Harpsichord Wire

[Fred S. Sturm]

Stephen,
    Actually, I'm not confusing tension with stress, but simply ignoring stress.
What I am pointing out is a very simple-minded relationship. Given
a) a particular speaking length,
b) a particular pitch to be produced,
c) a choice of two different diameters of wire,
the narrower wire will require less tension to produce the desired pitch. The
thicker wire will require more tension.
    Whether or not this means reaching breaking point for either is a more complex
issue, but from the point of view of scaling pianos and harpsichords, there is a
simple-minded way of looking at it, which is related to the Pythagorean scale you
mention. With the Pythagorean scale, which doubles length for every octave, a
given diameter will be at the same tension throughout the scale, as you state. But
if we foreshorten the scale (as we do in all cases), that means that if you used
the diameter that works for the top note throughout the scale, it would be at a
lower and lower tension as you move down the scale. And sound awful. So we use
thicker wire (and wrapped, eventually, in pianos) to increase the required tension
(again, stated in a very simple-minded way). We can be pretty certain that any
diameter wire that works somewhere in a scale (doesn't break) will not break if
used for any lower note.
    What this means, in practical terms, is that on any harpsichord or piano it is
very risky to increase diameter - say, use 14 gauge for C8 on a piano, or increase
from .016 to .018 brass on a tenor note of a harpsichord -  and less risky to
decrease diameter, in terms of likelihood of string breakage. So, contrary to the
intuitive notion that you should use a heftier string if you are having breakage
problems, the opposite is more likely to be true. That's all I was trying to
convey.

Regards,
Fred Sturm

Stephen Birkett wrote:

> Fred, you're confusing tension with stress = tension per cross sectional
> area. The latter is the factor that has to be considered when it comes to
> breaking wires. Breaking stress should be given in MPa (or nasty psi) for
> each gauge. Very often, though, wrie "strength" is expressed for each gauge
> by wire manufacturers in terms of maximum breaking tension. In a
> pythagorean scale every note will have the same stress level regardless of
> the diameters used. If there were no tensile pickup a single value only
> would have to be given for breaking stress for all the gauges, i.e. it
> would be a characteristic only of the wire material. In reality, there is
> tensile pickup. Thinner wires can withstand greater stress, so you have to
> give breaking stress as a function of diameter. Historical builders were
> very familiar with tensile pickup, but once high carbon steel started to be
> common the knowledge receded into the depths and was generally forgotten.
>
> Stephen
>
> Stephen Birkett Fortepianos
> Authentic Reproductions of 18th and 19th Century Pianos
> 464 Winchester Drive
> Waterloo, Ontario
> Canada N2T 1K5
> tel: 519-885-2228
> mailto: sbirkett[at]real.uwaterloo.ca
> http://real.uwaterloo.ca/~sbirkett
>
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