When a piano is properly tuned, the note A should have the frequency 440Hz and the note E should be at 659Hz. The tuner can determine this by listening to the beats between the third harmonic of the A and the second harmonic of the E.
-A tuner first tunes the A string very precisely by matching it to a 440Hz tuning fork. She then strikes the A and E strings simultaneously and listens for beats between harmonics. What beat frequency indicates that the E string is properly tuned?