How this calculator works
Equal temperament divides the octave into twelve equally spaced semitones, so every semitone multiplies the frequency by the twelfth root of two, about 1.059463. Starting from A4 at 440 Hz, the page counts semitones to the chosen note and applies that ratio. Middle C, which is C4, is nine semitones below A4 and comes out at 261.63 Hz. The wavelength follows from the speed of sound in air, about 343 metres per second at 20 degrees Celsius, divided by the frequency. A 440 Hz tone has a wavelength of about 78 centimetres.
Formula
frequency = A4 x 2^((MIDI note - 69) / 12), where the MIDI note is (octave + 1) x 12 + pitch class and A4 is 440 Hz by default. wavelength = speed of sound / frequency, with 343 m/s in dry air near 20 degrees Celsius.
Worked example
For C4, the MIDI note is (4 + 1) x 12 + 0 = 60. The exponent is (60 - 69) / 12 = -0.75, so the frequency is 440 x 2^-0.75 = 261.6256 Hz. The wavelength is 343 / 261.6256 = 1.3111 metres, about 4 feet 4 inches. A5 is an octave above A4, so it is exactly 880 Hz.
Advertisement
Frequently asked questions
Why is A4 440 Hz?
The 440 Hz standard was agreed at an international conference in 1939 and is now the common concert pitch, written as A440. Many European orchestras tune a little higher, around 442 or 443 Hz, and historical ensembles use lower pitches. Change the A4 field to match the group you are playing with.
Does the wavelength depend on temperature?
Yes. The speed of sound rises by about 0.6 metres per second for each degree Celsius, so the wavelength is a little longer on a warm day. Instrument tuning itself is affected more by the air inside the tube, so wind players warm up before tuning.
What is the difference between A4 and A440?
A4 names the note, the fourth A on a standard piano keyboard counting from the lowest. A440 names the frequency assigned to that note. Note names describe positions and intervals; a frequency fixes one point on the scale.
Why does my tuner show 442?
The tuner is set to a different reference, not detecting a different note. An A at 442 Hz will read slightly sharp against an A440 tuner. Most tuners let you change the reference, and the same edit can be made in the concert pitch field here.