Why A is 440 Hz: how concert pitch was standardised

A is 440 Hz because musicians and engineers agreed it should be. There is nothing physically special about 440 vibrations per second; it is a reference that lets instruments made and tuned anywhere play together. It was recommended by an international conference in London in 1939 and formalised by the International Organization for Standardization as ISO 16 in 1975. The note frequency calculator works out every other note from it, and lets you change the reference.

What A440 means

A440 sets the A above middle C, written A4 in scientific pitch notation, at 440 hertz: the air vibrates 440 times a second. Tuning forks, electronic tuners and the oboe's tuning note in an orchestra all start from it. Because an octave doubles the frequency, the other As follow at once: A3 is 220 Hz, A5 is 880 Hz, and the lowest key on a standard 88-key piano, A0, is 27.5 Hz.

How 440 became the standard

For centuries there was no common pitch. Surviving tuning forks and organs show the A above middle C anywhere from about 390 Hz to more than 450 Hz, varying between cities, churches and opera houses, and pitch tended to creep upwards over the 19th century. Several attempts were made to fix it. In 1834 the German physicist Johann Heinrich Scheibler recommended 440 Hz, and a meeting of German scientists in Stuttgart approved it, which is why A440 is sometimes called Stuttgart pitch. France instead set a standard of 435 Hz in the mid-19th century, and many countries adopted it.

The modern standard came from a conference held at the BBC's Broadcasting House in London in May 1939, with delegates from several European countries, which agreed on 440 Hz. One argument recorded for 440 over the 439 Hz then used by British piano tuners was practical: 440 is easier to produce electronically, while 439 is a prime number. The International Organization for Standardization adopted the figure as a recommendation in 1955 and published it as ISO 16 in 1975.

How every other note follows

Western instruments are mostly tuned in twelve-tone equal temperament, where every semitone multiplies the frequency by the same factor, the twelfth root of 2, about 1.0595. Twelve semitones therefore exactly double the frequency. Number the notes as MIDI does, with A4 as note 69 and middle C as note 60, and any note's frequency is 440 × 2^((n − 69) / 12). That gives:

• middle C (C4): about 261.63 Hz
• E4: about 329.63 Hz
• G4: 392.00 Hz
• the guitar's low E (E2): about 82.41 Hz
• the top piano key (C8): about 4,186 Hz

The calculator also runs in reverse: enter any frequency and it names the nearest note and how many cents sharp or flat it is, with 100 cents to a semitone. Music intervals explained: names, semitones and inversions explains how those semitone steps compare with the pure ratios of just intonation.

Orchestras, Baroque pitch and 432 Hz

A440 is a reference, not a law. Many orchestras tune a little higher, around 442 or 443 Hz, for a slightly brighter sound; the difference from 440 is under 8 cents at 442, small but audible to trained players. Ensembles playing Baroque music on period instruments often use 415 Hz, close to a semitone below 440, which lets players transpose by a semitone to match modern instruments. You may also see claims that 432 Hz is more natural or healing. There is no good evidence for that; it is a little over 30 cents flat of 440, and music tuned to it simply sounds slightly lower. Change the A4 box in the calculator to see every note shift.

What it means when you tune

For most players A440 is invisible: the guitar tuner and nearly every clip-on or app tuner default to it, so instruments tuned separately will agree. If you play along with a recording that sounds slightly out, the recording may use a different reference or have been sped up, and setting your tuner a few hertz away fixes it. To hear the reference itself, the tone generator can play a steady 440 Hz sine wave. One honest caveat: real pianos are stretch-tuned, with high notes set slightly sharp and low notes slightly flat of the exact equal-tempered values, because piano strings have overtones that are not perfectly in tune with the formula. For how hearing changes at the top of the frequency range, see Why adults can't hear the mosquito tone.