In the discussions and debates surrounding liturgical music of the past fifty years, music theorists, critics, and historians have contributed little, and their counsel has rarely been sought. Whenever the matter of liturgical music arises, most often in parishes, but sometimes in episcopal conferences or in the academy or in Vatican documents, the nature of the music, as music, almost never affects the discussion.

With Sacred Treasure, Joseph Swain, a distinguished musicologist and accomplished performer, attempts to change that. He offers a theory for building authentic...