As proportion, musical ratios and divine numbers in

As defined online by the EnglishOxford Living Dictionaries, proportion is ‘The relationship of one thing toanother in terms of quantity, size, or number; ratio’1  The term proportion covers a wide range ofaspects in architectural buildings and plays a significant role in the eras ofCistercian, Gothic and Renaissance architecture.

  The fascination and interpretation ofproportion, musical ratios and divine numbers in the building of monasteriesand churches during these times will be discussed and evaluated throughout thisessay.Cistercian architecture is mainly associated with thebuilding of monasteries.  During thetwelfth century, a fascination with creating the most ‘ideal’ monastery tookhold and followed the rules of the Roman Catholic Cistercian Order.  The vastness and grandeur of the monasteries,abbeys and churches that were being built immediately before this time shockedand appalled St. Bernard of Clairvaux who was the head of the Roman CatholicCistercian Order.  St.

Bernard believedchurches should not distract from the true meaning of religion and religiouslife and should therefore not incorporate any ornamental piece, big or small,that would usually exist in medieval churches. The crucifix was one of the only religious item to be allowed.2 St. Bernard of Clairvaux decided to set up his own monasticorder called the Cistercians later in the twelfth century.  This movement worked mainly in remote areasof Europe, building mundane and simplistic churches, abbeys and monasteries.  During this period, Cistercians expandedimmensely and by the end of the 12th Century ‘there were 530Cistercian Abbeys’.

3  Due to the need forself-sustainability, it was here that the monks introduced new innovativefarming methods such as waterwheels and hydraulic engineering.  They also worked the land.2 (Anon., n.d.).

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  Every day the monks would also gathertogether in the chapter house and sit on stone benches that lined the wall asthey listened to a chapter being read out from the Rule of St. Benedict. 4 While St. Bernard believed his monasteries to be of a simpleand pragmatic form, upon further analysis we discover this isn’t quite true inthe grander scheme of things.  As we lookfurther into the total shape and form of the monasteries built in thisCistercian era, we discover a recurring principle that guided the building andgreatly influenced what these monasteries eventually looked like.

  Harsh geometrical principles were followed inthe monasteries organisation and layout. These geometrical principles could first be found in the writings of St.Augustine who drew comparisons between architecture and music.  He believed both architecture and musiccontained the same system of ratios and proportions that govern the divine geometriescontained in the universe.5  Due to this rigid style and structure, most Cistercianchurches and monastery buildings pose the exact same qualities and have veryfew differences throughout the buildings as a whole (Carolinarh, 2016).

  ‘The sculptural decoration of churches,manuscript illumination, stone towers on churches, and stained glass were allsuccessively proscribed’ (Britannica, 2017). Throughout their time, as the monks kept repeating the same layout anddesign of their first monastery, they eventually became to perfecting thestructures. If one is to compare the interior of two Cistercian churches, theywould notice very few dissimilarities in the layout and other significant elements(Carolinarh, 2016).

 For example, ‘the pillars have almost the sametransverse section and the moldings are identical’6.  Similarities also occur in the chapter housethe where it was always square and divided up into nine groin vaults with fourpillars existing in the centre.   Thechapter house tended to be located to the east of the cloister (Carolinarh, 2016).  A typical monastery consisted of ‘a dormitoryfor sleep, a cloister for strolling, a chapterhouse for the monks morningmeeting, and a caldarium, or warming room where the monks could read andtranscribe (also sometimes referred to as a scriptorium)’ (Bolli, n.d.

).  Unlike other orders, the Cistercians added anextra wing for lay men to join and stay. This was a distinguishing feature and proved very popular at that time. (Bolli, n.d.)On their exterior, the churches tended to be built from stoneof a pale colour, smooth and with little diversity (Anon.

, n.d.).’Cistercian churches were built on a Romanesque plan that embellished, withvaulting and a multiplication of parts, that of the Early Christian Basilica’ (Britannica, 2017).  This meant the churches were long and boastedside aisles, they had a raised nave with a semi-circular design on the eastwall where the sanctuary was on the nave. Before the pointed arches of the Gothic era, Cistercian churches hadrounded arches (Britannica, 2017).The Abbey of Fontenay, which is situated in Burgundy, Franceis a Romanesque Abbey and is a perfect example of the Cistercian Order’sarchitectural abilities and preferences. (Bolli, n.

d.).  This abbey contains all the rooms a typicalCistercian abbey would possess.   In order to insure the cloister and the churchwere kept out of any harm’s way during eventual expansion, they were builtparallel to each other, open at each end (wikipedia, n.d.).    FollowingSt. Bernard of Clairvaux’s rules, the church is free of any extravagantornamentation, including a crossing tower which is usually present inRomanesque churches (Bolli, n.

d.).  The capitols were also left bare and therewere no paintings of religious figures anywhere (wikipedia, n.

d.).  The only ornament to be found is a small bellon the roof which was used to make the monks aware of when to go to mass (Bolli, n.d.).  The materials used in the construction ofthis particular church was ‘the finest of ashlar masonry’ (Bolli, n.d.).

  The load of the church was not carried by itsarches or columns but by its thick walls (wikipedia, n.d.).

 The church takes the shape of a Latin cross and can only be enteredthrough a single doorway (Bolli, n.d.).  The Abbey of Fontenay boasts ‘a nave 66metres long and 8 metres wide, two side aisles, and a transept measuring 19metres’ (wikipedia, n.d.).  St. Bernard believed one could only trulyexperience God through light and therefore wanted nothing else but light toenter the church (wikipedia, n.

d.). Light enters Fontenay church at the right of the side aisles, through’windows at the East and West ends, as well as windows that pierce the Eastwall of the crossing transept’ (Bolli, n.d.).  In the designing process of the glasswindows, St. Bernard ensured numerical ratios that directly corresponded tomusic were used.  (wikipedia, n.

d.). For example, ‘the seven windows in the west of the interior weredistributed according to a musical ratio of 3/4’ (wikipedia, n.d.). This fascination with proportion and numbers ensured symmetry throughoutthe Cistercian architecture and produced aesthetically pleasing, simplebuildings to appreciate.   Following on from Cistercian architecture, Gothicarchitecture first appeared around approx. 1144 in France.

(Pevsner, 1990). It lasted in Europe ‘from the mid-12th Century to the 16thCentury’ (Britannica, 2017). ‘For the Gothic, as against the Romanesque style, is so essentiallybased on a co-operation between artist and engineer, and a synthesis ofaesthetic and technical qualities’ (Pevsner, 1990).  The most predominant features of the Gothicstyle are the rib-vault, the pointed arch and the flying buttress.  All these features contributed to theaesthetics of the buildings and made them more distinguishable. (Pevsner, 1990).  According to Pevsner, the purpose of thesefeatures ‘was to enliven inert masses of masonry, to quicken spatial motion, toreduce a building to a seeming system of innervated lines of action’ (Pevsner, 1990).

  In other words, these features allowedimmense additional height to the churches, while also ensuring natural lightflowed throughout the building. (Britannica, 2017). It gave the effect of lightness andtransparency, ‘of air circulating freely, of supple curves and energeticconcentration’ (Pevsner, 1990).

Unlike the Romanesque groin vaults which were in need ofsquare bays to be structurally sound, the Gothic pointed arch allows forconstruction of vaults over bays of many different shapes and forms other thansquare.  That being said, the Gothicoblong vault was also built with ribs which had the advantage of alsostrengthening the groins at the same time. (Pevsner, 1990). This ribbed vault was ‘made up of intersecting barrel vaults, whosestone ribs supported a vaulted ceiling of thin stone panels’ (Collins, 2008). This greatly reduced the initial weight of the vault and in turn theoutward thrust of the ceiling vault. This meant the weight of the vault was nowspread along a particular stone rib.

  Asthe weight wasn’t transmitted along an extended wall edge, it ‘could bechannelled from the rib to other supports, such as vertical piers or flyingbuttresses, which eliminated the need for solid, thick walls’ (Collins, 2008).  The flying buttresses were invented toreplace the need for ‘the massive walls between the radiating chapels which nowform a continuous wavy fringe to the ambulatory’ (Pevsner, 1990). The pointed arches also worked to vertically distribute the vaultsweight.  This new innovative,mathematical way of building ensured the Gothic churches could be built a lothigher, cold have much thinner walls and in turn allowed the option of a greatdeal more windows, sometimes stained glass, throughout the building. (Collins, 2008).

  All these featured contributed to the distinct aesthetics ofGothic architecture.  During this period,the exterior became a lot more complex. The buildings soared to even greater heights, symmetrical lines could beseen of vertical piers that were connected by flying buttresses so they could reachthe upper walls, and stunning rose windows were inserted.  As Gothic architecture continued to evolve,decorative art became more important to those designing the new cathedrals andas a result, ornamental stonework, now known to be called tracery, wasadded.

  (Collins, 2008). Gothic Sculpture also become more prominent as the exterior of thechurches were heavily decorated with religious figures as well as sculpturesrelaying a religious narrative.  Decorativefeatures such as pinnacles, moldings, and eventually window tracery.

  (Collins, 2008). The Gothic window ‘plays so large a part in Gothic architecture that itstands sponsor to each successive period, which is named “lancet, geometrical,curvilinear, flamboyant, or perpendicular,” according to the character of thestone framing in which the glass is set’ (Jackson, 1975). For example, during the High Gothic period, the walls largely consistedof stained glass ‘with vertical bars of tracery dividing windows into sections'(Collins, 2008). Early Gothic Architecture is said to be from the year 1120 to1200.  (Collins, 2008). Headed by Abbott Suger, one of the most well known Early Gothicbuildings is that of St. Denis Abbey located in the vicinity of Paris,France.  According to Nikolaus Pevsner,’Whoever designed the choir of St.

Denis, one can safely say, invented theGothic style’ (Pevsner, 1990). A sequence of four specific horizontal floors developed in thistime.  These levels were the’ground-level, then tribune gallery level, then triforium gallery level, abovewhich was an upper, windowed level called a clerestory’ (Collins, 2008). The columns and arches that were designed to bare the weight of thesefloors, ‘contributed to the geometry and harmony of the interior’ (Collins, 2008).   St. Denis gave precedence to many more cathedrals hoping toimitate its grandeur and philosophies. Examples of these include, but not limited to, ‘Paris (Notre Dame, c.

1163 seqq.), Laon (c. 1170 seqq.), Chartres (c. 1195 seqq.), Rheims (1211 seqq.

),Amiens (1220 seqq.), and Beauvais (1247 seqq.)’ (Pevsner, 1990).

 The ground plans at Sens and Noyon show newer, more daring layouts.  A ‘slightly centralizing tendency can benoted: at Sens by a lengthening of the chancel between transept and ambulatory,at Noyon by semi-circular endings of the transept to the north and south’ (Pevsner, 1990).  That being said, the architect in Parisdecided to situate his transept close to half way between the two towers at thewest and the east end.  His nave andchancel boast double aisles and his transepts reach little outside the outeraisles.

  As a result of this, the’spatial rhythm’ becomes a lot smoother (Pevsner, 1990). The theory of musical ratios, divine numbers and proportioncan be seen in the balance of the interiors. ‘High Gothic balance is a balance of two equally vehement drives towardstwo opposite directions’ (Pevsner, 1990). The contrast between the width and the height of the nave lead to amesmerizing first impression of its astonishing height.  At Sens, the width to height ratio was only 1: 1.

4.  In Paris it was 1 : 2.75 whichtranslated to 115 feet in height, in Beauvais the ratio was 1 : 3.

4 (157 feet),and in Cologne, the relative proportion is an incredible 1 : 3.8.  (Pevsner, 1990).

 The mathematical series known as Fibonacci’s Series, where each term isthe sum of the two last terms, was also used in the building of GothicArchitecture.  It enabled the architectsto draw the flying buttresses, columns and towers. (Bork, 2011-2012).  The third era of architecture to be discussed is Renaissancearchitecture.  Renaissance architectureoriginally came from Florence in the 15th Century and quickly madeits way around Europe, replacing Gothic architecture.  It reflects the ‘rebirth of Classic culture’ (Britannica, 2009) and also lead to therevival of old Roman forms such as the round arch, columns, the tunnel vaultand the dome.

(Britannica, 2009). Some examples of architects that contributed to Renaissance architectureinclude Filippo Brunelleschi, who was influenced by the work of Alberti, DonatoBramante and Michelangelo.  Renaissancearchitectures fascination with proportion derived from the writings ofVitruvius and ruins of ancient buildings.

 Many associated beauty with proportion so therefore the architects drewparallels between the human form and buildings. This in turn ‘resulted in clear, easily comprehended space and mass’ (Britannica, 2009) which madeRenaissance buildings separate themselves from the more convoluted Gothicstyle.   Brunelleschi’sarguably most famous Renaissance building is the Cathedral of Florence and thespectacular dome that accompanies it. Peter Murray argues ‘Perhaps the most important thing about his dome isthe fact that it is a feat of engineering which could not have been carried outby anyone else in the fifteenth century’ (Murray, 1986).  Upon building the dome, Brunelleschi faced two major problems, nocentering of the usual type was possible, and the drum for over the octagonalready existed.  A typical hemisphericaldome would have said to have been Brunelleschi’s preferred shape because of itsperfect shape. However, due to these problems, he had to adopt a pointed dometo ease the side thrust.  The onlysolution was to ‘build a dome pointed in section and supported on ribs with thelightest possible infilling between them’ (Murray, 1986).

 The finished dome can be seen from every street in Florence and is thepride and joy of the city.His work on the façade of Foundling demonstrated more theneed for symmetry and proportion at this time. It consisted of a colonnade on the ground floor, Corinthian columns,wide semi-circular arched that allowed light and warmth into the loggia, afirst floor that had widely spaced and reasonably sized rectangular windowsunder trivial pediments directly aligning with to the arches beneath. (Pevsner, 1990).  Inside, the ground floor and the clerestoryare the same height, and the ratio width to height in the nave is 1 : 2.  The aisles have square bays that are in theratio of 1 : 2 also.  The nave ‘ consistsof exactly four and a half squares’ (Pevsner, 1990).  A great effort was made in the 15thcentury to master space.

 Therefore, theidea of perspective and using perspective in buildings gained popularity duringthe Renaissance period ‘so architects were now anxious to find rationalproportions for their buildings’ (Pevsner, 1990).  A discovery of linear perspective was made during the Renaissance.Architects kept to human scale as they designed their building which meant thatone never got overwhelmed by its size.  Anexample where this is used is Alberti’s S. Andrea in Mantua.  Alberti changed the traditional nave and aislearrangement to a ‘series of side chapels taking the place of the aisles and connectedwith the nave alternately by tall and wide and low narrow openings’ (Pevsner, 1990).  By keeping the same proportions throughout thechurch, leaves a ‘deeply restful harmony’ in its wake (Pevsner, 1990).

 In conclusion, while each had their own beliefs on how their buildingsshould look aesthetically, preferences with ornamentation, and pushing the mathematicallimits of their time, each Cistercian, Gothic and Renaissance architecture showa fascination for proportion, and include proportion, musical ratios and divinenumbers in their buildings.   1Anon., 2017. English Oxford LivingDictionaries. OnlineAvailable at: https://en. 30 12 2017. 2Anon., n.d.

Revolvy.. OnlineAvailable at: type=topic Accessed 04 01 2018.

3Anon., 2016. OnlineAvailable at: http://www. 05 01 2018.4Anon.

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