Soundboards and Inharmonicity

[Richard Moody]

> Richard Moody writes:
>
> >I am asking if soundboards DO have inharmonicity?   If so,
> >how do you find out how much?
>    ...snip...
> >I say that if a vibrating string has inharmonicity due to stiffness
> >and diameter, then a vibrating sound board MIGHT have inharmonicity
> >in itself due to stiffness and diameter.(thickness).
>
> Richard, let me see if I can clear up what the issue really is.
> In trying to answer the question "Does the soundboard affect the
> inharmonicity of the strings" it is a mistake to focus on the
> soundboard as a separate item with its own "inharmonicity".

I don't know. It is hard to see how a steel string changes in inharmonicity
unless it changes in tension.  That is the only thing you can do to a piano
string until you replace it.  That voicing would make the partials'
frequency change is hard to comprehend. They say Ih is due to stiffness and
all the formulas I have seen take only that into account besides length,
freq, diameter, and tension. A soundboard only vibrates when a string does.
So whether or not it (SB) has its own iharmonicity matters only if the way
it (SB) is vibrating affects the inharmonicity being measured.  After all
when using a microphone we are recording how the
soundboard itself is vibrating.  The string is only exciting the SB.  That
the SB is reproducing the exact freq of the partials of the string is being
assumed.  However I think a couple of issues should be resolved before we do
focus on
the SB.  The problem (question) is----that inharmonicity measurements have
been reported to be changed from day to day, does soundboard conditions
affect these readings?   I think before we consider these changes real, we
ought to focus on the measuring device and determine if that device is
giving consistant, accurate valid measurements.  This can only happen when
at least one other machine agrees with the machine being tested.  And even
then it is better to have two.

>The inharmonicity of a string sounding forte is going to
> be slightly different than a string sounding pianissimo.
>
> -Robert Scott
>  Ypsilanti, Michigan

Yes VERY slightly, as in too slight to measure.  The thesis that was
mentioned earlier stated that the experiments could find no difference in Ih
in different volume levels, or none more than 1 in 10,000.    In the
original experiments by R Young, he considered having a device play the
notes instead of a human to assure a consistant blow.
However he found that varying degrees of loudness did not produce measurable
differences in Ih, so they went ahead and struck the keys by hand.
>
> Soundboard resonaces will have an immeasureable effect
> on the overall inharmonicity of a sounding string.

Yes.


>
> In the search for a link between inharmonicity and something beyond the
> string itself, there other candidates to consider.
> Since inharmonicity is highly sensitive to stiffness and kinks near
> the bearing point, it is easy to see how random variations in
> the inharmonicity could result from the string sliding to a new
> position under the V-bar, or, for that matter, at the bridge.
> -Robert Scott


If this were true, and it does make for a good hypothesis to experiment on,
the advocates of string leveling would have to re-examing that practice
since how can you "level" a string wo affecting the bend at the pressure
bar?  Or not put another bend in the string to bring it to level?    Or
those of us who tune a piano to 442, then lower it back to 440?.   Surely
the effects you suggest should be observed here?
The old timers used to say a wire with a bend or kink in it is no longer
good for music wire.  But one quick (although abusive) experiment would be
to pull up on a string under the capo, or agraffe, or push down near the
upper termination in an upright  as to alter its bend, then re-measure the
inharmonicity. ---ric