Piano key frequencies


This is a list of the fundamental frequencies in hertz of the keys of a modern 88-key standard or 108-key extended piano in twelve-tone equal temperament, with the 49th key, the fifth A, tuned to 440 Hz. Since every octave is made of twelve steps and equals two times the frequency, each successive pitch is derived by multiplying or dividing the previous by the twelfth root of two. For example, to get the frequency a semitone up from A4, multiply 440 by the twelfth root of two. To go from A4 to B4, multiply 440 twice by the twelfth root of two. To go from A4 to C5, multiply 440 three times by the twelfth root of two,. For other tuning schemes refer to musical tuning.
This list of frequencies is for a theoretically ideal piano. On an actual piano the ratio between semitones is slightly larger, especially at the high and low ends, where string stiffness causes inharmonicity, i.e., the tendency for the harmonic makeup of each note to run sharp. To compensate for this, octaves are tuned slightly wide, stretched according to the inharmonic characteristics of each instrument. This deviation from equal temperament is called the Railsback curve.
The following equation gives the frequency of the th key, as shown in the table:
Alternatively, this can be written as:
Conversely, starting from a frequency on the idealized standard piano tuned to A440, one obtains the key number by:

List

Values in bold are exact on an ideal piano. Keys shaded gray are rare and only appear on extended pianos. The normally included 88 keys have been numbered 1–88, with the extra low keys numbered 89–97 and the extra high keys numbered 98–108.