Musical Note Frequency

Note frequency from MIDI number: formula and example

Under 12-tone equal temperament tuned to A4 = 440 Hz, MIDI note n sits at f = 440 · 2^((n − 69) / 12). So A4 (n=69) = 440 Hz, C4 (n=60) ≈ 261.63 Hz, A5 (n=81) = 880 Hz and A3 (n=57) = 220 Hz. If you prefer the Verdi pitch, A=432 Hz shows up often enough as an alternative reference.

Context and applications

Luthiers and piano tuners lean on the formula to set string frequencies. Synth designers use it to turn MIDI into oscillator pitch, and orchestras tune to A=440, or 442 in a lot of European halls. Historical performance is a different story. Players there work from older reference pitches: baroque A=415 Hz, which is roughly a semitone lower, and classical-era A=430 Hz. The upshot is that a baroque flute comes out at the pitch a modern flute would hit playing one semitone down.

FAQ

Why is the octave a factor of 2? Double the frequency and you go up exactly one octave, which the ear reads as the same note name. That's why 440 Hz and 880 Hz are both A. Equal temperament then chops the octave into 12 equal ratios of 2^(1/12) ≈ 1.0595.

What changes with A=432 Hz? Just scale every frequency by 432/440 ≈ 0.9818, so C4 drops to about 256.87 Hz. The ratios between intervals don't budge.

How precise is a cent? One cent is 1/100 of a semitone, the ratio 2^(1/1200) ≈ 1.000578. A trained ear picks up on roughly 5–10 cents, while tuners try to stay under 2 cents off A=440.