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.