Just wondering, you certainly know more than I do about composition. But could you give, boiled down, the 2-4 basic composition formats that are the most important.
Adam Marelli gave an excellent lecture at B&H that shows the basics without getting into the root system of design used in classical drawing.
http://www.youtube.com/watch?v=zwk3YFknyNA
As for composing using the root system of design, the book that you provided the link to is an excellent start. The root rectangles have a dynamic, repeating, harmonic geometry within the frame that can be used to establish a gamut and for placement of elements. The root system of design can be quite confusing for the beginner. I had a bit of head start. I used to draw and I was introduced to some of the basics by an art teacher in high school. Then I became familiar with dynamic rectangles in university while studying mathematics. Most recently, following Adam Marelli's advice, I went through Myron Barnstone's Foundation of Drawing and Design course. It improved my understanding of classical composition immensely and I actively started to employ it in my own photography.
Normally in classical drawing, the painter would choose a frame that is suitable for the subject. For example, for a head and shoulders portrait a Root-Phi rectangle (close to 3:4) may be chosen. For a seascape, a wide Root-4 or Root-5 rectangle will likely work best.
With photography, we often go the other way around - we start with the frame.
Personally, I use 35mm primarily and 6x6 and 6x9 in medium format and 4x5 large format. I avoided 6x7 because of the weird ratio. I'm attracted to 6x12 (a perfect Root-4) but I have enough cameras.
The 35mm frame is a 1:1.5 rectangle. It is close to the Golden rectangle, which is approximately 1:1.618. I normally use the same conventions used when composing using the golden rectangle. Finding a rebated square or two. Finding whirling squares. What I tend to do most is to try composing on the diagonal with its reciprocal.
The Root-2, which is approximately 1:1.414, is also close to 1:1.5. The 'rule of thirds' come into play with the Root-2 rectangle.
When using the root rectangles, one can stack and combine them. The Root-4 is handy because it is in the ratio of 1:2. Two identical squares joined together form a Root-4. A 1:1.5 frame can be constructed by overlapping two Root-4 rectangles. By drawing in all the diagonals and their reciprocals, you'll get a 1:1 rebated diamond in the centre, the frame can be divided horizontally in quarters and vertically in thirds or quarters where diagonal intersect (the eyes).
With 6x6 - I usually try to imagine a pentagram when composing. All the lines of a pentagram intersect each other on the golden section. Fra Bartolomeo's "Madonna and Child," which sold for $13 million a few days ago, is composed using the pentagram. Michelangelo's "Holy Family" is another example. Both are actually framed in a circle but composing can be the same for a square. I find square format quite difficult to deal with and I don't use it often enough to improve. Also I find framing with squares within a rectangle much more interesting than a square frame by itself. I often use my 6x6 cameras when I intentionally want to crop. The 6x6 negative is usually big enough for it. I'll likely abandon 6x6 eventually.
Despite being called a 6x9, my Bessa RF actually has a 3:5 frame and is closer to a golden rectangle than the 1:1.5 frame. However, my Bessa RF is more of a toy than a tool for me. I only use it when I want to have a break from my other cameras.
With 4x5, I take out 1/2 inch on the short side to get a 3.5:5 ratio. This is extremely close to the Root-2. Take a look a Marie Cosindas' work. She framed pretty much everything with the Root-2. Every line and angle is measured, every element positioned perfectly... Eileen Cowin's did similar work too. An aside: Cosindas and Cowin carefully constructed their frame whereas HC-B extracted a frame from chaos. For me, that is the what makes HC-B a genius; not only could he extract the perfect composition but also the emotion and significance of the moment. And that he made so many great photographs.
So, getting back to dynamic rectangles. in my opinion, the ones that come in handy are the Root-2, Root-4 and the Golden Rectangle. I don't consider myself an expert. Lets just say that I'm a big fan of classical drawing just as one may be a big fan of classical music. And I try to understand and employ the techniques of the past masters I admire into my own photography. For me, this means using employing the principles of the root system when composing.
