Interpretation
In this section I attempt a partial interpretation of the geometry. The objectivity which has marked the paper up to this point is now relaxed.
As a Lay Clerk at the cathedral, it is natural to think in musical analogies. Pipes or strings with sounding lengths in the ratio 2:1, other things being equal, give notes one octave apart. A ratio of 3:2 gives a fifth. A ratio of 4:3 gives a fourth etc. In the Renaissance, the analogy with ratios used in architecture was explicit. For Gothic architecture, the analogy does not hold, for pipes in the ratio of √2:1 or √3:2 or φ:1 would produce not only a dissonance, but an intolerable cacophony, whereas we have seen that these ratios were highly prized. But we can extend the analogy and treat these ratios as dissonances. In music it is the handling of dissonance which adds zest. Possibly these ratios can be thought to fulfil a similar purpose in architecture.
There was almost certainly the intention of representing heavenly order and harmony on earth and embodying it. This aspect has a parallel in the great programmes of sculpture and stained glass. They might have had a function in educating illiterate peasants, but their primary purpose was doubtless to anchor the universal in the particular location, and make it present.
One lady who attended a presentation of this paper said to me concerning the presence of geometry “That is why these buildings look so right.”
Continuing the musical analogy, if the individual ratios are like intervals, the effect of looking at all the geometry at once is that of a mighty geometrical symphony, or like the ratios and combinations of numbers governing section lengths in Tudor masses and other music which build up into a complex numerical structure.
The music of the spheres is another concept in the same family.
Eternal ruler of the ceaseless round
Of circling planets singing on their way…
What though in solemn silence all
Move round this dark terrestrial ball;
What though no real voice nor sound
Amid their radiant orbs be found…
As with all controversies, there is truth in both positions. There is no microphone that can record the music of the spheres, nor the interval of a minor third in the vicinity of the north door, with its ratio of 6:5. Evidently there are complicated geometrical relationships between the orbits of the planets, and the positions of stars and galaxies, and it is possible to wonder what music bears an analogy with them.
In one sense it is unnecessary to search for a meaning outside the geometry itself. Working with these figures for a long time, one starts to feel that the geometry is a language in its own right, and the intricacy and ingenuity and sheer skill have a meaning in themselves, or that an architect can say things in this language that are expressible in this language alone. We have seen how the designer of the nave “spoke” to the designer of the Lady Chapel at Llandaff. I have had the experience of going backwards and forwards between the elevations of the nave at Llandaff and the choir at Wells, and finding them “saying” similar things, for example, because there was a golden rectangle at Wells and other geometrical features were common to both buildings, I looked to see if there was one at Llandaff. Another “speaking” moment was when I saw how the circle in Figure 11 matched the curve of the door. The language is also capable of sustaining an argument. An example is in the West Font, where each placement depends on its predecessor in a lengthy chain. It was by following this argument that I discovered the golden rectangle in Figure 12. The musical analogy continues here, for one does not need to enquire concerning the extra-musical meaning of a Mozart symphony for example, for the meaning is in the symphony itself, and is communicated in musical language.
We have seen two instances in the west front where similar results were arrived at by a dual determination. As well as showing the superb skill of the designer, this was all to the good as it “locked” the additional determinations into the geometry. This is one of the meanings of the vesica piscis, to join opposing powers and give birth from the union. A deeper meaning is that the two circles represent duality, that which is manifest, and the intersection represents the Unity which is the source of all.
The pentagram is an ancient symbol of the Goddess, Venus, Aphrodite, Isis, She has many names. The clearest and largest pentagram is in the Lady Chapel.
In some places the pentagram with point downwards is viewed as a symbol of evil. No shape is inherently evil. If you choose to give this meaning to the pentagram round the door, you also see the Unity, symbolised by the circle, shining through every appearance of evil. The same meaning could be seen in the clerestory, but really evil has no place in beauty such as this.
One can never say that one has exhausted all the layers of meaning in a building. To those involved in the design, it may be that numbers possessed properties and meaning in themselves. It is therefore a legitimate line of enquiry to see if there is any consensus in writings on numerology, although the element of subjectivity is necessarily strong here, where it was absent in the demonstration of the pervasive presence of pentagons at Llandaff.
Gervais Frykman
2004
2014
As a Lay Clerk at the cathedral, it is natural to think in musical analogies. Pipes or strings with sounding lengths in the ratio 2:1, other things being equal, give notes one octave apart. A ratio of 3:2 gives a fifth. A ratio of 4:3 gives a fourth etc. In the Renaissance, the analogy with ratios used in architecture was explicit. For Gothic architecture, the analogy does not hold, for pipes in the ratio of √2:1 or √3:2 or φ:1 would produce not only a dissonance, but an intolerable cacophony, whereas we have seen that these ratios were highly prized. But we can extend the analogy and treat these ratios as dissonances. In music it is the handling of dissonance which adds zest. Possibly these ratios can be thought to fulfil a similar purpose in architecture.
There was almost certainly the intention of representing heavenly order and harmony on earth and embodying it. This aspect has a parallel in the great programmes of sculpture and stained glass. They might have had a function in educating illiterate peasants, but their primary purpose was doubtless to anchor the universal in the particular location, and make it present.
One lady who attended a presentation of this paper said to me concerning the presence of geometry “That is why these buildings look so right.”
Continuing the musical analogy, if the individual ratios are like intervals, the effect of looking at all the geometry at once is that of a mighty geometrical symphony, or like the ratios and combinations of numbers governing section lengths in Tudor masses and other music which build up into a complex numerical structure.
The music of the spheres is another concept in the same family.
Eternal ruler of the ceaseless round
Of circling planets singing on their way…
What though in solemn silence all
Move round this dark terrestrial ball;
What though no real voice nor sound
Amid their radiant orbs be found…
As with all controversies, there is truth in both positions. There is no microphone that can record the music of the spheres, nor the interval of a minor third in the vicinity of the north door, with its ratio of 6:5. Evidently there are complicated geometrical relationships between the orbits of the planets, and the positions of stars and galaxies, and it is possible to wonder what music bears an analogy with them.
In one sense it is unnecessary to search for a meaning outside the geometry itself. Working with these figures for a long time, one starts to feel that the geometry is a language in its own right, and the intricacy and ingenuity and sheer skill have a meaning in themselves, or that an architect can say things in this language that are expressible in this language alone. We have seen how the designer of the nave “spoke” to the designer of the Lady Chapel at Llandaff. I have had the experience of going backwards and forwards between the elevations of the nave at Llandaff and the choir at Wells, and finding them “saying” similar things, for example, because there was a golden rectangle at Wells and other geometrical features were common to both buildings, I looked to see if there was one at Llandaff. Another “speaking” moment was when I saw how the circle in Figure 11 matched the curve of the door. The language is also capable of sustaining an argument. An example is in the West Font, where each placement depends on its predecessor in a lengthy chain. It was by following this argument that I discovered the golden rectangle in Figure 12. The musical analogy continues here, for one does not need to enquire concerning the extra-musical meaning of a Mozart symphony for example, for the meaning is in the symphony itself, and is communicated in musical language.
We have seen two instances in the west front where similar results were arrived at by a dual determination. As well as showing the superb skill of the designer, this was all to the good as it “locked” the additional determinations into the geometry. This is one of the meanings of the vesica piscis, to join opposing powers and give birth from the union. A deeper meaning is that the two circles represent duality, that which is manifest, and the intersection represents the Unity which is the source of all.
The pentagram is an ancient symbol of the Goddess, Venus, Aphrodite, Isis, She has many names. The clearest and largest pentagram is in the Lady Chapel.
In some places the pentagram with point downwards is viewed as a symbol of evil. No shape is inherently evil. If you choose to give this meaning to the pentagram round the door, you also see the Unity, symbolised by the circle, shining through every appearance of evil. The same meaning could be seen in the clerestory, but really evil has no place in beauty such as this.
One can never say that one has exhausted all the layers of meaning in a building. To those involved in the design, it may be that numbers possessed properties and meaning in themselves. It is therefore a legitimate line of enquiry to see if there is any consensus in writings on numerology, although the element of subjectivity is necessarily strong here, where it was absent in the demonstration of the pervasive presence of pentagons at Llandaff.
Gervais Frykman
2004
2014