Figures are enlargeable.
Enlarge finished armatures to see them over the paintings.
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A composition is an arrangement of shapes, lines, colors and textures on a picture plane.
An armature is like the composition's underlying framework — the elements of the design are organized within its structure.
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Many armatures are essentially grids.
Grids are useful for transferring a design to a canvas or panel.
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Two scalable rectangular grids.
The one on the left is quadrisected.
The one on the right is divided into thirds.
In both cases the first step is to bisect the rectangle, then the diagonals are drawn to locate the vertices of the rectangles that comprise the grid.
To create a grid comprised of squares, it is necessary to begin with a square.
This is undoubtedly one of the reasons that the Renaissance armatures that are based on grids (mainly the Italian and Spanish armatures) utilize squares.
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Many armatures dictate the dimensions of the picture plane.
I have called these "format armatures".
The term "format" refers to the shape or proportions of the picture plane.
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Mrs. Frank Millet by John Singer Sargent (oil on canvas, 34 x 27), 1885-86.
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Armatures can be formal, like the ones presented in this paper, or informal.
It is highly unlikely that John Singer Sargent went to the trouble of drawing a triangle and an arc before he started painting Mrs. Millet's portrait, above.
Most portraits that include only the head and shoulders or torso are naturally triangular — a fact that portraitists understand implicitly.
Sargent was certainly aware of the arc suggested by Mrs. Millet's posture because it adds movement to the composition by creating an eye path for the viewer to follow.
The arc could well be the reason he posed her like this.
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Armatures can supply information about artistic styles and influences.
They can also help to identify and reconstruct damaged artworks.
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1.
Styles
- Armatures can help attribute works, or parts of works, to particular artists.
Example: In The adoration of the Lamb, Jan van Eyck appears to have altered his brother Hubert's design in order to impose a format armature on the painting.
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Armatures can help confirm that an artist was associated with a workshop.
Example: Petrus Cristus, who is thought to have been Jan van Eyck's apprentice, had an armature style similar to van Eyck's.
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Armatures can shed light on the stylistic development of an artist.
Example: Rogier van der Weyden appears to have learned simple, circle-based armatures from Robert Campin, for whom he worked.
Shortly after painting The descent from the cross, he began designing armatures based on golden rectangles.
(Did he have contact with van Eyck?)
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2.
Influences
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Armatures can help confirm that an artist was influenced by the artwork of another region.
Example: Jan van Eyck appears to have discovered overlapping squares in Portugal or Spain.
(Overlapping squares were used to create a center column with a different width than the side partitions.)
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The Reformation may have removed armatures from the iconography of religious paintings.
Example: Neither Bosch nor Bruegel appears to have used formal armatures.
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3.
Altered works
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A painting with an obvious format that extends past its edges may have been cut down.
Example: Piera della Francesca's Brera Madonna altarpiece.
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Art historians are attempting to reconstruct altarpieces have been dismembered and the pieces dispersed and lost.
Example: Duccio's Maestà.
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In creating the armatures presented in this paper I have tried to
- adhere to a painting's design;
- use shapes that can be drawn easily with a straightedge and compass;
- not read complex geometric figures (pentagrams, platonic solids, etc.) into simple symmetrical shapes (circles and squares).
In the two examples I discuss below, the armatures on the left are mine.
The armatures on the right are from The Painter's Secret Geometry: A Study of Composition in Art by Charles Bouleau, first published in English in 1963 by Harcourt Brace and World, Inc.
It is the seminal work on armatures in painting.
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Example 1.
The descent from the cross by Rogier van der Weyden (oil on panel, 220 x 262 cm), c. 1435, Prado.
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1a.
My armature:
The arcs in this design are apparent from the arrangement and attitudes of the figures.
What I could not understand was how van der Weyden arrived at the oddly proportioned rectangles that comprise the format.
After a lot of trial and error, I hit on the only construction that works for the main rectangle: a vesica inscribed in a rectangle.
The small rectangle at the top is not producible by overlapping squares, but a pair of arcs with center points on the vesica can establish both its height and width.
This is an elegant armature worthy of genius.
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1b.
Bouleau's armature:
After much painstaking analysis, Bouleau concluded that van der Weyden based the altarpiece's design on pentagons and the golden mean. (pp. 67-68)
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Example 2.
The Brera Madonna altarpiece by Piero della Francesca (tempera on panel, 98 x 59), 1472-74, Pinacoteca di Brera, Milan, Italy.
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2a.
My armature:
The central portion of the painting is either a 3:2 rectangle with a half-circle above it or two squares, at least one of which is inscribed with a circle.
The smaller circle makes the latter option the better choice — as the arcs reveal, its height, and consequently its circumference, are based on the quadrisection of the square.
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2b.
Bouleau's armature:
Instead of starting with the shape of the domed apse, Bouleau has based his armature on the format's 3:2 height-to-width ratio.
(Actually, it's 2.9:2.)
In pursuing these proportions he has found a circle inscribed with a hexagon and an equilateral triangle that determines the height of the dome.
"And so, in spite of an apparent recession in space, the composition is as symbolic as a Pythagorean solid." (p. 95)
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Symphonic composition (sometimes called "dynamic symmetry") is a system for organizing a design into spatial divisions based on the golden ratio (1:φ, or approximately 1.618.)
The system is thought to have originated in the ancient world; in Greece it was used in the design of both art and architecture.
A compass (which can be as simple as a human being with a string) is used to create rectangles derived from the root of a square (the golden rectangle is one such rectangle).
Lines drawn through the rectangles' vertices reveal the presumably harmonious spatial relationships that the elements of a composition might be organized upon.
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A composition based on a root-5 rectangle from The Geometry of Art and Life by Matila Ghyka, originally published by Sheed and Ward, New York in 1946.
The book builds on the work of Jay Hambridge, who wrote The Elements of of Dynamic Symmetry.
His book was originally published in 1926 by Brentano's, Inc.
Both books have been reprinted by Dover Publications, Inc.
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Charles Bouleau's armatures, above, are examples of symphonic composition.
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