Quadrivium

{{Short description |Liberal arts of astronomy, arithmetic, music and geometry}}
[[File:God the Geometer.jpg|thumb|upright=1.0|For most medieval scholars, who believed that God created the [[universe]] according to [[Musica universalis|geometric and harmonic principles]], [[science]]—particularly [[geometry]] and [[astronomy]]—was linked directly to [[divinity|the divine]]. To seek these principles, therefore, would be to seek God.{{Citation needed|date=December 2022}}]]

From the time of [[Plato]] through the [[Middle Ages]], the '''''quadrivium''''' (plural: quadrivia<ref name="JE">{{cite encyclopedia |url=http://www.jewishencyclopedia.com/articles/14950-wisdom |title=Wisdom |last=Kohler |first=Kaufmann |encyclopedia=[[Jewish Encyclopedia]] |access-date=2015-11-07 }}</ref>) 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,<ref name="nie">{{Cite NIE |wstitle=Quadrivium |year=1905}}</ref> and formed the basis of a [[liberal arts education]] in Western society until gradually displaced as a curricular structure by the [[humanitas#Revival|''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 ''quadrivium'', [[Latin]] for 'four ways',<ref>"Quadrivium (education)". ''[[Britannica Online]]''. 2011. [http://www.britannica.com/EBchecked/topic/485943/quadrivium EB].
</ref> and its use for the four subjects have been attributed to [[Boethius]], who
was apparently the first to use the term{{Sfn|Fried|2015|p=2}} when affirming that the height of philosophy can be attained only following "a sort of fourfold path" (''quodam quasi quadruvio'').<ref>{{cite book | vauthors=((Stahl, W. H.)) | date=6 November 1978 | title=[[Roman Science: Origins, Development, and Influence to the Later Middle Ages]] | publisher=Praeger |  isbn=978-0-313-20473-9}}</ref>{{rp|199}}. It was considered the foundation for the study of [[philosophy]] (sometimes called the "liberal art ''par excellence''")<ref>[[Daniel Coit Gilman|Gilman, Daniel Coit]], et al. (1905). ''[[New International Encyclopedia]]''. Lemma "Arts, Liberal".</ref> 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]].<ref>Onions, C.T., ed. (1991). The Oxford Dictionary of English Etymology. p. 944.</ref> 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.<ref>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.</ref> 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;<ref>'Philosophia ancilla theologiae'</ref> the separation of philosophy from theology and its elevation to an autonomous academic discipline were post-medieval developments.<ref>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.</ref>

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.{{Citation needed|date=December 2022}}

==Origins==
[[File:Boetius.png|thumb|224x224px|The Roman philosopher [[Boethius]], author of [[On the Consolation of Philosophy|''The Consolation of Philosophy'']]]]
These four studies compose the secondary part of the curriculum outlined by [[Plato]] in [[The Republic (Plato)|''The Republic'']] and are described in the seventh book of that work (in the order Arithmetic, Geometry, Astronomy, Music).<ref name="nie"/>
The quadrivium is implicit in early [[Pythagoreanism|Pythagorean]] writings and in the ''De nuptiis'' of [[Martianus Capella]], although the term ''quadrivium'' was not used until [[Boethius]], early in the sixth century.<ref>Marrou, Henri-Irénée (1969). "Les Arts Libéraux dans l'Antiquité Classique". pp. 6–27 in ''Arts Libéraux et Philosophie au Moyen Âge''. Paris: Vrin; Montréal: Institut d'Études Médiévales. pp. 18–19.</ref>  As [[Proclus]] wrote:

<blockquote>
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.<ref>Proclus. ''A Commentary on the First Book of Euclid's Elements'', xii. trans. Glenn Raymond Morrow. Princeton: Princeton University Press, 1992. pp. 29–30. {{ISBN|0-691-02090-6}}.</ref>
</blockquote>

==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.

==Modern usage==
In modern applications of the liberal arts as curriculum in colleges or universities, the quadrivium may be considered to be the study of [[number]] and its relationship to space or time: arithmetic was pure number, geometry was number in [[space]], music was number in [[time]], and astronomy was number in [[spacetime|space and time]]. [[Morris Kline]] classified the four elements of the quadrivium as pure (arithmetic), stationary (geometry), moving (astronomy), and applied (music) number.<ref>Kline, Morris (1953). "The Sine of G Major". In ''Mathematics in Western Culture''. Oxford University Press.</ref>

This schema is sometimes referred to as "classical education", but it is more accurately a [[Renaissance of the 12th century|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.<ref>{{cite web |url=http://www.boarding.org.uk/media/news/article/2352/Oundle-School-Improving-Intellectual-Challenge |title=Oundle School – Improving Intellectual Challenge |date=27 October 2014 |website=The Boarding Schools' Association |access-date=10 December 2015 |archive-date=15 August 2020 |archive-url=https://web.archive.org/web/20200815195502/http://www.boarding.org.uk/media/news/article/2352/Oundle-School-Improving-Intellectual-Challenge |url-status=dead }}<br />Each of these iterations was discussed in a conference at [[King's College London]] on "[http://www.kcl.ac.uk/artshums/depts/liberal/conference.aspx The Future of Liberal Arts] {{Webarchive|url=https://web.archive.org/web/20160525204125/http://www.kcl.ac.uk/artshums/depts/liberal/conference.aspx |date=2016-05-25 }}" at schools and universities.</ref>

==See also==
{{Wiktionary|quadrivium}}

* [[Andreas Capellanus]]
* [[Degrees of the University of Oxford]]
* [[Four arts]]
* [[Martianus Capella]]
* [[Trivium]]


==References==
{{reflist|30em}}

=== Book sources ===

* {{Cite book |last=Fried |first=Johannes |title=The Middle Ages |publisher=[[Harvard University Press]] |year=2015 |isbn=978-0-67405-562-9 |edition=3rd |publication-place=Cambridge, MA}}

{{Humanities}}
{{Classical education|state=collapsed}}
{{Authority control}}

[[Category:4 (number)]]
[[Category:Cultural lists|4 Quadrivium]]
[[Category:Liberal arts education]]
[[Category:Medieval European education]]

[[es:Artes liberales#Las siete artes: Trivium et Quadrivium]]