By Bernard Holland The Russian way of making music may not dominate American string-playing style as it once did: but the emigre Markov family is, in its own way, helping to revive the Slavic tradition of big sound and broad Romantic expression. The Markovs' principle advertisement has been their son, Alexander, who won the Paganini International Violin Competition in Genoa, Italy. His progress and development have been distinctly a family affair. The Markovs - father Albert, mother Marina and their son - emigrated from the Soviet Union in 1975, bringing with them a violinistic tradition, a pedagogical zeal and three strong performing talents. Mrs. Markov plays with the New York City Opera. Her husband has carried his solo career to this country and has also brought with him his deep interest in how the violin should be taught. The prime product of this work is Alexander, now involved in a promising career, who has no teacher except his father. Young Mr. Markov's success in international competition is bringing him immediate attention in Europe. Genoa is Paganini's birthplace, and as part of his victory ceremonies there, Alexander played Paganini's own violin. Another part of the prize, a series of engagements across Europe. Eager for a New Career The younger Markov is eager to get his career under way. "I don't just want to play at every opportunity." Alexander said "Too much playing makes you mechanical. I want every concert to be an event." "I was listed as a student at the Moscow Conservatory, " he said, "but I preferred to study with my father." Albert Markov responded: "He is the easiest student I ever had, I am happy to say we have absolute contact. I did not push him into music. He decided for himself." Alexander's mother added, "He was not a child prodigy, thank goodness." has she had a part in his education? "Absolutely not. I have no talent for teaching." Mr. Markov's Violin Method Albert Markov is eager to form what he calls an "American School" of violin playing - one that takes the best of the Russian and German teaching traditions and combines them to fit this country's musical life. "The Russian school, as embodied in players like Elman and Zimbalist, has that big freedom of expression and mood, but it sometimes lacks a knowledge of musical style and an organized system of learning the instrument," he said. "The German school - Carl Flesch in particular - is more analytical and tends toward a wider, more varied repertory. Flesch seems to be asking us to understand before we feel. It is a very valuable approach, but it can go too far." Mr. Markov's method avoids the traditional teaching of hand positions and fingerings on the violin and stresses the development of a more direct sense of exactly where tones lie on the strings. Mr. Markov also breaks the art of bowing into three basic positions - another departure from ordinary teaching practices. Just as Alexander Markov is balancing his committment to an older Romantic style with the popular music of his adopted country, so his family as a whole seems to be balancing an old life with a new one. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..