I am writing a program to help people learn guitar. To do this, I need to be able to look at a sample of time and see what note(s) they played. I looked at FFTW but I don't understand how to get this to work. I also tried to figure out the Goertzel algorithm but it seems like that is just for single-frequency notes like dial tones (not sure about that though). To be clear, I do need to be able to detect multiple notes (to see if a chord is played), but it doesn't matter too much if a few harmonics get in there too.
I'm coding this in C++, and would prefer a solution that is cross-platform.
UPDATE: I've realized it isn't so important to detect specific notes; what I really need is to check that certain frequencies are present, and that others aren't. For example, if someone plays a C, I want to check that a C frequency is present (about 262 Hz), as well as probably 524 Hz and 786 Hz, and check that nearby notes that are not near in the overtone series (like B and D) are not present.
Notes are not present in a wav file. Sampled sound is.
Humans might perceive some notes that might have been played to create the sound in some wav file, but doing automatic polyphonic pitch estimation/recognition from recorded sound into transcribed music for rich and complex waveforms, such as produced by guitars, still appears to be an advanced research topic.
When possible for certain very restricted types of music sounds, some non-trivial DSP will be involved. FFTW might be useful for a small part of the more sophisticated DSP processing needed for pitch estimation, Goertzel filtering less so.