That's easy for you to say!
I think you've shown me something. When I hear "sine wave" I imagine one cycle. I guess that's wrong, and a wave is a train of cycles.
Musical harmony is in a sustained interaction between trains of cycles. The interaction won't be simple enough to hear unless the quotient between the frequencies is a small integer.
When they talk about harmonics in an electrical wave, I guess they're talking about the potential for energy transfer. In that case, only odd multiples of the fundamental will stay in phase to tap the energy from the distortion. Where a wave is flattened it may resemble part of a sine curve with a longer period than the fundamental, but that doesn't count because you can't tap energy from the flat part.
If there's any truth in what I've said, I'll forget in a flash. In 1975 I was working in a repair facility. We'd use Bird Wattmeters to see forward and reflected power in antenna feeds. We knew the jargon and how to use the meters, but one day it struck me that none of us understood why they worked. I had a flash of insight and everybody stopped work to listen to me explain. Their faces lit up with comprehension. I felt pretty smart. The next day I couldn't remember whatever it was I'd figured out.