I became aware of harmonics and the sound of different shaped waveforms early in my electronics career (mid 1970’s) as I was an avid fan of [Emerson Lake and Palmer], [Pink Floyd], [Yes], and the list goes on. I knew every note of [Karn Evil 9] and could hear the sweeping filters and the fundamental wave shapes underneath it.
I remember coming to the understanding that a square wave, which is a collection of fundamental and (odd) harmonics frequencies, could then be used to give an indication of frequency response. If the high frequencies were missing the sharp edges of the square wave would round off. The opposite was then true, if the low frequencies were missing the square wave couldn’t “hold” its value and the top plateau would start to sag.