Voicing and Inharmonicity

[Robert Scott]

Jim Coleman Sr. wrote:

>There are those who have measured differences in inharmonicity as a
>result of voicing.  Whether or not we understand just why is not germaine
>to the issue. There are also some who have measured the difference in
>pitch produced by 3 identical strings individually as compared to the
>3 strings in unison. Whether or not we can explain it is inconsequential.
>It is just there.

  I'm not sure what you mean when you say understanding of why inharmonicity
changes is not germaine to the issue.  If you mean that we must accept
an observed phenomenon even when we can't explain it, then I agree with
you.  All I'm asking for is a solid observation.  But consider this.  The
stories
about inharmonicity changing as the result of voicing seem to be always
attributed to "others".  Not a single person has responded to my question
by saying that he has personally measured an inharmonicity change of
"x" cents on a particular string  after voicing.   Inharmonicity is difficult to
measure precisely in any case, and it is affected by a wide variety of other
things, including tuning.  Doesn't it stand to reason that if a person only
rarely observes the cause and effect that perhaps he is really experiencing
observational error?  Perhaps in the process of voicing, the tuning changed,
which changed the inharmonicity.  Also consider this:  if changing voicing
a little bit changes inharmonicity somewhat, then doesn't it stand to reason
that changing voicing a lot ought to change inharmonicity even more?  So if
you were trying to construct an experiment to measure the effect, it would
make sense that you would use a very large change in voicing so that
it would be easier to see the change in inharmonicity.  And what change
in voicing could be more severe than using a wooden paint stirring stick
instead of a felt hammer?  That's what I used and I didn't measure any
change in the inharmonicity.  Furthermore, if Inventronics recommends
plucking the string to measure the inharmonicity when the normal played
note doesn't have sufficient partial content, then aren't they implicitly
counting on the fact that it doesn't matter how the string is excited when
you are measuring inharmonicity?

By the way, the effect that you mentioned about unison pitches interacting
when played together as opposed to separately is real and was explained
quite well by Gabriel Weinreich in his excellent ariticle in Scientific
American,
January 1979, Pg. 118.

Jim goes on to say:

>My reasons for the inharmonicity differences that are measured due only
>to voicing changes go like this.  We know that piano string sounds are
>transient. Energy vaccilates between several partials as the piano sound
>decays.  Sonographs show this undulating effect. As one partial increases
>in amplitude (and hence its tension increase at that freq.) the pitch of
>that partial changes.

I think this is a misinterpretation of the sonographs.  Yes, the partials in
the sound do vaccilate up and down in amplitude, but that doesn't mean
the energy of the partial in the string is going up and down in the same
way.  The up and down component of the string vibration couples into
the bridge and soundboard a lot more than the side-to-side component, because
the bridge and soundboard are a lot more compliant in the up and down direction.
So if the vibration precesses between up and down and side to side, the sound
coming out of the soundboard will appear to vaccilate.  But the extent of
the vibrations in the string might not be changing at all.  So we cannot
conclude from the sonograph vaccilations that the string tension is vaccilating.

I agree that the change in string tension due to the amplitude of vibrations
does
affect the pitch of the fundamental and the partials.  But this is generally
noticeable only for quite heavy blows.  As the note dies out, the "extra"
tension
due to vibrations becomes an inconsequential part of the total string tension,
and I would think that most people would note consider the "true" pitch to be
the pitch that the string settles to as the note decays - not the pitch that is
observed just shortly after a heavy blow.  So if this vibration-induced tension
change is used to explain inharmonicity changes as a result of voicing, then all
it really might explain is inharmonicity changes as a result of how hard the
note
is played.

   -Bob Scott
    Ann Arbor, Michigan