Cistercian ratios. And each of the middle

architecture is a style of architecture associated with the churches,
monasteries and abbeys of the Roman Catholic Cistercian Order. It was headed by
Abbot Bernard of Clairvaux, who believed that churches should avoid superfluous
ornamentation so as not to distract from the religious life.

architecture is an architectural style that flourished in Europe during the
High and Late Middle Ages. It evolved from Romanesque architecture and was
succeeded by Renaissance architecture.

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architecture is the European architecture of the period between the early 14th
and early 17th centuries in different regions, demonstrating a conscious revival
and development of certain elements of ancient Greek and Roman thought and
material culture.






















The Old Registry (Burgerlijke Griffie)

By Jan Wallot and
Christiaan Sixdeniers


This is ‘a
typical example of the early Flemish Renaissance style. Gothic features are
combined with classical motifs to form a harmonious whole. The front is
dominated by huge windows and the engaged columns framing it at the side.’ (Markschies,
This view of the entire front façade from the market square is almost entirely
symmetrical with the obvious exceptions of the arch to access the rear of the
building, the front entrance being off centre and each of the statues across
the top representing Moses Justice and Arron. ‘The building underwent
considerable restoration in the late 19th century.’ (Markschies,

individual window pane is twice as high as it is wide which gives it a ratio of
1:2 one of the nine musical ratios. And each of the middle sections of windows
with six windows have a ratio of 2:6 or 1:3 another one of these musical ratios
which are engrained into the human subconscious for us to find these buildings



‘Johann Heinrich Müntz, Section of
the Octagonal Room for Mr Bateman’s House At Old Windsor, ink and wash 215mm x
370mm, 1761.’ (McCarthy, 1987)

This is a
perfect example of what gothic architects were trying to achieve they wanted to
thin out the walls and flood buildings with light to create a heavenly
environment. The pointed arch allowed them to build in this way.




This being
the only flat wall in this same image as on page 2 it is the only wall to show
its true shape allowing me to take accurate measurements from this drawing. The
window is once again twice as tall as it is wide making it 1:2 the same musical
ratio used on the Old Registry even though these designs are of two different
styles they each have the common trait of the use of musical ratios.

ornamentation flanking the window is only half the width of the window itself making
it once again the very same repetitive musical ratio of 1:2


Ratios break into three sections short, middling and long.

The short
ratios include: 1:1 2:3 and 3:4.

The middling
ratios include: 1:2, 4:9 and 9:16.

The long
ratios include: 1:3, 3:8 and 1:4.

‘The great cathedrals are a
symbol of the Middle Ages. By the middle Ages numbers had acquired a
metaphysical significance of their own, and were thought to be endowed with
occult power. Thus, they found their way into nearly every aspect of cathedral
design, from the numbers of the pillars in the choir and layout of the facade,
and, inevitably, to the division of the rose windows. In fact, the middle ages
were nuts about numbers and geometry.’ (Calter, 1998)

Dame de Paris

Notre Dame
in Paris, which was built in between 1163 and 1250 appears to have golden ratio
proportions in a number of its key proportions of design.  

Although it
is rather asymmetrical in its design and difficult to measure photographically
because of parallax distortions, which is a distortion that doesn’t allow us to
view objects or buildings in their true shape as they would be on an
architectural drawing. A simple everyday example of parallax can be seen in the
dashboard of vehicles that use a needle-style speedometer gauge. When viewed
from directly in front, the speed may show exactly 60; but when viewed from the
passenger seat the needle may appear to show a slightly different speed, due to
the angle of viewing.

The golden
ratio lines of the green, yellow and red rectangles conform closely to the
major architectural lines, which represent:

– Vertical height of base at ground level: Top of first level: Top of second
Vertical height of base of second level: Top of second level: Top of third
– Horizontal width of outside of left top section: Inside of top right section:
Outside of top right section.   Sénanque Abbey Near the
village of Gourdes in the Vaucluse Provence in France this Cistercian monastery
was built in 1178 and followed the words of St. Bernard of Clairvaux. ‘He
suggested the massive ornamental programme and the vast scale and height of the
churches and ancillary buildings not only went against the teaching of St.
Benedict but also seriously impeded spirituality. He set up a
new, puritanical movement called Cistercians (from Cîteaux) in the twelfth century. This
ascetic organisation renounced the architectural excesses of Cluny and instead
built stripped down simply organised structures located deliberately in remote
areas of Europe. Here, as well as listening the Rule in the chapter house, the
monks tilled the land and introduced new farming techniques and other
innovations.The apparent
simplicity of their buildings, however, is slightly misleading. Most Cistercian
monasteries followed strict geometrical principals in their organisation and
layout. These principals had their origins in the writings of St. Augustine who
compared architecture with music, suggesting both could contain the same system
of ratios and proportions that the divine geometries of the universe.’ (Boyd, n.d.) This is a view of the same arches in Sénanque
Abbey only flat on to show the geometry more accurately but unfortunately not
completely avoiding parallax distortions.The geometry
of these arches provides a nice effect especially with the repeated pattern in
this cloister. With the smaller arches being about a quarter of the radius of
the arch that it is set into makes it match up to another one of these musical
ratios, the long ratio of 1:4. I think this effect only really works because
the smaller arches are positioned on the diameters of the larger arches. The
middle arches and the larger arches also are concentric which is to say they
have the same centre points.             Santa Maria NovellaBy Leon Battista
Alberti’In designing
this church, Leon Battista Alberti (1404-72) takes his cue from a
pre-Gothic medieval design – that of San Miniato
al Monte. Following his Romanesque model, he
designs a small, pseudo-Classical, pediment-capped temple front for the upper
part of the facade and supports it with a broad base of pilaster-enframed arcades that incorporate
the six tombs and three doorways of the extant Gothic
building.In the organization of these elements, Alberti takes a long step
beyond the Romanesque planners.
The height of Santa Maria Novella (to the tip of the pediment) equals its
width, so that the entire facade can be inscribed in a square.

The upper structure. in turn, can be encased in a square one-fourth the size of
the main square; the cornice of the entablature that separates the two levels halves
the major square, so that the lower portion of the building becomes a rectangle
that is twice as wide as it is high; and the areas outlined by the columns on
the lower level are squares with sides that are about one-third the width of
the main unit.

Throughout the facade, Alberti defines areas and relates them to each other in
terms of proportions that can be expressed in simple numerical ratios
(1:1, 1:2, 1:3, 2:3, and so on).’ (LaChiusa, n.d.)  The Tempietto, San
Pietro In MontoripBy Bonato BramanteThis
small, round temple features a mix of classical references and elegant ratios
and it is also considered to be the prototype of the basilica of San Pietro in
the Vatican.’On the spot
where it was said St. Peter was crucified, the church of San Pietro in Montorio
sits overlooking the eastern slope of Gianicolo hill. Built in the 15th
century, the gorgeous church holds copious amounts of renaissance art including
frescoes from Italian masters and a chapel entirely designed by Gian Lorenzo
Bernini, but the true gem sits in the outer cloister. A smaller, circular
temple, the “tempietto” sits in the middle of the larger church’s rectangular
plaza, a hidden but influential piece of architectural history designed by one
of the most visionary architects of the Italian renaissance.Commissioned by
the King Ferdinand, the construction of the small temple probably started
around 1510 under the design and direction of Donato Bramante. Taking
inspiration from ancient buildings such as the Temple of Vesta (or what was
thought to be the Temple of Vesta at the time) and the Roman Pantheon, the
building is a single chamber temple with a hemispherical, concrete dome at the
top and a perfectly-spaced series of niches and pilasters on the main body. The
exterior is completed by a ring of columns built in Tuscanic (an offshoot of
Doric) Form.The temple
features so many well-mixed architectural references from Roman and Greek
culture that word of its beauty and harmony quickly inspired praise from
contemporary critics and artists such as Giorgio Vasari. In addition to
the accolades lauded on the building at the time of its construction, modern
critics also see the tempietto as the prototype for the greater Basilica
of Saint Pietro in the Vatican. Given the temple’s small size it does not seem
to serve a great deal of functional purpose, but as a show of architectural
precision and the multi-cultural influences of the burgeoning renaissance,
the little temple stands above all the rest.’ (F, n.d.)Florence Cathedral(The Cattedrale di Santa Maria del Fiore)by Filippo Brunelleschi’Classical number theory described in detail
by Plato and attributed to Pythagoras.  Using this theory and tying it to
Genesis and Plato’s Timaeus, a symbolic story of creation using the
arithmetical ideas of the monad, oneness, the dyad, twoness, the triad,
threeness, and on through the decade.  For example, fourness or the tetrad
related to the fourth day of creation in Genesis.  On the fourth day, “God
said, Let the waters under the heaven be gathered together unto one place, and
let the dry land appear.”  Geometrically, the tetrad or fourness is
represented by the four-sided polygon or a square.  Applying these theories into
recognizable form in architecture, we can look at a dome in a church especially
an early Christian church such as the Florence Cathedral.  A dome is a
sphere resting upon a cube.  In an even simpler geometric study, we see a
circle and a square.  Geometrically, the dome is composed of a square, the
tetrad, meeting a circle, the monad.  Applying Genesis to the dome in a
church, a dome is the location where heaven, the monad or oneness, meets the
dry land, the tetrad or square.  Therefore, the geometry symbolizes the meeting
of Heaven and earth, or the meeting of the Communion of Saints which occurs
during each Mass.  In some early churches, this union of Heaven and earth
was emphasized by the decoration on the pendentives which were the
four-triangular transition supports between the vertical columns and the dome.
Depictions of this unity such as the Annunciation of Mary, the Nativity, and
other Christmas scenes were painted on the pendentives to emphasize this
symbolic geometric parallel.’ (Yovanovic, 2012)Villa Hvezda (Star
Villa)By Ferdinand II and
Hans Tirol   ‘Around
1530, Ferdinand I established a large game park just outside Prague and this
was used in the 16th century principally for royal hunting parties.
Subsequently Ferdinand’s son, Archduke Ferdinand II of Tyrol (1529-95),
commissioned the construction of a villa in the park under the supervision of a
certain Hans Tirol, though the architects who oversaw the construction were
Italians, Giovanni Maria Aostalli and Giovanni Lucchese. Then, around 1558,
Bonifaz Wolmut, the architect of the Belvedere in Prague added Fortifications
to it in the Italian style.The plan for the building came from the archduke himself, to
which five signed drawings in his own hand now in the Austrian National Library
attest. The indicate how important the planning process had become in architectural,
as well as providing a further example of a client acting as his own architect.
Ferdinand II, who also dabbled in glass blowing metal casting and woodturning
employed ‘unimaginative artists so as to teach them what the had to do and
make’. The artists could thus be considered merely as vehicles for implementing
a client’s ideas.No Doubt this accounts for the idiosyncratic design of the
building of the building, both the ground plan and elevation with the roof are
star shaped. This is so unusual in architectural history that the ‘star’
epithet also became the name of the building. The ground plan reveals a
twelve-point central area vaulted by a dome, adjoining six narrow
barrel-vaulted corridors that lead to rhomboid shaped rooms. The visitor thus
experiences the villa as a labyrinth offering an endless series of surprising
spatial experiences. Convenience and functionality were sacrificed to symmetry
of ground plan for the purpose of visual effect. However, seen from the outside, the edifice looks
straightforward enough one might even call it austere. There is no main front.
The building thus reflects the theoretical ideal of 16th century
sculpture that work should be beautiful from every angle.The interior is decorated with stuccowork illustrating
Ovid’s metamorphoses, conferring stylistic up to dateness on the villa. Wall
niches in the rhomboid rooms were presumably originally intended to accommodate
statues or weaponry. Had this intention been realised the villa would have been
one of the earliest collections of art in the modern era.’ (Markschies,
2003, p. 102) 


Boyd, G. A., n.d. 1st Year H. and T.-The Monastery and
Monasticism. s.l.:s.n.
Calter, P. A., 1998. Geometry in
Art & Architecture. Online
Available at:
Accessed 2nd January 2018.
F, T., n.d. Atlas Obscura. Online

Available at:
Accessed 4th January 2018.
LaChiusa, C., n.d. Buffalo
Architecture and History. Online
Available at:
Accessed 4th January 2018.
Markschies, A., 2003. Icons of
Renaissance Architecture. 1st ed. s.l.:Prestel.
McCarthy, M., 1987. The Origins
of the Gothic Revival. 1sth ed. London: Yale University Press.
Yovanovic, G., 2012. The Way of
Beauty. Online
Available at:
Accessed 5th January 2018.