IT is hard to imagine Elisabeth Leonskaja doing anything trivial.

Reading a trashy magazine at the dentist's, watching naff telly on an overnight flight - the image just doesn't fit. Leonskaja is unrivalled doyenne of the Russian old school and an awesomely dignified persona. Born in Tblisi in 1945, once a regular duet partner of Sviatoslav Richter, her monumental performances of core 19th-century repertoire link us with a pianism of the past in which musical gravitas eclipses anything as potentially trite as flash technique or quirky presentation.

There is vast heritage to her playing but also clarity: in Schubert, in Beethoven, in Chopin, in Brahms, she strips away all gloss and ponders the music in deepest terms. Her performances don't make for easy listening, but then this isn't always easy music.

In person, too, Leonskaja is overwhelmingly un-trivial. She arrives in the lobby of a swish London hotel looking unhurried and stately, majestically old-world in black velvet and pearls. Her conversation is like her playing: no small talk, all substance.

Next week she brings two programmes to Scotland: Shostakovich's Second Piano Sonata and Piano Quintet with the Emerson Quartet on Sunday, then not one but both of Brahms's epic piano concertos with the Scottish Chamber Orchestra. She responds to my questions about the programmes in careful, heavily accented English. Yes, the Emersons are wonderful musicians; yes, she is looking forward to playing with the SCO, an orchestra she has long admired but has never worked with.

Does she enjoy new collaborations? "Of course," she replies. "We build something together: that is interesting. It takes concentration and much listening." Is it possible to achieve a profound result in just a couple of rehearsals? "Ah, I can do it with one rehearsal. This is called experience."

Leonskaja brings more experience to the stage than almost any other living pianist. She gave her first public concert at 11, studied at the Moscow Conservatory and forged that lasting friendship and musical partnership with the legendary Richter. She left the Soviet Union in 1978 for Vienna, but is unequivocal in stating that her roots are fixed in Russia's musical culture.

She knew Shostakovich personally and smiles warmly when I ask what kind of a man he was. "He was very friendly," she says, "and very encouraging to students. We went to his home and played for him often. I knew him quite well. He was modest. He was always being the gentleman. I can't say that I play his music differently because I knew him, but I'm Russian and this music is in my blood."

Then there is the herculean prospect of both Brahms concertos on one night. I attempt a slightly clumsy question about the contrast (is it a jolt to go from the troubled intimacy of Shostakovich chamber music to the grandeur of large-scale Brahms in just a few days?) but Leonskaja gently cuts me off.

"Listen, I'm not a student. It's not the first time that I play the concertos together. I know the distance of the music, when to give more, when to give less. It's true that you must have experience in each piece before you play them together, but my thinking was that if Leipzig Gewandhaus Orchestra can play all four Brahms symphonies across two nights, why can't I play both concertos?"

There is the small matter of physical stamina, I suggest. These are mighty, muscular works, two great pillars of the romantic repertoire; surely it must be tiring to play one after the other? She gives a gloriously slow Russian shrug. "Yes it is, but this is not a holiday."

Leonskaja softens most when she talks about Richter. "I can't write or express enough about him," she says. "The feelings I have about him are so deep down that I can't sum them up. But what was so special was that although I was a student and he was so great, he was always modest, always friendly. He didn't really teach me: we just discussed a lot. We played Mozart, Grieg. I remember him questioning why I was so businesslike about it all. He wanted me to play from the heart."

Unsurprisingly, she doesn't have much time for the classical music industry. She has recorded relatively little over her long career. "Concerts are necessary," she says, "not photo shoots and such. Maybe I'm a romantic, but I think that there is a special role for concerts. During the day people are working. In the evening, when it's dark, that is a time for hearing music."

The only name she mentions when we discuss today's generation of pianists is the whizzkid Daniil Trifonov, in some ways her descendant in the Russian school. She recently went to hear him in Vienna and afterwards found him backstage and said "thank you, that was wonderful". (Trifonov has had his share of praise in the past few years but Leonskaja's hard-won approval must have been worth gold.) "He is so exciting, so open," she explains. "Many pianists love themselves a bit too much; this is not the case with him. The music takes him."

It's a remark that equally applies to Leonskaja herself, of course. She tells me about her country house in Austria, nestled in the Alpine foothills between Vienna and Graz, where she has three pianos (a newish Yamaha, a Schiedmayer and a 1907 Blüthner) and where she says she does her best work.

"It is green there. I do a lot of walking. I'm not an alpinista, you understand, but I like to walk. My spirit is more open there than in the city; my heart can be very quiet among the hills." This is an image of the great Leonskaja that fixes easily in my head.

Elisabeth Leonskaja plays Shostakovich with the Emerson Quartet at Glasgow's City Halls on Sunday and Brahms with the Scottish Chamber Orchestra at Edinburgh's Usher Hall on November 13 and Glasgow's City Halls on November 14.