Nobody writes songs about the gibbous moon. It is in the sky more nights than any other shape and it has almost no folklore at all.

Crescents got beginnings, full moons got everything else, and the two lumpy phases in between got neither. Most languages have no native word for the shape and have to borrow the Latin one for a hunchback. If you want a moon phase that has never been used to sell anything, this is the one.