A theory of pure design

by Denman Waldo Ross

THE ORDER OF HARMONY

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. 9] and [Fig. 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 in [Fig. 7], but also a Harmony of Intervals.

Fig. 14

In this case the points are in a group and we have, as in [Fig. 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. In [Fig. 17] it 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.