The Best Teachers I Ever Had

The number of important, or influential or memorable teachers we have in life is probably quite limited. In fact, I have this sinking feeling that there are quite a number of people that may have never had a significant teacher. Other than their parents, for better or worse. Mine must have been ok, because as I recall, I arrived in Grade 1 already able to read. But that aside, here is a short list of teachers that made an impact on my life.

• In Grade 10 I had a class with the school principal, whose name I forget. The class was social studies or something. But it was important for two reasons: first, I remember him sitting on his desk, trying to give us some life advice which boiled down to: "Don't be mediocre!" The second reason was that he taught us the origins of the First World War so brilliantly, laying out all the over-lapping alliances and mutual defence pacts and so on, that when he said, "and then Archduke Ferdinand was assasinated" I nearly gasped because he had set it up so we could grasp the consequences. Some excellent teaching and that is rarer than you would think.
• The next outstanding teacher was the newly-minted PhD hire who taught Philosophy 100 in my first year at university. I doubt if I had ever previously encountered someone with a really trained mind. I won't mention his name, but that was his first year teaching and he did a brilliant job. He continued to teach at that same university for a few decades. The class was very small for a first year course, only 20-25 students. He would assign some reading and then in the next class we would argue about it. Since he was the best arguer, he won all the arguments! That was what got me hooked on philosophy, something that guides me to this day. I recall that I got A- minus on every essay assignment. I also recall that one day he said that only God got A+, so I guess that was pretty good. This was before the ubiquitous grade inflation.
• The next outstanding teacher was maestro José Tomás with whom I studied guitar in Spain for a year when I was twenty-three. Today, I barely remember a thing he said! The way he taught was, after listening to you stumble through the piece, he would quietly pick up his guitar and either play it from memory or read it off your score, to show how it should be done. One day I remember I was playing a Spanish vihuela piece and one phrase came out just right and he said, "ah."
• I had a couple of good teachers at McGill when I was there, both in theory, oddly enough. One taught form functional analysis and I learned that I could never use any of those forms! Another taught fugue, the most advanced counterpoint course at McGill and, again, oddly, the only counterpoint class I have ever taken. I tested out of the other undergraduate counterpoint classes by doing a little studying on my own. What I really remember about the fugue class was a couple of things. The first, at the very first class the instructor said, "lots of people have written fugues in one form or another over the last few hundred years, but the only composer we are going to look at is Bach." There really is no other form, nor composer, of which/whom that could be said. We spent quite a bit of time struggling to solve the problems of invertible counterpoint. Briefly, when intervals invert some dissonant ones become consonant and vice versa. If you use only thirds and sixths you will be ok. We were doing invertible counterpoint with two voices, of course, the minimum. Then one day we got to the Art of Fugue and it was explained to us that Bach wrote entire four-voice fugues, all four voices of which could be inverted!!! I nearly fell off my chair. I can't think of any other composer who even attempted that, by the way. They are called "mirror" fugues.
• Finally my last memorable teacher was not my teacher, but my colleague, the extremely fine violinist Paul Kling, who was famous, in Vienna, from when he was nine years old. We met when I was in my thirties and he was in his sixties. I remember the first time we read anything together, a Giuliani sonata for violin and guitar, afterward he casually asked about certain specific measures and phrases where I had gone astray. We shared a number of concerts and in one he decided to play the Bach Chaconne. As I was making up the program I asked him how long his performance would take. His answer: "Thirteen minutes and forty-three seconds." And I didn't doubt it for a minute. Paul once said to me that every great violinist of the century was either a Russian Jew from the Caucasus, or studied with one.

I don't have a recording of his of the Chaconne, but here is a violinist with a similar approach, Jascha Heifetz.

Let's have another one. Here are two right side up fugues followed by their inversions: