String Length Modulation

A number of stringed musical instruments have a ``nonlinear sound'' that comes from modulating the physical termination of the string (as opposed to its acoustic length in the case of tension modulation).

The Finnish Kantele [231,513] has a different effective string-length in the vertical and horizontal vibration planes due to a loose knot attaching the string to a metal bar. There is also nonlinear feeding of the second harmonic due to a nonrigid tuning peg.

Perhaps a better known example is the Indian sitar, in which a curved ``jawari'' (functioning as a nonlinear bridge) serves to shorten the string gradually as it displaces toward the bridge.

The Indian tambura also employs a thread perpendicular to the strings a short distance from the bridge, which serves to shorten the string whenever string displacement toward the bridge exceeds a certain distance.

Finally, the slap bass playing technique for bass guitars involves hitting the string hard enough to cause it to beat against the neck during vibration [263,366].

In all of these cases, the string length is physically modulated in some manner each period, at least when the amplitude is sufficiently large.

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Tension Modulation