Part 4

In this case, by omitting the long vertical line I have diminished the amount of convergence downward. In that way I have given predominance to the upward movement. Instead of altogether omitting the long vertical line, I might have changed its tone from black to gray. That would cause an approximate instead of complete disappearance. It should be remembered that in all these cases the habit of reading comes in to facilitate the movements to the right. It is easier for the eye to move to the right than in any other direction, other things being equal. The movement back to the beginning of another line, which is of course inevitable in reading, produces comparatively little impression upon us, no more than the turning of the page. The habit of reading to the right happens to be our habit. The habit is not universal.

80. Reading repetitions and alternations to the right, always, I, for a long time, regarded such repetitions and alternations as rhythmical, until Professor Mowll raised the question whether it is necessary to read all alternations to the right when there is nothing in the alternations themselves to suggest a movement in one direction rather than another. Why not read them to the left as well as to the right? We at once decided that the movement in a Rhythm must be determined by the character of the Rhythm itself, not by any habit of reading, or any other habit, on our part. It was in that way that we came to regard repetitions and alternations as illustrations of Harmony rather than of Rhythm. Rhythm comes into the Harmony of a Repeated Relation when the relation is one which causes the eye to move in one direction rather than another, and when the movement is carried on from repetition to repetition, from measure to measure.

81. The repetition of a motive at equal intervals, when there is no movement in the motive, gives us no feeling of Rhythm.

[Illustration: Fig. 102]

In this case, for example, we have a repetition in the line of a certain symmetrical shape. As there is no movement in the shape repeated, there is no Rhythm in the repetition. There is nothing to draw the eye in one direction rather than another. The attractions at one end of the line correspond with the attractions at the other.

82. The feeling of Rhythm may be induced by a regular diminution of measure or scale in the repetitions of the motive and in the intervals in which the repetitions take place.

[Illustration: Fig. 103]

In this case the shape repeated is still symmetrical, but it is repeated with a gradual diminution of scale and of intervals, by which we are given a feeling of rhythmic movement. The change of scale and of intervals, to induce a sense of rhythmic motion, must be regular. To be regular the change must be in the terms of one or the other of the regular progressions; the arithmetical progression, which proceeds by a certain addition, or the geometrical, which proceeds by a certain multiplication. The question may arise in this case (Fig. 103) whether the movement of the Rhythm is to the right or to the left. I feel, myself, that the movement is to the right. In diminishing the scale of the motive and of the intervals we have, hardly at all, diminished the extent of the tone-contrast in a given angle of vision. See Fig. 41, p. 27, showing the increase of attractions from one visual angle to another. At the same time we come at the right end of the progression to two or more repetitions in the space of one. We have, therefore, established the attraction of a crowding together at the right end of the series. See the passage (p. 43) on the attractiveness of a line. The force of the crowding together of attractions is, I feel, sufficient to cause a movement to the right. It must be remembered, however, that the greater facility of reading to the right is added here to the pull of a greater crowding together of attractions in the same direction, so the movement of the Rhythm in that direction may not be very strong after all. If the direction of any Rhythm is doubtful, the Rhythm itself is doubtful.

83. The feeling of Rhythm may be induced, as I have said, by a gradual increase of the number of attractions from measure to measure, an increase of the extent of tone-contrast.

[Illustration: Fig. 104]

Increasing the extent of tone-contrast and the number of attractions in the measures of the Rhythm in Fig. 103, we are able to force the eye to follow the series in the direction contrary to the habit of reading, that is to say from right to left.

A decrease in the forces of attraction in connection with a decrease of scale is familiar to us all in the phenomena of perspective. The gradual disappearance of objects in aerial perspective does away with the attraction of a greater crowding together of objects in the distance.

[Illustration: Fig. 105]

In this case the diminution of scale has been given up and there is no longer any crowding together. There is no chance of this rhythm being read from left to right except by an effort of the will. The increase of attractions toward the left is much more than sufficient to counteract the habit of reading.

84. The force of a gradual coming together of attractions, inducing movement in the direction of such coming together, is noticeable in spiral shapes.

[Illustration: Fig. 106]

In this case we have a series of straight lines with a constant and equal change of direction to the right, combined with a regular diminution of measures in the length of the lines, this in the terms of an arithmetical progression. The movement is in the direction of concentration and it is distinctly marked in its measures. The movement is therefore rhythmical.

[Illustration: Fig. 107]

In this case we have a series of straight lines with a constant change of direction to the right; but in this case the changes of measure in the lines are in the terms of a geometrical progression. The direction is the same, the pull of concentration perhaps stronger.

[Illustration: Fig. 108]

In this Rhythm there is an arithmetical gradation of measures in the changes of direction, both in the length of the legs and in the measure of the angles. The pull of concentration is, in this case, very much increased. It is evident that the legs may vary arithmetically and the angles geometrically; or the angles arithmetically and the legs geometrically.

85. If, in the place of the straight lines, which form the legs, in any of the examples given, are substituted lines which in themselves induce movement, the feeling of Rhythm may be still further increased, provided the directions of movement are consistent.

[Illustration: Fig. 109]

In this case the movement is in the direction of increasing concentration and in the direction of the convergences.

If the movement of the convergences be contrary to the movement of concentration, there will be in the figure a contrary motion which may diminish or even entirely prevent the feeling of Rhythm. If the movement in one direction or the other predominates, we may still get the feeling of Rhythm, in spite of the drawback of the other and contrary movement.

[Illustration: Fig. 110]

In this case the linear convergences substituted for the straight lines are contrary to the direction of increasing concentration. The movement is doubtful.

86. Corresponding rhythms, set in contrary motion, give us the feeling of Balance rather than of Rhythm. The balance in such cases is a balance of movements.

[Illustration: Fig. 111]

This is an example of corresponding and opposed rhythms producing the feeling, not of Rhythm, but of Balance.

ATTITUDES

LINES IN DIFFERENT ATTITUDES

87. Any line or linear progression may be turned upon a center, and so made to take an indefinite number and variety of attitudes. It may be inverted upon an axis, and the inversion may be turned upon a center producing another series of attitudes which, except in the case of axial symmetry in the line, will be different from those of the first series.

[Illustration: Fig. 112]

In this case the line changes its attitude.

[Illustration: Fig. 113]

In this case I have inverted the line, and turning the inversion upon a center I get a different set of attitudes.

[Illustration: Fig. 114]

In this case, which is a case of axial symmetry in the line, the inversion gives us no additional attitudes.

THE ORDER OF HARMONY IN THE ATTITUDES OF LINES

88. When any line or linear progression is repeated, without change of attitude, we have a Harmony of Attitudes.

[Illustration: Fig. 115]

This is an illustration of Harmony of Attitudes. It is also an illustration of Interval-Harmony.

89. We have a Harmony of Attitudes, also, in the repetition of any relation of two or more attitudes, the relation of attitudes being repeated without change of attitude.

[Illustration: Fig. 116]

We have here a Harmony of Attitudes due to the repetition of a certain relation of attitudes, without change of attitude.

THE ORDER OF BALANCE IN THE ATTITUDES OF LINES

90. When a line or linear progression is inverted upon any axis or center, and we see the original line and its inversion side by side, we have a Balance of Attitudes.

[Illustration: Fig. 117]

The relation of attitudes I, II, of III, IV, and of I, II, III, IV, is that of Symmetrical Balance on a vertical axis. The relation of attitudes I, IV, and of II, III, is a relation of Balance but not of Symmetrical Balance. This is true, also, of the relation of I, III and of II, IV. Double inversions are never symmetrical, but they are illustrations of Balance. The balance of double inversions is central, not axial. These statements are all repetitions of statements previously made about positions.

THE ORDER OF RHYTHM IN THE ATTITUDES OF LINES

91. It often happens that a line repeated in different attitudes gives us the sense of movement. It does this when the grouping of the repetitions suggests instability. The movement is rhythmical when it exhibits a regularity of changes in the attitudes and in the intervals of the changes.

[Illustration: Fig. 118]

In this case we have a movement to the right, but no Rhythm, the intervals being irregular.

[Illustration: Fig. 119]

In this case the changes of attitude and the intervals of the changes being regular, the movement becomes rhythmical. The direction of the rhythm is clearly down-to-the-right.

92. In the repetition of any line we have a Harmony, due to the repetition. If the line is repeated in the same attitude, we have a Harmony of Attitudes. If it is repeated in the same intervals, we have a Harmony of Intervals. We have Harmony, also, in the repetition of any relation of attitudes or of intervals.

We have not yet considered the arrangement or composition of two or more lines of different measures and of different shapes.

THE COMPOSITION OF LINES

93. By the Composition of Lines I mean putting two or more lines together, in juxtaposition, in contact or interlacing. Our object in the composition of lines, so far as Pure Design is concerned, is to achieve Order, if possible Beauty, in the several modes of Harmony, Balance, and Rhythm.

HARMONY IN THE COMPOSITION OF LINES

94. We have Harmony in line-compositions when the lines which are put together correspond in all respects or in some respects, when they correspond in attitudes, and when there is a correspondence of distances or intervals.

[Illustration: Fig. 120]

In this case the lines of the composition correspond in tone, measure, and shape, but not in attitude; and there is no correspondence in distances or intervals.

[Illustration: Fig. 121]

In this case the attitudes correspond, as they did not in Fig. 120. There is still no correspondence of intervals.

[Illustration: Fig. 122]

Here we have the correspondence of intervals which we did not have either in Fig. 120 or in Fig. 121. There is not only a Harmony of Attitudes and of Intervals, in this case, but the Harmony of a repetition in one direction, Direction-Harmony. In all these cases we have the repetition of a certain angle, a right angle, and of a certain measure-relation between the legs of the angle, giving Measure and Shape-Harmony.

95. The repetition in any composition of a certain relation of measures, or of a certain proportion of measures, gives Measure-Harmony to the composition. The repetition of the relation one to three in the legs of the angle, in the illustrations just given, gives to the compositions the Harmony of a Recurring Ratio. By a proportion I mean an equality between ratios, when they are numerically different. The relation of one to three is a ratio. The relation of one to three and three to nine is a proportion. We may have in any composition the Harmony of a Repeated Ratio, as in Figs. 120, 121, 122, or we may have a Harmony of Proportions, as in the composition which follows.

[Illustration: Fig. 123]

96. To be in Harmony lines are not necessarily similar in all respects. As I have just shown, lines may be in Shape-Harmony, without being in any Measure-Harmony. Lines are approximately in harmony when they correspond in certain particulars, though they differ in others. The more points of resemblance between them, the greater the harmony. When they correspond in all respects we have, of course, a perfect harmony.

[Illustration: Fig. 124]

This is a case of Shape-Harmony without Measure-Harmony and without Harmony of Attitudes.

[Illustration: Fig. 125]

In this case we have a Harmony of Shapes and of Attitudes, without Measure-Harmony or Harmony of Intervals. This is a good illustration of a Harmony of Proportions.

Straight lines are in Harmony of Straightness because they are all straight, however much they differ in tone or measure. They are in Harmony of Measure when they have the same measure of length. The measures of width, also, may agree or disagree. In every agreement we have Harmony.

Angular lines are in Harmony when they have one or more angles in common. The recurrence of a certain angle in different parts of a composition brings Harmony into the composition. Designers are very apt to use different angles when there is no good reason for doing so, when the repetition of one would be more orderly.

[Illustration: Fig. 126]

The four lines in this composition have right angles in common. To that extent the lines are in Harmony. There is also a Harmony in the correspondence of tones and of width-measures in the lines. Considerable Harmony of Attitudes occurs in the form of parallelisms.

[Illustration: Fig. 127]

These two lines have simply one angle in common, a right angle, and the angle has the same attitude in both cases. They differ in other respects.

[Illustration: Fig. 128]

In these three lines the only element making for Harmony, except the same tone and the same width, is found in the presence in each line of a certain small arc of a circle. Straightness occurs in two of the lines but not in the third. There is a Harmony, therefore, between two of the lines from which the third is excluded. There is, also, a Harmony of Attitude in these two lines, in certain parallelisms.

BALANCE IN THE COMPOSITION OF LINES

97. Lines balance when in opposite attitudes. We get Balance in all inversions, whether single or double.

[Illustration: Fig. 129]

Here similar lines are drawn in opposite attitudes and we get Measure and Shape-Balance. In the above case the axis of balance is vertical. The balance is, therefore, symmetrical. Symmetrical Balance is obtained by the single inversion of any line or lines on a vertical axis. Double inversion gives a Balance of Measures and Shapes on a center. We have no Symmetry in double inversions. All this has been explained.

[Illustration: Fig. 130]

We have Measure and Shape-Balance on a center in this case. It is a case of double inversion. It is interesting to turn these double inversions on their centers, and to observe the very different effects they produce in different attitudes.

98. Shapes in order to balance satisfactorily must be drawn in the same measure, as in Fig. 131 which follows.

[Illustration: Fig. 131]

[Illustration: Fig. 132]

Here, in Fig. 132, we have Shape-Harmony without Measure-Harmony. It might be argued that we have in this case an illustration of Shape-Balance without Measure-Balance. Theoretically that is so, but Shape-Balance without Measure-Balance is never satisfactory. If we want the lines in Fig. 132 to balance we must find the balance-center between them, and then indicate that center by a symmetrical inclosure. We shall then have a Measure-Balance (occult) without Shape-Balance.

99. When measures correspond but shapes differ the balance-center may be suggested by a symmetrical inclosure or framing. When that is done the measures become balanced.

[Illustration: Fig. 133]

Here we have Measure-Harmony and a Measure-Balance without Shape-Harmony or Shape-Balance. The two lines have different shapes but the same measures, lengths and widths corresponding. The balance-center is found for each line. See pp. 54, 55. Between the two centers is found the center, upon which the two lines will balance. This center is then suggested by a symmetrical inclosure. The balancing measures in such cases may, of course, be turned upon their centers, and the axis connecting their centers may be turned in any direction or attitude, with no loss of equilibrium, so far as the measures are concerned.

[Illustration: Fig. 134]

The Balance of Measures here is just as good as it is in Fig. 133. The attitudes are changed but not the relation of the three balance-centers. The change of shape in the inclosure makes no difference.

100. Measure-Balance without Shape-Harmony or Shape-Balance is satisfactory only when the balance-center is unmistakably indicated or suggested, as in the examples which I have given.

101. There is another form of Balance which is to be inferred from what I have said, on page 18, of the Balance of Directions, but it needs to be particularly considered and more fully illustrated. I mean a Balance in which directions or inclinations to the right are counteracted by corresponding or equivalent directions or inclinations to the left. The idea in its simplest and most obvious form is illustrated in Fig. 22, on page 18. In that case the lines of inclination correspond. They do not necessarily correspond except in the extent of contrast, which may be distributed in various ways.

[Illustration: Fig. 135]

The balance of inclinations in this case is just as good as the balance in Fig. 22. There is no symmetry as in Fig. 22. Three lines balance against one. The three lines, however, show the same extent of contrast as the one. So far as the inclinations are concerned they will balance in any arrangement which lies well within the field of vision. The eye must be able to appreciate the fact that a disposition to fall to the right is counteracted by a corresponding or equivalent disposition to fall to the left.

[Illustration: Fig. 136]

This arrangement of the inclining lines is just as good as the arrangement in Fig. 135. The inclinations may be distributed in any way, provided they counteract one another properly.

[Illustration: Fig. 137]

In this case I have again changed the composition, and having suggested the balance-center of the lines, as attractions, by a symmetrical inclosure, I have added Measure-Balance (occult) to Inclination-Balance. The Order in Fig. 137 is greater than the Order in Figs. 135 and 136. In Fig. 137 two forms of Balance are illustrated, in the other cases only one. The value of any composition lies in the number of orderly connections which it shows.

[Illustration: Fig. 138]

In this case I have taken a long angular line and added a sufficient number and extent of opposite inclinations to make a balance of inclinations. The horizontal part of the long line is stable, so it needs no counteraction, but the other parts incline in various degrees, to the left or to the right. Each inclining part requires, therefore, either a corresponding line in a balancing direction, or two or more lines of equivalent extension in that direction. In one case I have set three lines to balance one, but they equal the one in length, that is to say, in the extent of contrast. We have in Fig. 138 an illustration of occult Measure-Balance and the Balance of Inclinations. I have illustrated the idea of Inclination-Balance by very simple examples. I have not considered the inclinations of curves, nor have I gone, at all, into the more difficult problem of balancing averages of inclination, when the average of two or more different inclinations of different extents of contrast has to be counteracted. In Tone-Relations the inclinations are of tone-contrasts, and a short inclination with a strong contrast may balance a long inclination with a slight one, or several inclinations of slight contrasts may serve to balance one of a strong contrast. The force of any inclining line may be increased by increasing the tone-contrast with the ground-tone. In tone-relations the problem becomes complicated and difficult. The whole subject of Inclination-Balance is one of great interest and worthy of a separate treatise.

RHYTHM IN THE COMPOSITION OF LINES

102. We will first consider the Measure-Rhythms which result from a gradual increase of scale, an increase in the extent of the contrasts. The intervals must, in such Rhythms, be regular and marked. They may be equal; they may alternate, or they may be regularly progressive.

[Illustration: Fig. 139]

In this case I feel that the direction of the Rhythm is up-to-the-right owing to the gradual increase of length and consequently of the extent of contrast in the lines, in that direction.

[Illustration: Fig. 140]

In this case I have, by means of regularly diminishing intervals, added the force of a crowding together of contrasting edges to the force of a gradual extension of them. The movement is still more strongly up-to-the-right.

[Illustration: Fig. 141]

In this case a greater extension of contrasts pulls one way and a greater crowding of contrasts the other. I think that crowding has the best of it. The movement, though much retarded, is, I feel, down-to-the-left rather than up-to-the-right, in spite of the fact that the greater facility of reading to the right is added to the force of extended contrasts.

103. Substituting unstable for stable attitudes in the examples just given, we are able to add the movement suggested by instability of attitude to the movement caused by a gradual extension of contrasts.

[Illustration: Fig. 142]

The movement up-to-the-right in Fig. 139 is here connected with an inclination of all the lines down-to-the-right.

[Illustration: Fig. 143]

Here the falling of the lines down-to-the-left counteracts the movement in the opposite direction which is caused by the extension of contrasting edges in that direction. A crowding together of the lines, due to the diminution of intervals toward the left, adds force to the movement in that direction.

[Illustration: Fig. 144]

In this case a movement up is caused by convergences, a movement down by crowding. The convergences are all up, the crowding down. I think that the convergences have it. I think the movement is, on the whole, up. The intervals of the crowding down diminish arithmetically.

[Illustration: Fig. 145]

The convergences and the crowding of attractions are, here, both up-to-the-right. The Rhythm is much stronger than it was in Fig. 144. The intervals are those of an arithmetical progression.

[Illustration: Fig. 146]

The movement here is up-to-the-right, because of convergences in that direction and an extension of contrasts in that direction.

[Illustration: Fig. 147]