The DA effect works with the same logic of the DT.
It's not imbued into the songs, but it's granted by the weapon itself, according to how many songs you have.
This means you need to have Songs up, it doesn't matter if you cast those songs yourself, if you received them from another bard, if you cast them with Barfawc or Carnwenhan.
All that matters is that you have X songs buffs up on you, and then when you equip Barfawc you will receive additional bonuses.
Not sure if I made myself clear :x but this is how it works.