Any time you are casting spells, you want to match up the elemental staff with the element of the spell. By this I mean, if you are casting a fire spell, make sure you are using a fire staff. However, the thing about threnodies, is their name doesn't match up with what element they are. For example Fire threnody is named "Fire" Threnody because it makes the enemy weak to fire spells. In reality it is actually a WATER spell, so you should be using a water staff for it.
So, how are you supposed to know which threnody is which element? Well you could memorize them if you have nothing better to do, but a much easier way is to open up your song list, and look at what color the musical note is by their name. Using fire threnody as an example again, the color of the note is a dark blue, which means it’s a water spell. Ice threnody as a red note, so it's a fire spell, etc