This article is from the Final-Fantasy and other Square Soft Games FAQ, by firstname.lastname@example.org (Nick Zitzmann) with numerous contributions by others.
To learn the Hero's Song, called the "Level Song" in the USA release,
your party must play every piano in the first world.
Every town (except for Wix, Lonka, and a few others) has a piano in it.
Usually, the piano is found at the town pub.
You'll know when your players are getting closer to playing every piano
when they stop playing simple scales and start playing more and more
complex melodies on the piano. Play every piano, then talk to the bard
in Crescent Island. You'll receive one of the best songs for your bard,
the Hero's/Level Song.
Can't find all the pianos? Hint: There's one in the hidden town
southwest of Crescent Island that's rather difficult to find.