This is a list of the

fundamental frequencies The fundamental frequency, often referred to simply as the ''fundamental'' (abbreviated as 0 or 1 ), is defined as the lowest frequency of a periodic waveform. In music, the fundamental is the musical pitch of a note that is perceived as the l ...

hertz The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), often described as being equivalent to one event (or Cycle per second, cycle) per second. The hertz is an SI derived unit whose formal expression in ter ...

(cycles per second) of the keys of a modern 88-key standard or 108-key extended

piano A piano is a keyboard instrument that produces sound when its keys are depressed, activating an Action (music), action mechanism where hammers strike String (music), strings. Modern pianos have a row of 88 black and white keys, tuned to a c ...

twelve-tone equal temperament 12 equal temperament (12-ET) is the musical system that divides the octave into 12 parts, all of which are equally tempered (equally spaced) on a logarithmic scale, with a ratio equal to the 12th root of 2 (\sqrt 2/math> ≈ 1.05946). That resul ...

, with the 49th key, the fifth A (called A₄), tuned to 440 Hz (referred to as A440). Every octave is made of twelve steps called semitones. A jump from the lowest semitone to the highest semitone in one octave doubles the

frequency Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...

(for example, the fifth A is 440 Hz and the sixth A is 880 Hz). The frequency of a pitch is derived by multiplying (ascending) or dividing (descending) the frequency of the previous pitch by the

twelfth root of two The twelfth root of two or \sqrt 2/math> (or equivalently 2^) is an algebraic irrational number, approximately equal to 1.0594631. It is most important in Western music theory, where it represents the frequency ratio ( musical interval) of a se ...

(approximately 1.059463). For example, to get the frequency one semitone up from A₄ (A₄), multiply 440 Hz by the twelfth root of two. To go from A₄ up two semitones (one

whole tone In Western music theory, a major second (sometimes also called whole tone or a whole step) is a second spanning two semitones (). A second is a musical interval encompassing two adjacent staff positions (see Interval number for more deta ...

) to B₄, multiply 440 twice by the twelfth root of two (or once by the sixth root of two, approximately 1.122462). To go from A₄ up three semitones to C₅ (a

minor third In music theory, a minor third is a interval (music), musical interval that encompasses three half steps, or semitones. Staff notation represents the minor third as encompassing three staff positions (see: interval (music)#Number, interval numb ...

), multiply 440 Hz three times by the twelfth root of two (or once by the fourth root of two, approximately 1.189207). For other tuning schemes, refer to

musical tuning In music, there are two common meanings for tuning: * #Tuning practice, Tuning practice, the act of tuning an instrument or voice. * #Tuning systems, Tuning systems, the various systems of Pitch (music), pitches used to tune an instrument, and ...

. 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 In music, inharmonicity is the degree to which the frequency, frequencies of overtones (also known as Harmonic series (music)#Partial, partials or partial tones) depart from Integer, whole multiples of the fundamental frequency (harmonic seri ...

, i.e., the tendency for the

harmonic In physics, acoustics, and telecommunications, a harmonic is a sinusoidal wave with a frequency that is a positive integer multiple of the ''fundamental frequency'' of a periodic signal. The fundamental frequency is also called the ''1st har ...

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 (Hz) of the ^th key on the idealized standard piano with the 49th key tuned to A₄ at 440 Hz: :

,\right)^ \times 440 \,\text\, = 2^ \times 440 \,\text\,

where is shown in the table below. Conversely, the key number of a pitch with a frequency (Hz) on the idealized standard piano is: :

n = 12 \, \log_2\left(\right) + 49

List

Values in bold are exact on an idealized standard piano. Keys shaded gray are rare and only appear on extended pianos. The normal 88 keys were numbered 1–88, with the extra low keys numbered 89–97 and the extra high keys numbered 98–108. A 108-key piano that extends from C₀ to B₈ was first built in 2018 by Stuart & Sons. (Note: these piano key numbers 1–108 are not the keys in the equations or the table.)

References

{{Pitch (music) Piano Musical tuning

List

See also

References