Tempering an interval causes it to beat. Because the actual tone of a vibrating piano string is not just one pitch, but a complex of tones arranged in a harmonic series, two strings that are close to a simple harmonic ratio such as a perfect fifth beat at higher pitches (at their coincident harmonics), because of the difference in pitch between their coincident harmonics. Where these frequencies can be calculated, a temperament may be tuned aurally by timing the beatings of tempered intervals.