The abstract beauty of architecture can be understood without any knowledge of the purposes of buildings. A Hindu who knows nothing of our civilization cannot fail to be responsive to Notre Dame, any more than we can fail to admire the beauty of Taj Mahal. The very simplest architectural forms, like the pyramids or the Washington monument, provided they are of sufficient size and mass, speak an eloquent language which is immediately understood. And the content of their speech is not so abstract as might be judged from our previous studies of it; for in architecture, as in music, concrete emotions and sentiments flow into the channel cut by the form. Longing, aspiration, and mystery have universally been felt into a form pointing skyward; and the feeling of incompleteness has been lost, and security regained, in an overarching dome.

There is, however, this difference between architecture and music. In music, the emotional content is purely personal; while in architecture, it may become social and historical. Architectural purposes are all social: the purposes of a family, a nation, a cult. And the purposes of the greatest of buildings—of those which serve the nation and religion—are also historical; about them gather the traditions of a community. Centers of the life of a people, created by it and enduring with it, they become its symbols; or outlasting it, memorials and witnesses to it. The vague emotions aroused by the architectural forms are pointed and enriched by this spirit: the vastness, seclusion, magnificence, mystery, and aspiration of the Gothic cathedral become associated with the life of the medieval Catholic church; the fine balance, clarity, and simplicity of the Greek temple with the best in Greek culture. This interpretation of a building in terms of its purpose and history is necessary to a complete aesthetic appreciation. Without it, a building may have many beauties, all the beauties which we have analyzed; but they are all separate, and there is no beauty of the whole. It is the life which the many parts and aspects serve that makes them into one.

I shall close this chapter with a brief discussion of architectural composition. The unity of a building is constituted primarily by the necessary adjustment of part to part which makes possible the life that it incloses. How the parts serve this purpose is not immediately evident to intuition; nor can it be; yet it should be intelligible to a thoughtful study. The knowledge thus gained may then enter into an imaginative vision, for which the building will seem like an organism pulsing with life.

This purposive unity cannot well be secured without spatial contiguity; here, as in sculpture, a unified life demands a unified material. Yet sometimes detached structures belong together functionally, and may be felt as one aesthetically, provided they are similar in design and some one of them is dominant; otherwise, each claims to be a distinct individual, and aesthetic rivalry is the result.

Functional unity, although necessary, is not sufficient for aesthetic unity; in addition, there must be formal unity—design, composition. To study this adequately would require a separate treatise, which has not yet been written, so far as I know, with anything approaching philosophical depth and completeness; but for our plan it will be sufficient to show how the general principles of aesthetic form are illustrated in architecture; and because of the perspicuity of things spatial, these principles are nowhere else so lucidly manifest.

Since architecture is a spatial art, unity in variety is chiefly a matter of harmony and balance rather than of evolution, and of these harmony is perhaps the most conspicuous. Harmony is secured in many ways.

First, by giving the whole building or parts of the building a simple geometrical form readily perceived,—for example, the cruciform plan of many Gothic cathedrals, the oblong plan and oblong surmounted by a triangle in the facade of the Greek temple, the octagonal shape of a Renaissance chapel. A higher degree of harmony is obtained when the same shape is repeated throughout the various parts of the building,—the cylinder in the columns, the triangle or semicircle in the arches and gables. A step further is taken in the same direction when the different similar parts are all of the same size, as in the Greek temple, where the columns are all of one size, and similar parts of columns of equal size, and the metopes and triglyphs likewise.

A more complex type of harmony, since it admits of greater variety, is proportionality. Proportionality may be of various kinds. It may be merely the existence of a definite numerical relation between the dimensions of single parts, or the areas of various parts, of a building. This, in turn, may be either a simple arithmetical relation, such as exists between the parts of a Greek facade, each being some simple multiple of the unit or module; or a more complex relation like the Golden Section, where the smaller is to the larger dimension as the larger is to the sum of both; or like that which obtains when different parts form a geometrical series, where each is smaller or larger than the preceding by some fraction of the latter. The relation between the length and breadth of the facade of the Ducal Palace in Florence illustrates the Golden Section; the heights of the stories of the Peller House in Nuremberg form a geometrical series. This type of harmony is most complete when the proportion between the dimensions of the different parts is the same as that of the whole building,—by the ancients called concinnitas because it produces a feeling akin to that of musical harmony. Dominance of a particular kind of line, horizontal or vertical, also gives harmony. Finally, harmony is secured by sameness of direction of line: the alignment of windows or parallelism between moldings dividing the surfaces of walls, for example.

The relations, so seemingly mathematical, upon which architectural harmony is based, need not be exact, for two reasons: minor deviations are not perceptible, and even when perceptible, they give to the whole a feeling of life. Our experience with living things has taught us that, despite their orderliness, there is no exact mathematical regularity in their proportions; hence forms which cannot be precisely formulated are better fitted to symbolize life to us than the rigidly geometrical. The same experience has taught us that the curvilinear forms are closer to life than the angular; hence again the tendency, for aesthetic purposes, to introduce minute departures from the plumb-line and rule. There is, however, a type of life specifically human, the life of reason, which is best symbolized by mathematical relations; hence the Greeks, and all those who have followed the classical ideal, all who have had a passion for reason, have felt the circle and the square, and every other exact embodiment of clarity and intelligence, to be beautiful. In no other art has the passion for the intelligible been so perfectly expressed as in classical architecture.

Next in importance to harmony as a mode of unity in variety in architecture is balance. Balance implies emphatic variety, or contrast. One mode of balance, that between the upward and the downward tendencies, we have already discussed. There is another mode, similar to that which exists in painting and sculpture, the balance between the right and left members of a building. In order that this type of balance may be appreciated, there must be some axis or line of mediation between the parts, from which the opposing tendencies take their start; otherwise we view the parts together, instead of in opposition. For example, there is balance between two wings of a building which are separated by some central member or link; balance between the aisles of a church on either side of the nave; balance between the sets of three columns right and left of the door in the Greek hexastyle temple. Such cases of symmetry between equal right and left parts are the simplest examples of balance; but there are other, more complex types. For example, the parts may be unequal, yet balance nevertheless, provided their inequality is compensated for by some enrichment of design or ornament in the lesser part. Or again, there may be a balance between contrasting shapes, such as the square and the triangle, when they make an equal claim upon the attention.