Great Musicians generate 10 times your tourism at the time that the GM spawned. So if a GM spawned when you have +50 tourism/turn, the GM would generate 500 tourism. Unlike the Great Scientist, the Great Musician's strength does not increase as you increase in tourism output.
Finally, the GM will generate ~20% of it's value to every other civ that the one it was performing in. From the above example, if this GM did a concert tour in Greece, it would generate 500 tourism influence over greece, and ~100 tourism over every other civ for you.
This means that late game GMs are better for concert tours than early game ones.