Piano key frequencies
This is a virtual keyboard showing the absolute frequencies in hertz (cycles per second), of the notes on a modern piano (typically containing 88 keys) in twelve-tone equal temperament, with the 49th key, the fifth A (called A4), tuned to 440 Hz (referred to as A440). This effect is sometimes known as stretched octaves, and the pattern of deviation is called the Railsback curve. The following equation will give the frequency F of the nth key, as shown in the table: .For example, to get the frequency a semitone up from A4 (A♯4), multiply 440 by the twelfth root of two. For other tuning schemes refer to musical tuning. This list of frequencies is for a theoretical ideal piano.
On an actual piano the ratio between semitones is slightly larger, especially at the high and low ends, due to string thickness which causes inharmonicity due to the nonzero force required to bend steel piano wire in the absence of tension. Each successive pitch is derived by multiplying (ascending) or dividing (descending) the previous by the twelfth root of two.
To go from A4 to B4 (up a whole tone), multiply 440 by the twelfth root of two squared.
