Figure 29: The single defined field of this composition fits between the overlap of the figures’ boundaries (29·1).
Compare the same figures illustrated as a line drawing and absent the field (29·2).
Diagram 29·1: Aligned figures and defined field.
Diagram 29·2: Aligned figures drawn as line absent the field.
Figure 30: The field rendered as a ground plane lying between the original motivic figures.
Figure 31: The field rendered as a horizontal figure between the original figures in proportion to the original composition.
Figure 32: The field rendered as a figure placed so that the elevation mirrors the 1:3:6 geometry of the original motif.
In music, there are almost as many motifs as there are melodies, which is quite a large number. Similarly in architecture, there are as many motifs as there are arrangements of form – also a large number. However, the four rela-tionship categories help identify simple motivic structures. Between two or more figures, naming contrasts of size, shape and orientation, including the interval between them, identifies their elemental structure. Alignment speci-fies their spatial gesture, repetition marks the scope and principle of arrange-ment, while proximity designates any groupings. Thus the geometric motif for our first aligned composition might read:
· Two horizontal figures separated, proportioned as : and :, the smaller figure above and separated by an interval proportioned as :.
· The figures are parallel and aligned vertically such that the larger figure and the interval describe a square.
Notice that this description does not include any reference to the motif relative to the ground. Once we expand our point of view to include the larger field that is the ground, the dynamics of the composition become more involved.
Recalling the earliest analytic diagrams of the four compositions, we recog-nize that the fields drawn within those analyses make visible the formal rela-tionships within the composition. When we mark those as fields of tone, we begin to turn from the procedures of analysis to the possibility of extending the composition based on the original formal structure of the base composi-tional structure. If we assert that our initial simple composition acts as the Big Idea – the diagram of controlling order, then the analysis should lead us to visualizing a structure for coherent additions and modifications that fit within that order. The changes may alter the image of the project but the result remains connected to its intent.
Defined fields
Picking up from our earlier discussion, we start with a simple defined field – one that results directly from the boundaries of existing figures. In the case of the two parallel horizontal figures, there is only one, the : proportional neg-ative space between them (). The illustrations on the left show three varia-tions for interpreting the defined field. In all three variavaria-tions, the figures have a height equal to the width of the original compositional element resulting in near-cubic volume. As a result, the section along one axis mirrors the plan.
In the first illustration, the field remains as a ground plane, creating a courtyard connecting the two figures (). In the second, the field sponsors a slender connecting volume proportional to the elements in the two-dimen-sional plan but rearranged (). The final example shows another spanning volume that transfers the initial plan geometry on to the elevation of the com-positional solids.
Diagram 33·1: Staggered figures drawn as line.
Diagram 33·2: Edge-aligned figures drawn as line.
Diagram 33·3: Fitted figures drawn as line.
positions – staggered, edge-aligned and fitted – shown as line drawings.
As we examine all four of the original compositions – aligned, staggered, edge-aligned and fitted – as simple line drawings, we can perceive a degree of visual correspondence between the depiction of the figures, the boundar-ies and the underlying rules (··–). Such linear diagrams reveal align-ments and proportions among the elealign-ments. However, as we have seen in locating the defined field for the first composition, when we depict them as black figures on a white ground, we enhance the contrast between figure and field and objectify their spatial correspondence. This makes the gestalt dynam-ics more visible, helping to visualize additional elements in the ground that sustain or counter the basic motif.
The aligned forms define a single bounded, in-between field (·). In con-trast, the other three compositions define other possible fields of two kinds - and (·). Adjacent fields border a figure’s side and
extend to the parallel boundary of the other figure. Hybrids also border one form but derive their other measure from both the parallel and perpendicular boundaries of a second figure. Analyzing the complete set exposes subtle simi-larities and helps to illustrate the sequence of development of the composi-tions. Examining the figure-ground diagrams, we find the following:
· The staggered figures define one in-between field, two adjacent and two hybrid fields – five areas in all (·a). There are two adjacency-hybrid pairs and adding the hybrid areas to the in-between raises the total to ten recti-linear fields (·b).
· The edge-aligned figures share no in-between space, only two adjacencies and two hybrids totaling four fields (·a). There are three available pair-ings, bringing the total to seven defined rectilinear fields (·b).
· With three elements, the fitted-figures composition defines twelve fields.
In-betweens, adjacents and hybrids accrue to six fields. Adjacent pairs and a set of three betweens define six more rectilinear fields.
Variations in the figural elements will affect the character of each composi-tion type. This reminds us that the project is an exercise in proporcomposi-tion as well as an introduction to figures and fields on a ground. Our next observations will isolate individual fields and continue our analysis.
Diagrams 35·1 a&b: Five defined areas result from a staggered figures composition. Combining fields increases the possible fields to ten.
Diagram 34·1: An in-between field.
Diagram 34·2: An adjacent field.
Diagram 34·3: A hybrid field.
Diagrams 35·2 a&b: Four defined areas result from an edged-aligned figures composition. Combinations increase the possible fields to seven.
Diagrams 35·3 a&b: Six defined areas result from a fitted figures composi-tion. Combinations increase the possible fields to twelve.
Figure 34: Three general field types – in-between, adjacent and hybrid – arrayed in a prototype staggered motif.
Figure 35: The three derived compositions – staggered, edge-aligned and fitted – offer the possibility of multiple fields defined by various combina-tions of edges. The diagrams illustrate individual and grouped patterns to help visualize a complete inventory.
Figure 36: Five defined fields in the staggered composition – in-between, adjacent and hybrid – shown above in sequnce, starting at the center.
Figure 37: Two diagrams on the right show paired adjacent/hybrid combinations.
Figure 38: Combinations of the two hybrid areas with the in-between field yield multiple occupations of the visual middle as shown on the right.
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Figure 39: The four defined fields found in the edge-aligned composition consist of two adjacencies and two hybrids, shown on the right.
Figure 40: The three combined defined fields found in the edge-aligned composition occupy distinct precincts as shown on the right. Note their effect on the overall balance of the composition.
Diagram 36·1: Defined in-between field.
Diagram 36·2: Defined hybrid field.
Diagrams 36·4: Defined hybrid field.
Diagram 36·3: Defined adja-cent field.
Diagram 39·1: Defined upper adjacent field.
Diagram 39·3: Leftward defined hybrid field.
Diagram 39·4: Rightward defined hybrid field.
Diagram 39·2: Companion lower adjacent defined field.
Diagram 40·1: Defined com-bined field to the left.
Diagram 40·2: Opposite com-bined field to the right.
Diagram 40·3: Central com-bined defined field.
Diagram 37·1: Defined adja-cent/hybrid combined field.
Diagram 38·1: Defined com-bined field to the left.
Diagram 38·2: Opposite defined combined field.
Diagram 38·3: Central, shared defined combined field.
Diagram 37·2: Opposite com-bined field defined.
Diagram 36·5: Defined adja-cent field.
Figure 41: The in-between defined field found in the fitted figures composi-tion occupies a key posicomposi-tion, reflecting the structure of the underlying nine-square diagram. In contrast, the two adjacent fields accent our appreciation of the negative space.
Figure 42: The hybrid defined fields found in the fitted figures composition middle positions – shown on the left – reflecting the strategic structure of the basic nine-square diagram.
Figure 43: Three combined defined fields found in the fitted figures composition shift the balance. Those to the side of the composition tend to isolate the opposite figures, while the center field connects and unifies the overall configuration.
Figure 44: The other three combined defined fields found toward the center of the fitted figures composition also connect the upper and lower elements.
Those on the left or right suggest apparent mass or weight, while the center field unifies the whole.
· Single adjacent fields extend visual gesture within boundaries and along one axis (·, ·, ·, ·, ·–), as do some hybrid fields (·, ·,
·–). This is also the case with some combined fields (·, ·, ·–).
· Some extending combined fields touch two figures and create more complex
-shape figure-field outlines (·, ·, ·, ·).
· Certain hybrid fields also result in -shape figure-field outlines (·, ·).
· In some instances, the field connects two figures, resulting in a negative space that suggests a courtyard figure (·, ·, ·–). We can see a simi-lar suggested effect resulting from some hybrid fields (·, ·).
At this point, we should recognize that the interplay between figure and field follows from the precept of gestalt in which shapes and forms combine within a field to create a unified visual effect. The challenge of this exercise is noting where those effects are clearest and where further adjustments or addi-tions to the fields can lead to a more coherent overall composition.
Diagram 41·1: Defined lower adjacent field on the left.
Diagram 42·1: Defined hybrid field, mid-left.
Diagram 43·1: Defined com-bined field to the left.
Diagram 44·1: Defined com-bined field, left center.
Diagram 44·3: Defined com-bined field, right center.
Diagram 44·2: Combined field, spanning the center.
Diagram 43·3: Defined com-bined field to the right.
Diagram 43·2: Defined com-bined field in the center.
Diagram 42·2: Defined hybrid field, mid-center.
Diagram 42·3: Defined hybrid field, mid-right.
Diagram 41·3: Defined lower adjacent field on the right.
Diagram 41·2: Defined upper in-between field.
Comparing similar compositions holding different figures can improve both visual judgment and bolster the language for describing visual events. The image pairs to the left afford just such a comparison (·–). The left-hand column repeats examples from our four compositional strategies using fig-ures we can describe as large and small, and in close proximity. The right-hand column presents similar compositions that use more equally sized figures at greater distance from one another.
In the first pair, we observe the effect of scale and proximity in an aligned composition (·). The defined field in the first composition relates easily to the figures, effectively bridging and completing the proportional figures. In the second example, a larger field between two similar, mid-size figures forms a composition of opposing and independent elements.
The second set of examples, representing staggered figures, connects nor-mal faces to suggest partial courtyards within the negative space (·). The illustration on the left is the more intimate, the enclosure seemingly limited to enclosing the smaller central square bounded by the lower figure (compare to ·). In the second diagram (·b), the negative space stretches to the bounding edge of the upper figure. Both of these observations respond to the relative scale of the field as a visual influence.
In the third set, the scale of the field compared to the edge-aligned figures also leads to divergent gestalt readings (·). The primary visual sense of the first composition notes the field’s dependence from – and proximity to – the upper smaller figure, adding weight to the corner of an apparent rectangle and corresponding to the outer boundaries of the entire group (compare to ·).
In the example (·b), the dominant scale of the dependent field combined with the upper figure favors the negative space to its left from which the lower figure depends.
The final example set, being more complex, yields more subtle gestalt obser-vations (·). The combined fields in both connect two figures in an -shaped amalgam. In the first instance, the contrast of the larger square figure empha-sizes the negative space above, while the smaller figure on the upper right anchors within the negative space below and to its left. Together, they suggest two -shaped areas interlocked around the center. In the second composition (·b), the similar scale of the three figures and the combined field fuse into a more balanced assembly. The defined interior negative space merges, field-like, and the arrangement conveys a nuanced rectangle caught between the bound-ing perimeters.
Reviewing the diagrams prompts two observations. First, changes in pro-portion and proximity radically affect our apprehension of figure-ground, par-ticularly our awareness of resulting negative space (further examples can be found in ·.). Second, marking discreet defined fields modi-fies the overall composition profoundly and can shift our perception of the whole. Refining and adding to these observations brings us to implied fields, which further alter and add to our understanding of figures in composition.