On the face of it, music and science are two radically different subjects travelling on parallel tracks that are usually not destined to meet. Yet there are elegant overlaps between music and science, mathematicians and musicians. Take, for example, Pythagoras - the philosopher and mathematician who we remember mostly for his theorem. He believed that the universe could be understood in terms of whole numbers and devised a method of tuning music based on simple ratios of numbers. Musicians used this method to tune instruments for the next 2,000 years, till the early 16th century.
Talking of tuning instruments, this is what Grammy-winning tabla maestro Zakir Hussain has to say. "Our ears have been trained by our experienced gurus to spot the exact pitch and tune our musical instrument in such a way that there is perfect resonance between all the instruments and musicians on stage". Resonance. Now that is another of those elegant overlaps. The concept of resonance is widely used in mathematics and physics whether it be between resonant orbits in celestial mechanics, resonant wavelengths in particle-wave physics, resonant frequencies in nuclear physics, thermodynamics, particle physics, acoustics, electronics and so on. A giant orchestra on stage as well as a small radio on the streets rely on resonance to achieve a successful performance. Incidentally, one of the most widely used pitch notation systems in Western music was initially developed by the great German physicist Herman von Helmholtz, who is also known for the Helmholtz resonator, which is about tuning frequencies, resonances and feedbacks in acoustic physics.
Mathematical prodigy and Fields Medal winner Manjul Bhargava finds a beautiful resonance between mathematics, music and Sanskrit poems, which in turn helps the mutual learning of these subjects. "I find extremely interesting mathematical patterns in music and have learnt a lot about playing the tabla from Zakir Hussain," says the Princeton University faculty who calls Hussain a "good friend". Hussain believes that while speeding up the rhythm of the tabla is just a matter of doubling or quadrupling the speeds of existing composition and bols for him, Bhargava might have a different way of understanding and formulating the acceleration and deceleration of rhythms because of his grasp of mathematics. The exchange of ideas and mutual learning between the famous mathematician and the famous musician is possibly the greatest artistic-scientific collaboration of recent times. It brings to mind the Pulitzer-winning book by Douglas Hofstadter. Gödel, Escher, Bach: An Eternal Golden Braid looked at the overlaps between the works of eccentric logician Kurt Gödel, unconventional artist M.C. Escher and composer Johann Sebastian Bach and how important numbers are to art and music.
"I believe mathematics deals with logical structures that are appealing to the mind for their sense of purpose, internal consistency, unexpected connections and occasional surprises. For greater appeal, the structures should display a level of originality but also some amount of familiarity. I think the same words describe music very well," says Sunil Mukhi, eminent string theorist at TIFR, Mumbai, and IISER, Pune. Artistes come to the stage with a generic plan [familiarity] but the improvisations [originality] are spontaneous. Hussain says the freedom to improvise on the spur of the moment allows him to tread unexplored paths and patterns in music and often results in sheer musical magic.
"Of course emotions play a greater overt role in music. This probably constitutes the main difference between the two subjects," adds Mukhi. The tabla maestro confesses that the connection with his audience during a concert, the resonance and the feedback, give him more energy and motivation to enthral them further with much more challenging beats and notes. This is how music is able to strike the inner chord in human beings and bring their aesthetic sensibilities to life.
"Like science, music is one of the great inventions and virtues of humans. If there were evolved intelligent life elsewhere in the universe, it shall also bring both science and music into its life!" says noted astrophysicist Murthy Gudipati of NASA-JPL, Pasadena, the US. "Music takes you beyond the seeable, thinkable and reachable in your mind through the sounds it produces. And astronomy is that branch of science that looks beyond the seeable, thinkable and reachable in the real world," he adds.
Famous French mathematician Pierre-Simon Laplace first discovered the orbital resonance in the Galilean moons of Jupiter, namely Ganymede, Io and Europa. Hussain says that the many different levels of cycles and subcycles he constantly uses while playing the tabla are just like the orbits in the Solar System where the Moon goes around the Earth, then Earth goes around the Sun, and the Sun goes around the galactic centre. The rapid improvisation cycles and rhythm patterns he uses eventually has a fixed periodicity and boundary when it comes to the larger picture, he points out.
"The act of presentation itself, whether class, talk or concert, is an act of exposing one's innermost self to a critical audience. Like the musician's practice or sadhana, good scientists must practice all the time, keeping their instincts honed and sharp so as to not miss a beat," says Gautam Menon, acclaimed theoretical physicist at IMSc, Chennai. "When a scientist creates, he or she must do so within the bounds of what we know already, respecting every fundamental principle of physics and rule of mathematics. The astonishing thing is that there is so much to discover even within these boundaries, sometimes a whole new view and sometimes a fresh presentation," adds Menon.
Hussain agrees that it is striking that the act and practice of both music and physics or mathematics have so many parallels. "There is so much scope for different levels of improvisations and explorations even within the allowed bounds of classical tabla compositions. This makes us digress from certain set paths and lets us embark on journeys finding new directions and islands along the way," he says. The maestro points out that musicians enjoy the element of spontaneity on stage, depending on the emotions of co-artists. Such occasions test their presence of mind and sharpen their improvisation skills.
There are many interesting parallels between developing a new composition and style in music and the process by which a mathematician comes up with new theorems. Stalwarts such as Sir C.V. Raman took these studies to a new height by developing mathematical formalism to understand the frequencies of the tuning fork and tensions in an oscillating wire. His careful observations on mridangam playing and correlating the changes in musical tones to the increasing and decreasing radii, layers and thickness of membranes is one of the most comprehensive studies in this direction. Although most scientists and students are aware of the concept of Raman effect in spectroscopy, only very few have noticed Raman's effect and role in the technical and philosophical overlap in music and science. Renowned theoretical physicist Alladi Ramakrishnan used to consider his adventures in both physics and music equally challenging, beautiful and satisfying. If the new generation of students, of both music and maths, were made aware of just how rich the connections between science and music are then perhaps we can make these historically rich works and thoughts of legends like Raman and Ramakrishnan relevant again!
Here's to a symphony of science and music!
The writer is an Indian astrophysicist based at CEED, University of Oslo, Norway
