It's rumoured the Saxophone was a lucky mistake... he was trying to make a metal clarinet, but it wasn't very successful until he made the 'bore' conical instead of cylindrical... and the Saxophone was born!
It's so odd... the clarinet and flute are both cylindrical, yet the flute overblows on the octave, but the clarinet on the twelfth. Make the bore conical, and the 'clarinet' behaved like the flute!