randform

In theory it should be impossible to separate the notes in a chord. If you play a sine wave and add say a perfect 5th one perceives this either as a single note (now with a different timbre than the single sine wave) or as an interval – namely the perfect 5th. what one hears depends on several things. If for example both sine waves are given a slight vibrato of the same phase and rate one is more likely to hear this a one note. However in general it should be impossible to tell (algorithmically) whether the audiosignal is a chord or a timbre. Theoretically. In practice chords are allmost never tuned perfectly, the notes in a chord are likely to start with tiny (or even big) offsets, the instruments / strings / sources usually have their own characteristics. So it might be possible in practice to separate the notes in a chord. Still it should be a difficult task.
Now celemony – the company that makes the incredible Melodyne – anounced that they have takled the problem.
Here is a promo video that shows the possibilities (they use the slightly overused DNA acronym for their technology (this time as “direct note access”)) .
Impressive and somewhat scary.