A line of frozen stone rope runs its way around the warm red sandstone of Hospitalfield House in Arbroath.

Around the mass of the building it goes, circumnavigating towers, battlements and crenellations. Inside, too, coils of rope have been carved into mantelpieces and the grand central staircase.

This maritime detail came from the 19th-century mind of Patrick Allan Fraser, whose dream of what this imposing (if perhaps little known) Angus country house could be is this week inspiring a very contemporary Scottish show in one of the most prominent international locations for art. Allan Fraser first saw the rope detail in Venice when he took the Grand Tour of Europe. He brought it back and applied it to the ambitious project he built in Arbroath from 1850 to 1890 when, after becoming man of the house after marriage to the wealthy Elizabeth Fraser in 1843, the building was transformed into the impressive pile it is today.

And the rope he built into his house continues to run. The design is a visual emblem on the publicity material for the major show that Hospitalfield is staging at the biggest contemporary art show in the world, the Biennale of International Art in Venice, beginning tomorrow. There, at the Palazzo Fontana on the Grand Canal, Hospitalfield, led by director Lucy Byatt, is staging a show devised by Glasgow-based contemporary artist Graham Fagan in collaboration with Scottish composer Sally Beamish, reggae musician Ghetto Priest and music producer Adrian Sherwood. The show, at a classic Venetian palace, is primarily inspired by Robert Burns's The Slave's Lament, and is the official Scotland + Venice exhibition this year.

Much will be reviewed and reported from Venice this coming week; but what of this house in Arbroath where the Scottish show been planned and devised? Byatt, who I meet on a frigid, cold day in late March, has been director of the house and its programme since 2012. She and its board are in the process of turning the striking, large but architecturally challenging main house, with its many acres of land, into one of the most interesting and, when a multi-million pound capital programme is completed, state-of-the-art artistic locations in Scotland.

The show in Venice will therefore offer more than a stage for displaying Scottish contemporary art at the biggest festival of its kind; it will also be a very timely international presentation for Hospitalfield itself.

Allan Fraser was not of aristocratic birth himself, but was intelligent and charismatic, and an artist who was taught by Robert Scott Lauder at Edinburgh College of Art.

"He toured Europe so it was inevitable he visited Venice," Byatt explains. "And one of the things we noticed very quickly on our site visits to Venice - absolutely knitted into the architecture of Venice - is the rope carved into stone and wood. Hospitalfield has this same rope carved all the way around it; and this is also a port town with a harbour that was very important for the economy. Of course Allan Fraser was inspired by his Grand Tour, he lived in Rome for a time and was president of the Royal Academy in Rome in the latter part of his life, so he would have visited Venice many times."

As we talk, a busy group from the National Association of Decorative & Fine Arts Societies looks around. This is a building with several identities. It is a remarkable place of artistic heritage in itself. The house holds open weekends at certain times of the year for the public to discover its extraordinary architectural details, turrets and objets d'art. There are acres of paintings and walls of books. Allan Fraser was fascinated by the Arts and Crafts movement, and worked with local craftsmen to create beautiful interiors, baronial exteriors and a very large, lofty ceilinged, highly decorated Picture Gallery.

The couple had no children, and on Allan Fraser's death in 1890 the house and estates, collections and all, were left in trust. The couple wanted the house to become a residential art school - and it is still a place of artistic residencies and small-scale artistic happenings. It is also a venue for hire, which counts for 50% of its income, although it now also has a three-year funding deal from Creative Scotland.

Byatt says the Venice show is coming at a crucial time for the building. With architects Caruso St John, Byatt and the company's board want to build new studios both for artists residencies and for visiting groups to stay, and conserve the studios already in place (including Allan Fraser's own, with a lambent natural light and a huge fireplace). New facilities for a digital editing studio and ceramic studio will be added. The project will also conserve the old house and renovate the fernery - the only one on the east coast - in the walled gardens. With its location amid gardens in Arbroath, but close to the heart of the town, the sea and the train station, it is not hard to imagine an upgraded and expanded house as an attractive place for artists and cultural bodies to live, for a time, and work.

"Venice is important," Byatt admits, "especially for an organisation that is about to embark on such an important project, and for a place that is [seen to be] on the margins. Our future plan is to conserve the existing architecture [at the house], look after our collections, but add things to make the site work better for us. And so we have to raise quite a lot of money to do that."

The last Biennale, in 2013, drew more than 220,000 visitors, many of whom - collectors, curators, arts companies - may have money or connections useful for Hospitalfield's plan.

"I also think it provides the international platform for Graham [Fagan] that will be very useful for him, currently, and investment into a new commission that is comparatively substantial," Byatt adds. "It gives us the visibility that we really need to be able to realistically think about raising the funds to support what we do. And also to bring into sharp focus the fact that we really are a rather good arts organisation: we work with interesting artists and we do something which is very particular here."

Hospitalfield does not have an exhibition programme, but a programme of events (last year, in the extensive gardens, artist Laura Aldridge led a large Pit Firing). "It allows artists to do something that is outside their normal practice," Byatt says. "It's a bit of a protected environment that allows them to experiment a little more."

Byatt also wants the house to develop audiences in Angus, and especially with the four schools that are all within walking distance. Emphasis, too, is being placed on the location of Arbroath, which is within two hours of both Glasgow and Edinburgh, and so could be an easy day trip.

The fundraising campaign needs to raise £11.5m. Capital funds from Creative Scotland have already been granted to the tune of £1m, with £500,000 from Historic Scotland, and a bid to the Heritage Lottery Fund has also been submitted; other sums will be raised from trusts and foundations.

Key to Hospitalfield's plans will not only be the success of this year's Biennale, but how it balances the old and the contemporary. Byatt knows it is a fine balance, but also one that can be struck - and has been before, in Allan Fraser's own day.

"I think that he wanted this place to be about contemporary art," she says. "In 1892, when it was first open to the public, 2000 people came here over one weekend. And they were visiting the art of their time. They weren't visiting a heritage site, they were visiting a house in which a patron of the arts had left behind a collection of art from his peers, from that time. He commissioned them to make paintings and sculpture; we are commissioning them to make film and sculpture and performance because that is the material of our time.

"We are very lucky. A lot of heritage buildings are stuck in a preservation of history, and we have the responsibility to do that, but we also have a duty to create the history of the future."

Phil Miller will report from the Venice Biennale in The Herald and Sunday Herald over the coming week