The sustained overtones are only half the battle. Getting the attack correct (the sound profile of the first ~10 milliseconds) is really important for differentiating instruments. Plucking a guitar string and hammering a piano string have very different attack characteristics. A flute has a distinctively "breathy" attack.

Many synthesizers use a sampled recording of the actual instrument for the attack, then synthesize the sustained portion of the instrument.

> The sustained overtones are only half the battle.

Actually probably like 10% at most of the battle. My understanding is attack is overwhelmingly dominant in our perception of timbre.

This takes me back to when I played around with sound using the C64 midi. There were four attributes that you could adjust to try and emmulate the timbre of a particular instrument: attack, delay, sustain & release.

Was a lot of fun when I was young.