C/C++/Obj-C Real-time algorithm to ascertain Note (not Pitch) from Vocal Input

Question

I want to detect not the pitch, but the pitch class of a sung note.

So, whether it is C4 or C5 is not important: they must both be detected as C.

Imagine the 12 semitones arranged on a clock face, with the needle pointing to the pitch class. That's what I'm after! ideally I would like to be able to tell whether the sung note is spot-on or slightly off.

This is not a duplicate of previously asked questions, as it introduces the constraints that:

1. the sound source is a single human voice, hopefully with negligible background interference (although I may need to deal with this)

2. the octave is not important, only the pitch class

EDIT -- Links:
Real time pitch detection
Using the Apple FFT and Accelerate Framework

Answer 1

See my answer here for getting smooth FREQUENCY detection: https://stackoverflow.com/a/11042551/1457445

As far as snapping this frequency to the nearest note -- here is a method I created for my tuner app:

- (int) snapFreqToMIDI: (float) frequencyy {

    int midiNote = (12*(log10(frequencyy/referenceA)/log10(2)) + 57) + 0.5;
    return midiNote;
}

This will return the MIDI note value (http://www.phys.unsw.edu.au/jw/notes.html)

In order to get a string from this MIDI note value:

- (NSString*) midiToString: (int) midiNote {
    NSArray *noteStrings = [[NSArray alloc] initWithObjects:@"C", @"C#", @"D", @"D#", @"E", @"F", @"F#", @"G", @"G#", @"A", @"A#", @"B", nil];
    return [noteStrings objectAtIndex:midiNote%12];
}

For an example implementation of the pitch detection with output smoothing, look at musicianskit.com/developer.php