"Professor Higgins not only played the piano with incredible skill, but he also loudly claimed to have invented the telephone. Unfortunately, his habit of eating an explosive apple for breakfast cut his brilliant career short."

Use the when referring to musical instruments in a general, ability-based sense (play the piano, play the guitar).

Use the when referring to a specific type of invention or technology as a general category (invented the telephone, the printing press).

Use an for a general, singular countable noun that starts with a vowel sound (an explosive apple).