It is a good question and quite hard for an English speaker to explain! I will try! I can play the guitar/violin/saxophone - I am saying that I have the ability to play these instruments but I am not specifying where I play them (in a band/group/orchestra). I play guitar in our school band. Here I am specifying what my role is in the band - John plays drums, Joe plays trumpet. I could just as easily say "the" guitar/drums etc and my meaning would be the same. It is also more common in American English to omit "the" in this context I think. If members of al rock band were explaining their roles on stage, they would probably omit "the" from the name of their instrument. It is perhaps also more common to retain "the" for musical instruments associated with an orchestra - "he plays the violin in the Berlin Philharmonic" but "she plays fiddle in the country and western band". This could be something to do with the status of the instrument and its role in classical music. Just a few suggestions!

When talking about roles in a band, I think with or without "the" is fine.

THE article in English is called also DEFINITE Article. Definite means definite / course / clear. This article is used for something special or specific. Example: Open the door! Cut the cake! I love the girl. In the example above sentence, the article THE indicates that the object-specific, either speaker and listener already knows object in question. If it says "close the door! "means the speaker and listener already know which door should closed. "Cut the cake!" Means already know Which cake to be cut. Note: THE article can also be placed before plural noun (plural nouns), for example: The students, the books, the cars.