Correction Appended

In the last six years, the apartment building at 215 West 116th Street in Harlem has been sold five times, its price rising from $6,000 to more than $600,000. The fortunes of the building's tenants, meanwhile, have at best held even, and for them, even means miserable.

Once luxurious and now forlorn, long ignored but lately desired, 215 West 116th Street offers a dramatic case history of the real-estate speculation that has swept through Harlem since 1980.

The number of building sales in Harlem more than doubled in five years, to 1,131 in 1985 from 503 in 1980, according to figures compiled by the Harlem Urban Development Corporation. The average price per building climbed to period. Against such a backdrop, 215 West 116th is not the exception but the rule.

The building embodies almost a century of Harlem life - the neighborhood's passage from a failed middle-class district for whites to a diverse and self-supporting black metropolis to a crime-ridden, drug-ravaged slum to a prime candidate for the urban facelift called reinvestment by some and gentrification by others.

As Harlem's real-estate prices have soared, two alternative visions of the future have emerged, neither of them kind to longtime residents like those in 215 West 116th.

In one scenario familiar to Manhattan, the buildings being bought up will be rehabilitated and converted into cooperatives, with the affluent displacing the poor and whites supplanting blacks.

In the second, prices will so exceed the buildings' earning capacities that a new round of foreclosures and tax sales will be set off, visiting abandonment and neglect again on a neighborhood that knows both too well. Some early investors in Harlem have already pulled out.

The 38-unit building at 215 West 116th has been sold sequentially for $6,000, $190,750, $216,492, $305,000 and finally $613,000 - a cumulative increase of 10,000 percent. Its various owners, meanwhile, have been cited for 142 building code violations dating to 1977, and they owe $3,000 for emergency repairs made by the city since 1983, according to records in the Department of Housing Preservation and Development.

Throughout this period, few major repairs have been made. Residents point to rats, leaky ceilings, corroded pipes and broken drains. They tell of their confusion at a series of owners they rarely if ever met - owners who frankly say that their interest in the building was not large-scale renovation but rapid resale at a profit.

''No matter who buys it, it's all the same,'' said Alfred Price, a 60-year-old printer who has lived in the building for six years. ''Nobody changes it. They come out and make a list of what's wrong, tell you, 'We'll send somebody.' But they never do. And six months later, it's sold again.'' From Stylish To Squalid Four auburn granite pillars flank the entrance to 215 West 116th, and above them rests a bas-relief panel that announces the building as the Jerome. There are marble floors in the lobby, moldings in the shape of floral strands and a wrought-iron banister that winds up seven stories.

These details are jarring reminders that 215 West 116th, like much of Harlem, was built for comfort. The building was completed in 1901, the peak of the construction boom that was intended to turn Harlem from a sylvan retreat to which doctors dispatched respiratory patients to a kind of suburb-in-the-city for the white middle class.

But the whites never arrived in sufficient numbers, largely because of delays in building the Lenox Avenue subway. And so, in desperation, landlords began renting to blacks, although at double the prices that whites paid for comparable apartments elsewhere in the city.

Between 1900 and 1920, the black population of Harlem quadrupled, and by 1930 blacks owned Harlem property worth $60 million. With discrimination closing off many neighborhoods and most suburbs, Harlem became by necessity, as well as by choice, the home to a cross-section of black America -wealthy as well as poor, professionals as well as unskilled laborers.

''It is not a fringe, it is not a slum, nor is it a 'quarter' consisting of dilapidated tenements,'' the poet James Weldon Johnson wrote of Harlem in 1930. ''It is a section of new-law apartment houses and handsome dwellings, with streets as well paved, as well lighted and as well kept as any in any other part of the city.''

The older tenants in 215 West 116th remember when both their block and their building typified a stable Harlem.

''This was a beautiful place when I got here, really,'' said Lois King, a 76-year-old widow who has lived in the building 42 years. ''In the lobby we used to have throw rugs, chairs, mirrors. We had an elevator operator.''

''It was like a palace,'' added Mrs. King's friend, Willie Campbell, who moved into the building in 1940. ''We had iron gates on the front door. You weren't allowed to sit on the stoop. The super took out your garbage.''

Anything from a furniture showroom to an optometrist, meanwhile, could be found on West 116th Street. ''We had drug stores, variety stores, hardware stores,'' Mrs. Campbell said. ''You didn't have to go to 125th Street for anything. It was all right here.''