Note, frequency and tuning
Turn a note into a frequency and back, at A=440 or A=432, with the cents you are off. What you need to set an autotune or match a sample that was not tuned to standard pitch.
The formula, and the two checks that prove it
f = concert pitch × 2(midi − 69) ÷ 12
Equal temperament divides the octave into twelve steps of the same ratio, not the same distance in hertz — the twelfth root of two, about 1.0595. That is why the gap between two low notes is a few hertz and the same interval two octaves up is dozens.
Two results must always land exactly, and you can check them here: A4 is the concert pitch itself, and A5 is exactly double. If a converter fails either, it is not doing equal temperament.
Frequently asked
What is the formula?
f = concert pitch × 2^((midi − 69) ÷ 12). Equal temperament splits the octave into twelve steps of constant ratio — the twelfth root of two. Two checks always land exactly: A4 is the concert pitch itself, and A5 is double it.
Is 432 Hz better than 440?
No, and neither is 440. It is a choice, about a third of a semitone below the 440 Hz agreed in 1939. What is true, and it is the only thing that matters in a session: a sample tuned to one will fight an instrument tuned to the other. Pick one and keep it.
What is the period in milliseconds for?
It is the delay time that lands exactly on that note. Set a delay to the period of your root and the repeats reinforce the pitch instead of blurring it — the same trick as tuning a reverb's pre-delay to the tempo, but on frequency rather than on time.
Why does it show cents?
Because a frequency is almost never exactly a note. A cent is a hundredth of a semitone; past about five you start hearing it against a tuned instrument, and past about fifteen an autotune will pull the wrong way. The number tells you whether to retune the sample or move the whole track.