Mathematical sequences in music help us to understand why some songs evoke a physical reaction, writes Robert Matthews.
Symphony by the numbers
After just a few bars of his music, you're there - the vast, open spaces of Africa in Born Free, or some dank backstreet in Cold War Europe in The Ipcress File. John Barry, the celebrated British film composer who died last month, had an astonishing gift for painting pictures with music.
As the many obituaries of the Oscar-winning composer pointed out, Barry benefited from life-long immersion in the business, his father owning a chain of cinemas, his mother being a gifted pianist. It's said that the teenage Barry used to watch movies, notebook in hand, analysing what music worked well in specific scenes, and what didn't.
But what few of the obit-writers mentioned was Barry's use of a technique for musical composition that attempts to put the ineffable qualities of music on a scientific basis. It was devised during the 1920s by a Russian composer named Joseph Schillinger, who believed that the emotional content of music could be analysed objectively. By breaking down rhythm, melody and the other basic components of music into their components, Schillinger found simple mathematical rules - such as certain sequences of notes or symmetries in their appearance - that he claimed could be used to create music reflecting any mood.
What became known as the Schillinger System was taken up by such renowned composers as Glenn Miller, Benny Goodman and George Gershwin (who used it to compose his opera Porgy and Bess). Barry himself used Schillinger's method to pen the double Oscar-winning theme to the 1966 film Born Free in just 10 minutes.
Given the world-wide appeal of music, it is astonishing that scientists haven't taken a greater interest in the links between music and emotion. After all, the existence of objective rules for deciding what sounds pleasant or discordant has been recognised for millennia.
According to legend, the Greek mathematician Pythagoras uncovered one of the key principles more than 2,500 years ago while standing outside a blacksmith shop. Listening to the sound of hammers striking anvils, he wondered why the resulting sound seemed pleasantly musical. On investigation, he discovered that the blacksmiths were using anvils whose sizes happened to be simple ratios of one another, such as two to one and three to two. This led Pythagoras to link harmonious music to mathematical elegance - a connection that appears throughout music, from the construction of instruments to the art of composition.
Ever since, composers have sought to create unforgettable music using rules of thumb about the emotional appeal of certain combinations of sounds. During the Renaissance, composers began to recognise that notes arranged to form so-called major chords sound happy and upbeat, while those in minor chords sound mournful. For example, the Beach Boy's bouncy classic Wouldn't It Be Nice? is replete with major chords, while the Beatles' regret-filled Yesterday is dominated by minor chords. It is within the last few years only that scientists have begun to uncover how such combinations affect our minds. At McGill University in Quebec, Robert Zatorre and his colleagues have carried out ground-breaking studies in which volunteers listen to different types of music while their brain activity is monitored with medical scanners. The results suggest that the pleasure we get from music is very basic indeed: according to Mr Zatorre and his team, it triggers activity in some of the most primordial parts of the brain.
In one research project, he and his colleagues studied the response of aficionados of classical music to compositions renowned for their "tingle factor", such as Samuel Barber's Adagio for Strings and Rachmaninoff's 3rd Piano Concerto. The researchers measured the strength of the tingle factor through its effect on the respiration and heartbeat of the volunteers, while monitoring their brain activity using positron emission tomograph (PET) scanning.
Despite the sophistication of the music, the tingle factor proved to be correlated to activity in regions of the brain such as the amygdala, ventral striatum and orbitofrontal cortex, which are normally excited by such basic needs as food and sex.
In research published in the current issue of the journal NatureNeuroscience, Mr Zatorre and his colleagues have used scanning to look in more detail at the response of the brain. They've found that listening to music can trigger the release of dopamine - a neurochemical usually associated with basic pleasure - and say that this explains why some music can be almost addictive.
Other researchers have been examining that other celebrated feature of music - the irresistibility of rhythm. At the University of Oxford, Dr Joyce Chen and colleagues from the International Laboratory for Brain, Music and Sound Research in Montreal have carried out brain-scanning studies on healthy but musically untrained volunteers listening to rhythmic sounds. As one might expect, the sounds triggered activity in the auditory parts of the brain.
But the team also found that the mere act of listening to the rhythms also triggered activity in the motor regions of the brain, which are linked to active movement. This might explain why some tunes set our toes tapping: there may be a direct link between the auditory and motor regions. It might also explain why disabled patients often benefit from listening to music, which may help form new connections in the motor regions.
The upshot of these findings is that everything from the most basic drum beat to the sophistication of Wagner's Parsifal has the ability to excite very basic circuitry in our brains. But why? One possibility is that our love of music has its origins in the times when our very survival depended on tuning into the sounds of the creatures around us. Some years ago, the late curator of ornithology at the California Academy of Sciences, Dr Luis Baptista, claimed to have found many connections between music and birdsong.
Whatever the truth, the discovery that music excites brain circuitry linked to basic desires suggests that Shakespeare's line about music being the food of love may be more apt than he realised.
Robert Matthews is visiting reader in science at Aston University, Birmingham, England