The West Front
The extraordinary beauty of the geometry of the west front confirms the artistry and stature of the designer (Figure 11). It also confirms that the round headed Early English doorway was integral to the design of the whole. Such doorways are rare, but can be found in the great transept at Beverley Minster, in the Nine Altars and Refectory at Fountains, on the exterior of the south nave aisle at Exeter, and possibly at Thornbury Parish Church. The pentagonal nature of the geometry is disclosed by the angle of the gable, which is 72º, the angle at the centre of a regular pentagon. A further clue lies in the annulets on either side of the doorway, which indicate a pentagonal angle in conjunction with the centre of the base line. The shaft sections above and below the annulets are of equal length, which explains why the capitals are unusually tall in proportion to the length of the shaft. Another device used to disguise the low positioning of the annulets was to form them asymmetrically in their respective stones.
In Figure 11, the pentagon round the door has sides of 15'. It is enclosed in a pentagon of side 30', which is the width of the central part of the west front, being 1/5 of 150’, the length of the nave. The top of this pentagon aligns with the bottom of the opening of the upper window.
Two equilateral triangles of side 30' are shown. One has its base coinciding with a chord of the large pentagon. Its apex is at the lower edge of the hood mould at the apex of the central lancet, which is the level of the top of the capital of the south stair turret. The second equilateral triangle has its base at this level and its apex at the apex of the gable.
The width of the central lancet of the triplet, measured between the edges of the mouldings next to the openings, is equal to the width of the stair turret, which is derived from the bases of the piers of the nave arcade. The distance between the lancets is the same measure, so the inner edges of the outer lancets are defined. Two thirds of the distance from there to the stair turret or edge of the central part of the west front gives the position of the outer edges of these lancets. The remaining one third gives the width of the decorative band round the outer lancets. Naturally the band round the central lancet has the same width. We recall that the width of the windows in the clerestory is equal to the width of the wall between them. The openings of the lancets of the triplet are actually a little less than the widths defined above. This may reflect an aesthetic judgement, that the windows were too cavernous as first designed. The effect is a subtle one. In Figure 12, what looks like a band of glass quarries round the lancets is in fact stone as regards the vertical and curved edges. The windows as narrowed are shown in Figure 13, with actual quarries of glass round the edges. The position of the outer edge of the moulding round the outer lancets is given by the upper vertices of the 15’ pentagon in Figure 11. The width of the opening of the upper lancet is one seventh of 30’.
The pentagon in Figure 12 is centred on the apex of the lower equilateral triangle in Figure 11, and its circumcircle has a radius such that the upper vertices lie on the edges of the gable. The overall width of the pentagon is 30√3sin36° which evaluates to 30'6½". Two radii pass through the apices of the side lancets, just under the hood moulds. The part of the gable above the line joining the upper vertices can be reflected in that line, and the image of the apex falls at the centre of the pentagon. The circumcircle gives the position of the apex of the upper lancet. The lower faces of the pentagon, extended as shown to the points directly below the outer vertices define the level of the string course over the door. The outer vertex on the south side also appears to define the position of the angle shaft of the stair turret in a manner reminiscent of the clerestory geometry (Figure 9). A golden rectangle the width of the west front aligned on the string course gives the springing line of the arches of the lancets by an alternative method.
(2023) A pyramid triangle of base 11 units and height 7 units like that which locates the inner face of the south wall of the chapter house, where 11 units are 30 feet, based at ground level, gives the line of the lower edge of the window openings.
(2019) The first illustration below shows that the springing line on the south side is higher that that on the north side. This difference is not perceptible on the inside of the west front (Frontispiece). Nor is it shown on the drawing. The south lancet capitals have evidently been raised after they were built, for the decorative band on the south side of the lancet follows the line of the lancet pretty well, but on the north side of the south lancet, where there is a spur on account of the blind lancet which made it difficult to manipulate the stones, the band does not match the lancet.
The geometry of the inside of the west front is different, because the ground level is lower, and the width is greater, also the interior treatment of the door and windows is independent of the external treatment (Figure 13). Half the internal width of the west front, measured from the floor, gives the level of the bottom of the string course. The level of the edge of the sloping sill immediately over the string course is that of the springing line of the arches, a distance of d/4 from the floor. The sides of an equilateral triangle based on the floor cut the sill line at points which then determine the position of the strong verticals that divide the lancets of the west window and outline the door. Produced, they define the apices of the outer lancets in conjunction with the centre lines determined on the outside.
Another triangle, congruent with the first, is placed so that its apex is at the underside of the apex of the outer moulding of the central lancet. The upper apex of this moulding is at the level of the horizontal face of the large pentagon on the outside. The function of this triangle is to define the level of the openings at the base of the lancets. The triangle is confirmed by annulets in the outer lancets.
A third triangle, congruent with the other two and inverted, based on the level of the upper face of the clerestory pentagon defines the apex of the door. Let the side of the triangle be g. A point on the side, a distance g/3 from the door apex defines the shaft, and by analogy, all the other intermediate shafts and was marked with an annulet. A circle radius g/3 centered on this point necessarily passes through the apex of the door and touches the edge of the west front. It was also used to define the springing line of the arches of the lancets. When reflected in the centre line, a vesica piscis is formed.
The diameter of the vesica circles gives the height of the walkway in front of the central lancet from the floor.
The distance from the vertical outlining the door to the intermediate shaft of the central lancet was doubled to give the line of the inner shaft, and so the lines of all the inner shafts. The line of the inner shaft of the central lancet also aligns with the edge of the door opening. The difference between this and the edge of the opening on the west front is disguised by the door itself. It also provides a surface for the door to close against.
The point where the line of the door opening meets the floor, reflected in the centre line for illustration by a circle which defines the top step, is the centre of the extrados of the door. The curve also passes through the junction of the edge of the west front with the floor, and its highest point is its intersection with the opposite side of the equilateral triangle side g based on the floor. It also passes through the intersection of the vesica circle with the line of the door opening.
A construction would be to strike two sets of arcs from the apex of the door and the corner of the front, and join the two points thus determined with a line. This determines the centre of the extrados where it crosses the base line. Then noteworthy facts are the equal spacing of the shafts and the intersecting of the extrados at its highest point with the equilateral triangle.
Alternatively, draw a line at 45º from the corner of the west front and drop a perpendicular from its intersection with the lower equilateral triangle. Then the remarkable facts are the equal spacing of the shafts and the passing of the extrados through the apex of the door as defined by the inverted equilateral triangle, which it must do to be an extrados.
The centre of the extrados also defines a smaller equilateral triangle. The intersection of a side with the line of the door opening defines the intrados.
The apex of the inner face of the upper lancet is at a distance d from the floor. The apex of the gable is at a distance of 7d/6 from the floor.
With the quantity of geometrical relationships in the west front, both inside and out, particularly the apparent dual determination of the gable height, it is interesting to consider the ways in which measures depend on other measures. Presumably the geometry of the arcades came before that of the west front, as they are the principal members of the church and their geometry can wholly be expressed in terms of the initial 150 foot measure and the distance d. The height of the west front was then determined as 7d/6 (Figure 13) bearing in mind that it had to be a little greater than the four bay lengths indicated in Figure 10 (it calculates at 9”), and then the ground level outside the west front was determined by the geometry of Figure 11. There is rising ground to the west of the Cathedral, and some excavation was required in order to create sufficient level space. This is the reason for the steps (Figure 10). The designer could determine how much of the ground he had excavated on the outside. Obviously there were constraints on this, and it seems that here and elsewhere he knew approximately where he wanted the various elements to go, and then worked out a geometrical scheme to fix the positions exactly.
A further sophisticated feature is the way the two outer shafts of the outer sides of the outer lancets on the interior rest on the duplet shaft of the arcade where it meets the west front. Likewise the outer triplets outlining the central lancet rest, not on the sill, but on the triplet shafts that outline the door (second Illustration below). The result is a subtle merging of the arcade and the west front because the duplet shafts are clearly part of the arcade, and just as clearly part of the west front. Also because the plane of the wall above the lancets overhangs the plane of the west front at ground level, there is an interplay between the interior of the west front on these two planes and the main space of the church.
Some of the shafts outlining the lancets on the inside of the west front have fillets below but not above the annulets (Illustration below). This indicates that the west front may have been built in stages. Figure 12 shows a construction of two half-equilateral triangles which was loosely adhered to in the design of the arcade on the exterior of the west front. This looseness is reminiscent of the treatment of the eastern bays of the nave and confirms the impression that the west front may have been built in stages.
Figure 13 shows the roof to be more steeply pitched than the gable. This is to allow room for the parapet, which was a mediaeval feature as shown in Figure 22. The original roof, however, like the original roofs at Wells, overhung the walls. The approximate line of this roof, aligned with the gable, is shown in Figure 8. This represents a further intricacy in the geometrical design of the west front and the clerestory.
Here we may compare the cradling in stone of the shafts in the blind arcade with the similar motif in the Elder Lady Chapel at Bristol, which is attributed to Adam Lock, who was the master mason at Wells up to his death in 1229. 27 The development of this motif can be traced in the treatment of the shafts that flank the triplet of lancets and those in the clerestory. The coherence of the geometry of the arcades, west front and clerestory suggest that the designer of the blind arcade, probably Lock, retained the essential features of the earlier design of the gable. The similarity between the arcades at Wells and Llandaff as regards the geometry is so great that it is likely that one man designed both. Work at Wells started c. 1175, and the Choir design cannot be later than c. 1180, and possibly earlier. The design of Llandaff therefore probably dates from the same period. This means that Llandaff, with Wells and Lincoln, may be one of the earliest Gothic churches in Britain. The difference in style therefore need not imply any considerable break between the construction of the south door and the commencement of the west front, nor is there a reason why a campaign should be halted after the building of an aisle wall. It is attributable rather to a change of masons. It is not known why the masons from the Hereford-St David’s axis were replaced by those from Wells, but it may be because they were called away in 1181 to work at St David’s.
In Figure 11, the pentagon round the door has sides of 15'. It is enclosed in a pentagon of side 30', which is the width of the central part of the west front, being 1/5 of 150’, the length of the nave. The top of this pentagon aligns with the bottom of the opening of the upper window.
Two equilateral triangles of side 30' are shown. One has its base coinciding with a chord of the large pentagon. Its apex is at the lower edge of the hood mould at the apex of the central lancet, which is the level of the top of the capital of the south stair turret. The second equilateral triangle has its base at this level and its apex at the apex of the gable.
The width of the central lancet of the triplet, measured between the edges of the mouldings next to the openings, is equal to the width of the stair turret, which is derived from the bases of the piers of the nave arcade. The distance between the lancets is the same measure, so the inner edges of the outer lancets are defined. Two thirds of the distance from there to the stair turret or edge of the central part of the west front gives the position of the outer edges of these lancets. The remaining one third gives the width of the decorative band round the outer lancets. Naturally the band round the central lancet has the same width. We recall that the width of the windows in the clerestory is equal to the width of the wall between them. The openings of the lancets of the triplet are actually a little less than the widths defined above. This may reflect an aesthetic judgement, that the windows were too cavernous as first designed. The effect is a subtle one. In Figure 12, what looks like a band of glass quarries round the lancets is in fact stone as regards the vertical and curved edges. The windows as narrowed are shown in Figure 13, with actual quarries of glass round the edges. The position of the outer edge of the moulding round the outer lancets is given by the upper vertices of the 15’ pentagon in Figure 11. The width of the opening of the upper lancet is one seventh of 30’.
The pentagon in Figure 12 is centred on the apex of the lower equilateral triangle in Figure 11, and its circumcircle has a radius such that the upper vertices lie on the edges of the gable. The overall width of the pentagon is 30√3sin36° which evaluates to 30'6½". Two radii pass through the apices of the side lancets, just under the hood moulds. The part of the gable above the line joining the upper vertices can be reflected in that line, and the image of the apex falls at the centre of the pentagon. The circumcircle gives the position of the apex of the upper lancet. The lower faces of the pentagon, extended as shown to the points directly below the outer vertices define the level of the string course over the door. The outer vertex on the south side also appears to define the position of the angle shaft of the stair turret in a manner reminiscent of the clerestory geometry (Figure 9). A golden rectangle the width of the west front aligned on the string course gives the springing line of the arches of the lancets by an alternative method.
(2023) A pyramid triangle of base 11 units and height 7 units like that which locates the inner face of the south wall of the chapter house, where 11 units are 30 feet, based at ground level, gives the line of the lower edge of the window openings.
(2019) The first illustration below shows that the springing line on the south side is higher that that on the north side. This difference is not perceptible on the inside of the west front (Frontispiece). Nor is it shown on the drawing. The south lancet capitals have evidently been raised after they were built, for the decorative band on the south side of the lancet follows the line of the lancet pretty well, but on the north side of the south lancet, where there is a spur on account of the blind lancet which made it difficult to manipulate the stones, the band does not match the lancet.
The geometry of the inside of the west front is different, because the ground level is lower, and the width is greater, also the interior treatment of the door and windows is independent of the external treatment (Figure 13). Half the internal width of the west front, measured from the floor, gives the level of the bottom of the string course. The level of the edge of the sloping sill immediately over the string course is that of the springing line of the arches, a distance of d/4 from the floor. The sides of an equilateral triangle based on the floor cut the sill line at points which then determine the position of the strong verticals that divide the lancets of the west window and outline the door. Produced, they define the apices of the outer lancets in conjunction with the centre lines determined on the outside.
Another triangle, congruent with the first, is placed so that its apex is at the underside of the apex of the outer moulding of the central lancet. The upper apex of this moulding is at the level of the horizontal face of the large pentagon on the outside. The function of this triangle is to define the level of the openings at the base of the lancets. The triangle is confirmed by annulets in the outer lancets.
A third triangle, congruent with the other two and inverted, based on the level of the upper face of the clerestory pentagon defines the apex of the door. Let the side of the triangle be g. A point on the side, a distance g/3 from the door apex defines the shaft, and by analogy, all the other intermediate shafts and was marked with an annulet. A circle radius g/3 centered on this point necessarily passes through the apex of the door and touches the edge of the west front. It was also used to define the springing line of the arches of the lancets. When reflected in the centre line, a vesica piscis is formed.
The diameter of the vesica circles gives the height of the walkway in front of the central lancet from the floor.
The distance from the vertical outlining the door to the intermediate shaft of the central lancet was doubled to give the line of the inner shaft, and so the lines of all the inner shafts. The line of the inner shaft of the central lancet also aligns with the edge of the door opening. The difference between this and the edge of the opening on the west front is disguised by the door itself. It also provides a surface for the door to close against.
The point where the line of the door opening meets the floor, reflected in the centre line for illustration by a circle which defines the top step, is the centre of the extrados of the door. The curve also passes through the junction of the edge of the west front with the floor, and its highest point is its intersection with the opposite side of the equilateral triangle side g based on the floor. It also passes through the intersection of the vesica circle with the line of the door opening.
A construction would be to strike two sets of arcs from the apex of the door and the corner of the front, and join the two points thus determined with a line. This determines the centre of the extrados where it crosses the base line. Then noteworthy facts are the equal spacing of the shafts and the intersecting of the extrados at its highest point with the equilateral triangle.
Alternatively, draw a line at 45º from the corner of the west front and drop a perpendicular from its intersection with the lower equilateral triangle. Then the remarkable facts are the equal spacing of the shafts and the passing of the extrados through the apex of the door as defined by the inverted equilateral triangle, which it must do to be an extrados.
The centre of the extrados also defines a smaller equilateral triangle. The intersection of a side with the line of the door opening defines the intrados.
The apex of the inner face of the upper lancet is at a distance d from the floor. The apex of the gable is at a distance of 7d/6 from the floor.
With the quantity of geometrical relationships in the west front, both inside and out, particularly the apparent dual determination of the gable height, it is interesting to consider the ways in which measures depend on other measures. Presumably the geometry of the arcades came before that of the west front, as they are the principal members of the church and their geometry can wholly be expressed in terms of the initial 150 foot measure and the distance d. The height of the west front was then determined as 7d/6 (Figure 13) bearing in mind that it had to be a little greater than the four bay lengths indicated in Figure 10 (it calculates at 9”), and then the ground level outside the west front was determined by the geometry of Figure 11. There is rising ground to the west of the Cathedral, and some excavation was required in order to create sufficient level space. This is the reason for the steps (Figure 10). The designer could determine how much of the ground he had excavated on the outside. Obviously there were constraints on this, and it seems that here and elsewhere he knew approximately where he wanted the various elements to go, and then worked out a geometrical scheme to fix the positions exactly.
A further sophisticated feature is the way the two outer shafts of the outer sides of the outer lancets on the interior rest on the duplet shaft of the arcade where it meets the west front. Likewise the outer triplets outlining the central lancet rest, not on the sill, but on the triplet shafts that outline the door (second Illustration below). The result is a subtle merging of the arcade and the west front because the duplet shafts are clearly part of the arcade, and just as clearly part of the west front. Also because the plane of the wall above the lancets overhangs the plane of the west front at ground level, there is an interplay between the interior of the west front on these two planes and the main space of the church.
Some of the shafts outlining the lancets on the inside of the west front have fillets below but not above the annulets (Illustration below). This indicates that the west front may have been built in stages. Figure 12 shows a construction of two half-equilateral triangles which was loosely adhered to in the design of the arcade on the exterior of the west front. This looseness is reminiscent of the treatment of the eastern bays of the nave and confirms the impression that the west front may have been built in stages.
Figure 13 shows the roof to be more steeply pitched than the gable. This is to allow room for the parapet, which was a mediaeval feature as shown in Figure 22. The original roof, however, like the original roofs at Wells, overhung the walls. The approximate line of this roof, aligned with the gable, is shown in Figure 8. This represents a further intricacy in the geometrical design of the west front and the clerestory.
Here we may compare the cradling in stone of the shafts in the blind arcade with the similar motif in the Elder Lady Chapel at Bristol, which is attributed to Adam Lock, who was the master mason at Wells up to his death in 1229. 27 The development of this motif can be traced in the treatment of the shafts that flank the triplet of lancets and those in the clerestory. The coherence of the geometry of the arcades, west front and clerestory suggest that the designer of the blind arcade, probably Lock, retained the essential features of the earlier design of the gable. The similarity between the arcades at Wells and Llandaff as regards the geometry is so great that it is likely that one man designed both. Work at Wells started c. 1175, and the Choir design cannot be later than c. 1180, and possibly earlier. The design of Llandaff therefore probably dates from the same period. This means that Llandaff, with Wells and Lincoln, may be one of the earliest Gothic churches in Britain. The difference in style therefore need not imply any considerable break between the construction of the south door and the commencement of the west front, nor is there a reason why a campaign should be halted after the building of an aisle wall. It is attributable rather to a change of masons. It is not known why the masons from the Hereford-St David’s axis were replaced by those from Wells, but it may be because they were called away in 1181 to work at St David’s.