time changes
the shape of the traveling wave on the string.  The shape of the wave on the
string is not completely determined until the moment the hammer leaves the
string. Why is the different from the consensus model above?  The consensus
model has the hammer resting against the string and high frequency waves
returning from the termination points of the string being absorbed and
essentially killed by the hammer still in contact with the string. The
assumption is that these little high frequency wavelets return from the
termination points first.  My idea is that these little wavelets do not
separate themselves from the main impulse and travel at a faster speed down
the string. In fact, that's not possible in the standard string equation
model except for the longitudinal modes of the string. 

In the case of non-level strings,the wave shape due to the contact of the
hammer's twisting while contacting would certainly give a more out of the
ordinary shape to the wave on the string. 
++++++++++++++++++++++++++++++++++
Michael J. Wathen, Rpt
Cincinnati, Ohio USA
michael.wathen@uc.edu

http://ucccm56.ccm.uc.edu