The role of inventors is arguably underappreciated. For example, if I were to ask you who you thought most influenced music in the twentieth century, you might name The Beatles or Pink Floyd, who doubtlessly inspired whole generations of teenagers to become rock musicians. Maybe you'd go back a little further, and pick Chuck Berry or Jimi Hendrix.
However, these are just the bands and musicians that happened to be very good at their job — writing and performing songs — at a time when rock music was starting to take off. Rock music would still have been created without their influence. Better candidates might be the inventors of the electric pickup, whose invention allowed guitarists to amplify their instruments. Without this amplification, rock music would not have been possible (or at least would have featured the piano instead of the guitar as its main instrument, significantly altering its sound).
Similarly, both Mozart and Beethoven were stunningly influential, but perhaps pale in comparison to the lesser known Bartolomeo Cristofori. Cristofori invented the piano, which allowed a much greater dynamic range than the harpsichord that came before it, in turn allowing a greater range of artistic expression.
Given how radically synthesisers have changed the sound of music, spawning countless genres from hiphop, techno, house and rave to jungle, drum'n'bass and IDM, you could easily make a case for Bob Moog being much more influential than any musician, as he turned the synthesiser from a complicated device into something musicians could actually play. The same could be said for John Chowning, whose pioneering work in the field of FM synthesis allowed synthesisers to access previously untapped sounds.
Going back further to the root of what made these inventions possible, it could be argued that the inventors of the transistor influenced music in the twentieth century more than anyone else, just as they pushed the state of the art in every other medium, as it was this invention that allowed the subsequent invention of the synthesiser and multitrack tape recorder, and eventually the home computer that would replace both. Without them, the state of the art would be instruments that use vacuum tubes. There's a sobering thought to consider while you next load up Pro Tools.