Research – Golden Section and Rule of Thirds

The Golden Mean (aka Golden Ratio or Golden Section) is a mathematical formula equivalent to 1.618.  Without going into too much mathematical detail, what this means in art is using a rectangle where (in landscape format) the horizontal line is 1.618 times larger than the vertical (a golden rectangle).  By drawing a vertical line at the point on the horizontal equivalent to the length of the short edge, the “golden rectangle” is sub-divided into a square and a rectangle (the resulting rectangle) also being of golden proportions.  This rectangle can subsequently be sub-divided in the same way as the original ad infinitum.  By drawing a curved line round the rectangles (the line clipping the edge of the rectangle at the right angles where the dividing lines meet) a spiral is formed.  See this diagram for all that information in visual form!

As with the “rule of thirds” (dividing the picture plain into three equal sections horizontally and vertically and placing areas of interest on these lines or intersections), the principle behind using the Golden Mean is that many compositions work better with a degree of asymmetry (i.e. not placing your focal point in the centre of the canvas) as this has the effect of leading the eye through a painting.

The rule of thirds is a simplified, rough and ready guide to composition which can be applied quickly and easily at any time, whether in a studio or painting en plein air.  Most cameras and cropping tools on imaging software even have a overlaid grid so you can easily divide an image up in this way.  The Golden Mean is a more complex compositional tool which requires a little pre-planning on the maths front but can be used in a number of ways (whether using the straight division lines as a guide or the curling spiral).  Areas of a painting can also be sub-section and divided according to either of these compositional devices for more detailed subjects.

Rule of thirds:

Bathers at Asniere – Georges Seurat. 

As well as strong diagonals and compositional consonance (repetition of the C curve on the backs of five of the figures), Seurat has used the third lines to place his figures.  The top third horizontal exactly meets the bridge in the distance while the bottom third line runs (left to right) through the three hats, the laying man’s eyeline, the top of the largest figure’s shorts, the bottom of the distant bather’s bath and the shoulders of the boy at the front.  To add interest in the water, Seurat has added a sailing boat on the intersection of the third lines.

Music in theTuileries Garden – Edouard Manet.  

If you divide this painting up using the rule of thirds, you find that Manet has placed the most prominent figures on the third lines – the older lady in cream staring out of the canvas, as well as the well dressed gentleman in top hat and tails.  To further emphasise this he has placed strong areas of contrast on these figures where the lines bisect each other – where the black jacket meets the cream trousers on the man, and where the blue scarf meats the cream coat on the woman.  Tree trunks are also placed on the third lines with the top horizontal third roughly correlating with the tonal change of the tree line.

Golden section:

One Renaissance painting I found which exactly correlates to the golden mean is Jacapo Tintoretto’s Saint George and the Dragon (in the National Gallery).  This painting has a number of compositional devices.  The most obvious one is the shape of the canvas, domed at the top representing sacred geometry (the circle over the square) with the bottom of the imagined circle finishing at the slain body laying on the ground.  In terms of the golden mean, if you square off the top of the dome, the proportions of the canvas are that of the golden mean.  By drawing a square at the bottom, the first line of the golden mean runs directly across the top of the horse and so through Saint George.  The next horizontal line to bisect the first created rectangle runs directly through God appearing from the clouds.  The next bisecting horizontal line forms the line of the clouds, and then the next bisecting line running horizontally down through the outline of the distant castle.  If you then add the spiral to the golden mean, you find that the line of the spiral (beginning in the bottom left corner) runs directly through the woman, following the line of her leg and up through her shoulder.  This line then mirrors that of the top of the dome and eventually finishing at the top of the castle’s battlements.