One day while I was discussing sculpture and music
with my friend and fellow artist Paul Willers, he said with an encouraging
smile: You must do something with the treble clef!
Among Paul’s diverse interests are points of contact between aesthetic fields
of human expression, such as music and sculpture. While the desire to
integrate distinct modalities of art can lead to beautiful things, as I
looked at the treble clef that he drew for me, I thought it would be taking
on a headache. The treble clef figure seemed too complicated as a starting
point for a sculpture, by which I mean a formalistic one, designed as a
composition of elements from the cross product of figures that can be seen on
A swan emerged.
I put the idea aside, but after a few weeks I returned to it. First, I had to
learn to be more flexible in my own requirements and mathematical severity in
creating sculpture. I was willing to accept that instead of using the whole
range of elements of the cross product, the sculpture would have to be formed
by only one element, the kernel. Secondly, I allowed myself to change the
appearance of the treble clef, so that it would be possible to make a cross
product with this figure. That left me ready to work out the design and as
soon as I began, it became clear that the resulting sculpture would have a
bird-like appearance, resembling a swan. As I worked on the design it emerged
as the reflection of a swan, the surface of the water mirroring its trunk,
neck, and head.
I then had to create the outline for the swan-like treble clef sculpture.
Should it be a freehand design or a geometrical translation of the treble
clef? I decided upon a geometrical translation because I have found that it
often leads to unexpected beauty and harmony. The first translation resulted
in a description of the treble clef by a system of 26 curves (17 ellipses and
9 circles), but that was much too complex. I was occupied for several weeks
in the mathematical struggle of avoiding that chaos to find simplicity and
harmony. During that process, I made 7 physical models of the sculpture to
examine the spatial effects of the changes in the two-dimensional system of
curves. I finally ended with a system of 19 curves (13 ellipses and 6 circles)
and the result seemed harmonious. However, I thought it should be possible
with 16 curves or less. Later on, when I had finished the sculpture and my
mind was free again, I discovered that even 15 curves could do the job
nicely, still leaving the character of the shape intact without losing any
power of expression.
Casting and finishing.
Once I had finished the design, I cut it out from a block of polystyrene and
took it to a foundry to have the sculpture cast in bronze. The foundry made a
casting mould which, because of the complexity of the figure, they split into
two parts. This was a very difficult task and because the result was not
perfect, some parts had to be cast again. To make matters worse, some
fractures occurred while I was finishing the sculpture, and these
necessitated welding, grinding, and polishing.
But after some months, the sculpture was ready to be exhibited. I named it
The film about Harmony.
In 2008, I talked with my neighbour Bas Wersch about Harmony. Bas is a
photographer and is responsible for several pictures on my website. I was
pleasantly surprised when he offered to make a film about my sculpture. I
admire Bas: with people and in his work, he always has a relaxed, committed,
and professional attitude. He also has an amazing capacity to see beautiful
lighting where I might see nothing special. To distinguish invisible nuances
of light is a special skill of professional photographers.
Since the treble clef had emerged as a swan, it seemed quite natural to use
part of Tchaikovsky’s Swan Lake for the accompanying music (act II. scene
10). The film opens with a swimming swan to set the scene for the sculpture.
Future of Harmony
The sculpture cast in bronze is a starting point. I have the following steps
1) Designing process
The sculpture Harmony is now based on a design with 19 curves (ellipses and
circles). Later on I found that it can be made with 15 curves and that is a
big step forward with regard to geometrical purity. The next Harmony will be
based on 15 curves!
2) Producing a huge sculpture
I would like to construct a version of Harmony as a monumental sculpture
having a height of 10 meters or more, and therefore I need a commission to
carry out the project.
3) Producing Harmony as a trophy
In a version with a height of 25 to 40 cm and with an adapted socle, the
sculpture could be a marvellous trophy in music or in cultural crossing
points between mathematics, ornithology, and music. I would be pleased to
discuss this with anyone who is interested.
4) Producing Harmony as a tiny sculpture for large-scale production.
I would like to produce Harmony as a small sculpture of 16 to 25 cm, at an
affordable price. A suitable production procedure may be the water cutting
technique by which the sculpture can be cut out of blocks of light metal,
hardwood, Perspex or other synthetic material, or even unbreakable glass. I
would need to examine two main aspects: marketing strategies and technical