The songs on their own just give party members a slight crit buff.
For you to get the special effects of the song, you have to have DoTs ticking on one or more mobs. The more DoTs you have ticking, the more opportunities you have for one of those ticks to crit. Every time a DoT crits, you get a Repertoire stack (or for Ballad, your Bloodletter/RainOfDeath finishes cooling down immediately).
This is why Mage's Ballad is so good on trash. If you DoT everything, you get a free Rain of Death pretty much every three seconds for the duration of the encounter. It's also why you should not kill the mobs with lower health--you want your DoTs to tick longer so you get more Rains.