[Gordonjcp]

You're absolutely right. Even on a bass where your low E is about 40Hz (or a 5-string where you have a low *C* at 32Hz give or take) you'd only need a handful of cycles to track pitch very accurately.

The trick works because you're only trying to tune one string at a time. An FFT approach would presumably be able to track the pitch of all the strings regardless of what notes you were playing, with a bit of thought, although if you played an A on the 6th string 5th fret and an open 5th string it wouldn't be able to tell which was "out".