This is an impossible question to answer. However I really thought about how to answer this if I were to give the most logical answer.
The answer I came up with is Guido d'Arezzo who is the inventor of modern music notation circa 1000 AD. d'Arezzo is to the history of music what Gutenberg (inventer of the printing press) is to the history of literature.
That said, if one were to ask who was the most influential writer of all time and the answer suggested was Gutenberg that would surely be a mediocre answer since Gutenberg's importance however great, is merely from a mechanical standpoint and not a creative standpoint.
If I were to guess from a creative standpoint I would say Beethoven and Bach are at the very top, but I feel The Beatles, James Brown, Bob Dylan, have all been enourmously influential and it is unfair to compare such newcomers to 300 year old legacies. I believe between the Beatles, Brown and Dylan you essentially have the 3 strands of popular music completely at its focal point...... The Beatles are the champion of pop / rock. Brown is the champion of soul / funk / a precursor of hip hop and an awesome showman ala Michael Jackson, and Dylan is the first musician to break into the mainstream who wrote (and was able to chart with) meaningful lyrics and songs dealing in folk, country and blues.
In my opinion those 3 artists are the most influential of the past 100 years.
But Beethoven and Bach are clearly higher up on the ladder, but not really fair.