strings and things

The problem of figuring out the partials that will sound when a
nonuniform string is plucked is dealt with in

Kalotas and Lee, ``Transverse modes of a string with variable mass
density", Acustica Vol 76 (1992).

This paper provides a matrix method that allows you to segment the
string into sections, each with its own properties, and to then
calculate the partials of the complete system. Thus, for Gary's twist
tie string, you could divide the string into three parts, (regular string
on left and right, twist tie version in middle) and use Kalotas'
method.

However, the inverse problem is far more interesting from a musical
perspective: define a desired set of partials, and find a string with
contour so as to generate the desired partials. Unfortunately, this
inverse problem is as yet unsolved.

On a slightly different topic, Glen said: I can't imagine the air
conducting the sound from one string to the other.

I believe that sympathetic strings do indeed work by transferring
the energy through the air. As a simple experiment, sing into a string
on a guitar, and you can easily set the string to vibrating
(sympathetically) with your voice.


-Bill Sethares

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