As proportion, musical ratios and divine numbers in

As defined online by the English
Oxford Living Dictionaries, proportion is ‘The relationship of one thing to
another in terms of quantity, size, or number; ratio’1  The term proportion covers a wide range of
aspects in architectural buildings and plays a significant role in the eras of
Cistercian, Gothic and Renaissance architecture.  The fascination and interpretation of
proportion, musical ratios and divine numbers in the building of monasteries
and churches during these times will be discussed and evaluated throughout this

Cistercian architecture is mainly associated with the
building of monasteries.  During the
twelfth century, a fascination with creating the most ‘ideal’ monastery took
hold 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 shocked
and appalled St. Bernard of Clairvaux who was the head of the Roman Catholic
Cistercian Order.  St. Bernard believed
churches should not distract from the true meaning of religion and religious
life 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 monastic
order called the Cistercians later in the twelfth century.  This movement worked mainly in remote areas
of Europe, building mundane and simplistic churches, abbeys and monasteries.  During this period, Cistercians expanded
immensely and by the end of the 12th Century ‘there were 530
Cistercian Abbeys’.3
  Due to the need for
self-sustainability, it was here that the monks introduced new innovative
farming methods such as waterwheels and hydraulic engineering.  They also worked the land.2 (Anon., n.d.).  Every day the monks would also gather
together in the chapter house and sit on stone benches that lined the wall as
they listened to a chapter being read out from the Rule of St. Benedict. 4

While St. Bernard believed his monasteries to be of a simple
and pragmatic form, upon further analysis we discover this isn’t quite true in
the grander scheme of things.  As we look
further into the total shape and form of the monasteries built in this
Cistercian era, we discover a recurring principle that guided the building and
greatly influenced what these monasteries eventually looked like.  Harsh geometrical principles were followed in
the 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 music
contained the same system of ratios and proportions that govern the divine geometries
contained in the universe.5 

Due to this rigid style and structure, most Cistercian
churches and monastery buildings pose the exact same qualities and have very
few differences throughout the buildings as a whole (Carolinarh,
2016).  ‘The sculptural decoration of churches,
manuscript illumination, stone towers on churches, and stained glass were all
successively proscribed’ (Britannica, 2017). 
Throughout their time, as the monks kept repeating the same layout and
design of their first monastery, they eventually became to perfecting the
structures. If one is to compare the interior of two Cistercian churches, they
would notice very few dissimilarities in the layout and other significant elements
(Carolinarh, 2016).  For example, ‘the pillars have almost the same
transverse section and the moldings are identical’6.  Similarities also occur in the chapter house
the where it was always square and divided up into nine groin vaults with four
pillars existing in the centre.   The
chapter house tended to be located to the east of the cloister (Carolinarh,
2016).  A typical monastery consisted of ‘a dormitory
for sleep, a cloister for strolling, a chapterhouse for the monks morning
meeting, and a caldarium, or warming room where the monks could read and
transcribe (also sometimes referred to as a scriptorium)’ (Bolli, n.d.).  Unlike other orders, the Cistercians added an
extra 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 stone
of a pale colour, smooth and with little diversity (Anon., n.d.).
‘Cistercian churches were built on a Romanesque plan that embellished, with
vaulting and a multiplication of parts, that of the Early Christian Basilica’ (Britannica, 2017).  This meant the churches were long and boasted
side aisles, they had a raised nave with a semi-circular design on the east
wall where the sanctuary was on the nave. 
Before the pointed arches of the Gothic era, Cistercian churches had
rounded arches (Britannica, 2017).

The Abbey of Fontenay, which is situated in Burgundy, France
is a Romanesque Abbey and is a perfect example of the Cistercian Order’s
architectural abilities and preferences. (Bolli, n.d.).  This abbey contains all the rooms a typical
Cistercian abbey would possess.   In order to insure the cloister and the church
were kept out of any harm’s way during eventual expansion, they were built
parallel to each other, open at each end (wikipedia, n.d.).    Following
St. Bernard of Clairvaux’s rules, the church is free of any extravagant
ornamentation, including a crossing tower which is usually present in
Romanesque churches (Bolli, n.d.).  The capitols were also left bare and there
were no paintings of religious figures anywhere (wikipedia,
n.d.).  The only ornament to be found is a small bell
on 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 of
this particular church was ‘the finest of ashlar masonry’ (Bolli, n.d.).  The load of the church was not carried by its
arches or columns but by its thick walls (wikipedia, n.d.). 
The church takes the shape of a Latin cross and can only be entered
through a single doorway (Bolli, n.d.).  The Abbey of Fontenay boasts ‘a nave 66
metres long and 8 metres wide, two side aisles, and a transept measuring 19
metres’ (wikipedia, n.d.).  St. Bernard believed one could only truly
experience God through light and therefore wanted nothing else but light to
enter 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 East
wall of the crossing transept’ (Bolli, n.d.).  In the designing process of the glass
windows, St. Bernard ensured numerical ratios that directly corresponded to
music were used.  (wikipedia, n.d.). 
For example, ‘the seven windows in the west of the interior were
distributed according to a musical ratio of 3/4’ (wikipedia, n.d.). 
This fascination with proportion and numbers ensured symmetry throughout
the Cistercian architecture and produced aesthetically pleasing, simple
buildings to appreciate. 


Following on from Cistercian architecture, Gothic
architecture first appeared around approx. 1144 in France. (Pevsner, 1990). 
It lasted in Europe ‘from the mid-12th Century to the 16th
Century’ (Britannica, 2017). 
‘For the Gothic, as against the Romanesque style, is so essentially
based on a co-operation between artist and engineer, and a synthesis of
aesthetic and technical qualities’ (Pevsner, 1990).  The most predominant features of the Gothic
style are the rib-vault, the pointed arch and the flying buttress.  All these features contributed to the
aesthetics of the buildings and made them more distinguishable. (Pevsner, 1990).  According to Pevsner, the purpose of these
features ‘was to enliven inert masses of masonry, to quicken spatial motion, to
reduce a building to a seeming system of innervated lines of action’ (Pevsner, 1990).  In other words, these features allowed
immense additional height to the churches, while also ensuring natural light
flowed throughout the building. (Britannica, 2017). It gave the effect of lightness and
transparency, ‘of air circulating freely, of supple curves and energetic
concentration’ (Pevsner, 1990).

Unlike the Romanesque groin vaults which were in need of
square bays to be structurally sound, the Gothic pointed arch allows for
construction of vaults over bays of many different shapes and forms other than
square.  That being said, the Gothic
oblong vault was also built with ribs which had the advantage of also
strengthening the groins at the same time. (Pevsner, 1990). 
This ribbed vault was ‘made up of intersecting barrel vaults, whose
stone ribs supported a vaulted ceiling of thin stone panels’ (Collins, 2008). 
This greatly reduced the initial weight of the vault and in turn the
outward thrust of the ceiling vault. This meant the weight of the vault was now
spread along a particular stone rib.  As
the weight wasn’t transmitted along an extended wall edge, it ‘could be
channelled from the rib to other supports, such as vertical piers or flying
buttresses, which eliminated the need for solid, thick walls’ (Collins,
2008).  The flying buttresses were invented to
replace the need for ‘the massive walls between the radiating chapels which now
form a continuous wavy fringe to the ambulatory’ (Pevsner, 1990). 
The pointed arches also worked to vertically distribute the vaults
weight.  This new innovative,
mathematical way of building ensured the Gothic churches could be built a lot
higher, cold have much thinner walls and in turn allowed the option of a great
deal more windows, sometimes stained glass, throughout the building. (Collins, 2008). 

All these featured contributed to the distinct aesthetics of
Gothic architecture.  During this period,
the exterior became a lot more complex. 
The buildings soared to even greater heights, symmetrical lines could be
seen of vertical piers that were connected by flying buttresses so they could reach
the 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 and
as a result, ornamental stonework, now known to be called tracery, was
added.  (Collins, 2008). 
Gothic Sculpture also become more prominent as the exterior of the
churches were heavily decorated with religious figures as well as sculptures
relaying a religious narrative.  Decorative
features such as pinnacles, moldings, and eventually window tracery.  (Collins, 2008). 
The Gothic window ‘plays so large a part in Gothic architecture that it
stands sponsor to each successive period, which is named “lancet, geometrical,
curvilinear, flamboyant, or perpendicular,” according to the character of the
stone framing in which the glass is set’ (Jackson, 1975). 
For example, during the High Gothic period, the walls largely consisted
of stained glass ‘with vertical bars of tracery dividing windows into sections’
(Collins, 2008). 

Early Gothic Architecture is said to be from the year 1120 to
1200.  (Collins, 2008). 
Headed by Abbott Suger, one of the most well known Early Gothic
buildings 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 the
Gothic style’ (Pevsner, 1990). 
A sequence of four specific horizontal floors developed in this
time.  These levels were the
‘ground-level, then tribune gallery level, then triforium gallery level, above
which was an upper, windowed level called a clerestory’ (Collins, 2008). 
The columns and arches that were designed to bare the weight of these
floors, ‘contributed to the geometry and harmony of the interior’ (Collins, 2008).   

St. Denis gave precedence to many more cathedrals hoping to
imitate 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 be
noted: 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 Paris
decided to situate his transept close to half way between the two towers at the
west and the east end.  His nave and
chancel boast double aisles and his transepts reach little outside the outer
aisles.  As a result of this, the
‘spatial rhythm’ becomes a lot smoother (Pevsner, 1990). 

The theory of musical ratios, divine numbers and proportion
can be seen in the balance of the interiors. 
‘High Gothic balance is a balance of two equally vehement drives towards
two opposite directions’ (Pevsner, 1990). 
The contrast between the width and the height of the nave lead to a
mesmerizing 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 which
translated 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 is
the sum of the two last terms, was also used in the building of Gothic
Architecture.  It enabled the architects
to draw the flying buttresses, columns and towers. (Bork, 2011-2012).


The third era of architecture to be discussed is Renaissance
architecture.  Renaissance architecture
originally came from Florence in the 15th Century and quickly made
its way around Europe, replacing Gothic architecture.  It reflects the ‘rebirth of Classic culture’ (Britannica, 2009) and also lead to the
revival of old Roman forms such as the round arch, columns, the tunnel vault
and the dome. (Britannica, 2009). 
Some examples of architects that contributed to Renaissance architecture
include Filippo Brunelleschi, who was influenced by the work of Alberti, Donato
Bramante and Michelangelo.  Renaissance
architectures fascination with proportion derived from the writings of
Vitruvius and ruins of ancient buildings. 
Many associated beauty with proportion so therefore the architects drew
parallels between the human form and buildings. 
This in turn ‘resulted in clear, easily comprehended space and mass’ (Britannica, 2009) which made
Renaissance buildings separate themselves from the more convoluted Gothic

arguably most famous Renaissance building is the Cathedral of Florence and the
spectacular dome that accompanies it. 
Peter Murray argues ‘Perhaps the most important thing about his dome is
the fact that it is a feat of engineering which could not have been carried out
by anyone else in the fifteenth century’ (Murray, 1986).  
Upon building the dome, Brunelleschi faced two major problems, no
centering of the usual type was possible, and the drum for over the octagon
already existed.  A typical hemispherical
dome would have said to have been Brunelleschi’s preferred shape because of its
perfect shape. However, due to these problems, he had to adopt a pointed dome
to ease the side thrust.  The only
solution was to ‘build a dome pointed in section and supported on ribs with the
lightest possible infilling between them’ (Murray, 1986). 
The finished dome can be seen from every street in Florence and is the
pride and joy of the city.

His work on the façade of Foundling demonstrated more the
need 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, a
first floor that had widely spaced and reasonably sized rectangular windows
under trivial pediments directly aligning with to the arches beneath. (Pevsner, 1990).  Inside, the ground floor and the clerestory
are the same height, and the ratio width to height in the nave is 1 : 2.  The aisles have square bays that are in the
ratio of 1 : 2 also.  The nave ‘ consists
of exactly four and a half squares’ (Pevsner, 1990).  A great effort was made in the 15th
century to master space.  Therefore, the
idea of perspective and using perspective in buildings gained popularity during
the Renaissance period ‘so architects were now anxious to find rational
proportions 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 that
one never got overwhelmed by its size.  An
example where this is used is Alberti’s S. Andrea in Mantua.  Alberti changed the traditional nave and aisle
arrangement to a ‘series of side chapels taking the place of the aisles and connected
with the nave alternately by tall and wide and low narrow openings’ (Pevsner, 1990).  By keeping the same proportions throughout the
church, leaves a ‘deeply restful harmony’ in its wake (Pevsner,

In conclusion, while each had their own beliefs on how their buildings
should look aesthetically, preferences with ornamentation, and pushing the mathematical
limits of their time, each Cistercian, Gothic and Renaissance architecture show
a fascination for proportion, and include proportion, musical ratios and divine
numbers in their buildings.  


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John Olley, ‘Sustaining the Narrative at Kilmainham’
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