Before I discuss today's topic, I should explain this painting. It's watercolor and was painted many years ago. The title is

*Measured Life at 51* and it's about a time in my life when I underwent chemotherapy for the first time. I began to think of all the ways my life was being measured: dosage of pills, timing of dosages, losing weight, measuring everything I ate, etc. Glad those days are behind me! It's not a very masterful painting, but it expresses how I felt at the time.

In the last post, I left you with Arnheim's idea that

*The great works of art are complex, but we also praise them for having simplicity, by which we mean that they organize a wealth of meaning and form in an overall structure that clearly defines the place and function of every detail in the whole. This way of organizing a needed structure in the simplest possible way may be called its ***orderliness**.

Over the past year I made it a point to study

**composition**, and specifically Renaissance designs. Talk about making the complex simple! Although I haven't yet applied too much of what I learned, I plan to start a whole new series of paintings in 2010 that employs the mathematical division of space developed by the Ancients. The idea that a work of art will be more beautiful if it is made according to numerical relationships began in mid-fifth century BCE. Renaissance artists utilized that math, as do a growing number of contemporary artists.

*Everything old is new again!*For those of you who are brave enough to follow this line of reasoning, I'll briefly depart from Arnheim's book to discuss how the

*Masters* placed shapes to create "orderliness." It's not a comprehensive analysis; just some tidbits.

I'll start with a very simple concept. You want to paint on a rectangular canvas or paper. According to Renaissance artists, the length and width of that rectangle should be a specific proportion to yield the best results. These are called

**root rectangles.*** *Here's how it works:

1. Start with a square of any dimension (example - each side is 3")

2. Measure its diagonal (for a 3" square, that would be 4.25")

3. Calculate the square root of the diagonal (the square root of 4.25" is 2.06")

4. Add that number to the length of the base of the square (3" + 2.06" = 5.06")

5. Draw a line that defines the length of the base of the new rectangle

6. Draw the other three sides of the rectangle. (your rectangle has a height of 3" and length of 5.06")

**This is a root 2 rectangle.**

You can keep going, like the figure below, by drawing the diagonal of the new rectangle, taking its square root, and drawing the next larger rectangle. That would be a root 3 rectangle, etc.

Figure from Hambidge, 1920

**GUESS WHAT?? **If you use pre-made canvases/papers they're already sized according to these proportions!

OK, so you've decided on the size of your rectangular canvas/paper. Now, you must create a balanced (harmonic) composition to create "orderliness." For now, I'll forego a discussion of the size and color of the shapes. How did the "ancients" figure this out? Pythagoras, a Greek mathematician/philospher who lived around 500 BCE, discovered harmony through proportions, or ratios. This is the foundation of our modern musical harmonic scale, and also the foundation for Roman architecture and Renaissance art.

Eventually, Pythagorean theory on harmonics made its way to the Renaissance, when artists wanted to create a less complicated way to organize the elaborate designs of their predecessors, the medieval artists. These designs, or ways of creating orderliness, were eventually identified as the

**armature of the rectangle **by Charles Bouleau in his book

*The Painter's Secret Geometry.* Here's a complex armature:

Notice that the diagonal lines are drawn from either the corners or middle of each side. The verticals are calculated by halves, thirds, fifths, (sevenths?).

**Nodes **occur where lines cross, and it's on those some of these nodes that the artists would place focal points.

Here's the armature used by Johannes Vermeer in his painting,

*The Astronomer. *Notice that he ony used a few of the diagonals, verticals, and horizontals from the more complex armature in the diagram above. Also, notice the central nodes that define the placement of the globe, wrist, and shoulder in the middle of the composition. The left hand is immediately below the right wrist on another node, and the toe of the left shoe is below that. The angle of the light follows the two diagonals drawn from the upper left to the bottom right. And so on. (Figure taken from

*Classical Painting Atelier* by Juliette Aristides, 2008).

There are many variations on this basic armature, and certainly any artist can invent one. They may be very simple, or include all the lines found in the figure above. Some artists included circles and arcs in the armatures. What do they all have in common? Harmonic symmetry.

Does an artist have to use these geometric principles? No, not at all. As I said earlier, I plan to experiment with it in 2010 to see if I can correct many of the design flaws I've been noticing in my work. This gives me a great opportunity to marry my two "selves": the nerd and the aesthete!

So, for those of you who made it this far -

**thank you**! and here's a great quote as a reward meant to provide a counterweight to all that precedes it:

*There are some things in painting which cannot be explained, and that something is essential.* - Pierre August Renoir