You have to know the tune. Everyone in the band has to know the tune. It has to be totally committed to memory by everyone so you can focus on performing in the moment.
This is one reason that playing blues tunes is a good idea for guitar players in formative years. There is a solid, predictable set of chord changes over a set amount of bars. You can do the same thing with pop, country, jazz, rock tunes. But the same thing has to happen. You play the tune so many times that it becomes automated, it's second nature, you don't have to count all the time, or worry about getting lost.
This is also why it's so important to play lines that target chord tones & form melodic phrases. You are playing the form of the song & making statements that outline the song form so the lead lines & the chord changes are all integrated.
It helps if the bass player or drummer is also cognizant of the song form & adds a dramatic fill or crescendo at the end of an 8 or 16 bar section. Not only does it let the other members know where you are in the tune, it makes the performance more musical for the listeners. Everyone knows, "Here comes the end of this section! Get ready for the next!"
All great performers do this as a matter of craftsmanship. In some cases it's so automated, or ingrained in their subconscious that it seems instinctual. They don't even have to talk about it. They've done that sort of thing for so long it just happens naturally. But it is a learned art.
So, to answer your question, the responsibilities of the players don't change. It remains the same: everyone is supposed to know the tune ahead of time. It's just that in a 3 piece it becomes more obvious if someone or everyone doesn't know the tune! More members means it's easier to hide a weak link!
Learn the tune to the point that it doesn't matter if someone else screws up. You can keep playing confidently & hopefully they are listening & will be able to jump back in following your lead. It's a natural & necessary part of becoming a better musician.
Hope that helps!
Thanks Chris! I will take you advice and apply it. One obvious issue was using a tablet to help me remember some of my songs š³. I will make sure I have them memorized!
