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From the time of Plato through the Middle Ages, the quadrivium (plural: quadrivia, Latin for "four ways""Quadrivium (education)". Britannica Online. 2011. EB. ) was a grouping of four subjects or arts—arithmetic, geometry, music, and astronomy—that formed a second curricular stage following preparatory work in the trivium, consisting of grammar, logic, and rhetoric. Together, the trivium and the quadrivium comprised the seven liberal arts, and formed the basis of a liberal arts education in Western society until gradually displaced as a curricular structure by the studia humanitatis and its later offshoots, beginning with Petrarch in the 14th century. The seven classical arts were considered "thinking skills" and were distinguished from practical arts, such as medicine and architecture.
The four mathematical arts were recognized by Pythagoreans such as Nicomachus, but the use of quadrivium as a term for these four subjects has been attributed to Boethius, when he affirmed that the height of philosophy can be attained only following "a sort of fourfold path" ( quodam quasi quadruvio). (1978). 9780313204739, Praeger. ISBN 9780313204739 It was considered the foundation for the study of philosophy (sometimes called the "liberal art par excellence")Gilman, Daniel Coit, et al. (1905). New International Encyclopedia. Lemma "Arts, Liberal". and theology. The quadrivium was the upper division of medieval educational provision in the liberal arts, which comprised arithmetic (number in the abstract), geometry (number in space), music (number in time), and astronomy (number in space and time).
Educationally, the trivium and the quadrivium imparted to the student the seven essential thinking skills of classical antiquity.Onions, C.T., ed. (1991). The Oxford Dictionary of English Etymology. p. 944. Altogether the Seven Liberal Arts belonged to the so-called 'lower faculty' (of Arts), whereas Medicine, Jurisprudence (Law), and Theology were established in the three so-called 'higher' faculties.By way of example, until well into the 1970s, the faculty of Medicine of the University of Würzburg (Germany) was still officially referenced as a 'Hohe Fakultät' by its doctoral students in their written doctoral dissertations. It was therefore quite common in the middle ages for lecturers in the lower trivium and/or quadrivium faculty to be students themselves in one of the higher faculties. Philosophy was typically neither a subject nor a faculty in its own right, but was rather present implicitly as an 'auxiliary tool' within the discourses of the higher faculties, especially theology;'Philosophia ancilla theologiae' the separation of philosophy from theology and its elevation to an autonomous academic discipline were post-medieval developments.This separation is partly attributable to topical developments within philosophy itself, and due in part to Martin Luther's rejection of philosophy as 'useless for theology' as the Protestant Reformation evolved.
Displacement of the quadrivium by other curricular approaches from the time of Petrarch gained momentum with the subsequent Renaissance emphasis on what became the modern humanities, one of four liberal arts of the modern era, alongside natural science (where much of the actual subject matter of the original quadrivium now resides), social science, and the arts; though it may appear that music in the quadrivium would be a modern branch of performing arts, it was then an abstract system of proportions that was carefully studied at a distance from actual musical practice, and effectively a branch of music theory more tightly bound to arithmetic than to musical expression.
The Pythagoreans considered all mathematical science to be divided into four parts: one half they marked off as concerned with quantity, the other half with magnitude; and each of these they posited as twofold. A quantity can be considered in regard to its character by itself or in its relation to another quantity, magnitudes as either stationary or in motion. Arithmetic studies quantities as such, music the relations between quantities, geometry magnitude at rest, spherics astronomy magnitude inherently moving.Proclus. A Commentary on the First Book of Euclid's Elements, xii. trans. Glenn Raymond Morrow. Princeton: Princeton University Press, 1992. pp. 29–30. .
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 handWright, Craig (2001). The Maze and the Warrior: Symbols in Architecture, Theology, and Music. Cambridge, Massachusetts: Harvard University Press. and geometry and cosmology on the other.Smoller, Laura Ackerman (1994). History, Prophecy and the Stars: Christian Astrology of Pierre D'Ailly, 1350–1420. Princeton: Princeton University Press.
The subject of music within the quadrivium was originally the classical subject of , 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.
This schema is sometimes referred to as "classical education", but it is more accurately a development of the 12th- and 13th-century Renaissance with recovered classical elements, rather than an organic growth from the educational systems of antiquity. The term continues to be used by the classical education movement and at the independent Oundle School, in the United Kingdom.
Each of these iterations was discussed in a conference at King's College London on " The Future of Liberal Arts " at schools and universities.
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