Just keep in mind if using "madrigal" that it's usually not used to describe a singer, but a type of song. Nothing wrong with using it differently, just best to be aware that people with certain musical backgrounds may misunderstand your meaning at first.
You also have the typical words - minstral (if they play and sing) or bard (if they write and sing) or troubadour (which I think carries more of a just singer context). Or you could always come up with a different and unique word. I think the most important part is for the word you choose to sound thematically similar to other titles you're using