Question

Notes that are shorter in duration than quarter notes have flags on their stems. What is the purpose of the flag?

Answer 1

They sort of serve almost like a half fraction that you multiply the original duration by, I believe. So if you have a quarter note, you add the flag, thus multiplying the quarter note by one half and getting an eighth note. Then you multiply that eighth note by adding another flag, and you get a sixteenth note. Beams serve the same purpose.

Answer 2

So for example, a note with like, say 4 flags is effectively a one-sixtyfourth note.