I took Latin in secondary school and my teacher, several classmates and I concluded that the derivation of the Noun, though unclear, indicates several possible related origins:
From dialectal madregal < from medieval Latin matricale < from neuter of matricalis simple < from late Latin of the womb < from Latin: matric-, matrix womb , from mater mother.
Thus, the vocal music and poem forms of the Madrigal Nouns possibly mean "in the mother tongue".
I researched the Madrigal Surname family tree, and the consensus was that the surname originated in the municipality Madrigal de las Altas Torres in Spain, From there, it propagated to Madrid, and later to the rest of the Spanish peninsula, reached the Islands of Sicily and Sardegna in Italy, got established in the Americas, and continues to spread geographically around the Globe.
Incidentally, if your surname is Madrigal you might want to find our group in facebook.