Piano tuners tune pianos by listening to the beats between the harmonics of two different strings. When properly tuned, the note A should have the frequency \(440 \mathrm{~Hz}\) and the note \(\mathrm{E}\) should be at \(659 \mathrm{~Hz}\). The tuner can determine this by listening to the beats between the third harmonic of the \(\mathrm{A}\) and the second harmonic of the \(\mathrm{E}\). A tuner first tunes the A string very precisely by matching it to a \(440 \mathrm{~Hz}\) tuning fork. She then strikes the A and E strings simultaneously and listens for beats between the harmonics. What beat frequency indicates that the E string is properly tuned?