There's nothing more unnatural about odd-order harmonics than even-order harmonics. The brain picks up on both of them because any harmonic sound is good eviden

There's nothing more unnatural about odd-order harmonics than even-order harmonics. The brain picks up on both of them because any harmonic sound is good evidence that some living thing is nearby (non-living things like flowing water and falling rocks typically produce inharmonic sounds). The idea that there is something "unnatural" or inferior about odd-order harmonics is propaganda invented by valve-amplifier enthusiasts, because their amplifiers predominantly produce even-order harmonic distortion. A stopped pipe wind instrument produces odd-order harmonics, and they were invented long before chiptunes.