Thinking about instruments like saxophones or violins I find it really hard to imagine how people figured out those shapes, let alone without modern computers.
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Like everything else, trial and error. Hominids have been making music for tens, if not hundreds, of thousands of years. You start with “banging things together makes sound”, move to “banging on hollow things makes different sound”, and after a few different iterations, you have a good-sounding drum. Same with blowing into a shell leading to wind instruments, rubbing or plucking strings for stringed instruments, etc. Anything that sounded good was iterated on, and anything that sounded bad was abandoned.
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