⁷For example, a doubling of force results in a frequency increase of 1.414 (precisely equal to ). A four-fold increase in pressure would be necessary to double the string’s resonant frequency. This particular form of nonlinearity, where diminishing returns are realized as the applied stimulus increases, yields excellent rangeability. In other words, the instrument is inherently more sensitive to changes in pressure at the low end of its sensing range, and “de-sensitizes” itself toward the high end of its sensing range.