Of course, given the chance to travel in Dr Who's Tardis time machine, it would be nice to look in on the 1930s, when such groups as the Busch, Pro Arte, Léner and Budapest were at their peak. But in the euphoria that followed the Second World War, something remarkable happened in the rarefied sphere of the string quartet. Ensembles emerged – the Smetana of Prague, the Amadeus of London, the Quartetto ltaliano, the Hollywood of the American west coast – that played with a tonal clarity and a technical skill not previously heard. Although in Cold War days it was unknown to listeners in the West, the Moscow Philharmonic Quartet was cut from the same fabulous cloth. lts 1945 founders were Rostislav Dubinsky, Vladimir Rabeij, Rudolf Barshai and Mstislav Rostropovich (soon succeeded by Valentin Berlinsky). In 1947, the year of the group's first interaction with Dmitri Shostakovitch, a change of second violinist brought in Barshai's wife Nina. Mozart recordings show that the ensemble was of first-class quality, but in 1952 Nina Barshai was replaced by Jaroslav Alexandrov. ln 1953 Rudolf Barshai moved to the short-lived Tchaikovsky Quartet, ceding his chair to Dmitri Shebalin, son of the composer Vissarion Shebalin. In 1955, under the new name "Borodin Quartet," the formation of Dubinsky, Alexandrov, Shebalin and Berlinsky was allowed to visit East Germany and Czechoslovakia in the first of many foreign tours.

With a repertoire founded on Borodin, Tchaikovsky and Shostakovitch, a sprinkling of Viennese classics and individual works by composers such as Myaskovsky, Shebalin, Vainberg, Szymanowski and Stenhammar, the Borodin Quartet became the most familiar Russian ensemble in the rest of the world – the more rugged Beethoven Quartet, which kept the same personnel from 1923 to 1964 and toured no farther than Czechoslovakia. In 1974, when Alexandrov had to resign from the Borodin Quartet owing to illness, Andrei Abramenkov came in as second violin. In 1976, when Dubinsky emigrated, Mikhail Kopetman became leader. The next two decades saw the Borodin concentrate on the Beethoven and Shostakovitch repertoires – candlelight performances of the latter's Fifteenth Quartet were especially notable. When, in 1996, Kopelman moved to the Tokyo Quartet and Shebalin retired, their replacements were the outstanding Armenian violinist Ruben Aharonian and the superb violist Igor Naidin. Finally, in 2007, Berlinsky made way for the prize-winning Vladimir Balshin.

What strikes one most forcibly about the "new" formation is its prowess in the Viennese classics. While the Borodin Quartet always played the occasional piece by Haydn, Mozart, Schubert or Brahms and gradually concentrated more on Beethoven. In the Dubinsky era, such music suffered from the leader's somewhat narcissistic style; and in the Kopelman era, while one can recall memorable performances of the classics, the style could be too heavy and self-conscious. Interpretations seemed to be policed meticulously by Berlinsky, so that in concert one encountered little details which one recalled from innumerable previous performances. One simply cannot envisage the earlier personnel performing Schubert and Brahms with the straightforward enjoyment to be seen and heard on this programme. The tonal sheen of the ensemble remains, but the musical approach has been lightened and refreshed. In conversation, Aharonian freely admitted that, having been a soloist, he took something like five years to come fully to terms with quartet playing. His success may be gauged by the dazzling way in which the present line-up plays Haydn, a world away from the exotic style imparted to the Lark, Op. 64 No. 5, by the Dubinsky-led group.

There is no Haydn here, but there is the similarly joyous Schubert E flat, a favorite in the past with both the Smetana Quartet and the Quartetto ltaliano. Written for domestic use in November 1813, when the composer was not quite seventeen, it was his eighth quartet and his most skillful so far, although unusually he elected to have all four movements in the same key. Schubert himself would have played the viola in home performances, and the music shows that he knew the music from the inside: the texture is transparent, the balance among the voices excellent. A fairly solemn Allegro moderato is followed by a brief, bright Scherzo with a poignant Trio, an affecting Adagio and a delightful finale in which the players can kick up their heels.

Next on the program is a masterpiece, one of those frustrating unfinished torsos that we encounter from time to time in Schubert's repertoire. In December 1820 he began a C Minor Quartet; but having achieved a dramatic Allegro assai and progressed forty-one bars into an Andante, he laid the work aside, never to return to it. The one completed movement is in the repertoire of every professional quartet, under the title Quartettsatz.

A great admirer of Schubert was Johannes Brahms who, for years, labored under a kind of paralysis when it came to writing quartets. The example of Beethoven was too daunting, and Brahms destroyed goodness knows how many quartets before allowing the two of Op. 51 to be published. Completed in the summer of 1873, the A Minor is the more lyrical and autumnal of the pair. The Hungarian-style episode in the Andante moderato and distinctly Magyar atmosphere of the vigorous Finale are tributes to Brahms's close friend, the Hungarian violinist Joseph Joachim, whose ensemble gave the premiere. As an encore, the Borodin Quartet plays the Agitato from Brahms's bucolic Third Quartet in B flat, Op. 67, of 1875. This lovely movement, which fulfills the function of a scherzo, pits the bronze viola tone of Igor Naidin against the other instruments, which are muted. Brahms confided to the singer and conductor George Henschel that it was "the most amorous, affectionate thing" he had composed.

© Tully Potter/ICA