That results in what is called transient intermodulation distortion (TIM), and enhancement of particularly objectionable odd-order distortion components.
It is this last bit wherein you see so much variance in amplifier design: odd orders as stated are very objectionable, in no small part because the human ear/brain system uses them to determine how loud a sound is. It is arguable that our ears are more sensitive to this than actual frequency response errors- so electronics that distort these harmonics will have a false loudness and brightness to them. Audiophiles use terms like 'hard', 'harsh', 'brittle', 'bright' to describe this phenomena.
This is why of two amps that have flat frequency response, one might sound bright and the other might not.