Soundboards and Inharmonicity

[Clark]

Hi there,

Robert Scott:

> The soundboard all by itself
> does have resonances, but they are not strong resonances.

The tuning of these resonances is an important aspect to building fine
string instruments. In fact, their top and back resonances should not be
so defined as for pianos, since their 'rims' only are thin or kerfed
liners joining ribs to the plates.

> assuming you could find more
> than one such resonance, there is no reason for two such resonances 
> to be even approximately harmonically related.  For example, if you
> found a soundboard resonance at 10 Hz and another at 28 Hz, what would
> you conclude about inharmonicity?

In the violin family these are carefully adjusted into a faintly
harmonic order, but they also are inside the range of played pitches.
Coincidences of a resonance and sounded pitch are another so-called
wolf-tone which is audible as pronounced false beats.

In "The Physics of Harpsichord Sound", John Sankey explores the effect
of soundboards on the dissipation of string energy: "...the relative
radiated power of each partial was calculated and is shown compared with
the theory for a non-resonant 'piston' soundboard. The soundboard seems
to be acting primarily as a non-resonant element. And, it seems close to
being a rigid piston...the high partials [are] a bit higher in power
than expected. That should be due the deviations of the soundboard from
those of a piston, i.e its resonances." (from
http://www.geocities.com/Vienna/Studio/1714/energy.html )

Another factor affecting the power of higher partials has been mentioned
here in discussion of the Wapin bridge-pinning system. One version of
the invention can be installed in recapped bridges, obviously which
shouldn't much change the existing board resonances. Sankey explores a
similar effect in "Bridge Pins of Harpsichords", where he concludes that
differences in the apparent string lengths between horizontal and
vertical modes had been exploited in antique instruments (i.e. two
different, but phase-locked sets of partials). 

Ric:

> 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

The higher effective wire stiffness at these points is described to
cause an apparent elongation of the speaking length of a vibrating
string; however, introducing the desired bend might cause a second.


Clark