The remaining four, the quadrivium are mathematics, music, geometry, and astronomy. These relate to the range of material that is taught, engaging on the four basic kinds of learning. Mathematics is abstract, absolute thought, encompassing the complexities of calculus and the systematic careers of scientific formula. Music is aesthetic awareness, including not only the performance and appreciation of music, but also, for the Ancients, the study and enjoyment of poetry. Astronomy meant the observation and study of the stars, but by extension this can stand for the whole range of empirical knowledge, the careful observation of nature that is the hallmark of all sciences.
Geometry relates to spatial knowledge, the apprehension of objects and their relationships in space.
For the Ancients, this would include architecture and the visual arts and could be extended to the contemporary disciplines of design and even engineering. Philosophy was also considered a natural science, since it dealt with truth about objective existence. Moral Science dealt with knowledge of human beings. This would include the study of human interaction, encoded in law and what we would call political science. Today, moral science would include what we term the social sciences, as well as the humanities.