If I understand the intended meaning, I believe that the sentence could be rephrased into something like, "Many of his poems were set to music and later/eventually developed into Scottish folk songs."I agree that the 'become' is problematic. What are you trying to say exactly? It almost sounds like the setting of the text to music made them folk songs. That is not the case. Were they set to existing folk tunes?
I just wanted to ask if "put to music" and "set to music" means the same thing. Would you tell me what I should have asked?No.
Why would you want to alter a standard collocation?
The poem was put to music in a collaboration with Curly Musgrave on his Cowboy True CD.