Young Brunette Girl Reveals At The Old Piano With An Antique Chair

Tuning
The relationship between two pitches, called an interval, is the ratio of their absolute frequencies. Two different intervals are perceived to be the same when the pairs of pitches involved share the same frequency ratio. The easiest intervals to identify, and the easiest intervals to tune, are those that are just — which have a simple whole-number ratio. The term temperament refers to a tuning system which tempers the just intervals (usually the perfect fifth which has the ratio 3:2) in order to satisfy another mathematical property; in equal temperament, a fifth would be tempered by narrowing it slightly, achieved by flattening its upper pitch slightly, or raising its lower pitch slightly. A system of temperament can also be known as a set of bearings.
Tempering an interval causes it to beat, which is a fluctuation in perceived sound intensity due to interference between close (but unequal) pitches. The rate of beating is equal to the frequency differences of any harmonics that are present for both pitches and that coincide or nearly coincide.