Chatres and the Mystery of the Pythagorean Comma
Chartres is a pleasant French town about an hour’s train journey, southwest from Paris. It is famous for its cathedral. Every year hundreds of thousands of people pass through its doors, and the number continually grows.
For the tourist who has spent too many hours in too many cathedrals, it is no doubt a colossal bore. Yet, for the pilgrim who is seeking a miracle, not a moment is wasted time.
Perhaps they have come to pray through Mary, mother of Jesus. For there are many ikons of her here, hundreds in statue and in stained glass. There is even the sancta camisia, a garment supposedly worn by Mary when she gave birth to Jesus. But then there is another legend about it which says it is the veil she wore at the Annunciation. Neither possibility seems factual, both flights of fancy. However, there is no mistaking the devotion on the faces of the faithful who have come to pray. For those in need we may ask whether it is the history of the ikon or the power of faith which transforms the heart?
Certainly, many visit Chartres because it is a triumph of the human spirit. For the student of architecture, there is the style itself. Chartres is the first and the best preserved of the Gothic cathedrals. For those with a sense of artistry in glass, Chartres has been called “jewelled darkness”, creating an atmosphere of deep meditative mystery. And there are those who come to walk the labyrinth, the only one of its kind to remain intact in the French medieval cathedrals.
So they come, a vast procession, seeking who knows what, during all the long summer months. It is something that has been going on for over a thousand years, and maybe for much longer. One by one, from the bored atheists to the pious of every faith, Chartres works a kind of alchemical magic upon the individual. The church of the Assumption of Our Lady of Chartres changes people.
To enter the cathedral of Chartres is not just to go inside a great church building, rather it is to confront the universe within one’s own self. It is to plunge deep into an extraordinary vision of the cosmos and be brought face to face with the very geometry of existence. Silence expands into its vast spaces, but every ear is filled with a music. It is the harmonies of deep space, the music of the spheres, the last exultant trumpet note of praise that “untunes the sky”. It is music that is unsounded.
Geometry. Cosmos. Music. God’s pilgrims. An unlikely combination: but at least possible, even likely, more than probable, certain because of Chartres itself. But, how to explain it?
At school we learn a little geometry, maybe with reluctance. We play with the shapes of triangles, squares, rectangles, and circles. We find that some shapes are similar to other shapes, while others are congruent, identical in nature, while others not similar at all, and from all this grows a sense of proportion and ratio. Some ratios are just right, like the strings of a guitar gently strummed, but others are exquisite, gorgeous as if the forces of nature had crushed numbers together into a lustre of diamonds. There is an inward fire to their equations.
Inside Chartres one is confronted everywhere by these ratios, by these similarities, by these harmonics. They multiply up in the interior spaces, a profusion of proportions bounded by floors, walls, windows, pillars, columns, the vaulted ceilings and even in the statues and carvings and craft in stone. Outside, the visual geometry is just as remarkable. It is an exterior of flying buttresses and arches distributing massive forces, allowing the whole structure to stand not statically, but as a dynamic space.
But astonishingly, paradoxically, there is no final unity to the building, it is chaotic, a mess. Nothing quite fits together. Everything is right in Chartres, and yet something is wrong in it. Like an individual’s life it is all of a unity, yet a flawed unity.
There is a rich history to the site. There are clues in it, pointers to the origin of that contradiction. The present cathedral is at least the fifth church to be built here, each of four previous destroyed by fire or war or both. There is strong evidence of Christianity that dates back to the 4th century. Yet long before then, legend has it, the druids had some kind of association with this spot. A well with healing waters, a sacred grotto, something or some idea reaching back even to the time of Abraham or before: these were misty traditions even to the medieval church historians and the modern mind will probably relegate it as stuff and nonsense.
It is not, however, to be so lightly dismissed. The ancient world speaks a truth that most of the moderns and the post-moderns block their ears from, for they cannot comprehend it: their philosophy is too small, their sense of geometry, of proportions, stunted.. In fact, the myths and legends of the druids have actually conveyed a concrete truth in the foundations and footings of the building itself. The clue is in its orientation, how it lies to the sun and the stars.
For the orientation of the cathedral of Chartres is unique among European cathedrals. It is not aligned east-west as we would expect (the altar to the east, the entrance or narthex to the west) but rather the whole cathedral is rotated 47° NE. The significance of this is that the cathedral at Chartres is almost aligned parallel with Stonehenge in England, along with other pre-Christian megalithic sites around Europe. This is an astronomical alignment to the mid-summer solstice. And excavations seem to show that all the previous churches on the Chartres site were similarly aligned.
Stonehenge is not aligned precisely to the solstice, being a fraction over one degree out. This is not due to ancient inaccuracies. Quite the reverse. The alignment of Stonehenge is unbelievably accurate for its purposes. The amount of the difference from the solstice is a particular number called the Pythagorean Comma. A celebrated number. In fact, it has tormented musicians and watchers of the skies down the ages. And it is the Pythagorean Comma which causes the disunity of the cathedral building. It is built into the design of Chartres itself. That is not the only similarity to Stonehenge. As Gordon Strachan points out, the outer Sarsen ring of Stonehenge fits exactly the circumference of the pillars of the cathedrals crossing. Archaeo-astronomy gives us cause to think very deeply about what the people of the past knew. Had, in fact, their hearts and minds been opened to the geometries of existence in ways of wisdom that have now been lost?
Chartres is the architectural masterpiece of teams of craftsmen who, building between 1194-1220 seem to have synthesized three profound concepts: manipulating the symbolic imagery of numbers and letters, which is the ancient art of gematria found in the Bible; the geometry of the Pythagoreans, and the technological brilliance from Islamic architecture in the form of the pointed arch. Australian architect Dr John James has written authoritatively on the construction of Chartres from a lifetime of “reading the stones”. It is science at its best: painstaking measurements, direct observations, patient accumulation of data, and the slow growth of sure knowledge.
It is impossible to summarise in a couple of brief articles what the reading of the stones involves. And if we look beyond the architecture to the other art-forms there are over 10,000 characters carved in stone, scenes and people depicted from the Bible, from history and from contemporary French society. There is some 2,700 square meters of stained glass depicting likewise over 5,000 figures. The detail is overwhelming yet the geometry profound, reflected in the architecture, the design of the windows, the statues themselves, and the placing of the labyrinth.
For many Chartres is its labyrinth. It is certain that the labyrinth determined much of the overall cathedral design. It is 12.8 meters in diameter, and to walk through its path is close to 261 meters. If the huge rose window of the west wall were laid over the labyrinth it would fit exactly.
Not all were pleased by the labyrinth; it annoyed some clergy later on. They thought it was a distraction, and pilgrims played games on it.
Unlike a maze a labyrinth is but a single path, which leads from the circumference to the centre. The maze offers choices, dead-ends; the labyrinth offers none.
The idea of the labyrinth first appears in ancient Greek mythology. The architect Daedalus built a labyrinth underground, beneath the palace, for King Minos at Knossos on the island of Crete. At the centre of the labyrinth the King kept the minotaur, a fierce creature with the head of a bull on the body of a man. Today some artists like to reverse the two halves, but the result is not quite as spectacular.
The minotaur demanded human sacrifices, young flesh, which King Minos supplied. Theseus was moved by the plight of the children delivered up for the slaughter and sailed to Crete to do battle with the minotaur. Ariadne, the king’s daughter fell in love with Theseus and pledged herself to help him in return for marriage. She gave Theseus a ball of thread to unwind in his journey into the labyrinth and thus have a way of finding his way out again. She also gave him a sword with which he could slay the minotaur.
Theseus fought and won and returned from the darkness. But he did not marry Ariadne, instead he sailed back to Athens. According to the story King Minos was enraged by what had happened The minotaur had been killed, Theseus had escaped victorious, and Ariadne had been scorned.
Minos looked like a fool So he imprisoned Daedalus and his son Icarus in the labyrinth. But they were clever and plotted an escape in an unforseen way. They built wings. They got out of the labyrinth, found their way to the castle walls, put on the wings and flew up into the sky. But Icarus flew to close to the sun and perished in the flames.
It will not have escaped the notice of the thoughtful reader that Theseus did not need Ariadne’s ball of thread. The path alone would have taken him to meet the enemy and if he survived, as we know he did, the path of the labyrinth would have led him out. But he certainly needed the magic or in Christian terms the virtue in Ariadne’s gift of weapon: for it was by her sword alone that the minotaur could be slain.
The labyrinth is but one of many examples of how Christianity has always appropriated mythology for its own symbolic purposes.
The priests of Chartres used the labyrith for Christian purposes, just as they used gematria and geometry, astrology and astronomy. In the case of the labyrinth all people journey through life and have their own minotaurs of the soul to confront, to slay or even to befriend. The entrance to to to the labyrinth of life is birth and the centre to which inevitably we are drawn is death. Ariadne’s thread is the Church’s gift of divine grace at every step of the pilgrimage. Sometimes pilgrims were forced to do penance by walking the labyrinth on their knees.
But in symbolic terms it was the object of the exercise to come to the centre and thence to confront death with grace. Physically the exact centre of the labyrinth determined the exact placement of the high altar in Chartres. The altar itself symbolizes the same: death confronted by redeeming love.