PROPORTION (see also references to the subject under ARCHITECTURE, PERSPECTIVE, and RHYTHM).
The term proportion, when used in a non-technical sense, signifies frequently little more than measurement. When we say that a house has the proportions of a palace, or a growing boy the proportions of a man, we mean merely that the one is as large as the other, or has the same general measurements. In addition to this, however, there is often connected with the term, when carefully used, a conception of a comparison of measurements. When we say of a man that his feet are out of proportion, or of a copy of a Greek temple, that its pediment is out of proportion, we are probably recalling a normally developed man or an ancient Greek temple. If so, we mean that, in the specimen before us, the measurements of the parts mentioned are not the same as in the specimen of which we are thinking.
There may be two reasons why these measurements are not the same: one reason, because they are absolutely larger or smaller than in this specimen; the other reason, because they are relatively so, a hand or a limb being said to be in proportion because its measurements, whether large or small, bear the same relation to the parts or to the whole of a body that they do in the typical man which is supposed to be the artist’s model.
But proportion has still another meaning. From this, any conception of imitation, whether or not suggested by any particular model, is absent; and a part is said to be in proportion because of the relationship which its measurements sustain to the measurements of other parts or to the whole of a product. This seems to be the meaning when we speak of the proportions of the human figure, irrespective of any references to attempts to copy any particular model; and it certainly is the meaning when we speak of the proportions of a building in a style such as has never before had existence, . . . in this sense, proportion includes the ideas, both of ratios or relationships, as in I : 2, and also of likeness or equality in ratios, as in i : 2: : 3: 6.Proportion and Harmony of Line and Color, II.
The view expressed in Gwilt’s “Encyclopedia of Architecture, ” and still quite prevalent, to the effect that pro-portion is “but a synonym for fitness,” is entirely ignored. This is not because of any undervaluation of the aesthetic importance of fitness, but because it is recognized that this latter characterizes many other artistic arrangements of form, as those of rhythm, tune, and color; and because it is recognized also that no amount of mere fitness could cause, or even suggest, that which is generally meant not only by artists but by people in general when they speak of pro-portion. When using this term in any strict or technical sense they almost invariably refer to an effect of measurements indicating a certain mathematical relationship between the parts of a product as compared with one another and with the whole.Idem, Preface.
Artistic proportion is based in this volume, as all acknowledge rhythm to be, upon the principle of comparison. It is held that, fundamentally, measurements go together because they appear to be exactly alike, that is, as i : i ; and that the mind accepts the ratios of certain small numbers that are not alike, like i : 2 or 2 : 3, because it is able to recognize in the first that which corresponds to I : i +I, and in the second that which corresponds to 1+1: + I + I . Idem, Preface.
If, however, the relationship be not that of I : i, the next easiest to recognize is that of I : 2. . . Nor is it difficult to recognize the relationship of I : 3, as between the second pair of lines in this figure, or of 2 : 3, as between the third pair.
But it is evident that as the values of the numbers represent ing the ratios increase, these become less recognizable; as, for instance, when they are as 4: 5 or as 5:7, as between, respectively, the fourth and fifth pairs of lines in this Fig. 16. When, at last, we get to a relationship that can be expressed only by large numbers like 1o: 11, or 15:16, the mind is no longer able to recognize even its existence.Idem, Iv.
What has been said will show us a good reason, too, why, as affirmed by W. W. Lloyd in his “Memoir on the Systems of Proportion,” published with Cockerill’s ” Temples of Aegina and Bassae,” p. 64, “the Greek architects attached great value to simple ratios of low natural numbers.” Of course, the simpler the ratio, and lower the number, the more easily could each be recognized.Idem,
Notice, again, that proportion, as it is thus attributed to measurements that are compared, is merely a statement of a fact; nor is it essential that the mind, before stating this fact, should recognize what the ratio is, only that it has existence. The same principle applies here as in rhythm. To experience the effects of this, we do not need to be able to tell what the metre iswhether long or short, iambic or trochaiconly that there is a metre. But while this is true, the metre must be capable of being analyzed; and we must feel that it is so, although, perhaps, we our-selves do not actually go through with the analytic process. Idem, ii.
The mind takes satisfaction not in the ratio per se, but in that which the ratio enables it to recognize, which is that, in fulfilment of the fundamental art-method, measurements have been put together which are alike as to their parts… . This is not the explanation usually given for effects of proportion. But it is the explanation most consistent with that usually given for effects of rhythm; it is the explanation most consistent with all the methods of art as unfolded in ” The Genesis of Art-Form” (see also chart on page 89 of the present volume) ; and, finally, it is the explanation which can render most easy and simple the practical application of the principle to all possible visible effects. Idem, VIII.
As rhythm starts by putting together similar small parts such as feet and lines, and produces the general effect of the whole as a result of the combined effects of these parts, so does artistic proportion. For instance, the height of the front of the Parthenon is to its breadth as 9:14. But we need not consider the architect as aiming primarily at this proportion; or that it is any more than a secondary, though, of course, a necessary result of the relations, the one to the other, of the different separate measurements put together in order to form the whole.Idem, Preface.
PROPORTION AND RHYTHM NATURAL TO MAN.
There is no primitive kind of ornamentation, no matter how barbarous the race originating it, of which one characteristic, perhaps the most marked, is not an exact division or subdivision of spaces, the mind, apparently, deriving the same sort of satisfaction from rude lines of paint and scratchings upon stone, made at proportional distances from one another, that it does from the rhythmical sounds drummed with feet, hands, or sticks to accompany the song and dance of the savage.Idem, II.
An appreciation of rhythm is usually supposed to furnish the earliest evidence of aesthetic capability on the part of either a child or a savage. In fact, almost the only form of musical harmony over large sections of the earth to-day continues still to be merely a rude development of rhythm. But what is rhythm? A result of making, by series of noises or strokes, certain like divisions of timesmall divisions, and exact multiples of them in large divisions. But the moment that the smaller become so numerous that the fact that they exactly go into the larger divisions is no longer perceptibleas often, when we hear more even than eight notes in a musical measure, or more even than three syllables in a poetic foot,the effect ceases to be rhythmical. A like fact is true of proportion. Owing to the very great possibilities and complications of outlinings, as in squares, angles, and curves, its laws are intricate and difficult to apply; but, as will be shown in the volume of this series entitled ” Proportion and Harmony in Painting, Sculpture, and Architecture,” the harmonic effects of proportion all result, in the last analysis, from exact divisions and sub-divisions of space in every way analogous to the methods effects, which, in addition to those of proportion, were deemed desirable. As said in the preceding chapter, a chief reason why the requirements of proportion are supposed to be involved in impenetrable mystery, and why, therefore, the neglect of them in our own day is supposed to be excusable, is traceable to this confounding of these two entirely different subjects of inquiry.Idem, Iv.
As the principles of proportion have reference to appearances and to these alone, they cannot be fulfilled in a satisfactory way without regard to circumstances. A number of straight lines enclosed within a space, for instance, in-crease the apparent length of that space in the direction in which they point or incline. Any other spaces containing no such lines, yet intended to appear of equal length with it, ought really, therefore, to be a little longer. Again, if when we are looking at a building a projecting cornice hide part of a wall, window, pediment, or roof that is above the cornice, so that this upper part appears too short or too low to be in good proportion, then, as we shall find was the case in the Parthenon, it must be made longer or higher, no matter what its real measurement may be. The end to be attained is not factors with like or related measurements, but factors that appear to have these.Idem, IX.
Whether applied to exteriors or interiors, the important consideration is that there should be some apparent relation-ship between the length, height, and breadth. If we perceive that there is such a relationship, our minds are satisfied. If we fail to perceive it, they are confused; the effects are distracting and disquieting. As will presently be shown, the use, on exteriors, of window-caps, string-courses, cornices, pilasters, pillars, and also of some of these, as well as of color and of upholstery in interiors, may some-times counteract a confusing tendency. But sometimes, too, it cannot ; and when needing to suggest relationships that do not really exist, it can never do so except by apparently shortening or lengthening actual dimensions.Idem, Ix.
It is well-nigh impossible to distinguish such effects as are attributable to the measurements, from such as are attributable to the outlines that are measured. For instance when one says that the angles described by the coverings over the gable-windows, turrets, and different parts of the roof in Fig. 27, page 51, are not in proportion, he necessarily refers to appearances produced both by measurements and by shapes. In the mind of the observer, therefore, the two different classes of effects are often confounded.Idem, Ix.
PROPORTION DEPENDENT ON APPEARANCES.
A very convincing proof of this may be obtained from the façade of St. Sulpice, Paris. Has any one ever looked at this church without finding himself involuntarily asking why it is that its proportions seem so unsatisfactory? And yet it is not because the measurements, as applied to the building as a whole, violate any of the principles of proportion. The extreme width of each tower is to the width of the space between the towers exactly as 1:2. Could any scheme of ratios be more simple? Why, then, does it not appear so? Why, but because of the five divisions made by the pillars in the space between the towers? How can the mind recognize that each tower’s width is to the space as 1:2, or, what is the same thing, as 2:4, when it sees five instead of four divisions in this space? It cannot do so, or, at least, not without at first being confused. Were there a pediment above the cornice over the nave, the apex of this would divide the space there into two equal parts; or were the central door of the nave made more prominent than the two doors each side of it, then the present unfortunate effect would be prevented. But if such changes cannot be made, the mind would be better satisfied, in that it would judge the proportions to be more correct, even on a supposition that they were 2:4, in case there were between the towers only four divisions of the width of the present ones, making the proportions, in fact, less correct.Idem, Ix.
PROPORTION, GREEK, MISUNDERSTOOD.
There were many of the dimensions which the modem Hellenist would follow slavishly, which the Greeks used on account not of what they were, but of what they appeared to be. Nor, even admitting that the proportions were used on account of what they were, is it certain that the parts of the buildings which modern students suppose these pro-portions to determine are the parts which the Greeks intended them to determine. When, for example, the height of a temple, pediment included, is to its breadth as 7:12, or 9:14, is this ratio the cause of these dimensions, or only an incidental and, therefore, almost accidental result of arrangements for which the cause is to be sought elsewhere,for instance, in a desire to make the entablature and pediment appear of the same height, and both together to appear to sustain a certain ratio to the columnar space below them?Idem, XI.
PROPORTION IN ARCHITECTURE.
Architecture, like music, deals with forms that to only a limited extent can be said to result from an imitation of nature. In some regards, this fact gives the builder greater freedom for invention than is possible in painting and sculpture. He is not expected to accept forms as he finds them. Like the musician, who is at liberty to shorten and lengthen sounds so as to make them rhythmical, he is at liberty to shorten and lengthen shapes so as to make them proportional. But this fact places him, in some regards, under peculiar restraints. If the effects of the proportion produced by him must depend upon his own invention, it is particularly necessary for him to understand what the right proportions should be. A painter not knowing this may succeed because he may be able to copy accurately the proportions of objects that form his models. But the architect, barring the instances, necessarily limited, in which he may exactly imitate the buildings of others, must design his own forms. In such circumstances, so far as beauty depends on proportion, if ignorant of its requirements, he will fail as certainly as a musician attempting to compose a march, without knowing how to produce rhythm.Idem, Ix.
PROPORTION IN ARCHITECTURE, THE RESULT OF EXPERIMENTING.
The Parthenon was not sketched in its completed form upon paper, and then let out to some contractor to be erected in so many months. It took, as some say, ten years, and, as others say, sixteen years to complete it; and most of the marble in iteach column, for instance, with its capital is said to have been shaped after being lifted to its place. We know that some of the Gothic cathedrals were almost entirely pulled down and rebuilt, because their appearance was not satisfactory. Why should it not have been the same with the Greek temples? In the age in which they were constructed other artists believedwhy should not the architect ?that a man should study upon a product, if he intended to have it remain a model for all the future. It is natural to suppose that the structural arrangements intended to counteract optical defects, or to produce optical illusions, were largely the results of the individual experiments of individual builders. If they were not so, why were they invariably different in different buildings? But if they were so, and if, therefore, it be justifiable to compare the methods of arranging the out-lines of these buildings to the methods of arranging outlines according to the laws of perspective in painting, then why is not the general principle which these ancient architects endeavored to fulfil of more practical importance than any particular manner in which, in any particular case, they fulfilled it? More than this, why might not the architects of our own time, by applying, each for himself, as a result of his individual experiments, the same general principle, produce approximately successful results? But these they certainly cannot produce (for reasons stated on page 26) until they get out of their heads the conception that the measurements in the ancient buildings are merely representativein some mysterious way not possible to fathomof ratios related to one another as are those of pitch in music. As applied to this case, at least, we have an illustration of how utterly destructive of true practice in art is a false theory.Idem, XIV.
PROPORTION IN ARTISTIC PAINTING OF NATURAL SCENERY.
Natural speech is not always rhythmical, at least not in that higher sense in which it is also metrical. Yet a drama-tic poet, in his artistic representation of speech, may make it so. In the same way, why may not a painter or sculptor, whether or not a form or collection of forms manifest pro-portion in nature, make it do so in his artistic treatment? The main requisite of proportion, as we have found, is to have some apparently like standard of measurement into which certain parts or sets of parts in an object of sight are divided; and there are innumerable methods, not involving any lack of exactness in imitation, through which this result may be attained. Take a mountain scene. A selection of one point of view only a hundred feet away from another may entirely change the suggestion of like divisions afforded by the lines of distant and nearer ridges, of snow or flora of different characters, or of the borders of lakes or rivers.Idem, vi.
The painting accurately represents nature, and nature deprived of none of its variety. But if the artistic representation did not fulfil the requirements of proportion, it might be no more entitled to be considered a work of art than would be a poem, if devoid of rhythm.Idem.
PROPORTION IN HUMAN FORMS, AND CLOTHING.
To speak of the originator of styles of clothing, it is sometimes supposed that these latter need fulfil no aesthetic principles,that men will think beautiful any style to which they have become accustomed. But they will not think it beautifulwhatever word they may use in order to express their thought of it; at best, they will merely think it fitting, because it is conventional; and for the same reason, too, they may think any other style inappropriate. But in some way, which possibly they cannot explain, perhaps not even recognize, life for them will be deprived of certain legitimate esthetic influences, the presence of which might enrich their experience. This statement applies not only to the use of form and color, but also of proportion. How easy it would be to cause the cut of the garments to reveal the four, five, six, or eight parts of equal lengths into which the height of the well proportioned body is divisible! A line below the knee, whether of skirt or breeches; a line at the middle, whether of girdle or waistcoat; a line in the centre of the breast, whether of bodice or vest, together with other lines, always divide the figure satisfactorily.Proportion and Harmony of Line and Color, VI.
PROPORTION IN HUMAN FORMS, AS DETERMINED BY REAL OR IMAGINED LINES.
When we come to consider the human body it might be supposed that the influence of such lines as are drawn through it or through parts of it, might not be felt because they are not actually present. Nevertheless, because they are ideally present, they have some influence. If, for instance, a person be facing us, it is almost impossible not to suppose an imaginary vertical straight line drawn from the middle of his forehead to the middle of his chin, and if we find this line passing through the middle of his nose, we obtain an impression of regularity which, so far as concerns it alone, is an aid to the agreeableness and consequent beauty of the effect; but in the degree in which the middle of the nose is out of this vertical line, not only irregularity but ugliness is suggested. A similar tendency of thought causes us to suppose other imaginary vertical straight lines, drawn, at equal distances from this central line; and from them we may gain an impression of relative regularity by noticing to what extent the lines pass through corresponding sides of the face. Besides this, we are prompted to suppose horizontal lines drawn, across the forehead, eyes, and mouth; and from these lines, too, we form judgments with reference to the degrees of regularity. If the hair be farther down on one side of the forehead than on the other, or if the arch of the eyebrows be not symmetrically rounded, or if the sides of the mouth incline down-ward or upward, or a lip be larger on one side than on the other, we notice the fact. Of course we do this, only so far as we compare the result with that of an imaginary straight line drawn through the feature. The same is true, too, with reference to lines dividing other parts of the body. If one part of an eye or ear or if a neck, or hand, or trunk, or leg, be, relatively to other features of the frame, ‘ too long, or too short, we perceive the defect almost immediately; but we can only do it as a result of ideally drawing such lines and measuring and comparing the distances between them. In the same way, the similarity in curvature suggested by the outer lines of calves, thighs, and shoulders, prompts us to imagine similar curves drawn; and in case there be any deviation in outline from conformity to a segment of one of these curves, the eye will observe the fact; and the parts of the contours about which they are described will not seem to be constructed on the same lines, as we say, and, therefore, will not seem to be in proportion. So much as to the general principles in accordance with which such lines are made the basis of aesthetic judgments, either because they are actually delineated or are merely imagined.Idem, VII.
For instance, take the outlining conditions of pictures produced upon stained glass, especially in windows. Such windows are always constructed on a network of bars which cannot be hidden; and these necessitate dividing whatever is represented on the glass into certain parts. Why has it never occurred to artists to have these bars divide human forms, when crossing them, into parts of like longitudinal dimensions? Straight lines, cannot give us, perhaps, the most important indication of the measurements determining the proportions of the human form. But such lines can give us some indication, and, so far as they do this, the artist, alive to his opportunities, will utilize them, it being an elementary principle in art that its necessary limitations should be made to add to its effectiveness.Idem, VI.
PROPORTION IN HUMAN FORMS INDICATED BY LIKE CURVES.
Figures of various outlines can be made to seem to be in proportion, when they are, or can be, framed not only in like rectangles, but in any like figures whatever. The rectangle is used as an actual or ideal standard of comparison merely as a matter of convenience. It is comparatively easy to recognize whether or not straight lines, such as rectangles have, are of the same lengths, or are the same distances apart, or have, in other regards, other measurements that are in proportion. It would be a mistake, however, to suppose that the standard of measurement is, or, in all cases, can be rectangular. Take the human form. It is ordinarily divided into equal parts by horizontal lines, and these lines are undoubtedly an aid in determining the proportions. But, as will be shown on page 68, effective aid may be afforded by circles also.
There is a reason for the use of these circles as a standard of measurement derived from the physiological requirements of the eye, especially in binocular vision. This reason will be found unfolded in Chapter XVI. Here it is sufficient to say . . . that when all the circumferences of the circles described about the same figure are the same, the eyes are supposed to be focussed for distinct vision at exactly the same distance. At a certain distance from the form, for instance, all the circles are of one size, but nearer than this all of them are of another size.
A very interesting illustration of the aid afforded by. . . the perception of the fact that like is put with like, may be observed in . . . the curve which Ruskin, in his ” Mod-ern Painters,” declares to be the most common in nature. The curve is one so described as to show a constant tendency to become straight, although never becoming straight.
Any one who will go over any representations of the human figure with compasses will be surprised to find how large a part of a segment of exactly the same curve fits either the bend of the calf, forearm, thigh, abdomen, chest, or back. If then his experiencesay at a bathing-placecauses him to recall the aesthetic influences of such formations as a long arm or leg combined with great leanness, or a small chest combined with an abnormally large abdomen, he will find upon reflection that the effects of disproportion, while attributable partly to association, are also attributable partly to a recognition of an absence of like curves. Or, to illustrate this fact from a contrary condition, everybody ad-mires a small ankle and a good-sized calf. Yet the moment the calf becomes so large proportionately as to interfere with the suggestions of a like curve in this, and in the out-lines of the hip, almost everybody is conscious of receiving a suggestion of disproportion.Idem, V.
PROPORTION VS. PERSPECTIVE (see also GENERAL AND DISTANT VS. SPECIFIC AND NEAR EFFECTS, and PERSPECTIVE).
As indicated in either opinion or production, the artistic intelligence of our own time has, as yet, scarcely an apprehension, and no comprehension whatever, of that which is acknowledged to have formed the chief visual excellence of Greek art. The author is convinced that this fact is owing almost wholly to a misunderstanding of the aims of proportion, together with a confounding of it with perspective.Idem, Preface.
It will be recognized that the supposition that all these buildings were constructed with primary reference to producing a certain apparent effect when viewed from some point or points at a distance, is the only one that can furnish the same reason, and a sufficient one, for all the different methods of producing these effects,methods as different, for instance, as that in the forward curve of the entablature and as in the upward curve of the entablature or of the stylobate. Moreover, such a supposition is the only one that can give the same reason, and a sufficient one, for the application of the same method in order to produce the same effects, yet with almost infinite differences in measurements, in different temples. Here are some of these measurements . . . they probably have nothing to do with proportion, per se, but merely with producing the appearances to which, after being made to appear as they do, the principles of proportion apply. The best clue to the interpretation of these irregularities seems to be afforded by the methods of introducing perspective into painting. It is not considered necessary in this latter art to apply the laws of perspective with mathematical exactness. Each draftsman, in arranging his outlines, feels at liberty to stand off from his drawing, and, as a result of repeated examinations and experiments, to use his own ingenuity. Indeed, even if these laws were applied with mathematical exactness, the required measurements would differ with every foot by which a man stood nearer to his product, or farther from it. Precisely so in architecture . . . as Vitruvius says, very unequivocally, in book iii., chapter iii., “To preserve a sensible proportion of parts, if in high situations or of colossal dimensions, we must modify them accordingly, so that they may appear of the size intended.” Idem, XIV.
Every painter knows that colors and shadows as examined close at hand in the external world often differ greatly from what they appear to be to one who judges of them by the image on the retina. To him an actually checkered surface may appear to be of a single color, and a color, owing to the influence of surrounding hues, may appear unlike that which it actually is. The same fact is true with reference to out-lines. The eye is rounded and therefore the mind behind it sees everything through a rounded surface. If one look into a convex mirror he will find all of the dimensions of the natural world slightly altered. As a rule, for instance, the straight upward lines of a square object with its base on the middle line of the mirror will appear not to be parallel but to approach one another. The effects in the mirror merely exaggerate the effects already exerted upon nature by the rounded formation of the eye. As applied to natural surroundings, we become accustomed to these effects and never judge lines to be curved or lacking in parallelism merely because they are so in the image on the retina. On the contrary, unless they were so in this image, we should judge the lines to be neither straight nor parallel. Accordingly, when men try, as in drawing a picture, to reproduce the appearance of such an image, it becomes important for them to carry out what are termed the laws of linear perspective. These are laws, as will be explained in Chapter XIV., in accordance with which all the outlines of an artificial image, whether drawn, painted, carved, or constructed, or however changed in size, are made among other things to sustain somewhat the same relations as in an image naturally produced on the retina.
Notice, moreover, that to fulfil these laws of perspective so as to make this artificial image correspond to the image in the eye is one thing; and that to make the respective dimensions of this image appear to fulfil, each to each, the laws of proportion is another thing. Yet it is quite easy and natural to confound the two. We need not be surprised, therefore, to find them almost invariably con-founded in theories of proportion, especially in those which have had most influence in causing men to think that the subject is too complex and mysterious for solution. Those who have advanced these theories have failed to recognize that the analogue of proportion is not harmony but rhythm. Moreover, as rhythm is an effect of the conscious action of the mind, its general principles are comparatively easy to ascertain; and, by carrying out the analogies suggested by them, the explanation of the effects of proportion may be rendered comparatively easy. But the processes through which the ear becomes cognizant of the harmonic relations between musical notes and chords are difficult to ascertain, for the very reason that the mind is not conscious of these processes. No wonder, therefore, that a theory identifying with them those of proportion by which the mind, through the eye, becomes cognizant of the relations existing between spaces, should involve difficulties.Idem,