Note to frequency

The modern reference is A4 = 440 Hz. From it, each semitone above multiplies the frequency by the twelfth root of two (about 1.05946) and each semitone below divides by it, so an octave is exactly double: A3 is 220 Hz and A5 is 880. That one rule fills the whole table, from C0 at 16.35 Hz to C8 at 4186.01 Hz.

Guitar strings in standard tuning sit at E2 82.41 Hz, A2 110.00, D3 146.83, G3 196.00, B3 246.94 and E4 329.63. A guitar sounds lower than it is written, which is why its open high string is E4 while the piano note people call high E sits two octaves above it.

The table assumes 12-tone equal temperament at A4 = 440. A piano that has not been tuned this year, or a recording made to another reference, sits somewhere else: if the A is 438, a string tuned to it reads about eight cents flat on a 440 tuner, and a violin tuned to the baroque A = 415 reference sits about 102 cents below a modern one. Just intonation gives a major third a slightly different frequency again.

Type any frequency and the page gives the nearest note and the cents offset, which is also the quickest way to name a hum or a room mode: mains hum is 50 Hz in the UK, a third of a semitone above G1 (49.00 Hz), and 60 Hz in North America, about half a semitone below B1 (61.74 Hz).