[Editorial] Music and prime numbers

June 2022 Editorial

[The Queen and the mystery of prime numbers]

Queen and their use of prime numbers

Author: Lucio Cadeddu - TNT Italy
Published: June, 2022

Maths and music have always shared a common path: these disciplines are not for everyone, and both hide mysteries that are hard to understand to many people. Hence, it is not surprising there have always been interactions between these two forms of art: mathematicians have studied music (the first musical scale has been created by Pythagoreans!) while musicians have applied mathematical ideas and structures to their compositions: symmetries and anti-simmetries, scale-reductions as in fractal geometry and...prime numbers. You might remember your early days at school when you were asked to factorize numbers into their prime factors. Since any number which is not prime can be decomposed into a product of its prime factors, these are considered the smallest atoms that compose the universe, or the mathematical universe, if you prefer. Musical notes, as well, if taken singularly don't have any particular meaning or attractiveness, but they can become masterpieces when organized into harmonies and melodies.

Mathematicians used prime numbers to associate musical intervals to a particular scale of listening pleasure. This has been done by Pythagoreans and finally, in a much more sophisticated way, by Euler in 1739. Some 230 years later Brian May, the guitarist of the British band Queen, used prime numbers to record their hit “We will rock you” (1977). May was quite familiar with numbers and their bizzarre properties, since he had a degree in physics. After a long break, in 2007, he received a PhD in Astophysics with a thesis on zodiacal dust particles.

The problem with the recording of “We will rock you” was the boom boom clap sound, which is the rhythmic skeleton of the song. The band performed this rhythm on the Sex Pistols's drum kit riser (the Pistols were recording their “Never mind the bollocks” in the same studio, at the same time) but May's aim was to trasform it into something that seemed like played by a crowd. Adding time delays was the solution but, if not done properly, this would have generated harmonics of the fundamental notes, creating an innatural and metallic sound. To avoid this harmonic resonance May decided to use time delays that were co-prime, that is, pairs of numbers that have no common divisors (e.g. 15 milliseconds and 32 milliseconds). This way he could reduce the amount of generated harmonics. As a result, the sound of that boom boom clap appeared as if it was performed by a crowd, and not by Queen members. This brilliant mathematical intuition was so successful than one year later Lexicon designed and built their first digital time delay unit, the Prime Time. That name wasn't a coincidence. When selecting a pair of delays a led indicated whether the numbers had common divisors or not. The same trick can be found nowadays in modern plug-ins (such as PrimalTap and EchoBoy, by Soundtoys) that make everything the old digital delays did, and much more! Unfortunately, the manuals of the Lexicon units and of these plug-ins don't cite Brian May as the inventor of the trick.

The whole story, with more details and anecdotes, can be found in a just published paper, written by yours truly for the magazine Civiltà delle Macchine (you might remember I'm a researcher in mathematics, in real life). Unfortunately it's in Italian, but Google Translate will give you an idea of its content.