Bk

On the left is Bartók Béla. He used a symmetrical plan for several pieces of music, which employed of five movements. This arrangement is often referred to as an arch. The most symmetrical of these pieces is the fourth string quartet. The main themes of the first and last movements are identical. They are like a little arch of notes. The themes of the second and fourth movements are also very similar, differing only in tempo. Each looks rather like a perspective view of a bridge with three arches receding into the distance. Supported in the centre of all this is a an eloquent and passionate piece of music. It contains elements from the sounds of nature and from folk music.

On the right is Kodály Zoltán, a composer, and a collaborator and friend of Bartók.

These busts are close together on Margit-sziget in Budapest. After Bartók heard Dósa Lidi singing, in 1904, he became very interested in folk music, as did Kodály, and in time their music became a bridge between "art music" and "folk music".

In the case of Bartók, the music is perhaps also a bridge connecting nature, art and science, three areas of great interest to him.

Composing a piece of music presents technical problems, like building a bridge. You have some idea of the span of time that needs to be filled . You have to decide on the number of sections or movements. You also have to decide on a means of relating these movements to create a coherent whole . This process goes on right down to the smallest details, until the construction is as satisfactory as you can make it.

The artistic person can create whatever she or he likes, as long as a living can be made from it, or by some other means.

Building a bridge is different . Economy is far more important than in art. The bridge designer is forced to work with what nature offers, rather than with a blank sheet of paper. The width of the crossing, the type of ground, the depth of water, the range of the tides, and the navigational requirements, for example, are not under the designer's control. But he or she can use art and science to produce the best solution to the problems. And solving the problems may lead to great ideas, just as the search for a line with the right rhyme and rhythm may lead to an idea that a poet might not otherwise have had.

At the beginning of Beethoven's quartet Opus 131, or Bartók's Music for Strings, Percussion and Celeste, both seem not so much like tuneful music as constructing something. The Bartók piece literally builds up, towards a tremendous climax, from which it descends quite rapidly on the other side.

The Beethoven piece gives a great sense of density, in terms of music per minute. A musician could explain this, but as with bridges or nature, we can enjoy things without understanding most of the details. But nothing is lost if we learn more - science does not spoil pleasure - it provides an extra dimension.

Many kinds of art and science involve structure and symmetry. In another part of this web-site there will be pages about symmetry and broken symmetry in physics.

Perfect symmetry in art would be rather boring. On the other hand, an art in which nothing is related to anything else would be very odd. Even in a painting by Jackson Pollock, there is relationship between the components, and the paintings are recognisably different from each other. They have not much structure, and not much symmetry.

On the other hand, poetry that rhymes and has metre is both well structured and highly symmetrical. The most symmetrical poem would consist of the same word repeated many times.

The symmetry is reduced by breaking it into lines, and grouping these into stanzas. The lines are generally all different. But the poem is held together by the rhyming scheme and the metrical pattern. So we have an example of broken symmetry.

There may be occasional imperfect rhymes or feet that are not a part of the rhyming scheme. But these may even be used to emphasise a point.

Prof Ian Stewart, in "Life's Other Secret (Penguin), shows how broken symmetry and simple rules can generate complicated structures and behaviour. So symmetry and patterns arise in nature as well as in art and engineering.

What are the differences between "popular" music, "folk" music, and "classical" music? In fact there are so many forms of music that this probably cannot be answered. But at least we can ask how they differ in complexity of structure and the degree of ornamentation of those structures.

In an article about Bartók, Kodaly wrote that art and science are not unrelated, and that someone can achieve greatness in both. This is surely true of the best bridge builders, whether the bridge is a humble footbridge or a great span. The article is quoted in "Bartók Remembered", by Malcolm Gillies, published by Faber and Faber.

C P Snow made a cause out of "The Two Cultures". In fact there are thousands of cultures and sub-cultures, from angling to zebra breeding. What does it matter, as long as we respect what other people do?