All of us apply mathematics in our daily lives. As an exercise, we think of it as cold and rational. Music, on the other hand, brings more enlivening sentiments with it. We think of music and a favourite song may come to mind. Instinctively, we delight in it.
Though it may seem unlikely at a glance, there is, in fact, a connection between the steely, rational logic of mathematics and the creative, warm art of music. Of the relationship between mathematics and music, Igor Stravinsky, the twentieth century Russian composer said, “Mathematics swims just below the surface (of music).”
Interestingly, the Fibonacci numbers—1, 2, 3, 5, 8, 13, 21—and their growing patterns are numbers that point to a hidden, even mystical code, still under study. They reflect in our world in the micro and macro—in the sunflower, for instance, as well as in the proportions of the Milky Way. In music, the Fibonacci numbers reflect in the work of composers from Bartok to Debussy, in the way their compositions grow organically. This, most likely, was an inadvertent exercise reflecting the subtle but strong linkages between the mind, mathematics and music.
Visual and spatial links
Studies over the last few decades have repeatedly established a link between mathematics, music and inclinations of the brain. Children who are inclined towards music usually show a greater propensity towards analytical thought and arithmetic. They are good at jigsaw puzzles and chess.
These skills are stronger in children who play a musical instrument rather than in those who might simply listen to music casually. Practising an instrument requires them to be attentive to detail and to work their way to greater precision. This strengthens the power of concentration as well as coordination in such students.
The 1990s saw interesting cognitive research on the connection between mind, maths and music. Participants in a study demonstrated better spatial-visual abilities after listening to a particular sonata by Mozart. They were better able to visualise a boat and then build it with Lego pieces after listening to the sonata. Termed the 'Mozart effect', this study fuelled the discussion on the linkage between brain, music and mathematical patterns.
Structure, patterns and maps
The Greeks considered music as a science—the science of sound, harmony, rhythm and pitch. All four have mathematical foundations. Rhythm depends on arithmetic—on equal, precise intervals between two notes. As for pitch, when we hear two notes an octave apart, we are hearing the same note though the frequencies are different. The ratio of the frequencies is exactly 1:2.
Beyond numbers and deductions, mathematics is essentially about arriving at structure and patterns. This affinity it shares most evidently with music, which, too, is about structure and pattern.
Much of the research done on the brain so far points again in the same direction—there are patterns and structural movements that the brain evolves and functions with. These significantly impact thinking, behaviour and individual growth.
While mathematics is trying to map phenomena, experts are beginning to consider musical patterns as maps of the mind. A composition thus reflects a map of the composer’s mind—how he thinks, which linkages are stronger and what his emotions and propensities are. It, therefore, seems a possibility that the ability of all three combined may lead us to a more sublime map of the universe.