Bach: INTP 9w1 I don't know much about his life, but his mastery of counterpoint and craftsmanship suggest t-dom. Counterpoint requires entertaining multiple melodies at once (ne works), and he was a traditionalist (si). He had a big family, which suggests fe.
Mozart: ESTP 3w4 I see se in his hedonism, aestheticism, and focus on the present. He was ti-fe; he produced all his music from his head fully formed, never amending or correcting (ti), and he was social and emotionally open (fe).
Beethoven: INTJ 4w5 A really obvious fi-te; he had no regard for politeness, social standards, or the feelings of others, but he had a very rich inner world of emotion (fi). Unlike Mozart, he would constantly rework his scores until he had them just right (te, implied xxxj). Like House, his inferior se can make him look like a perceiver; he was definitely a slob. But he was also directive, driven, arrogant, single-minded, selfish, uncompromising and controlling. He was an introvert who preferred to focus on his private work rather than form social connections. And he was a Ni user with a strong appreciation for metaphor and archetype (fate knocking at the door...). Of the three big composers, he was the only major innovator (ushering in the romantic movement), and he was certainly ahead of his time. It makes strong intuitive sense for Bach to be a t-dom, Mozart to be an s-dom, and Beethoven to be an n-dom. And I see little ne, he was single-minded and obsessive. INTJ 4s are rare, which is why he's often typed as a fi-dom. Not every tortured artist is fp.