Not nearly that simple. Each moment of audio sample has so many overtones that detecting individual notes stored within a chord is a herculean task.

A given vibrating string will have several overtones, many of which are shared with completely different notes, especially considering that the overtones tend to fall in the same areas that we consider harmonically pleasing (fifths, thirds, sevenths, etc.), so the odds that you're going to have other notes in the chord that already share overtones is high.