> ... different amplitudes for various harmonics ...

Different phases too.

> If I wanted to speculate even more, I'd wonder if there's any coupling 
> between the strings that would disfavor having them stay 180 out of 
> phase.  

Interesting and plausible idea.

> ...  But that's the facile answer.

I suspect the correct answer relates to an interaction between (and
superposition of) the three effects you mention.




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