Listen to extracts from the performers at Cheltenham Music Festival
People just love the idea that there’s a connection between music and maths. Or rather, frighteningly brainy music-loving mathematicians love it. They’ve been saying it since Pythagoras’s day, and right now the idea is enjoying a new lease of life, encouraged by fresh insights into how music stimulates the brain.
Next month the Cheltenham Festival jumps on the bandwagon with a series of debates between mathematical and philosophical luminaries including Marcus de Sautoy, Tim Gowers and Roger Scruton.
But is music really a kind of “unconscious calculation”, as the philosopher Leibniz once described it? I’m sceptical.
Of course, all music is rooted in counting. It goes ONE-two, ONE-two, or ONE-two-three, ONE-two-three. Sometimes the counting might go as high as five, or even 12. Tunes are basically patterns, a kind of dancing in sound. Think of how a typical tune is made; two steps up, pause, two more, pause, then the same in reverse. We’ve all been dimly aware of these symmetries and patterns when we tried to pick out tunes on the piano.
But it’s very basic stuff. Our love of music can’t be rooted in something so primitive, surely? Raise this thought and the mathematics and music brigade immediately bring out their big guns. What about the connection between music, astronomy and maths, they’ll say. The conjunction inspired a lofty metaphysics about the “harmony” of the human soul, which was mirrored in the “harmony” of the heavenly bodies, and in music.
All true, and inspiring in its way. But it’s only a metaphor which limns the music we listen to with an extra light.
And it only works if it’s the right music. These thoughts are helpful for a Monteverdi madrigal, not so helpful for a Tchaikovsky ballet; which shows these things aren’t really rooted in the music at all.
But the mathematicians aren’t done yet. Harmony only sounds harmonious, they’ll say, because it’s rooted in mathematics. Intervals sound “harmonious” because they obey simple arithmetical ratios. It’s been shown that the more complex the ratio between two notes, the more unpleasantly it buzzes in our ears.
Well, yes and no. The fact is that our tuning system in the West is, mathematically speaking, a mess. It grew up over centuries as a compromise between different tunings, so none of the intervals it contains are pure, apart from one. Are we bothered by this? Do we wince every time we hear a C-major chord? No. We’ve learnt to hear something that is mathematically impure as glorious. Harmony isn’t something nature gives us ready-made. It’s a cultural creation, like language.
But what is it that does the creating? The human brain, of course. And (say the maths-and-music fans), the way the brain functions is itself mathematical. It’s an amazingly sophisticated computer. When we listen to music, we’re processing information in a way that is mathematical.
Well, maybe. But music isn’t enjoyed by brains, it’s enjoyed by human beings. When we listen to an irresistible rhythm, it’s not our brains that drum the rhythm on the table. We respond to music with all of our selves. In any case, when we’re moved to tears by a harmonic progression, it’s not our brains that are moved, it’s our minds.
It’s undoubtedly true that music is mathematical in all sorts of fascinating ways when contemplated from outside. But we don’t contemplate music from the outside. We listen to it, and thrill to it, from the inside. And once you’re inside music, all thoughts about mathematics become irrelevant.
The Cheltenham Festival, June 29-July 10 (01242 505444; www.cheltenhamfestivals.com