Single vs. three string unisons

[Jim]

Dear Joel:

I did do the test where I use a length of soft felt placed lengthwise
between two strings of a unison to see if there was a difference.  I
could not see that the weight of the rubber mutes was a factor.

I believe that the cause has to do with string coupling at the bridge.
There is a book of five lectures on "The Acoustics Of The Piano" which is
edited by Anders Askenfelt.  It is publication #64 of the Royal
Swedish Academy of Music.  This was done in Stockholm in 1990.  One
of the lectures deals with string coupling at the bridge.  I don't
understand all I know about coupling, but it seems to me that here is
where the cause of the difference between single string and full unison
frequencies occurs.

I must emphasize that there is little difference of freq., but still some;
and, it is most noticeable from around notes 49 to around 66.

A simple test, to show that a rubber mute does take on hammer energy, is to
merely touch the rubber mute while a string is struck.  If you feel any-
thing, that is energy.  A mute is a damper, felt is a damper. fingers can
be used as dampers.  I liked Dave Porritt's comment about all 3 strings
receiving the same hammer energy.  The two damped strings just
refuse to get in line with the free string.

Jim Coleman, Sr.

On Wed, 6 Nov 1996, Joel Rappaport wrote:

> Dave Porritt has and interesting observation that I have been wondering
> about while following this subject.  Does a rubber mute absorb energy
> from a hammer blow, or does it transform the muted string(s) into
> immovable objects so that *all* of the hammer energy goes into the
> unmuted string(s)?
>
> If we make an assumption that a _rubber_ mute will not take on hammer
> energy and a _felt_ mute, however, will absorb the energy - taking
> energy away from the unmuted string(s) - maybe there is a measurable
> difference.  Maybe the pitch level (not to mention energy output) of the
> individual strings vs. the whole unison can be measured.  Has anyone
> tried these tests with both kinds of mutes?
>
> I use felt mutes made of hammer head material, cut and shaped
> appropriately.  Of course, if the above assumption is not true, there is
> always the <Delete> button up there.....
>
> Joel Rappaport
>
> David Porritt wrote:
> >
> > --snip
> >
> > > Dean observed that a given "hammer blow strength" might generate
> > > greater amplitude in a single string  with the other two muted compared to
> > > the amplitude of all three strings excited by an equal blow - that more of
> > > the force of the blow would be focused on one string, and that this might
> > > account for the pitch difference between single and three string unisons. I
> > > think that is the most satisfctory explanation I have heard, but I don't see
> > > why the SAT wouldn't pick it up.
> >
> > --snip
> >
> > The hammer is still striking 3 strings even when 2 are muted.  The energy
> > is going in to all the strings, it's just that the energy from two of
> > them is being dissipated by the mute.  I really think the 1 singing
> > string doesn't get any more energy in either case.
> >
> > dave
> >
> > _______________________________________________
> >
> > David M. Porritt, RPT
> > Meadows School of the Arts
> > Southern Methodist University
> > Dallas, Texas
> > _______________________________________________
>