[impedance]

[Clark]

Ric, et al,

I found (and recently posted here) a linear formula describing this
pitch increase, from Ian Firth, "Overwrapped Strings", JCAS 45:

Df/f=[(3/16)*pi*E*(max displacement/length)^2]*(pi*(core
diameter)^2)/Tension

where Df/f is the proportion of the raised and theoretical pitches.

You'll notice (which Firth describes) that up to a point the effects to
length and tension cancel. I'm a little suspicious about using it
directly, however, without accounting for some of the less linear
factors involved such as hammer/shank behavior, vertical and horizontal
modes, coupling, winding inertia, terminations, ad infinitum. But you
can hear a momentary pitch increase in low-tension tenor strings easy
enough.


Clark