Like so many of you who’ve learnt to play a musical instrument, I too was guided by my teacher to go through the hoops of the British-based music exams. We’d take successive exams each year, even though we played other music as well. A lot of my ‘other’ playing involved church music, in our São Tomé chapel and wherever in Goa our parish priest and founder of our Santa Cecilia music school Fr. Martin Fernandes took us. Even today, I have a sense of déjà vu when I visit a very remote church or chapel, and realise with a start that we had played at a feast or novena mass there in my childhood. And although the violin is not common used today in tiatr, I have fond memories of playing in a few, as also in school operettas.

But when it came to solo playing, apart from a few violin tutors (Eta Cohen was and still is a favourite with violin teachers), we spent a lot of time on “exam pieces.” Whenever in the exam hierarchy one need to study theory and “form” in music, we were directed to prescribed textbooks that addressed these, I have to say, quite technically and dispassionately. There were seen as “necessary evils” to be temporarily addressed for the sake of the exams, and then promptly forgotten.

It took a visit by the great cellist Mstislav Rostropovich (1927-2007) to Goa in 1988 to open my eyes to the importance of structure and form in music.


I was in my final year MBBS at the time. I think I can safely say that Goa has not been graced by a public concert by a musician of greater eminence than he. His visit to India created a veritable stir in musical circles nationwide as well. I know of at least one eager cellist who shadowed Rostropovich on his concert itinerary, attending every recital of his, in Mumbai, Goa, Delhi & Calcutta.

When it was announced that Rostropovich would take the time during his stay in Goa to do a little teaching, we were ecstatic. I couldn’t sleep the nights before that day, so nervous was I at the prospect of playing before someone larger than life.

But my apprehensions were unfounded, as he was such a gentle, unassuming man. He greeted us in typical Russian fashion, with a bear hug and a kiss on either cheek, and then got us started.

I remember I had chosen the first movement (Adagio) of Johann Sebastian Bach’s sonata in G minor for solo violin. He listened patiently as I played, and then he floored me with a question: “Where is the “golden point?”

He then compared a musical phrase to an arch, how each phrase has its own pinnacle, how phrases are part of a larger design, and the importance of studying a piece architecturally as it were, before proceeding to play it.

But the term he used, the “golden point”, intrigued me. His parting shot to me was an enigmatic “Find the golden point!” Did he mean in the Adagio I had just played for him? Or in general? Perhaps both.

This took place before the internet and Google, so my “searches” were confined to the limited books available to me, either my own or in the library, and asking whoever I thought might be able to shed more light on this. I did not get anywhere.

A decade or so later, things had changed. Not only was the internet firmly entrenched in our lives (although I still did not have a computer of my own), but I was now in London, and had access to the wonderful library at the Barbican Centre. One of the first things I began to look up was this “golden point”.

And as if on cue, around this time, I watched a fascinating BBC documentary on this very subject. Briefly, the “golden proportion” is at least as old as ancient Greece. The famous Parthenon in Athens utilises the template of a rectangle whose sides are in the “golden proportion of 1:1618, or 0.618:1.

This “golden ratio”, known as ‘phi’, also finds application in some (but obviously not all) music composition. In pieces where it is employed, the “climax”, or “golden point” occurs at 61.8% of its length.

And so I’ve gone back to study the piece I played for Rostropovich, the Bach Adagio from his first sonata for solo violin. It is 22 bars long, and there is a major turning point in the music at bar 13, exactly 61.8% (22 times 0.618 equals 13.596) into the work.

Coincidence? I think not. Bach’s obsession with numbers and their mystical, often religious significance and symbolism is by now well-known. New facets to his prolific output are still being discovered, as his music gets painstakingly analysed, bar by bar, phrase by phrase.

So did I finally find the “golden point” that Rostropovich urged me to seek? Or is it somewhere else? Was he speaking metaphorically? I’ll never know. But I’ll always be grateful to him for setting me upon this quest.

(An edited version of this article was published on 16 August 2015 in my weekend column ‘On the Upbeat’ in the Panorama section of the Navhind Times Goa India)