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.
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.
In this case the attitudes correspond, as they did not in Fig. 120. There is still no correspondence of intervals.
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.
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.
This is a case of Shape-Harmony without Measure-Harmony and without Harmony of Attitudes.
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.
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.
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.
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.