Music and Mathematics

Music and Mathematics Ramesh Gangolli Quite often, during the course of the small talk thatwe all engage in at parties, I am asked about what I do. When I respond by saying that I am retired, they ask about what I did while I was working, and how I spend my time in retirement. I try to respond guardedly, but truthfully,that Iworked as amathematician professionally, but also had an interest inmusic, and that I continue to pursue both my interests at present. A common response from my questioner is along the lines of "Oh yes, of course music and mathematics are related, aren't they?" As is common with small talk, the subject is soon dropped, and I usually do not seek to pursue itmuch further.Once in a while, the conversation proceeds to a slightlymore detailed level, but often I find thatmy ques tioner is thinking that the supreme example of the connection between these subjects istied up with the process of counting matras^ in various talas,2 and its application in arriving accurately at the sam$ in a perfor mance. Usually the conversation ends there, but the exchange usually stimulates further reflection, and I have often tried to understand for 52 PerspectivesofNew Music myself, however tentatively, how the two subjects are related and why. What follows is a modest effort to share some of my thoughts, and I offer them humbly. As every student ofmusic knows, there is surely a connection between counting and musical performance, of the kind mentioned above: we undoubtedly need to understand the structure of the different talas, their divisions into the different vibhagas4 etc. in order to have a basic vocabulary and control ofthe material with which we work asmusicians, whether in theoretical study or inperformance. However, it seems tome that this connection is at best at a superficial level. Understanding the basis of this kind of counting, and acquiring the ability to use it in per formance is an important technical prerequisite, but no more. To think that one can become a good musician by mastering the technique of such counting is akin to thinking that one can become a good writer by learning all thewords in the dictionary, or a good painter by learning all the properties of various colors of paint. Acquiring these tools is a neces sary step, but much more is needed for reaching artistic goals. The connection between music and mathematics lies at a much deeper level, and ismuch harder to understand and describe. The two activities are similar in three respects: 1. They require substantially similarmental attitudes and intellectual processes for the acquisition of knowledge and skills. 2. The strategies used in the creative aspects of both activities are remarkably similar in spirit. 3. When one is engaged in either activity one is fundamentally oriented towards one's inner self (3i<-t^