From the time ofPlato through theMiddle Ages, thequadrivium (plural:quadrivia,[2] Latin for "four ways"[3]) was a grouping of four subjects or arts—arithmetic,geometry,music, andastronomy—that formed a second curricular stage following preparatory work in thetrivium, consisting ofgrammar,logic, andrhetoric. Together, the trivium and thequadrivium comprised the seven liberal arts,[4] and formed the basis of aliberal arts education in Western society until gradually displaced as a curricular structure by thestudia humanitatis and its later offshoots, beginning withPetrarch in the 14th century. The seven classical arts were considered "thinking skills" and were distinguished from practical arts, such asmedicine andarchitecture.
The four mathematical arts were recognized by Pythagoreans such asNicomachus of Gerasa, but the use ofquadrivium as a term for these four subjects has been attributed toBoethius,[5] when he affirmed that the height of philosophy can be attained only following "a sort of fourfold path" (quodam quasi quadruvio).[6]: 199 It was considered the foundation for the study ofphilosophy (sometimes called the "liberal artpar excellence")[7] andtheology. Thequadrivium was the upper division of medieval educational provision in the liberal arts, which comprised arithmetic (absolute number), music (relative number), geometry (magnitude at rest), and astronomy (magnitude in motion).[8]
Educationally, thetrivium and thequadrivium imparted to the student the seven essential thinking skills ofclassical antiquity.[9] 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.[10] 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 typicallyneither a subjectnor a faculty in its own right, but was rather presentimplicitly as an 'auxiliary tool' within the discourses of the higher faculties, especially theology;[11] the separation of philosophy from theology and its elevation to an autonomous academic discipline were post-medieval developments.[12]
Displacement of the quadrivium by other curricular approaches from the time of Petrarch gained momentum with the subsequentRenaissance emphasis on what became the modernhumanities, one of four liberal arts of the modern era, alongsidenatural science (where much of the actual subject matter of the original quadrivium now resides),social science, andthe arts; though it may appear that music in the quadrivium would be a modern branch ofperforming arts, it was then an abstract system of proportions that was carefully studied at a distance from actual musical practice, and effectively a branch ofmusic theory more tightly bound to arithmetic than to musical expression.[citation needed]
These four studies compose the secondary part of the curriculum outlined byPlato inThe Republic and are described in the seventh book of that work (in the order Arithmetic, Geometry, Astronomy, Music).[4]The quadrivium is implicit in earlyPythagorean writings and in theDe nuptiis ofMartianus Capella, although the termquadrivium was not used untilBoethius, early in the sixth century.[13] AsProclus wrote:
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.[14]
At manymedieval universities, this would have been the course leading to the degree ofMaster of Arts (after theBA).[citation needed] 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 (theB.Phil andB.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 byProclus (AD 412–485), namely arithmetic and music on the one hand[15] and geometry and cosmology on the other.[16]
The subject of music within the quadrivium was originally the classical subject ofharmonics, in particular the study of the proportions between the musical intervals created by the division of amonochord. 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.
In modern applications of the liberal arts as curriculum in colleges or universities, the quadrivium may be considered to be the study ofnumber and its relationship to space or time: arithmetic being pure number, geometry number inspace, music number intime, and astronomy number inspace and time.Morris Kline classified the four elements of the quadrivium as pure (arithmetic), stationary (geometry), moving (astronomy), and applied (music) number.[17]
This schema is sometimes referred to as "classical education", but it is more accurately adevelopment of the 12th- and 13th-century Renaissance with recovered classical elements, rather than an organic growth from the educational systems of antiquity.[citation needed] The term continues to be used by theclassical education movement and at the independentOundle School, in the United Kingdom.[18]
The dictionary definition ofquadrivium at Wiktionary
