There are two famous silences in the history of classical music: those of Rossini and Sibelius. Rossini's, which lasted nearly 40 years, was a worldly, cosmopolitan silence, much of it spent in Paris, during which time he co-invented tournedos Rossini. Sibelius's, which lasted nearly 30 years, was more austere, self-punishing and site-specific; and whereas Rossini finally yielded again to music, writing the late works he referred to as "the sins of my old age", Sibelius was implacable. He fell silent, and remained silent.

I first got to know his music almost half a century ago in recordings by Anthony Collins and the London Symphony Orchestra. The sleeves of those old Ace of Clubs LPs featured black-and-white photos of appropriately Nordic scenes: snowscapes, fjords, towering pine trees, and so on. I think these images were mixed up with my early appreciation: there was a cool yet turbulent melancholy to them which I also found in the music, and which seemed to harmonise with my unrestful late-adolescent soul. But the music has stayed with me all my life, and, though generally uninterested in the lives of composers, I make an exception for Sibelius. I admire his mixture of puckish humour and obdurate high principle. During a conducting tour of England, he said in one post-concert speech, "I have plenty of friends here, and, naturally, I hope, enemies." He consoled a young colleague for a bad review with the words: "Always remember, there is no city in the world which has erected a statue to a critic." And during his final, silent years—he lived to the age of 91—he noted at one point in his diary: "Cheer up! Death is round the corner." So for years I have wanted to visit Sibelius's house, 40 kilometres north of Helsinki, a region of lakes and pine forests and towering silver birches. For me it has always been a place with a dual, divided reputation: for both creation and destruction, for both music and silence.

Most artists' houses have had previous and subsequent owners. In some you feel only a vestige of the artist's presence; others have had their spirit crushed by museumification, by curatorial intervention and the accretion of study centres. The Sibelius house is one of those rare places where no other presence interferes with the genius loci: it is a house of, for, by, with and about Sibelius. He bought a one-acre plot at Järvenpää near Lake Tuusula in 1903. There was already an artists' colony here, but Sibelius was as much attracted by the empty landscape in which he loved to walk, by the swans and geese passing overhead.

In September 1904 he moved his family into the still unfinished house which he named Ainola (the suffix "-la" meaning "place of") after his wife Aino. Here they brought up their five daughters (a sixth died in infancy). Here Sibelius composed most of his major works, from the violin concerto of 1905 to the last five of his seven symphonies, and here he spent three decades not publishing a single note. When, in 1957, death's long round-the-corner wait ended, he was buried in the grounds; Aino lived on here for another 12 years; their joint tomb, a six-foot square low bronze slab—which has the monumental inevitability of the later symphonies—was designed by their architect son-in-law Aulis Blomstedt. The five daughters, old themselves by the time of Aino's death at the age of 97, sold the house and contents to the Finnish state in 1972, and it opened as a museum in 1974.

The house was designed (for no charge) by an architect friend, Lars Sonck, in the "National Romantic" style. It is essentially a grand log villa built on a heavy stone base and clad with weatherboard; in the grounds Aino designed a sauna house (with laundry room), laid out vegetable and flower gardens, and planted fruit trees, some of which still survive. Inside, the main rooms have heavy pine beams and those typically Scandinavian high stoves finished in glazed brick or tile. There is the feel of solid, continuous living to the place. Even the Sibeliuses' two housemaids were solid and continuous: both lasted nearly 60 years.

Almost nothing has changed (though Sibelius's original manuscripts have been removed to the national archives); and the place which once held Sibelius and his music still holds them both. The composer's white summer suit rests on a hanger in his study; his broad-brimmed Borsalino and stick are on a nearby table. Here is the Steinway grand he was given on his 50th birthday (though he composed in his head, not at the piano); there is a run of the National Geographic magazine covering the last five years of his life. On the Russian oak desk at which he worked from the time of his marriage in 1892 lies the wooden ruler Aino carved for him, with which he ruled his scores; also, an empty box of Corona cigars, and an elegant Tiffany photo frame, containing a portrait of Aino, through which the light streams. Open on the desk is a facsimile score of his greatest symphony, the Fourth. But the homely is never far away: in the kitchen, screwed to the wall, is an apple-coring machine which Sibelius brought back from one of his trips to America. Made of black cast iron, it is a Heath Robinson contraption of prongs, screws and blades which will peel, core and slice your apple at the turn of a handle. From the same trip he also brought his wife a Tiffany diamond; but it is the apple corer that sticks in the mind.

Reminders of his fame are everywhere, from an enormous laurel wreath (now much dried) which once encircled him on a notable birthday, to the multiple commemorative images made of him. Every time a plaster medallion of Finland's greatest artist was cast, he was given a personal copy, and most seem to have ended up on his walls. But genius had to co-exist with family life, and it was not always easy. "Our souls are worn down through continuous contact with one another," Sibelius wrote in his diary. And: "I am building a studio for myself—at least one. Next to me are all the children whose babbling and pranks ruin everything." But he never did build himself a studio; instead, he relocated his study upstairs and forbade the noise of any instrument while he was in the house. The children had to wait until he had gone for his daily walk to do their music practice.

The house, though comfortable and practical, is by no means extravagant. The visitor might reasonably conclude this was just a summer home, used by Sibelius to get away from the city. Not a bit of it. For most of his life he was in serious debt. At first these were a young man's debts, caused by his taste for high living: he was a committed drinker who would often go missing for days (but could always be located in "the best restaurant serving oysters and champagne"). And though the drinking was lifelong, and his tastes remained luxurious—that white suit came from Paris, his shoes and shirts were made for him in Berlin—this was not the reason why Aino kept chickens, laid out a vegetable garden, planted fruit trees and schooled her own children. Sibelius took on a huge debt when he built Ainola, and wasn't able to clear it for more than two decades. The website sibelius.fi contains a terrifying graph of his indebtedness for the period 1892-1926: it peaks at the equivalent of €300,000 today.

But, you will say, he was a world-famous composer. His music was constantly played; he was feted everywhere, not least in Britain—"the land without chauvinism", as he called it (we are to presume he was only talking musically). Constant Lambert, in his 1934 study "Music Ho!", extravagantly called him "the most important writer [of symphonies] since Beethoven". Yale gave him a doctorate in 1914. How could such a man not afford to pay off the debts on his house? How come he was only saved from bankruptcy in 1910 by the intervention of generous patrons?

The answer lies mainly in history and the curious laws of copyright. When Sibelius started composing, Finland was part of the Russian empire, and Russia was not a signatory to international copyright treaties. So—apart from performing fees (and he often conducted)—Sibelius's income came from selling his work outright to music publishers. In 1905, for instance, he signed an agreement with Robert Lienau in Berlin to supply "four major works" in the coming year, the first of which went to pay for the sauna house Aino designed. Finland gained independence from Russia in 1919, but didn't sign the Berne Convention on Copyright until 1928—by which time Sibelius had entered into his silence.

And in any case, you couldn't retrospectively claim copyright on what you had previously sold outright. To take the most egregious example: Sibelius composed his famous "Valse Triste" as part of the incidental music to "Kuolema" (1903). The following year he made two arrangements of the piece, each of which he sold outright for 100 marks (a little less than €3,000 in modern money). This may have seemed canny at the time. But "Valse Triste" was to become the best-known piece of music Sibelius ever composed; in the 1930s it was estimated to be the world's second most-played tune after "White Christmas"—yet from all the recordings and playings and sheet music Sibelius didn't receive a cent. He survived with the help of donations, national collections and a government pension; in 1912, he even thought of emigrating, whereupon the government raised his stipend and there were relieved newspaper headlines reading "Jean Sibelius remains in Finland". He finally became solvent at the age of 62, in 1927, and was eventually to die a fairly rich man. But it is an instructive story at a time when copyright is once again an issue, music piracy rife, and "Don't-be-evil" Google has illegally digitalised hundreds of thousands of books still in copyright.

There is something heroic about those writers and artists who choose silence when it would be easier to supply profitable titbits to an adoring audience. Sibelius struggled with his Eighth Symphony for many years. He was constantly badgered about its progress; conductors and concert impresarios begged a foretaste. He always refused. Some believe that in the decades he worked on it he had finished only one movement. Sibelius himself claimed that he had "completed" the Eighth "many times"—though perhaps only in his head. In any event, at some point in the early 1940s, he piled the manuscript sketches of the Eighth plus a large quantity of other unfinished or (in his view) inadequate works into a big laundry basket, took them to the dining room, and, with Aino's help, began to feed them into the stove. After a while, Aino no longer had the strength to watch, and left the room, so she was unable to confirm exactly what had gone into the flames. But she reported that afterwards, "My husband became calmer and his attitude was more optimistic. It was a happy time."

The stove, made at the local brickworks, is chunky and rustic, with a glistening green finish (Sibelius saw colours as keys: green was F major, yellow D major). I bent down and tried to open the small steel doors, to see exactly where all that potential music had turned to ash. But they were screwed shut—not, it transpired, out of any piety, rather because in the years of Aino's widowhood the stove had been converted to electricity. Electricity also powered the library's shiny walnut-cased radiogram which the head of Philips gave Sibelius in the early 1950s. This was the last of a series of such instruments on which, all through the three decades of his personal silence, music had come into Ainola from Berlin, London, Paris and New York. Or from just 40 kilometres away. At the exact time Sibelius lay dying, on September 20th 1957, the Helsinki City Orchestra was playing his Fifth Symphony under Sir Malcolm Sargent. Naturally, the concert was being broadcast on Finnish radio, and Aino later recalled that she had been tempted to turn on the radiogram, in the hope that her husband's music might bring him back to consciousness; but in the end, she decided not to.

In his last year, Sibelius wrote in his diary:

The swans are always on my mind, and they lend magnificence to life. It is strange to note that nothing in the whole world, not in art, literature or music, has such an effect on me as these swans and cranes and bean geese. Their calls and their appearance.

If you stand in the grounds of Ainola today you are more likely to hear the steady thrum of traffic from a nearby road than the honk and wail of any passing wildlife. But the place retains its magic as a meeting-point of high art and practical living, of musical fame and apple-peeling machines, of conjured sounds and final silence.

Ainola is open May 2nd to September 30th 2012, 10am-5pm, closed Mondays and June 22nd. ainola.fi