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4 Use of the Twelve- and the Ten-Part System

Published onApr 22, 2021
4 Use of the Twelve- and the Ten-Part System
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The Acropolis at Athens, 530–437 B.C.

The Acropolis at Athens was inhabited for about three thousand years. Its various transformations during this long period, and particularly during its golden age, in the fifth century B.C., have been the subject of investigation since the beginning of archaeological studies. Unfortunately, the remains of individual buildings of the earlier periods are few and do not permit a complete reconstruction of the structural changes and developments of the site. Several theories, some partially conflicting, have already been put forward; I shall therefore not attempt to describe the development of the Acropolis in historical or philosophic terms but simply examine the organization of its architectural space.1

I have divided this development into three phases, beginning with the era of Pisistratus (560–527 B.C.) and his successors, when the general layout of the Acropolis is already recognizable, and passing over the earlier period, when the existence of only one building, the ancient temple of Athena,2 is definitely known. During the first phase, 530–480 B.C., alterations were made to the ancient temple of Athena, a surrounding colonnade (pteron) was added, and the first stone Parthenon and the pre-Persian propylon were built.3 In 506 B.C. a bronze quadriga was erected to celebrate a victory over the Boeotians and Chalcidians. There is no evidence, however, as to whether the Acropolis at this stage was consciously planned as a whole (Fig. 3).

During the period I have termed Acropolis II, 480–447 B.C., the pre-Parthenon, or Parthenon II, was built. Although there has been controversy as to whether this building was erected before or after the Persian invasion (480 B.C.), the prevalent opinion is that construction began in pre-Persian times and was never completed.4 In addition to the Parthenon II, the Acropolis of this period consisted of the ancient temple of Athena, the adjacent sacred precinct of Pandrosos, remnants of the early propylon,5 the southwestern building, and northern stoa. It seems certain that the last two buildings date from this period. It is generally accepted that both were built after the Persian invasion, and they must have been built before the Periclean era, since they were removed at that time to make room for other structures.6
The plan of Acropolis II (Fig. 4) relates to the time before 447 B.C. when the building of Parthenon III began, heralding the new plan proposed by Pericles.

During the phase of Acropolis III, 447–437 B.C. the Acropolis was undoubtedly designed as a unity by Pericles and his advisers, even though it proceeded at first with gradual improvements7 and due to political and religious circumstances was never fully completed.

The plan of Acropolis III (Fig. 5) shows the Parthenon, 447–432 B.C.; the Propylaea built by Mnesicles, ca. 435 B.C.; the Erechtheion, 421–407 B.C.; the Chalkotheke, completed before 400 B.C.; the colossal statue of Athena Promachos, 447–438 B.C. (C on the plan); the bronze quadriga, re-erected ca. 446 B.C. (K on the plan);8 a square building northwest of the Erechtheion that covered the east part of the old north stoa.9

Acropolis I, 530–480 B.C.

Organization of the Site. The main entrance is through the early propylon.10 Point A on the plan (Fig. 3) is at the center of the edge of the stylobate facing toward the ancient temple of Athena.

SIGHT LINES FROM POINT A
a to left corner of the ancient temple of Athena

b to right corner of the temple of Athena (B on the plan), passing the right comer of the quadriga (E on the plan)

c to left (northeast) corner of the Parthenon I (D on the plan)

d to the middle (northwest) comer of the Parthenon I (C on the plan)

e to the right (southwest) comer of the Parthenon I

ANGLES OF VISION FROM POINT A
Angles ab, bd, and de are all equal.

Angle ae = 50°.

DISTANCES FROM POINT A
Along the line AD we construct AB′ equal to AB and AC′ equal to AC.

We then find that AD = AC′ + CD = AC + CD.

We also find by measurement that AB = 80 m and AD = 160 m.

Hence AD = 2AB.

If AC′ = x, AB = y, CD = z,
xy = yz and y:(x + z) = 1:2.

This is an example of arithmetic progression.

We do not know the exact position of the relevant comers, nor can we be certain how much attention was paid to views of the distant landscape, since nothing remains of several buildings that are known to have existed11 and that, with their accompanying monuments, may have been important elements of the layout. It can be asserted, however, that the field of vision between the ancient temple of Athena and the Parthenon I was then free of structures, for, to the extent that we can trust present evidence, it always seems to have been kept open. This view is directly oriented toward the east. The assumption that the space between lines b and c was always held free is supported by the situation of the quadriga, which was placed in position E on the plan: this position takes the line b into consideration and avoids blocking the field of vision between b and c.

Acropolis II, 480–447 B.C.

Organization of the Site. There is a single main entrance through the western propylon (Fig. 4). Point A remains in the same position as in Acropolis I.

SIGHT LINES FROM POINT A
a to left corner of the southwestern building.

b and b′ to right corner of the southwestern building and left comer of the northern stoa. It is possible that b and b′ are identical, since the exact position of the northeast corner of the northern stoa (H on the plan) is uncertain.

c to right comer of the northern stoa (D1 on plan) and left corner of the “northern wall.”

d to right corner of this northern structure; d′ to middle corner.

e to left corner of the enclosure sacred to Pandrosos.

f to the left (northwest) corner of the ancient temple of Athena.

g to the right (southwest) comer of the ancient temple of Athena (D2 on the plan).

h to the left (northeast) comer of Parthenon II (G on the plan).

i to the right (southwest) corner of Parthenon II.

ANGLES OF VISION FROM POINT A
Angles bd, dg = 30° = 180°/6.

Angles ab, fh = ca. 30°.

Thus the plan is organized on the basis of an equilateral triangle AE1E4 with AE1 = AE4 = E1E4 = 92.40 m.

DISTANCES FROM POINT A
If arcs of a circle are described from point A to corners of the buildings, the following observations can be made.

The distance along line g to point D2 at the corner of the ancient temple of Athena is equal to the distance along line c to point D1 at the corner of the northern stoa;

i.e., AD2 = AD1.

Also, the distance to the middle (northwest) corner of the Parthenon (E3 on the plan) is equal to the probable juncture of the Pandroseian precinct with the Hecatompedon (E2 on the plan);

i.e., AE3 = AE2 (uncertain).

Further, a series of arcs touching one comer of each of the buildings cuts the line h at equal intervals;

i.e., AB = BC = CE = EF = FG = 30.8 m.

The distance AD does not appear in this series. It represents the height of the equilateral triangle AE1E4;

i.e., AD = AE(3/2\sqrt{3}/2) = 92.40 × 0.866 = 80.02 m.

Measurements show AD = 80.0 m.

The basic division of line h (AB = 30.8 m) is probably equal to 100 pre-Periclean feet (100 × 0.308 m). If this is accepted, all subsequent distances from point A are established at 100-ft intervals (100, 200, 300, 400, 500). Neither the size nor even the existence of the pre-Periclean foot as a unit of measure has been completely proved, however (see Chapter 3, note 4).

If AE = x, then AD = 3x/2 and

x/3 = 30.8 m = 100 Attic feet.

Therefore the distances of B, C, E, F, G from point A can be expressed

x/3, 2x/3, x, 4x/3, 5x/3.

FIELD OF VISION FROM POINT A
From point A, looking from left to right, the following views are possible:

the southwestern building within an angle of 30°

the northern stoa and the “northern wall” together within a second angle of 30°

a field of vision that is apparently open but is actually closed by the Lycabettos Hill, the sacred precinct of Pandrosos, and the ancient temple of Athena—all three within a third angle of 30°

a completely open field of vision together with Parthenon II within a fourth angle of 30°

The entire architectural scene is thus divided into four 30° sectors, and the central division, along line d, lies on the axis of the propylon. This means that the two remaining angles, left and right, between lines a and i and the face of the propylon, are also each 30°. In other words, the entire space is divided into six identical angles, each 30°, and this division, with the equilateral triangle that is derived from it, forms the organizing principle of the layout. The general view is enclosed on all sides except for a single open field of vision directly toward the east; the background of the other opening is entirely occupied by the Lycabettos Hill.

Acropolis III, 447–437 B.C.

Organization of the Site. The layout was probably determined either in 447 B.C., when Parthenon III was started, or in 437 B.C., when the new Propylaea was started. The plan was never fully carried out.

The main entrance is still through the Propylaea, and point A remains in the center of the front edge of the stylobate.

SIGHT LINES FROM POINT A
(* indicates that the exact position of these structures is uncertain.)

a to left corner of the steps beside the old north stoa on the northern slope of the Acropolis.

a′ to nearest corner (southwest) of the house of the Arrephoroi.

b to right (southeast) corner of the same building.

c to left corner of the unbuilt, but probably planned, west porch of the Erechtheion* and left comer of the stylobate of the north porch of the Erechtheion.

c′ to right corner of the west porch of the Erechtheion* (D2 on the plan).

d to left side of the base of the statue of Athena Promachos (only the foundations remain, and I have assumed a conventional base). This line also leads to the right corner of the base of the porch of the caryatids of the Erechtheion (H on the plan) as well as to the right (southeast) corner of the stylobate and architrave of the east porch of the Erechtheion (E on the plan).

e to right corner of the base of the statue of Athena Promachos and left comer of the altar of Athena* (F on the plan).

f to right corner of the altar of Athena* and left corner of the altar of Zeus*.

g to left (northeast) corner of the lowest step of the Parthenon (G on the plan).

h to middle (northwest) corner of the lowest step of the Parthenon (D3 on the plan).

k to left (northeast) corner of the wall of the Chalkotheke (D4 on the plan) and right (southwest) corner of the lowest step of the Parthenon.

k′ to middle (northwest) corner of the Chalkotheke (C′ on the plan).

l to right (southwest) corner of the wall of the Chalkotheke*. As the position of the southern wall of the Chalkotheke has not been precisely determined, its southwest corner cannot be located with certainty, but it was probably at the end of line l.

ANGLES OF VISION FROM POINT A
Angles ac, cg, gk, kl, all = 30° = 180°/6.

Thus an equilateral triangle AD1D4 is bounded by two symmetrical sectors of 30°, with its axis on AG (line g).

The four equal angles ac, cg, gk, kl are divided into two parts (see Fig. 5), each of which has angles of 17° 30′ and 12° 30′ (approximately in the proportion 18°: 12°, or 3:2).

Angle ac = aa′ + ac = 17°30′ + 12°30′ = 30°.

Angle cg = cd + dg = 12°30′ + 17°30′ = 30°.

Angle gk = gh + hk = 12°30′ + 17°30′ = 30°.

Angle kl = kk′ + kl = 12°30′ + 17°30′ = 30°.

But angle ch between the right comer of the west porch of the Erechtheion* and the nearest corner of the Parthenon = 36° = 180°/5. By dividing this important angle (18° and 18°) we arrive at line f′, which may determine the right corner of the altar of Zeus*.

DISTANCES FROM POINT A
If an arc is described with center at A and radius AD3 (the nearest comer of the Parthenon), it passes through the following points (from left to right):

D, the northeast corner of the house of the Arrephoroi (sensed but not visible from point A) = 79.25 m;

D2, the southwest corner of the unbuilt western porch of the Erechtheum*;

D3, the northwest corner of the lowest step of the Parthenon = 79.25 m;

D4, the northeast corner of the wall of the Chalkotheke = 79.70 m; i.e., AD = AD2 = AD3 = AD4 = ca. 79.60 m.

If another arc is described with center at A and radius AC′ (the nearest corner of the Chalkotheke), it passes through the center of the statue of Athena Promachos and is found to measure 39.80 m; i.e., AC = AC1 = 39.80 m.

Hence AC = AD/2.

We also find that DE = 39.80 m.

Hence AC = CD = DE = 39.80 m; i.e., if AD = x, then AC = x/2 and AE = 3x/2.

If a line is drawn from point D3 (the nearest corner of the Parthenon) parallel to the line AD4 (the northeast corner of the Chalkotheke), it will cut AG (axis of the equilateral triangle) at point K.

Similarly, if a line is drawn from point H (southeast corner of the porch of the caryatids of the Erechtheion) parallel to AD1 (the line c leading to the northwest corner of the north porch of the Erechtheion), it will also cut AG at point K.

Point K possesses similar remarkable relationships with other buildings (see Fig. 5).

FIELD OF VISION FROM POINT A
From point A, the field of vision from left to right comprises the following:

within the first angle of 30°, the house of the Arrephoroi and an open view terminated by the Lycabettos Hill

within the next angle of 30°, the Erechtheion, the statue of Athena Promachos, the altars of Athena* and Zeus* and a completely open field of vision

within the third angle of 30°, the Parthenon

within the fourth angle of 30′, the Chalkotheke*

The layout is thus organized within four 30° sectors.

Consequently, the location of the various buildings is determined by a division of the space into six or twelve parts, or by the angles and sides of an equilateral triangle derived from this division of space.

In certain instances, angles of 36° (180°/5), 18° (180°/10), and 12° (180°/15) seem to play an important role.

The field of vision from point A is enclosed on all sides except along the eastern axis (see Fig. 2). The buildings form two groups, the left group having an opening out into the landscape, which is closed in the distance by the Lycabettos Hill. This layout has many close similarities with that of Acropolis II. Most important, the open view to the east was retained in all three periods, although its relation to the entrance point A differed in each layout.

THE STRUCTURES
The proportions of the ground plans of the chief buildings were as follows:

Parthenon

1:51:\sqrt{5}

Chalkotheke*

1:51:\sqrt{5}

Erechtheion

1:231:2\sqrt{3}

Propylaea

1:31:\sqrt{3}
(to the outer walls of the wings).

 


South Side of Acropolis

North Side of Acropolis



Mycenaean palace shrine
1. Primitive temple of Athena (Doxiadis’ “ancient temple of Athena”)

ca. 570–566 B.C.

2. Hekatompedon (Doxiadis’ “Parthenon I”)


529–520 B.C.


3. Pisistratid temple of Athena

488–480 B.C.

4. Older Parthenon (Doxiadis’ “Parthenon II”)


480–479 B.C.

PERSIAN

DESTRUCTION

479 B.C.


5. Temporary shrine of Venerable image

447–432 B.C.

6. Parthenon (Doxiadis’ “Parthenon III”)


439–437 B.C.


(Opisthodomos refinished)

421–405 B.C.


7. Erechteion

353 B.C.


(Opisthodomos demolished)]


Works Consulted by the Author

Dörpfeld, Wilhelm. “Das Hekatompedon in Athen.” Deutsches Archäologisches Institut. Jahrbuch 34, 1919.

Judeich, Walter. Topographie von Athen. 2nd ed. Munich: Beck, 1931.

Rodenwaldt, Gerhard. Die Akropolis. Berlin: Deutscher Kunstverlag, 1930.

Wiegand, Theodor. Die archaische Poros-Architektur der Acropolis zu Athen. Leipzig: Fisher, 1904.

Additional References

Bundgaard, Jens A. Mnesicles: A Greek Architect at Work. Copenhagen: Gyldendal, 1957.

Dinsmoor, William B. “The Burning of the Opisthodomos at Athens.” American Journal of Archaeology 36, 1932, pp. 143–172, 307–326.

———. “The Hekatompedon on the Athenian Acropolis.” AJA 51, 1947.

Dörpfeld, Wilhelm, and Schleif, Hans. Erechtheion. Berlin: Mittler, 1942.

Raubitschek, Antony E. Dedications from the Athenian Akropolis. Cambridge, Mass.: Archaeological Institute of America, 1949.

Stevens, Gorham P. “Architectural Studies Concerning the Acropolis of Athens.” Hesperia 15, 1946, pp. 75–106.

———. The Erechtheum. Edited by James M. Paton. Cambridge, Mass.: Harvard University Press, 1927.

———. The Periclean Entrance Court of the Acropolis of Athens. Cambridge, Mass.: Harvard University Press, 1936.

———. “The Setting of the Periclean Parthenon.” Hesperia, suppl. 3, 1940.


1   Athens, Acropolis. View from point A, 1968.


2   Athens, Acropolis III, after 450 B.C. Perspective from point A.


3   Athens, Acropolis I, circa 530 B.C. Plan.


4   Athens, Acropolis II, circa 480 B.C. Plan.


5   Athens, Acropolis III, after 450 B.C. Plan.


6   Athens, Acropolis II and III. Plan. (Dinsmoor.)


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