POSITIONS

DRAWING AND PAINTINGIN PURE DESIGN

POSITIONS

14. Take a pencil and a piece of paper. With the pencil, on the paper, mark a dot or point.

Fig. 3

By this dot (A) three ideas are expressed: an idea of Tone, the tone of lead in the pencil; an idea of Measure, the extent of the space covered by the dot; and an idea of Shape, the character given to the dot by its outline or contour. The dot is so small that its tone, its measure, and its shape will not be seriously considered. There is another idea, however, which is expressed by the dot or point,—an idea of Position. That is its proper meaning or signification. There is presumably a reason for giving the dot one position rather than another.

15. Put another dot (B) on your paper, not far from dot “A.”

Fig. 4

We have now a relation of two positions,—the relation of position “A” to position “B.” The relation is one of Directions and of Distances. Proceeding from “A” in a certain direction to a certain distance we reach “B.” Proceeding from “B” in a certain direction and to a certain distance we reach “A.” Every position means two things; a direction and a distance taken from some point which may be described as the premise-point.

16. Directions may be referred either to the Horizontal or to the Vertical. Referring them to the horizontal, we say of a certain direction, that it is up-to-the-left, or up-to-the-right, or down-to-the-left, or down-to-the-right, a certain number of degrees. It may be thirty (30°), it may be forty-five (45°), it may be sixty (60°),—any number of degrees up to ninety (90°), in which case we say simply that the direction is up or down. Directions on the horizontal may be described by the terms, to the right or to the left.

Fig. 5

The method of describing and defining different directions from any point, as a center, is clearly explained by this diagram.

17. The definition of Distances in any direction is well understood. In defining position “B,” inFig. 4, we say that it is, in a direction from “A,” the premise-point, down-to-the-right forty-five degrees (45°), that it is at a distance from “A” of one inch. Distances are always taken from premise-points.

18. If we mark a third dot, “C,” on our paper and wish to define its position, we may give the direction and the distance from “A,” or from “B,” or, if we prefer, we may follow the principle of Triangulation and give two directions, one from “A” and the other from “B.” No distances need be given in that case. The position of “C” will be found at the intersection of the two directions.

Fig. 6

The principle of Triangulation is illustrated in the above diagram.

19. We shall have occasion to speak not only of Distances, but of Intervals. They may be defined as intermediate spaces. The spaces between the points “A” and “B,” “A” and “C,” “B” and “C,” inFig. 6, are Intervals.

20. Given any relation of positions, the scale may be changed by changing the intervals, provided we make no change of directions. That is well understood.

Before proceeding to the considerations which follow, I must ask the reader to refer to the definitions of Harmony, Balance, and Rhythm which I have given in the Introduction.

IN POSITIONS: DIRECTIONS, DISTANCES, INTERVALS

21. All Positions lying in the same direction and at the same distance from a given point, taken as a premise-point, are one. There is no such thing, therefore, as a Harmony of Positions. Positions in Harmony are identical positions. Two or more positions may, however, lie in the same direction from or at the same distance from a given point taken as a premise-point. In that case, the two or more positions, having a direction or a distance in common, are, to that extent, in harmony.

22. What do we mean by Harmony of Directions?

Fig. 7

This is an example of Direction-Harmony. All the points or positions lie in one and the same direction from the premise-point “A.” The distances from “A” vary. There is no Harmony of Intervals.

Directions being defined by angles of divergence, we may have a Harmony of Directions in the repetition of similar angles of divergence: in other words, when a certain change of direction is repeated.

Fig. 8

In this case the angles of divergence are equal. There is a Harmony, not only in the repetition of a certain angle, but in the correspondence of the intervals.

Fig. 9

This is an example of Harmony produced by the repetition of a certain alternation of directions.

Fig. 10

In this case we have Harmony in the repetition of a certain relation of directions (angles of divergence). In these cases,Fig. 9andFig. 10, there is Harmony also, in the repetition of a certain relation of intervals.

23. Two or more positions may lie at the same distance from a given point taken as a premise-point. In that case the positions, having a certain distance in common, are, to that extent, in Harmony.

Fig. 11

This is an example of Distance-Harmony. All the points are equally distant from the premise-point “A.” The directions vary.

We may have Distance-Harmony, also, in the repetition of a certain relation of distances.

Fig. 12

This is an illustration of what I have just described. The Harmony is of a certain relation of distances repeated.

24. Intervals, that is to say intermediate spaces, are in Harmony when they have the same measure.

Fig. 13

In this case we have, not only a Harmony of Direction, as inFig. 7, but also a Harmony of Intervals.

Fig. 14

In this case the points are in a group and we have, as inFig. 11, a Harmony of Distances from the premise-point “A.” We have also a Harmony of Intervals, the distances between adjacent points being equal. We have a Harmony of Intervals, not only when the intervals are equal, but when a certain relation of intervals is repeated.

Fig. 15

The repetition of the ratio one to three in these intervals is distinctly appreciable. In the repetition we have Harmony, though we have no Harmony in the terms of the ratio itself, that is to say, no Harmony that is appreciable in the sense of vision. The fact that one and three are both multiples of one means that one and three have something in common, but inasmuch as the common divisor, one, cannot be visually appreciated, as such (I feel sure that it cannot), it has no interest or value in Pure Design.

Fig. 16

The relation of intervals is, in this case, the relation of three-one-five. We have Harmony in the repetition of this relation of intervals though there is no Harmony in the relation itself, which is repeated.

Fig. 17

In this case, also, we have Interval-Harmony, but as the intervals in the vertical and horizontal directions are shorter than the intervals in the diagonal directions, the Harmony is that of a relation of intervals repeated.

25. In moving from point to point in any series of points, it will be found easier to follow the series when the intervals are short than when they are long. InFig. 17it is easier to follow the vertical or horizontal series than it is to follow a diagonal series, because in the vertical and horizontal directions the intervals are shorter.

Fig. 18

In this case it is easier to move up or down on the vertical than in any other directions, because the short intervals lie on the vertical. The horizontal intervals are longer, the diagonal intervals longer still.

Fig. 19

In this case the series which lies on the diagonal up-left-down-right is the more easily followed. It is possible in this way, by means of shorter intervals, to keep the eye on certain lines. The applications of this principle are very interesting.

26. In each position, as indicated by a point in these arrangements, may be placed a composition of dots, lines, outlines, or areas. The dots indicate positions in which any of the possibilities of design may be developed. They are points from which all things may emerge and become visible.

IN POSITIONS: DIRECTIONS, DISTANCES, AND INTERVALS

27. Directions balance when they are opposite.

Fig. 20

The opposite directions, right and left, balance on the point from which they are taken.

28. Equal distances in opposite directions balance on the point from which the directions are taken.

Fig. 21

The equal distances AB and AC, taken in the directions AB and AC respectively, balance on the point “A” from which the directions are taken.

29. Two directions balance when, taken from any point, they diverge at equal angles from any axis, vertical, horizontal, or diagonal.

Fig. 22

The directions AB and AC balance on the vertical axis AD from which they diverge equally, that is to say, at equal angles.

30. Equal distances balance in directions which diverge equally from a given axis.

Fig. 23

The equal distances AB and AC balance in the directions AB and AC which diverge equally from the axis AD, making the equal angles CAD and DAB. Both directions and distances balance on the vertical axis AD.

31. The positions B and C inFig. 23, depending on balancing directions and distances, balance on the same axis. We should feel this balance of the positions A and B on the vertical axis even without any indication of the axis. We have so definite an image of the vertical axis that when it is not drawn we imagine it.

Fig. 24

In this case the two positions C and B cannot be said to balance, because there is no suggestion, no indication, and no visual image of any axis. It is only the vertical axis which will be imagined when not drawn.

32. Perfect verticality in relations of position suggests stability andbalance. The relation of positions C-B inFig. 24is one of instability.

Fig. 25

These two positions are felt to balance because they lie in a perfectly vertical relation, which is a relation of stability. Horizontality in relations, of position is also a relation of stability.See Fig. 28, p. 21.

33. All these considerations lead us to the definition of Symmetry. By Symmetry I mean opposite directions or inclinations, opposite and equal distances, opposite positions, and in those positions equal, corresponding, and opposed attractions on a vertical axis. Briefly, Symmetry is right and left balance on a vertical axis. This axis will be imagined when not drawn. In Symmetry we have a balance which is perfectly obvious and instinctively felt by everybody. All other forms of Balance are comparatively obscure. Some of them may be described as occult.

Fig. 26

In this case we have a symmetry of positions which means opposite directions, opposite and equal distances, and similar and opposite attractions in those positions. The attractions are black dots corresponding in tone, measure, and shape.

Fig. 27

In this case we have a balance of positions (directions and distances) and attractions in those positions, not only on the vertical axis but on a center. That means Symmetry regarding the vertical axis, Balance regarding the center. If we turn the figure, slightly, from the vertical axis, we shall still have Balance upon a center and axial Balance; but Symmetry, which depends upon the vertical axis, will be lost.

34. The central vertical axis of the whole composition should predominate in symmetrical balances.

Fig. 28

In this case we do not feel the balance of attractions clearly or satisfactorily, because the vertical axis of the whole arrangement does not predominate sufficiently over the six axes of adjacent attractions. It is necessary, in order that symmetrical balance shall be instinctively felt, that the central vertical axis predominate.

Fig. 29

The central vertical axis is clearly indicated in this case.

Fig. 30

Here, also, the central vertical axis is clearly indicated.

35. All relations of position (directions, distances, intervals), as indicated by dots or points, whether orderly or not, being inverted on the vertical axis, give us an obvious symmetrical balance.

Fig. 31

This is a relation of positions to be inverted.

Fig. 32

Here the same relation is repeated, with its inversion to the right on a vertical axis. The result is an obvious symmetrical balance. If this inversion were made on any other than the vertical axis, the result would be Balance but not Symmetry. The balance would still be axial, but the axis, not being vertical, the balance would not be symmetrical.

36. In the case of any unsymmetrical arrangement of dots, the dots become equal attractions in the field of vision, provided they are near enough together to be seen together. To be satisfactorily seen as a single composition or group they ought to lie, all of them, within a visual angle of thirty degrees. We may, within these limits, disregardthe fact that visual attractions lose their force as they are removed from the center of the field of vision. As equal attractions in the field of vision, the dots in any unsymmetrical arrangement may be brought into a balance by weighing the several attractions and indicating what I might call the center of equilibrium. This is best done by means of a symmetrical inclosure or frame. In ascertaining just where the center is, in any case, we depend upon visual sensitiveness or visual feeling, guided by an understanding of the principle of balance: that equal attractions, tensions or pulls, balance at equal distances from a given center, that unequal attractions balance at distances inversely proportional to them. Given certain attractions, to find the center, we weigh the attractions together in the field of vision and observe the position of the center. In simple cases we may be able to prove or disprove our visual feeling by calculations and reasoning. In cases, however, where the attractions vary in their tones, measures, and shapes, and where there are qualities as well as quantities to be considered, calculations and reasoning become difficult if not impossible, and we have to depend upon visual sensitiveness. All balances of positions, as indicated by dots corresponding in tone, measure, and shape, are balances of equal attractions, and the calculation to find the center is a very simple one.

Fig. 33

Here, for example, the several attractions, corresponding and equal, lie well within the field of vision. The method followed to balance them is that which I have just described. The center of equilibrium was found and then indicated by a symmetrical framing. Move the frame up or down, right or left, and the center of the frame and the center of the attractions within it will no longer coincide, and the balance will be lost. We might say of this arrangement that it is a Harmony of Positions due to the coincidence of two centers, the center of the attractions and the center of the framing.

37. It will be observed that the force of the symmetrical inclosure should be sufficient to overpower any suggestion of movement which may lie in the attractions inclosed by it.

Fig. 34

In this case the dots and the inclosure are about equally attractive.

Fig. 35

In this case the force of attractions in the symmetrical outline is sufficient to overpower any suggestion of instability and movement which may lie in the attractions inclosed by it.

There is another form of Balance, the Balance of Inclinations, but I will defer its consideration until I can illustrate the idea by lines.

IN POSITIONS: DIRECTIONS, DISTANCES, INTERVALS

38. In any unsymmetrical relation of positions (directions, distances, intervals), in which the balance-center is not clearly and sufficiently indicated, there is a suggestion of movement. The eye, not being held by any balance, readily follows this suggestion.

Fig. 36

In this case we feel that the group of dots is unbalanced in character and unstable in its position or attitude. It is easy, inevitable indeed, to imagine the group falling away to the right. This is due, no doubt, to the visual habit of imagining a base-line when it is not drawn. Our judgments are constantly made with reference to the imagined standards of verticality and horizontality. We seem to be provided with a plumb-line and a level without being conscious of the fact.

Fig. 37

In this case there is a suggestion of falling down to the left due to the feeling of instability. A symmetrical framing holding the eye at the center of equilibrium would prevent the feeling of movement, provided the framing were sufficiently strong in its attractions. In the examples I have given (Fig. 36andFig. 37) we have movement, but no Rhythm.

39. There is another type of movement which we must consider,—the type of movement which is caused by a gradual crowding together of attractions.

Fig. 38

There is nothing in this series of dots but the harmony of corresponding attractions and intervals repeated in a harmony of direction. If, instead of the repetition of equal intervals, we had a regular progression of intervals, either arithmetical or geometrical, we should feel a movement in the direction of diminishing intervals.

Fig. 39

In the above example the changes of interval are those of an arithmetical progression.

Fig. 40

InFig. 40the changes of interval are those of a geometrical progression. The movement to the left through these sequences is, no doubt, somewhat checked or prevented by the habit of reading to the right.

Fig. 41

The angle FAB is the angle of vision within which the sequence is observed. At the end F of the sequence there is a greater number of attractions in a given angle of vision than at the end B, so the eye is drawn towards the left. The pull on the eye is greater at the end F because of the greater number and the crowding together of attractions. In the examples just given (Figs. 39,40), we have not only movements in certain directions, but movements in regular and marked measures. The movements are, therefore, rhythmical, according to the definition I have given of Rhythm.

40. It is evident that any relation of positions, balanced or unbalanced, may be substituted for the single dots or points in the figures just given. Such substitutions have the following possibilities.

41. First. When the points lie in a series, at equal intervals, the substitution of a symmetrical group of positions at each point gives no Rhythm, only Harmony.

Fig. 42

There is no movement in this series of repetitions. There is consequently no Rhythm. Disregarding the habit of reading to the right, which induces the eye to move in that direction, it is as easy to move toward the left as toward the right. It requires more than repetitions at equal intervals to produce the feeling of Rhythm. There must be movement, and the movement must have a definite direction.

42. Second. The substitution at each point of a symmetrical group at equal intervals, as before, but with a progressive change of scale, will give us Rhythm. The movement will be due to the gradual crowding together of attractions at one end of the series.

Fig. 43

In this case we have the repetition of a symmetrical relation of positions at equal intervals with a gradation of scale in the repetitions. The result is a Rhythm, in which the movement is from left to right, owing to the greater crowding together of attractions at the right end of the series. The feeling of Rhythm is no doubt somewhat enhanced by our habit of reading to the right, which facilitates the movement of the eye in that direction.

43. Third. The substitution of an unstable group at each point of thesequence, the repetitions being at equal intervals, gives us a Rhythm, due simply to the movement of the group itself, which is unstable.

Fig. 44

Taking the relation of positions given inFig. 36and repeating it at equal intervals, it will be observed that the falling-to-the-right movement, which is the result of instability, is conveyed to the whole series of repetitions. To make it perfectly clear that the movement of this Rhythm is due to the suggestion of movement in the relation of positions which is repeated, I will ask the reader to compare it with the repetition of a symmetrical group inFig. 42. There is no movement in that case, therefore no Rhythm.

44. Fourth. The movement inFig. 44may be increased by a diminution of scale and consequent crowding together of the dots, provided the movement of the groups and the crowding together have the same direction.

Fig. 45

In this case, as I have said, the movement ofFig. 44is enforced by the presence of another element of movement, that of a gradation of scale and consequent crowding together in the groups. The two movements have the same direction. The movement of the crowding is not so strong as that which is caused by the instability of the group itself.

45. Fifth. A symmetrical relation of positions, being repeated in a series with gradually diminishing intervals between the repeats, will give us a feeling of rhythmic movement. It will be due to a gradual increase in the number of attractions as the eye passes from one angle of vision to another.See Fig. 41. The Rhythm will, no doubt, be somewhat retarded by the sense of successive axes of symmetry.

Fig. 46

In this case a symmetrical group is repeated in a progression of measures. The movement is toward the greater number of attractions at the right end of the series. This increase in the number of attractions is due simply to diminishing intervals in that direction. The eye moves through a series of angles toward the angle which contains the greatest number of attractions. The reader can hardly fail to feel the successive axes of symmetry as a retarding element in this Rhythm.

46. Sixth. Symmetrical relations of position may be repeated in progressions of scale and of intervals. In that case we get two movements, one caused by a gradual increase in the number of attractions in successive angles of vision, the other being due to a gradual crowding together and convergence of attractions in the same series of angles.

Fig. 47

Comparing this Rhythm with the Rhythm ofFig. 43, the reader will appreciate the force of a diminution of scale in connection with a diminution of intervals.

47. Seventh. Unstable groups may be repeated in progressions of intervals, in which case the movement in the group is conveyed to the whole series, in which there will be, also, the movement of a gradual increase of attractions from one angle of vision to another. In all such cases contrary motion should be avoided if the object is Rhythm. The several movements should have a harmony of direction.

Fig. 48

In this case the movement in the group is felt throughout the series, and the force of the movement is enhanced by the force of a gradual increase of attractions from one visual angle to another, in the same direction, to the right. By reversing the direction of increasing attractions and so getting the two movements into contrary motion, the feeling of rhythm would be much diminished. Such contrary motions are unsatisfactory unless Balance can be achieved. In that case all sense of movement and of rhythm disappears.

48. Eighth. Unstable groups may be repeated, not only in a gradation of intervals, but in a gradation of scale, in which case we have a combination of three causes of movement: lack of stability in the group repeated, a gradual increase in the number of attractions in the sequence of visual angles, and a crowding or convergence of the attractions. Rhythms of this type will not be satisfactory unless the three movements have the same direction.

Fig. 49

Here we have the repetition of an unstable group of attractions in a progression of scale and also of intervals. The arrangement gives us three elements of movement, all in the same direction.

49. Two or even more of such rhythms as I have described may be combined in one compound rhythm, in which the eye will follow two or more distinct movements at the same time. It is important in all compound rhythms that there should be no opposition or conflict of movements, unless of course the object is to achieve a balance of contrary movements. Corresponding rhythms in contrary motion balance one another. If one of the movements is to the right, the other to the left, the balance will be symmetrical.

RELATIONS OF POSITION IN DIFFERENT ATTITUDES

50. Given any relation of positions (directions, distances, intervals), it may be turned upon a center and so made to take an indefinite number and variety of attitudes. It may be inverted and the inversion may be turned upon a center, producing another series of attitudes. Except in cases of axial balance, the attitudes of the second series will be different from those of the first.

Fig. 50

In this case the relation of positions being turned upon a center changes its attitude, while the positions within the group remain relatively unchanged. There is no change of shape.

Fig. 51

In this case the same group has been inverted, and a second series of attitudes is shown, differing from the first series.

Fig. 52

In this case, however, which is a case of axial balance, the inversion of the group and the turning of the inversion on a center gives no additional attitudes.

51. Among all possible attitudes there are four which are principal or fundamental, which we may distinguish as follows:—

Fig. 53

These principal attitudes are: First, I, the original attitude, whatever it is; second, II, the single inversion of that attitude, to the right on a vertical axis; third, III, the double inversion of the original attitude, first to the right then down; and, fourth, IV, the single inversion of the original position, down across the horizontal axis.

52. The repetition of any relation of positions without change of attitude gives us Harmony of Attitudes.

Fig. 54

In this case we have not only a Harmony in the repetition of a certain relation of positions and of intervals, but a Harmony of Attitudes. We have, in the relation of positions repeated, a certain shape. In the repetition of the shape we have Shape-Harmony. In the repetition of the shape in a certain attitude we have a Harmony of Attitudes.

Fig. 55

In this case we have lost the Harmony of Attitudes which we had inFig. 54, but not the Harmony of a certain shape repeated.

53. The possibilities of Harmony in the repetition of any relation of positions in the same attitude has been discussed. A Harmony of Attitudes will occur, also, in the repetition of any relation of attitudes.

Fig. 56

Here we have Harmony in the repetition of a relation of two attitudes of a certain group of positions. The combination of the two attitudes gives us another group of positions and the Harmony lies in the repetition of this group.

54. It is to be observed that single inversions in any direction, for example the relation of attitudes I and II, II and III, III and IV, IV and I, inFig. 53, shows an opposition and Balance of Attitudes upon the axis of inversion. The relation of positions I and II and III and IV, the relation of the two groups on the left to the two groups on the right, illustrates the idea of Symmetry of Attitudes, the axis of balance being vertical. By Symmetry I mean, in all cases, right and leftbalance on a vertical axis. All double inversions, the relation of positions I and III, and II and IV, inFig. 53, are Attitude-Balances, not on axes, but on centers. The balance of these double inversions is not symmetrical in the sense in which I use the word symmetry, nor is it axial. It is central.

55. When movement is suggested by any series of attitudes and the movement is regulated by equal or regularly progressive intervals, we have a Rhythm of Attitudes.

Fig. 57

In this case the changes of attitude suggest a falling movement to the right and down. In the regular progression of this movement through marked intervals we have the effect of Rhythm, in spite of the fact that the relation of positions repeated has axial balance. The intervals in this case correspond, producing Interval-Harmony. The force of this Rhythm might be increased if the relation of positions repeated suggested a movement in the same direction. We should have Rhythm, of course, in the repetition of any such unstable attitude-rhythms at equal or lawfully varying intervals.

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