Aleksandar Mlazev, developer of a bunch of fun effects apps, released Chord Detector. This app attempts to display chords played by a single instrument, as heard by your iOS device's microphone. There's an experimental audio to MIDI converter in here as well.
Chord Detector App Store Description:Chord Detector is closer to science than just an app. It is an experimental music recognition method that I have made according to my understanding about the mechanics of sound perception. The app is real time chord tracker that uses the microphone of the device.
The found chords are displayed with big letters on the screen but you can also see individual music tones with small letters at the bottom.
MIDI recording is an experimental feature. I do not know of any 100% successful audio to MIDI converter yet but this one I have made works relatively good for solo instruments. However full songs with drums and noises are not so good :)
Audio to MIDI conversion is also real time so some tones may be missed because the CPU may not catch up (depends on the device)
At the moment chord detection is limited to major, minor, 5th and 7th chords.