Article by Eden Muir for le Tour Sutton, October 2010.
THIS ISSUE'S THEME: "HARMONY"
The Search for Harmony in Architecture
Click images to expand...
Let's travel back in time 2,500 years to the Greek island of Samos.
A mathematician is investigating musical intervals and harmonics
by tuning a singlestring instrument, the monochord. He discovers
that if the string length is reduced by half, its pitch is exactly
one octave higher. Certain ratios such as 2:3 and 3:4 produce pleasing
sounds, others create irritating disharmony. Pythagoras (570  495 BCE) had discovered
the mathematics of consonance and dissonance, the foundation of musical harmony.
Ever since that brilliant insight, Pythagoras and others
speculated on the existence of a similar mathematical
basis for harmony, proportion and beauty in art and architecture.
We all remember the Pythagorean theorem explained by the familiar
triangle with sides of 3 and 4
and hypotenuse of 5 units. Could there be a geometry as simple as
that for aesthetic coherence and harmony?
Pythagoras is said to have advanced the Golden Section, a 1.618 to 1 ratio
which corresponds to certain fundamental proportions of the human body. The regular pentagram,
which also contains that ratio, became the Pythagoreans' symbol.
For centuries researchers have superimposed
Golden Sections over building plans
to prove that architectural beauty is derived from
invisible regulating lines. The Roman architect Vitruvius (8015 BCE) encouraged
a more holistic approach:
harmonious design must consider multiple factors: the building,
site, orientation, wind, light, shade, elevation and materials.
Vitruvius was also fascinated by architectural
units and numbers. He documented the proportions of
the classical orders: the height
of a Tuscan column was 7 times its lower diameter; Doric 8;
Ionic 9.
Vitruvius saw the human figure as the ultimate
inspiration for proportional design systems
just as it had generated dimensional units since the time of the Egyptians:
the palm equals 4 fingers; the foot is 4 palms;
the cubit six palms; the man's height 4 cubits.
Fastforward 12 centuries: mathematician Fibonacci (11701250) introduces his famous number
series (1, 1, 2, 3, 5, 8, 13, 21, etc.) which approaches the Golden Ratio.
It has the added advantage of being expressed as an attractive spiral within the
Golden Rectangle. Later, Leonardo da
Vinci (14521519) investigates human anatomy directly, through
dissections of cadavers, and sketches the Vitruvian Man to
illustrate his discussion of symmetry and harmony in temple architecture.
Alberti looks to the human frame
to inspire his system of proportions, and Pacioli
describes the "divine" properties of the Golden Ratio, which had already gathered
mystical connotations.
For many centuries, harmony and beauty in a building were judged by how
carefully the architect followed the classical Vitruvian rules which had
evolved into a sophisticated proportional system.
But with the 20th Century came the revolutionary new ideas of
Frank Lloyd Wright (18751950) who rejected the past and
developed his own "organic" architecture
with proportions, ornament and forms inspired by landscape and plant life.
Le Corbusier (18871965) went further, stripping away all ornament on his
white stucco villas perched on stilts. But this did not mark the end of "magic" ratios.
In 1948 Le Corbusier published his own proportional
system based on the body, summing it up as "a range of
harmonious measurements to suit the human scale, universally applicable
to architecture." This radical Swiss Modernist felt compelled to pursue a mathematical
basis for architecture and he obsessively traced Golden Rectangles to guide his
design decisions.
In the late 1870s, with the railroad coming to Frelighsburg,
the visionary Mayor Joseph Landsberg decided
to build what would be for a time
the finest imported goods store in eastern Canada.
The masons laid up the thick brick walls using
a foolproof geometry worthy of the Greeksthe building
was 80 by 60 feet in plan, forming a perfect 3/4/5 triangle with a
convenient 100 foot hypotenuse. Perhaps more surprisingly, the main
facade also measures 60 feet to the top of the cupola. This sturdy tribute to Pythagoras
still sits proudly on rue Principale!
Today, most architects would say that harmony is
not based on numbers but on design intuition, or simply having a "good eye" for form, materials,
colours and context. But architects and master builders
have always found it hard to resist a juicy mathematical ratio.
If you look carefully, you'll find 1.618 to 1 proportions in the oddest places,
from Toronto's CN Tower to small town commercial facades.
Check out the older buildings on your own Main Street
and see how many ancient Golden Sections are hiding in plain sight!
1. Pythagorean theorem demonstrated with a 3/4/5 triangle
2. Golden Section constructed geometrically
3. Golden Section with Fibonacci spiral superimposed on the Parthenon
4. The classical orders aimed at harmony down to the smallest detail
5. Vitruvian Man by Leonardo da Vinci
6. Le Modulor, Le Corbusier's architectural design guide based on the Golden Ratio
7. The Landsberg Building, Frelighsburg, 1879, built on a Pythagorean plan
8. CN Tower. Golden Ratio between heights of tower (555.3 m) and glass floor (342 m). Using the official
published heights, we get 555.3 / 342 = 1.62 / 1, or the Golden Ratio.
© Tous droits réservés Eden Greig Muir, architecte
Architect Eden Greig Muir's website is www.ateliermuir.ca
