Originally Posted by NimbleTurtle
Does the balance of the frequency response around that higher region really fundamental in the way we hear the overtones? For instance, if we heard some note at A = 440, and the headphone had extended very well into the overtone range (880, 1760, etc.) would the A at 440 sound richer?
The frequency response affects fundamental tones just as it does overtones. It's not like the playback gear can tell which is which. If it's 5 dB too soft at 880, 1320, etc. compared to 440 Hz, then the balance is off whenever an A440 is played because the overtones will be too weak compared to what it's supposed to sound like. If it's 5 dB too loud at 880, 1320, etc. compared to 440 Hz, then the balance is off whenever an A440 is played because the overtones will be too strong compared to what it's supposed to sound like.
If overtones are emphasized, that can sound richer. Then again, different frequencies could be fundamentals and overtones for different sounds. Let's say that 400 Hz is too loud relative to everything else. Then a 200 Hz (or 100 Hz, etc.) tone may sound funky, with the 400 Hz overtone too loud. Then when a note is played with 400 Hz fundamental, then all the overtones sound too soft (so unrich? who knows). You have problems with balance in both directions, not to mention the main issue that notes at 400 Hz sound too loud in the first place.
Originally Posted by bigshot
Overtones are what make an oboe sound different than a flute. Accuracy always helps.
Nah, it's the oboist, not to mention the dedication to the dark arts of bending reed chips in half and woodcrafting.