Boethius’ De musica…“Geometrical harmony”…
The Platonists of Chartres…Timaeus…
God the Architect…God the Geometer …
Architecture as the image of the Heavenly City…
A century after Augustine, his pupil Boethius quickly eclipsed him as the supreme authority for the Middle Ages and the Renaissance on both music and mathematics, on which he wrote separate and seminal treatises. In his own De musica, Boethius explains how to visualize the perfect consonances of music in explicitly geometrical terms. He points out that the proportions of double and half, triple and third—the perfect consonances of the Pythagorean monochord—are as easily perceived visually as they are acoustically, since, as he continues, “the ear is affected by sounds in quite the same way as the eye is by optical impressions”.
Applying this doctrine of synesthesia not only to proportions in a line but also to three-dimensional geometry, Boethius discovers “geometrical harmony” in the cube, since the number of its surfaces, angles, and edges, 6, 8, and 12, respectively, includes the ratios of octave, fifth, and fourth.
Though in the centuries that followed Boethius, there was no lack of “musical mysticism”–as expounded, for instance, by the Pseudo-Dionysius and John Scotus Eriugena,–it was the Platonism of the cathedral school at Chartres that produced the blueprint, if you’ll forgive the pun, by which musical harmonies were translated into the stone of the Gothic cathedral.
The poets, theologians, and philosophers who gathered at Chartres beginning in the second quarter of the twelfth century were even more avidly dedicated than their patristic forerunners, if that is possible, to effecting a grand synthesis of Platonic and Christian ideas. Their principal interest was Platonic cosmology, and thus their thinking was almost entirely based on the Timaeus.
Of that dialogue, only a fragment was available in the original Greek, but the Chartrains had, and were happy to depend upon, the translations and commentaries by Chalcidius (late-fourth century) and Macrobius (c. 400) (whose commentary on Cicero’s Somnium Scipionis we have alluded to so often). Both, of course, were pagan Platonists who, as indicative of the success of the harmonistic project, were nonetheless assumed from the outset to have been Christians. In any case, the original fragment of the Timaeus and the two commentaries were the Chartrain Bible, held by the theologians there in no less reverence—probably greater, if they had dared to admit it—than the Book of Genesis.
In the Timaeus, as Thierry of Chartres (the younger brother of Bernard, and second Magister at the School) points out, Plato described the division of the World-Soul according to the ratios of the Pythagorean tetractys (1:2, 2:3, 3:4). That is to say that for Plato, according to Thierry, musical proportion and harmony were the organizing principles of cosmogony and cosmology.
The conjunction of these themes–music and cosmogony–was hardly the invention of Chartres, of course. From the very nascency of the Church, God’s creation of the world (as we noted in a passage quoted from Clement’s Protrepticus) appears as a symphonic composition. Both Chalcidius and Macrobius had insisted that by dividing the World-Soul into the ratios of the tetractys, the Demiurge established a world-order based on musical intervals. The same argument is rehearsed in the ninth century by the Christian Platonist and biblical exegete John the Scot, and inevitably the idea was seized upon by the School of Chartres.
But the masters at Chartres go further in representing the harmony of the cosmos as a work not merely of musical composition, but of architecture, and God as the Master Architect. For example, in his late-twelfth century mythological allegory, The Complaint of Nature, Alan of Lisle (doctor universal and perhaps the greatest exponent of the Platonism of Chartres) describes God the Creator as the “artful architect” who builds the cosmos as his “regal palace”, composing and harmonizing the diversity of created things by means of the “subtle chains” of musical concord.
As you will hardly be surprised to learn, the conceit of God the Creator as Master Architect of the cosmos was already by the twelfth century a longstanding topos. It went right back to Plato’s description in the Timaeus of the Father and Maker of the universe as a “Demiurge”, a “Craftsman”. Of course, for Plato the Demiurge was no ordinary artisan; his techne or praxis as builder expressed the most eruditetheoria, and in conceiving the plan of his cosmic house, he depended upon the highest and most perfect theoretical knowledge of all, that of mathematics and geometry. Accordingly, in Gothic sculpture and painting, and especially on the facades of the Cathedrals, we encounter the ubiquitous image of God the Geometer standing astride the globe with his compass and rule in hand.
The idea that the building of the edifice of the world involved the application of the geometrical and arithmetical laws of proportion was, as we have seen, originally Platonic, but it soon found a happy biblical home in the verse from Proverbs (8:27): “When he prepared the heavens, I was there: when he set a compass upon of the face of the deep”.
With this joint Platonic and scriptural sanction, the architect of the early Christian basilica, the Gothic cathedral, the Renaissance church, or even great house, saw himself quite self-consciously in the divine role as creator, imitating the Master Architect in disposing his buildings in accordance with the same laws of geometrical proportion and harmony. Early buildings, especially churches, were indeed regarded as visible images or models of God’s cosmic creation, which itself was regarded pre-eminently as an image and symbolic expression of the Ideas in the Divine Mind, including and above all that ineffable principle of order according to which the world was made and is governed.
That order is most especially manifest in the harmony of the heavenly spheres, which in turn, as in Dante, for example, becomes identified with the celestial habitations of the blessed: the eternal Heaven of God. This explains why the medieval cathedrals, while modeling the cosmos as a whole, were above all conceived by the bishops and abbots who designed them as images of the Heavenly City. If the medieval architect designed his church according to the laws of harmonious proportion, he did so that is,in imitation not only of the order and harmony of the visible world of creation, but especially as an intimation of the world to come.
The symbolic resonances that linked the created cosmos, the Celestial City, and the earthly sanctuary are dilated upon in a famous passage in Abelard’s Theologia Christiana. Abelard identifies the World-Soul of Plato’s Timaeus with the harmony of the spheres, which he then in turn connects with the heavenly habitations in which angels and saints “in the ineffable sweetness of harmonic modulation render eternal praise to God”. (That the harmony of the spheres is in fact the hymn of praise that the angelic choirs intone in God’s presence was a natural enough inference, since, as I mentioned earlier, the biblical angels were identified with the Platonic Intelligences as the indwelling souls of the planets who revolved, held in their orbits by love, around God.)
Abelard then transposes his musical analogy into an architectural one. The Celestial Jerusalem, he says, is the archetype of the historical Jerusalem of ancient Judea, and more specifically, of the Temple erected there by Solomon.
As Von Simson observes, “No medieval reader could have failed to notice with what emphasis biblical description of a sacred edifice, particular those of Solomon’s Temple, of the Heavenly Jerusalem, and of the vision of Ezekiel, dwells on the measurements of these buildings”. To these measurements, Abelard gives an explicitly Pythagorean significance. Solomon’s Temple, he says, is reverberant with the same divine harmonies as produced by the heavenly spheres; moreover, its length, width, and height of 60, 20, and 30 cubits respectively, as recorded in I Kings 6, yield the proportion of the perfect musical consonances of third, fourth, and octave.
In Christian biblical commentary, the dimensions of Solomon’s Temple were regarded as ideal, in both the vernacular and Platonic sense of that word, and indeed practising architects felt obliged to heed them. The famous Renaissance architect Philibert Delorme thus recommends the proportions not only of Solomon’s Temple, but of Noah’s Ark and Moses’ Tabernacle, as having been prescribed by “the great architect of the universe”.