convert frequency to keyboard note

Question

I'm trying to write an audio application.

I can play a cin wave from a frequency of 20 to 20K to hear sounds. my question is how can i convert frequencies to keyboard notes in order to create a virtual keyboard (or piano) ? is there some kind of formula to achieve this ?

The programming language that I use is not important because I don't want to use other tools that calculate it for me. i want to write it myself so i need to understand the math behind it. thanks

update

i found the following url: http://www.reverse-engineering.info/Audio/bwl_eq_info.pdf

that contains the octave prequency chart. do i need to store that list or is there a formula that can be used instead ?

Answer 1

There are a few different ways to tune instruments. The most commonly used for pianos is the 12 tone equal temperament, a formula for which can be found here. The idea is that each pair of adjacent notes has the same frequency ratio.

See also equal temperament on Wikipedia.

Answer 2

You can calculate frequency of a tone as

f = 440 * exp(x*ln(2)/12)

where x is number of semitones above A in the middle of the piano keyboard.