Parsing the Parthenon (III)

In the first two posts of this thread, we've looked at the history of the Parthenon and it's perception by the Western intelligentsia up to the beginning of the 20th century.

What was at first rejected out of hand by many - that the Parthenon was not composed of flat planes and orthogonal relationships - gradually came to be an accepted view by the 1950's. In a quote attributed to Schopenhauer (1913) "Every problem passes through three stages on the way to acceptance: First, it appears laughable; second, it is fought against; third, it is considered self-evident. It is no surprise this sort of thing goes on among those with more limited educational backgrounds, but it is approaching irony when those who purport to be of a scientific or 'rational' mindset do the very same thing.

Now, personally, up until the past few months, I had some vague familiarity with the Parthenon, having heard that the building featured effects to counter foreshortening effects, however I really had no idea just how utterly the structure was designed and built with that aim in mind - or, well, perhaps it is more accurate to say it was built with aesthetic ideals in mind which made the building look perfect and yet it does so without using elements which are flat or plumb for the most part. For this insight, I am thankful for a 1999 publication of The University Museum at the University of Pennsylvania entitled Appearance and Essence: Refinements of Classical Architecture- Curvature. This book represents the proceedings from the 2nd William Symposium on Classical Architecture. As such, it represents very recent scholarship in this field.

And in getting acquainted with scholarship in this field has brought me fact to face with a vast amount of specialized lingo. I used a couple of those terms in the previous posting without providing definitions, namely the words 'entasis' and 'Centauromachy'.

I have struggled at times simply to understand the material due to such a large quantity of new vocabulary items in a specialized academic work such as this one. And I was laboring under the delusion, I guess, that I already had a pretty decent vocabulary.

See how well you do with defining the items on the following list:

• Krepis
• Euthynteria
• Stereobate
• Peripteral
• metope
• toichobate
• antae
• guilloche

I'll try to keep the technical jargon to a minimum in the following material, recognizing of course that one man's jargon is another's precise language.

In the previous post, I showed a photograph, now quite famous, taken from L'acropole d'Athènes. La Parthnon, by G. Fougères (1910):

The foundation. Let's start with that. The Parthenon's foundation rests atop the earlier Parthenon, or 'Pre-Partheon, construction of which was begun in 490 B.C.. That building was razed to the ground by the Persians, who sacked the city and burned the Acropolis. The Pre-Parthenon also had curved foundation courses, though it was a slightly smaller structure than the later Parthenon.

The foundation is curved in both directions, so as to produce a building floor which is convex. The first question that comes to mind, of course, is why? Vitruvius, whose work De architectura, written between 30 and 15 BCE and comprising 10 books, or scrolls, was the first work of architectural theory and in it the reason for a convex floor is stated, Book 3, Chapter 4:

"...for if it is laid perfectly level, it will look to the eye as though it were hollowed a little."

 -Link-

Vitruvius, of course, lived quite a while after the ancient Greeks had built their monuments, and lived within a different social context, so while he is the earliest observer and theorist we have in writing, it is by no means assured that his interpretations are the only, or correct ones.

This modification of a surface to alter how it looks to the naked eye is termed an 'optical refinement'. The Ancient greeks had realized at some point that the naked eye views objects, especially those especially large or far away, with a certain distortion that occurs due to the spherical shape of the eye’s retina.

We can consider this issue of a 'certain distortion' as follows:

First we have the issue of linear perspective, which is most directly shown, perhaps, by the phenomenon of railway tracks appearing to converge in the distance:

This optical phenomenon happens because the field of view changes. Look at the tracks up close, in the foreground of the above picture, and we can gauge the width of the tracks, a distance which occupies most of our field of view. We assume this dimension to be constant of course, but when we look at the tracks off in the distance, the portion of our field of view occupied by the tracks is now a much smaller portion of out field of view, and as a result, the tracks appear to converge.

We can say that the lines of the tracks converge to a vanishing point. Our field of view, therefore essentially is one in which all we see is converging to vanishing point(s):

Now, if we place across this view a pair of horizontal lines such as would be seen if we were in a large building and down towards one end we see the line of the floor and of the ceiling, we have the following optical situation:

This illusion is termed the Hering Illusion: the parallel lines in our field of view appear to curve, the lower one bowing downward, and the upper one bowing upward. Hence, when looking at a large expanse of floor off in the distance: if the floor were perfectly flat it would appear to sag downward. The remedy for this situation is to make the floor curve upwards slightly, so that when viewed it would thereby appear to be perfectly flat.

In Japanese ceiling work, large room ceilings, especially those with a grid work pattern of framed elements, are typically dropped slightly down in the middle, so as to counteract the visual effect that they are domed upward.

This phenomenon was known to the ancient Greeks, and after it was observed at the Parthenon, further research has revealed it was common to many Greek classic structures. In fact, it has now been determined that the degree of upward curvature on both long and short axes of rectangular buildings in classic Greek architecture has itself changed over time, possibly as a result of a process of gradual refinement and/or changing tastes:

As you can see, over time, the degree of curvature on the narrow sides of the buildings was decreased at the same time the degree of curvature on the long sides was increased.

So, the aspect of viewing point relative to the way in which the eye perceives objects off in a distance strongly influenced the design of a structure such as the Parthenon. The degree to which this refinement was taken however is quite staggering.

Here's a model of the Acropolis showing the site as it would have looked shortly after completion:

Notice that, in entering, one passes through a large gate, then walks upward along a path, the parthenon being positioned up and to the right of one's view. note also that there is a large flight of steps in front of the Parthenon.

Work by M. Korres to analyze the foundation of the Parthenon has revealed that the four corners of the structure are not all at the same height. This had been observed earlier by Penrose, however the reason for the height differential at the four corners had been ascribed to errors in workmanship by the ancient Greeks.

Korres, however, argues that the height differentials at the four corners are not accidental, but a deliberate positioning of the structure to further counter optical effects the result from the view of the building, along with the large bank of steps immediately in front, as one sees it from a distance and approaches.

In this first sketch, we have a view at top of three levels of the krepis (also termed the krepidoma) of the Parthenon, the three steps composed of the Stylobate, top, and stereobate, middle and bottom), along with the terraced steps in front, if they were made entirely flat:

At the bottom of the sketch is shown the perspective view seen in approaching the structure, with a note, '!' , to indicate that there would be a discordance between the lines of the krepis and the upper line of the staircase platform.

Now, if one made the foundation of the Parthenon convex as usual, and made the lines of the terraced staircase similarly curved (for the same optical reasons) there would be a couple of points of conflict in the lines of the two structures:
 

To solve this, the foundation of the Parthenon is kicked up diagonally at the front left corner and down at the rear right corner, thus bringing the foundation lines into visual harmony with the steps in front:

Of the steps, Korres notes,

"Surveying along length of the extant steps indicated that the curves were asymmetrical, as already stated by Choisy, but in a different, more complicated, manner: their apexes are shifted to the north of the temples axis, but not equally. The shifting increases gradually from the second step up to the last: the first exhibits no shifting at all."

Consider that these refinement had to have been considered from the outset of construction. Someone had to clearly perceive what the optical conflicts would be and make the adjustments to compensate, right from the moment the building foundation was being carved in the bedrock.

As Korres notes,

"It is amazing that the architect should have foreseen these almost imperceptible problems even prior to the beginning of work on the new building. The manner in which they were grappled with is equally impressive. The architect eschewed the horizontality of both groups of lines to a degree that would render them compatible when seen in perspective. As a result of this modification, the northwest corner of the temple lay 3cm higher than the east facade, the curvature of the steps of the terrace had its apex shifted to the north of the axis, and the southwest corner of the Parthenon lay 2cm higher than the northwest corner and consequently 5cm higher than the east facade. It is even more remarkable that these refinements were executed not solely on the lines of the relatively lightly constructed terrace, but also on the heavy and expensive construction of the temple itself! 

....The decision to correct the perspective of the temple, with modifications applied not only on the terrace (evidently constructed after the Parthenon) but also on the heavy structure of the temple itself, indicates a refusal on the part of the architect to choose the easier, more practical option. He preferred to risk a solution that might be misconstrued as an indication of erroneous leveling - a trap that even pedantic specialists from intellectually rigorous times have fallen into...." 

So, we consider the convex foundation as one wonderment in this structure. If one were to take ordinary columns, cut square across their bases, and place them atop a convex base, the columns would all flare outward, would they not? The builders of the Parthenon compensated by adjusting the bases and capitals of the columns, along with every drum of which they were composed, so that the columns lean inward. Not only do they lean inward, but they do so differentially, long side compared to short side, and the columns out on the corners leaning, in compound manner, the most of all. Here is an exaggerated view:

If one extended the centerlines of all the columns up into space, the lines of the narrow sides building columns would meet some 3 miles (4950m) above the building, as follows:

The lines of the long side columns would meet 2200m, or 1.36 miles, above.


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Above the columns there is the pediment, it is not plumb. Again, Vitruvius explains, in Chapter 5, section 13:

13. All the members which are to be above the capitals of the columns, that is, architraves, friezes, coronae, tympana, gables, and acroteria, should be inclined to the front a twelfth part of their own height, for the reason that when we stand in front of them, if two lines are drawn from the eye, one reaching to the bottom of the building and the other to the top, that which reaches to the top will be the longer. Hence, as the line of sight to the upper part is the longer, it makes that part look as if it were leaning back. But when the members are inclined to the front, as described above, they will seem to the beholder to be plumb and perpendicular.

This fact is well known as well in Japanese architecture, and gable ends on buildings are not made plumb, but lean slightly forward.

Another aspect concerning the gable pediment is an optical illusion which results from an increasingly flattened triangular shape

Notice how the effect of a slack-pitched gable, if the pediment's lines are doubled, intensifies the effect of the horizontal base of the pediment downward sag? As with the floor issue, the remedy is to curve the base of the pediment upward so that it will appear to be flat.

In the Parthenon, surfaces or members which are set true to perpendicular are exceptional. Perhaps the end walls are the only exception. All the columns lean inward toward the sides of the building, and the corner columns lean inward diagonally The side walls lean inward more than the columns. The antse, or flat pilasters at the ends of the side walls, lean forward. The vertical faces of the platform steps and of the architrave and frieze lean inward, whereas the acroteria and antefixae, the vertical face of the cornice, and the vertical front faces of the abaci, or square slabs between the architrave and capital, lean forward. The door jambs lean slightly toward one another, in the rising direction.

The Parthenon's intercolumniations are not of even widths, the spacing crowning in towards the corner columns. It kind of emphasizes the corners of the building by increasing the visual density of the posts there, and the corner posts are also larger in diameter than the other columns.

Besides lending increased visual density to the corners, the change in column spacing addressed an issue which has been termed 'the corner conflict'.

Above the column there is the supported beam and above that the frieze with applied triglyphs, a component which takes the form of a vertically channeled tablet. It is thought to be a representation of wooden beam ends. The frieze, part of the architrave, was greater in width than the columns below. In archaic examples, the trigylph was placed right at the corner of the frieze:

As you can see, this causes an irregularity in the spacing of the triglyphs along the frieze.

In classical Greek architecture, the column spacing was gradually shifted over, crowding in towards the corners, so that a corner-mounted triglyph in the frieze appeared as parts of a even rhythm of elements:

This is a subtle and beautiful solution to the problem of triglyph spacing. it's a useful solution to file away for those situations where one is designing with elements that have different widths to fit within and yet must relate to other elements in the same facade, for instance, exposed rafters and post spacing rhythms.

In Roman architecture, sometimes a third solution is shown, in which the triglyph is not placed directly as the corner but over the column:

Above three sketches from:  The Corner Conflict.

The Roman solution, 'C' above, leaves a less finished, open-ended look to the corner of the frieze.

I wanted to illustrate some details which show that there is much more to the Parthenon than meets the eye. Indeed, since these features of the Parthenon have been uncovered, similar design detailing has been found at many other classical Greek architectural ruins. Again, the work Appearance and Essence: Refinements of Classical Architecture- Curvature is a highly recommended read if this sort of subject is of interest to you.

That concludes this short series on the history and design of the Parthenon. I hope you enjoyed. Other scholars have of course written much more extensively upon this topic, so for those whose interest may have been piqued, I can assure you there is much more depth to that particular rabbit hole to be found. Have fun!