Library to identify musical note

Developing for iphone/ipad/mac

I have an idea for a music training app, but need to know of supporting libraries for recognizing a musical note's fundamental frequency in close to real time (100 ms delay) Accuracy should be within a few cents (hundredths of a semi tone)

A search for "music" resolved the core-midi library -- fine if I want to take input from midi, but I want to be open to audio input too.

And I found MusicKit, which seems to be a programmer's API for digging into Meta questions:

Should I be using different search terms:

Where are libraries listed?

Who are the names in 3rd party libraries.