About Harmony

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 this website.
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.

Geometry.

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 Harmony.

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 in mind.

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 possibilities.

E-mail

peter.g.meijer@gmail.com

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