The link between mathematics and music has been recognised for thousands of years, with many great mathematicians also being noted for their musical talent. Our old friend Pythagoras, of right-angled triangle theorem fame, has also been called the father of musical theory.

He used numerical ratios to define the different notes in the musical scale, leading to an understanding of harmony.

Indeed, music has been credited with stimulating an increase in intelligence. In 1993 researchers at the University of California (Rauscher, F. H., Shaw, G. L, & Ky, K. N. (1993). Music and spatial task performance. Nature, 365, 611) found that a group of 36 college undergraduates improved their spatial-temporal intelligence (the ability to mentally manipulate objects in three-dimensional space) after listening to 10 minutes of a Mozart sonata, the so-called Mozart effect. Pythagoras’ B-flat note at 233Hz has gained particular popularity recently, as it is the note played by thousands of vuvuzelas in every football match at the 2010 World Cup finals in South Africa. If you are one of the many viewers who find the noise irritating, we can offer you some comfort – since Pythagoras’s work led to the theory of fifths.

This diagram shows groups of notes, five steps apart, which provide pleasing harmonies. So all we need to do is persuade one-third of the spectators to switch to an E-flat vuvuzela, and another third to invest in a vuvuzela tuned to F, and we would then be rewarded with a much more pleasant and harmonious sound. Which leads to an intriguing thought. Perhaps if the crowd at Rustenburg last Saturday had been equipped with a set of harmonic vuvuzelas, England goalkeeper Robert Green would not have suffered from his embarrassing lapse of spatial-temporal intelligence. Now, where did I put Fabio Capello’s phone number?