contrapunctus series @
essential pivot of metered composition.
beyond logic, art invention,
beyond words, art logic.

beyond logic, art invention:
the invention turns previous forms - continuous radical transformation.
beyond words, art logic:
the logic is succinct, yet it cannot be consumed by theory.

(Poetic form taken from Zazenshin by Zen Master Dogen)

3. Contrapunctus

The Logic, Counterpoint And The Visual Forces
That Shape Root2Art Composition

Counterpoint in Composition 1.

Vertical/Horizontal and Tonal Logic

The scale I use, seen as percentages of black, is 0%,25%,50%,75%,100%. The Contrapuctus 3D piece seen at the top of this page, was actually the first composition I created using this 5 tone scale. All previous motifs were defined using only black, white and a mid grey (50% black). I actually produced some of my most distinct motifs using just 3 or 2 tones. Many of the later works on this site use both a 7tone scale and a full (8-bit) 256 greyscale, although this number has little significance as it is simply the means by which I render a full black to white graduation.
The tone chart, above right is a scale I designed to assess values for printed output. The printing technology I now use, however, is so well calibrated that the ideal values described above left produce perfect printed results.

Tonal Symmetry Logic
One key device I have evolved in my work is something I call tonal symmetry. A simple demonstration of this can be seen in the logic diagram above. In essence it is a simple tonal counterpoint exercise where horizontal elements @ (25% grey) is balanced by vertical elements @ (75% grey). This provides an interlocked grid structure onto which the composition is set. The real invention comes at the point where vertical and horizontal intersect. The simplest solution to this might be something like that seen below left, but that would be plane dull.

The rotating squares in the animation below, indicate how the Square root of 2:1 proportion* meters the growth of this simple motif.

*In a square of sides = 1, the distance between opposite corners = root2.

Counterpoint in Composition 2.

Directional Emphasis

Comp 1 and 2

Comp 3

Compositional Movement
Directional force and movement within a visual composition is produced by all shapes to some degree or another. Essentially, ordered variety of form will create movement around a composition as the eye will naturally move from areas of activity to areas of inactivity and vice versa. All the motifs from 3 through to 10 have a diagonal directional emphasis, but achieve it in varying ways. Compositions No.1 and No.2 contrast strong diagonal forces with a non-directional, centrally focus motifs.
No.5 is an invention on a theme of symmetric form and tone which creates a diagonal passage through the composition without using any significant linear components. The ‘type’ of symmetry here is a conceptual symmetry of themes and parts as opposed to a literal axial symmetry like that created by a mirror and seen in No.10. This thematic symmetry, however, in this motif does operate about an central x and y axis.
We might think a simple bold arrow or bold stripes might produce the strongest directional movement, but I believe there are much stronger compositional solutions at hand with the use of a little invention. Take a look at No.4. We see two points of focus at the ends of the arrows, but this intensity is quickly lost as we move into the composition leaving dead areas. The square composition is cut in half by the arrow and there is no essential and continuous unity between the negative spaces around the arrow. A simple jarring and discordant arrangement like that in No.4 may well be desirable if this is the expression that is sought. Compare No.4 with the continuous and evolving movement in No.6. This is one of my favourite motifs and I have pretty much exhausted its use over the years. Its geometry is very pure and it creates a flowing varied movement with very little fuss.
No.9 is quite amorphous by comparison to the rest of the motifs, but still, nonetheless creates some varied forces. No.11 and No.12 create a rotational movement with no diagonal emphasis. As I have discussed previously on this site, very rarely do I utilise linear stripes in my work like those shown in No.8. This is partly due to the somewhat arbitrary nature of the geometry needed to define them, but more simply, it is to do with their intrinsic lack of progressive variety. One way I have gotten round both of these ‘problems’ can be seen represented in No.7. The type of visual dynamic however creates another problem of its own. This is the ‘Op Art’ phenomenon, which whilst providing an instant effect, for me has more to do with sensation and illusion, than order and beauty. Both No.7 and No.8 are still, however examples of emphasised directional movement within a visual composition.

Historical Context

Directional and Tonal Counterpoint

Campidoglio designed by Michelangelo

Detail of photo by QT Luong

Michelangel Campidoglio Capitoline Museum

Michelangelo’s vertical elements spanning two stories, in a supreme example of balance and counterpoint.

Jameh Masjid, Isfahan, Iran

Detail of photo by Keith Mellnick

Both these buildings show a bold use of counterpoint between relief and flat elements. This simple contract creates a powerful dynamic which I tried to employ in the 3D piece seen at the top of the page.

Detail from David Best's Temple of Honor from the Burning Man Festival

Images from
David Best @ wikipedia

Detail from David Best's Temple of Honor

David Best’s Temple of Honour 2003 is a feast of intricate greyscale geometric designs contrasted against bold sculptural forms. The geometric patternation he has used emphasizes the 2dimensionalness of the plane surfaces making this contrast very powerful. I would love to know the source of these ‘Islamic-like’ designs, they may well be Best’s own invention. I only discovered David Best whilst making this site and am keen to see more of his work.

cezanne - The Large Bathers

Note the opposing diagonal emphasis created by the left and right halves in Cezanne’s Large Bathers. For me this is one of the very great compositional masterpieces of the last 200 years. Cezanne is widely known for his pioneering uses of colour modulation in creating pictorial space. However, the tonal structures seen in his vast body of paintings, work equally hard to create form, movement and space. I’ve been fascinated with this painting for many years and its strong directional counterpoint is something I’ve attempted to examine with the Contrapunctus pieces. See Comp 1,2 and 3.

islamic Calligraphy

Hokusia - Great Wave

College Piece

Michelangelo Creation of Adam


Key Compositions

contrapunctus series @