The Great Mathematics Bazaar II: Music lectures

It came as an enormous (and pleasant) surprise when Prof. Raghunathan asked me, nearly a year ago, whether I would be willing to give a lecture or two on Indian classical music appreciation at the ICM. The idea would be to present some aspects of Indian culture to the participants, specially those from outside India, and to prepare them to some extent for the planned live concert. Accordingly I gave two lectures, one on Sunday August 22 and the second on Tuesday August 24. The vocal concert by Ustad Rashid Khan took place on August 25.

During my first lecture the sound and video (files embedded in my powerpoint presentation) worked well, and speaking in Hall 2 was a thrill since it was there that Vishwanathan Anand, a couple of days later, played simultaneous chess against 40 participants (apparently unmoved by the gratuitous questions about his Indian-ness or lack thereof).

The second lecture was held in the infinitely larger Hall 4, and like everything conducted there, was videotaped. Hall 4 was even more of a thrill given that I was on the stage where the President of India and the Fields medallists had stood a few days earlier, but for me the thrill quickly evaporated when the sound failed to work and some time was wasted getting things in order. The video of this session can be viewed by going to this page and selecting Part 3 under "24th Aug 10 Time 15:00 – 18:00 /Hall4" or you can download this flv file. Unfortunately due to the sound problem, by the end of an hour I was only 45 minutes into the talk. Since the video was programmed for an hour, it failed to capture the last 20 minutes (in which incidentally Pandit Kumar Gandharva features twice).

Now about the content of the talks. I was asked by the press unit there (= R. Ramachandran, better known as "Bajji") to send a writeup for the ICM daily newsletter, so I might as well reproduce that here.

Titled "A Mathematician's Guide to Hindustani Classical Music", this pair of talks on the musical tradition of North India has been put together specially for the ICM. The first talk presented a brief history of Indian music, which has its roots in religious chanting from Vedic times around 5000 BCE. The textbook "Natya Shastra " by Bharata, the basis for the Bharata Natyam dance form presented at the ICM on Friday, has some reference to this music, and more details including an embryonic concept of raga appear in Matanga's Brihaddeshi in the 8th century. By around the 11th century Persian and Arabic influences started to enrich the music and around this time the North and South Indian streams of music began to diverge. The present lectures focus exclusively on the North Indian or "Hindustani" tradition, which will be presented at the ICM in a live concert by Ustad Rashid Khan on Wednesday.

The nature of Hindustani music evolved during the 12th to 18th centuries, partly in response to the Bhakti movement in Hinduism, in which participatory and devotional love for the divine being (rather than formal worship of God as an idealised entity) became the principal theme. Another contributing factor was the patronage of the Mughal emperors. By the 18th century the "khayal" form of music was established. It remains an oral tradition even today, despite many books and treatises on the subject, some of which have established a rudimentary notation.

In the first of these talks, the notion of raga is introduced by playing short clips of pairs of performances, by different musicians, of the same raga. The common features between the members of a pair serve to illuminate the concept of the raga, even to a complete novice. A definition can then be built up through a series of successive approximations. In its barest form, a raga is a set of notes selected from the 12 notes of the musical scale. But then these notes must be combined into patterns following certain rules. One can emulate the definition of a topological space in mathematics by saying that a raga R={S,U,T} is a subset S of notes from the musical scale together with a collection U of subsets of S and a set T of rules for combining elements of U! But art is not mathematics, so we need to add an aesthetics clause: the rules for combination must give rise to desirable results and create an appropriate mood. It is this mood that lies at the heart of a raga, which some authors consider to be a "living entity" rather than a mere combination of proportions and form. Parallel to raga, the concept of tala (rhythm) is briefly developed.

In the second talk the notion of "gharanas" or schools of music is briefly introduced (parallels with mathematics are quite strong!) and video clips used to illustrate some of the instruments and show how they are played. This is followed by a description of the structure of a typical performance, the different types of movements (introductory, slow and fast) and the complementary role of compositions and variations. The bulk of the talk consists of audio and video clips of performances by some of the leading musicians of India (many of them sadly no more) illustrating different segments and features of a performance. In selected cases the lyrics and their significance are highlighted. The association of ragas with times of day and seasons is also briefly discussed. The talk closes with a short outline of the "lighter" forms: thumri, tappa and bhajan that are usually performed towards the end of a concert.