Audio to midi conversion for an IOS app

Hi, We're looking someone for to develop some software for us that would convert audio input (microphone in) to midi. The software should be built to run native on IOS. We would expect this to be built using established techniques such as FFT. Are would you recommend another approach? The expected input via the microphone would be a range of acoustic instruments and vocals. Please let us know if you have the knowledge to do this is, which technique you would recommend and how much you would expect it to cost. Best regards, SR