Anne Bulckens’ Analysis of the Proportions of the
Parthenon and its Meanings
New Jersey Institute of Technology
University HeightsNewark, NJ 07102
Based on the PhD thesis of Anne Bulckens, the proportional system of the Parthenon is examined. With the appropriate choice of a module and the length of a “Parthenon foot,” all dimensions areshown to be integers. These integer values are shown to be related to the musical scale of Pythagoras. Among the many musical relationships expressed by this structure, this paper focuses on a pentatonic scale made up of lengths, widths and heights of the outer structure and the inner structure or cella.
The Parthenon, dedicated to Athena Parthenos, is one of the most measured buildings thathas survived antiquity. It was constructed between 447-438 B.C., which places it between the ages of Pythagoras (570-497 B.C.) and Plato (428-347 B.C.). It has been shown by scholars to have been built with extraordinary precision [1,2]. It is a Doric temple with some Ionic features. There are eight columns along the East and West facades and 17 columns to the North and South (see Figure 1).The outer temple is adorned by metopes depicting scenes from Greek mythology. Within the outer structure is an inner structure called a cella, consisting of two chambers: the naos housing the statue of Athena and the opisthodomos, which once served as the treasury for the Delian league (see Figure 2). The cella is ringed by a continuous frieze depicting the four yearly Panathenaic procession ofordinary Greek citizens. Though it is generally agreed that the temple’s overall proportions of width to length and height to width follow the ratio 4:9 (see Figure 2) , no one has adequately determined the temple’s underlying proportional scheme and its meaning, which was the raison d’être for such precise measurements.
Anne Bulckens has addressed these questions, in her recent Ph.D thesisfrom Deakin University in Geelong, Australia [3,4,5], by her discovery of a single module of length 857.6 mm., the average width of a “theoretical triglyph”, following the writings of Vitruvius’ who stated that “Within a temple a certain part should be selected as a standard …the size of the module for Doric temples should equal the width of a triglyph.” The width of this Parthenon module isequal to the width of a “theoretical triglyph”, which was the width of a triglyph in the first design stage of the Parthenon before the frieze became shorter than the stylobate. This measure of a module agreed well with the result of a computer analysis carried out in 1984 by the scholar, Ernst Berger, in which 858 mm was found to occur most frequently as a common denominator of the length, width,and height measurements. Bulckens then discovered that when this module is divided by 2.5 to obtain a Parthenon foot of length 343.04 mm, and when this foot is subdivided into 16 equal parts, as was the convention of the time, referred to as “dactyls” (D), all of the main measurements of the Parthenon can be represented as integers. (The use of the dactyl as main measuring unit might have startedwith the Great Temple of Apollo at Delos, begun 460 B. C.). This measurement of a foot is larger than the common Greek foot measurement of 293-295 mm. Bulckens has also drawn on the history and mythology of the Parthenon and the mathematics and numerology of Pythagoras. This paper addresses why this structure may be regarded as one of the finest examples of Pythagorean theory at work....
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