String bending

String bending is a

There are numerous mechanical and acoustic properties which heavily influence the resultant pitch from a string bend. Analysis of the physics of string bending ^[3] suggests that the resultant pitch of a string bent at its midpoint is given by

${\displaystyle \nu ={\frac {1}{2L}}{\sqrt {\frac {T+\cos \theta (T-EA)}{\mu _{o}}}}}$

where L is the length of the vibrating element, T is the tension of the string prior to bending, ${\displaystyle \theta }$ is the bend angle, E is the

and ${\displaystyle \mu _{o}}$ is the

Thus, the pitch is not only dependent on the bend angle, but on material properties of the string such as Young's modulus; this may be interpreted as a measure of the stiffness of the string. The force required to bend a string at its midpoint to a given angle ${\displaystyle \theta }$ is given by

${\displaystyle F_{B}=2\left(T+EA\left({\frac {1-\cos \theta }{\cos \theta }}\right)\right)\sin \theta .}$

It is important to note that the resultant pitch from string bending is not linearly correlated with the bending angle, and so a player's experience and intuition is important for accurate pitch modulation.

See also

• Finger vibrato
• Finger vibrato#Axial pitch-shifting

References