But for all his popularity, most of the works for orchestra-without-piano are heard in the concert hall only infrequently. For four decades or so after the Second World War, it seemed that "serious" music had to be atonal and could be written only by composers with degrees in maths from American universities or computer science from French research institutes. That made Rachmaninov deeply unfashionable; all those gorgeous melodies, that sumptuous scoring, couldn't be good for you, couldn't command respect. But tastes are less prescriptive these days, and "Hidden Perspectives", the major Rachmaninov festival which begins at the Royal Festival Hall tomorrow evening, will show us something of what we've been missing.
"Hidden Perspectives" intends to live up to its name. It will, of course, feature core Rachmaninov, with three of Russia's most dazzling keyboard lions - Yevgeny Kissin in the Second Piano Concerto tomorrow night, Arcadi Volodos in No 3 on 11 May (don't miss it; Volodos' Third at the Proms last year was one of the most thrilling things I have ever heard), and Mikhail Pletnev in the Paganini Rhapsody on 16 May. (All three works featuring the same forces are also in Symphony Hall, Birmingham, tonight and on 10 and 17 May.) But it's not all mainstream: the festival directors, the conductor/ pianist Vladimir Ashkenazy and the South Bank's head of classical music, Amelia Freedman, will also be shining lights into little-explored corners.
Tonight's concert, for example, concludes with a real rarity, the resplendent choral symphony The Bells, which sets texts by Edgar Allan Poe. Rarer yet, the concert on 11 May begins with the tone poem Prince Rostislav, composed in 1891 while Rachmaninov was a student in Moscow. And, rarest of all, on 16 May there is a concert performance of Francesca da Rimini, one of Rachmaninov's three operas - all of them thoroughly neglected.
Ashkenazy feels strongly that the man has not had his due. "People know Rachmaninov basically as the composer of the Second - and now especially the Third - Piano Concertos. First of all, they are very good compositions - people never think of that; they just think it's lots of good tunes, great piano-playing. But when they listen to the symphonies or Symphonic Dances or The Bells, there is no more piano-playing, there is nothing to distract you from the fact that he was a great composer. Let them just listen to the idiomatic orchestration, the tremendous harmonic inventiveness and the sweeping melodies. People started realising he was a great composer only a couple of decades ago, even less than that. They always thought he was a kind of sentimental piano composer. Far from it! He had a lot to say. And what he said is of timeless value."
That message still hasn't got across to everyone; you still hear the view that, for example, the Second Symphony (11 May) is a rambling piece of orchestral self-indulgence. Ashkenazy will have none of this, and recalls his own student encounter with the piece. "Rachmaninov could put his music into a well-defined and eloquent form. His Second Symphony is very well put together; the compositional form is tremendous. When I heard it for the first time, in Moscow, I went to see the orchestra backstage after the concert (I had many friends in the orchestras in Moscow) and I said: `What a fantastic piece!' They looked at me with a perplexed expression and said: `Look, we think it's the best Russian symphony.'"
Rachmaninov left Russia shortly after the Revolution and never returned, though his music never fell from favour there. He lived first on a small estate in Switzerland, from where he toured as conductor and virtuoso pianist, squeezing in his composition between the engagements that fed him. And in 1935 he settled in the United States. But every bar of the music portrays his allegiance to his native land. Ashkenazy, another emigre Russian virtuoso, savours his home country in that sound. "Rachmaninov combines, in his expression, various Russian characteristics. I find his music could be called the most Russian of all Russian composers. It's a dangerous thing to say, and it's very much a generalisation. But I can support it by the fact that it has generosity and fatalism, it has the black earth and idealism, it has the eternal elevated feeling about it and yet it also has the Russian abandon. It has so many qualities that you find in one or other Russian composer, but never all together as in Rachmaninov's music. To me, he has this synthesis of everything in the Russian mentality, in Russian music."
Yet ask your average classical-music enthusiast about Russian music in the 20th century and the chances are he'll talk about Prokofiev and Shostakovich, and maybe Scriabin. Rachmaninov takes his place, in this view, as an eccentric loner, a stylistic anachronism. But there's an entire tradition that has somehow been lost from view, represented only by Rachmaninov's toe- hold on the repertoire. Now that the CD is familiarising us with neglected masters such as Medtner and Grechaninov, who also left Communist Russia and failed to re-establish their reputations in the West, we can see Rachmaninov as being bang in the middle of an alternative history of Russian music - one that relishes luxury of thought and texture.
Ashkenazy blames Lenin for its elimination: "Actually, Prokofiev's Romeo and Juliet has very luxurious moments and the Fifth Symphony, too - I don't think it disappeared totally from the Russian mentality. But life after the Revolution was very different in Russia. There was more tragedy and drama and darkness and depressiveness. Music reflected what life was like. That didn't prevent some composers giving a lot of generosity from their inner world, but the luxuriousness disappeared because life wasn't so kind. It was a very difficult time for the country."
Rachmaninov the composer was one of the best-known musicians of his day. Rachmaninov the man was a different matter. He was reputedly stand-offish to a fault - Stravinsky, indeed, described him as "a 6-ft scowl". But then Stravinsky himself was a mean, petty character, "made of angles", in Nathan Milstein's equally memorable phrase. He may have resented the sheer open-heartedness of Rachmaninov, who came to the rescue of impecunious friends again and again and again. Ashkenazy sums him up. "He was a very good person. He didn't say much: he was very reticent. He didn't talk about his compositions - he didn't like to. And being a very reserved man, generally, in life, he was incredibly generous and open in his music. It's very interesting - as if it was his release. His music was his inner life, and he gave it to everybody."
`Hidden Perspectives: Rediscovering the Music of Rachmaninov', Royal Festival Hall, SBC, London SE1, further details from the box office: 0171- 960 4242, website: www.sbc.org.uk, tomorrow to 23 May. Symphony Hall, Birmingham (0121-212 3333) tonight, 10 and 17 May