Quadrivium

==Medieval usage==
[[File:Woman teaching geometry.jpg|thumb|''Woman teaching how to construct geometric shapes''. Illustration at the beginning of a medieval translation of Euclid's Elements, ({{circa|1310}})|200x200px]]
At many [[medieval universities]], this would have been the course leading to the degree of [[Master of Arts]] (after the [[Bachelor of Arts|BA]]). After the MA, the student could enter for bachelor's degrees of the higher faculties (Theology, Medicine or Law). To this day, some of the postgraduate degree courses lead to the degree of Bachelor (the [[Bachelor of Philosophy|B.Phil]] and [[British degree abbreviations|B.Litt.]] degrees are examples in the field of philosophy).

The study was eclectic, approaching the philosophical objectives sought by considering it from each aspect of the quadrivium within the general structure demonstrated by [[Proclus]] (AD 412–485), namely arithmetic and music on the one hand<ref>Wright, Craig (2001). ''The Maze and the Warrior: Symbols in Architecture, Theology, and Music''. Cambridge, Massachusetts: Harvard University Press.</ref> and geometry and cosmology on the other.<ref>Smoller, Laura Ackerman (1994). ''History, Prophecy and the Stars: Christian Astrology of Pierre D'Ailly, 1350–1420. Princeton: Princeton University Press.</ref>

The subject of music within the quadrivium was originally the classical subject of [[harmonic]]s, in particular the study of the proportions between the musical intervals created by the division of a [[monochord]]. A relationship to music as actually practised was not part of this study, but the framework of classical harmonics would substantially influence the content and structure of music theory as practised in both European and Islamic cultures.