Note Frequency Calculator

Convert between notes, octaves, frequencies, MIDI numbers, cents and wavelength - in equal temperament, with an adjustable reference pitch.

Note

Octave

A4 reference

Or a frequency

Note: A4
Enharmonic: A
Octave: 4
Frequency: 440.000 Hz
Equal-tempered: 440.000 Hz
MIDI number: 69
Cents offset: 0.0 cents
Wavelength: 0.780 m

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Wavelength assumes a speed of sound of 343 m/s — dry air at about 20°C. It changes with temperature, so treat it as an approximation.

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The formula

Equal temperament divides the octave into twelve equal ratios, so every semitone multiplies the frequency by the twelfth root of two - about 1.0595. From a reference of A4 = 440 Hz and its MIDI number of 69, any note is 440 x 2^((n-69)/12), and the reverse is 69 + 12 x log2(f/440). Both directions are exact here, not table lookups.

Cents

Cents are a logarithmic measure: one hundredth of a semitone, so 1200 to the octave. The formula is 1200 x log2(f1/f2). That logarithm matters - the same musical interval is the same number of cents whether you are at 30 Hz or 3 kHz, which is not true of a plain frequency difference. A tuner that treats cents as a percentage of frequency is roughly right near unison and visibly wrong at the edges.

MIDI numbers

MIDI numbers each note from 0 to 127, with middle C at 60 and A4 at 69. They map exactly onto semitones, which makes them a convenient integer form for calculation. C4 is middle C in scientific pitch notation, which is what this uses; some manufacturers label the same key C3.

Enharmonics

C sharp and D flat are the same pitch in equal temperament and are shown together. Which spelling is correct depends on the key you are in, not on the sound - a piece in D major has C sharp, one in A flat major has D flat, and writing the wrong one is legal but reads as a mistake to a musician.

Wavelength

Calculated at 343 metres per second, the speed of sound in dry air at about 20 degrees Celsius. It varies with temperature - noticeably so - and changes completely in water or a solid, so treat it as an approximation for air at room temperature.

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