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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They did it through trial and error. The original horns were actual rams’ horns that had been hollowed out. Pipes were hollow reeds or bones or sticks. People would make something, and if it worked they’d make another copy. Eventually you’d get professionals who knew they could make good money by coming up with something new.
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