[Illustration: Fig. 67]
In this case we have a Harmony of Direction in the line, because it
does not change its direction.
63. Harmony of Angles. We may have Harmony in the repetition of a
certain relation of directions, as in an angle.
[Illustration: Fig. 68]
The angle up 45° and down 45° is here repeated seven times.
[Illustration: Fig. 69]
In this case we have a great many angles in the line, but they are all
right angles, so we have a Harmony of Angles.
[Illustration: Fig. 70]
In this case we have Harmony in the repetition of a certain relation
of angles, that is to say, in the repetition of a certain form of
angularity.
64. Equality of lengths or measures between the angles of a line means
a Harmony of Measures.
[Illustration: Fig. 71]
In this case, for example, we have no Harmony of Angles, but a Harmony
of Measures in the legs of the angles, as they are called.
65. We have a Harmony of Curvature in a line when it is composed wholly
of arcs of the same radius and the same angle.
[Illustration: Fig. 72]
This is a case of Harmony of Curvature. There is no change of direction
here, in the sequence of corresponding arcs.
[Illustration: Fig. 73]
Here, again, we have a Harmony of Curvature. In this case, however,
there is a regular alternation of directions in the sequence of
corresponding arcs. In this regular alternation, which is the
repetition of a certain relation of directions, there is a Harmony of
Directions.
[Illustration: Fig. 74]
In this case the changes of direction are abrupt (angular) as well
as gradual. There is no regular alternation, but the harmony of
corresponding arcs repeated will be appreciated, nevertheless.
66. Arcs produced by the same radius are in harmony to that extent,
having the radius in common.
[Illustration: Fig. 75]
This is an example of a harmony of arcs produced by radii of the same
length. The arcs vary in length.
67. Arcs of the same angle-measure produced by different radii are in
Harmony to the extent that they have an angle-measure in common.
[Illustration: Fig. 76]
This is an example.
Arcs having the same length but varying in both radius and angle may be
felt to be in Measure-Harmony. It is doubtful, however, whether lines
of the same length but of very different curvatures will be felt to
correspond. If the correspondence of lengths is not felt, visually, it
has no interest or value from the point of view of Pure Design.
68. Any line may be continued in a repetition or repetitions of
its shape, whatever the shape is, producing what I call a Linear
Progression. In the repetitions we have Shape-Harmony.
[Illustration: Fig. 77]
This is an example of Linear Progression. The character of the
progression is determined by the shape-motive which is repeated in it.
69. The repetition of a certain shape-motive in a line is not,
necessarily, a repetition in the same measure or scale. A repetition of
the same shape in the same measure means Measure and Shape-Harmony in
the progression. A repetition of the same shape in different measures
means Shape-Harmony without Measure-Harmony.
[Illustration: Fig. 78]
Here we have the repetition of a certain shape in a line, in a
progression of measures. That gives us Shape-Harmony and a Harmony of
Proportions, without Measure-Harmony.
70. In the repetition of a certain shape-motive in the line, the
line may change its direction abruptly or gradually, continuously or
alternately, producing a Linear Progression with changes of direction.
[Illustration: Fig. 79]
In Fig. 79 there is a certain change of direction as we pass from
one repetition to the next. In the repetition of the same change
of direction, of the same angle of divergence, we have Harmony. If
the angles of divergence varied we should have no such Harmony,
though we might have Harmony in the repetition of a certain relation
of divergences. Any repetition of a certain change or changes of
direction in a linear progression gives a Harmony of Directions in the
progression.
[Illustration: Fig. 80]
In this case there is a regular alternation of directions in the
repeats. The repeats are drawn first to the right, then up, and the
relation of these two directions is then repeated.
71. By inverting the motive of any progression, in single or in double
inversion, and repeating the motive together with its inversion, we are
able to vary the character of the progression indefinitely.
[Illustration: Fig. 81]
In this case we have a single inversion of the motive and a repetition
of the motive with its inversion. Compare this progression with the one
in Fig. 77, where the same motive is repeated without inversion.
[Illustration: Fig. 82]
Here we have the same motive with a double inversion, the motive
with its double inversion being repeated. The inversion gives us
Shape-Harmony without Harmony of Attitudes. We have Harmony, however,
in a repetition of the relation of two attitudes. These double
inversions are more interesting from the point of view of Balance than
of Harmony.