The dependence on amplitude of the fundamental resonant frequency for the free vibration of a string is derived for the two systems of mounting used in vibroscope measurements. It is found that in both systems a correction term of order e^-1(A/l)² applies, where A is the amplitude, l the gauge length, and e a number we call the incremental strain. As this strain e is usually small (of the order 1% from most textile testing), the correction term can be important at apparently low amplitudes.