In one aspect thereof this invention provides a method to estimate pitch in an acoustic signal. The method includes initializing a function ƒt and a time t, where t=0, x′0=ƒ0(F0), x′0 is a pitch estimate at time zero and F0 is a frequency of the acoustic signal at time zero; determining at least one pitch estimate using the function x′t=ƒt(Ft) by an iterative process of creating ƒt+1(Ft+1) based at least partly on pitch estimates x′t, x′t−1, x′t−2, x′t−3, . . . , and functions ƒt(Ft), ƒt−1(Ft−1), ƒt−2(Ft−2), ƒt−3(Ft−3) . . . and incrementing t; and calculating at least one final pitch estimate. Embodiments of this invention can be applied to pitch extraction with various different input acoustic signal characteristics, such as just intonation, pitch shift in the frequency domain, and non-12-step-equal-temperament tuning.