You can use the Harmonic Product Spectrum method to estimate the distance (frequency difference) between overtone peaks in a frequency spectrum (FFT results), even if some peaks are missing, as long as there are not too many spurious frequency peaks (noise).
To do a Harmonic Product Spectrum, print the FFT out on semi-transparent paper and roll it up into a cylinder (or do the equivalent in software). Wrap the cylinder tighter and tighter until the greatest amount of peaks overlap. The circumference will be a good estimate of the pitch. This works for any musical sounds that have lots of harmonics, even if a fundamental pitch frequency peak is missing or weak.