String Pitch Distortion - Firth, JCAS#45

[Clark]

Hi,

While reading Ian Firth's "Overwrapped Strings: A Design Guide
Incorporating Acoustical Limitations", (Journal of the Catgut Acoustical
Society #45, May 1986. p7-9), I came across this:

"String pitch distortion occurs when a string is plucked, or excited.
The deflection of the string lengthens it and this increases the tension
of the string. The increase in length lowers the pitch of the string,
whereas the increase in tension increases the pitch. The effect which is
dominant in bass musical instrument strings is the rise in pitch and
this has a maximum value of

Df/f=[(3/16)*pi*E*([delta]/l)^2]*(pi*dc^2)/T

where Df/f is the fractional rise in pitch for the fundamental of the
string, E is Young's modulus for the core material and [delta] is the
transverse maximum deflection, for instance the initial pluck. [dc I
take as d<sub>c, which he uses throughout as the core diameter; l is
length, T is tension, and pi is 3.14...] The effect is heard in the
plucked string as a momentary uncertainty in the pitch, and in some
cases as a definite fall in pitch in the transient note." (p7-8)


By setting Df/f = 1, [delta] will not equal zero, implying that up to a
point the increased tension and string length due displacement cancel
each other out.

This is the only instance I've seen this equation. Has anyone else
encountered it before?


Clark