Prof. Jürgen Richter-Gebert speaks about the exhibition "La La Lab. The Mathematics of Music"

"Music is usually based on mathematics"

Which musical phenomena have a mathematical basis?

It starts with the fact that a sound is actually air in motion – in other words, a vibration. And a vibration is a function of time. Everything I hear can therefore be described in a mathematical function. The question of why certain tones sound good together and others do not was already investigated by Pythagoras and his followers. They studied string instruments and deduced that the sounds of two strings are harmonious when the ratios of the string lengths are equal to those of certain natural numbers. Today we know that the sound of a string is not just a single tone, but rather a series of overtones. That means that, along with the fundamental tone, the frequencies we hear are integer multiples of it. The harmony depends on this so-called frequency spectrum. The fact that many combinations of tones sound unpleasant on bells but are harmonious on other instruments results from the overtone spectrum: It is not pure. The overtone frequencies are multiples of the fundamental frequency – another example of mathematics at work.

How can you present such an abstract topic in an exhibition?

I'm a professor of geometry and visualization. So we've put a lot of optical elements into "La La Lab". We link visual and musical concepts and present the underlying mathematics. The visualization can enhance the perception of music or transform it: When I listen to a piece by Chopin while watching a screen where every note descends visually, the music sounds much sadder. And when I see a piece being played on a piano keyboard and graphically represented as a spiral, I suddenly have a deeper understanding of the music, and have a better sense of what's coming next. The visualization opens up a new dimension.