[cnity]

This is basically how you'd do it with non-negative matrix factorization. You take the spectrogram of a bunch of known notes for that type of guitar, and store them in a template library (just a vector of vectors, where each inner vector is a spectrogram of that note). Then NNMF determines how much of each template contributes to some given signal. The templates are the "harmonics look like this" thing you're talking about. It works pretty well.

By the way, the reason it is easier to use NNMF than try to implement your suggestion as a heuristic is because there's much more overlap between the different notes than you might think, and (worst of all) the timbre of the note:

1. evolves over time!

2. depends on the velocity of the note (how hard the string was strum)

3. and the notes actually interact with each other. If you play an E, the A string will mildly reverberate too because of the shared harmonics