Toronto, Canada

Like a pair of jugglers, Brigitte Shim and Howard Sutcliffe approached the Integral House, in Toronto, as a balancing act—creating a building that seems to defy basic forces of architecture. By anchoring the horizontal thrust of the project’s floor plans to the vertical force of its tumbling section, and spinning intimate elements off of grand gestures, they made a 15,000-square-foot house perched on the side of a steep ravine appear effortlessly connected to its site and the larger context of the city’s cultural topography. Fluid yet orthogonal, handcrafted and digitally produced, the house performs by reconciling opposites.

Designed for James Stewart—a mathematician who has made a fortune writing calculus textbooks and is a violinist and music patron—the house serves as a performance space as well as a home. The name of the project derives from the role of integrals in calculus and Stewart’s request that the design incorporate curves (remember those sine and cosine curves from math class?). The integral symbol also echoes the shape of a violin’s sound holes and the S in the client’s and architects’ last names. “I didn’t give Brigitte and Howard any specific integrals to work with,” says Stewart. “As a mathematician, I just find curves more interesting. As soon as you have curves, you need calculus.”

Curves, though, had never been part of Shim and Sutcliffe’s design vocabulary. “It took a while for us to figure out how to integrate this new geometry into our work,” admits Sutcliffe. The architects started by spending a month working out of the 1960s stucco house that came with the property and that they would later tear down. The experience helped them understand the intricacies of the site: the way it begins as tableland near the street then drops 65 feet down a wooded slope; the way views work through the ravine; and the way changing light animates interior spaces. “Toronto is a city of hidden landscapes,” says Shim, referring to the ravines that slice through the local terrain but remain mostly out of view.

Capturing this sense of discovery became a key part of the architects’ scheme. They designed the street elevation as a relatively modest, two-story pavilion with a translucent-glass upper story floating above a wood-and-clear-glass entry level. A reflecting pool wrapping around one corner of the front reinforces the fluid geometry. From the driveway, visitors have no idea that the house sprawls over five stories or is any larger than the typical home in this affluent neighborhood. “The house unfolds,” explains Shim. “You are unaware of the total volume until you move through it.”

Once inside, visitors face a living room that spreads out toward a view of the ravine and spills down a grand stair to a lower level. The two-story living room serves as a space for musical performances, with seating for up to 150 people, but also offers more intimate areas for relaxing and conversation. Shim and Sutcliffe enveloped this multifunctional space on three sides with an undulating perimeter of clear glass and oak fins. “We wanted to create a foregroud to the ravine, to modulate the relationship between the man-made and the natural,” says Shim.

The fins—each set at a different angle and distance from the one adjacent to it—create a syncopated rhythm that varies from one floor to another. On the entry level, the fins stand fairly close together, offering narrow view slots out to the trees and piquing our curiosity about what lies beyond. “At this level, you are between the city and the forest—a suspended place floating among the trees,” states Sutcliffe. One flight down, the wood-clad fins provide more generous views, establishing a more direct connection to the ravine. Because the fins are angled, the view through them depends on your vantage point. Looked at straight-on, they frame a big view of the ravine; turn your head a bit, and they close off most of the scenery. In Philip Johnson’s Glass House or Mies’s Farnsworth House, large glass panes frame static views. But at the Integral House, the fins create changing views as you move through space. “It’s the difference between cinema and still photogrpahy,” says Shim.

To anchor the liquid forms of the house to a more stable visual language, Shim and Sutcliffe designed a trio of freestanding concrete elements that rise through all five floors: a stairwell, a chimney, and an elevator shaft. The architects also designed a trio of “performance pieces”: the grand stair connecting the two living-room levels, a large hearth, and a saturated blue-glass installation created with artist Mimi Gellman in the stair leading to the bedrooms on the top floor. The installation, which surrounds a steel-frame stair with translucent-glass treads, features indigo-colored glass shingles suspended from cables with bronze clips. Set within a building that has a mostly subdued material palette, the striking glass art piece “has a complex relationship with the rest of the house,” says Sutcliffe. “It’s like a geode, a private crystalline object that’s almost undigested.”

A concrete frame and concrete floor slabs serve as the structural system for most of the house. Slender triangular steel columns with pin connections, though, run approximately every 8 feet through the sinuous wall overlooking the ravine. The architects, who admit they don’t care much about expressing structure in their work, hid the columns in some of the wood fins (most have no column inside). The top floor has its own structural system: a lightweight steel frame.

To maintain proper humidity levels for musical instruments, the house has almost no operable windows. But triple glazing reduces energy loss, and 23 geothermal wells connected to multiple heat pumps provide most of the energy needed to operate the house. On the lowest floor, a 35-foot-long glass wall sitting on a steel beam can slide below grade to open an indoor swimming pool to the outdoors.

Shim and Sutcliffe used both digital technologies and traditional fabrication methods in creating the Integral House. For example, they made a clay model of a custom bronze door handle, converted it to a digital drawing and a CNC-milled model, and then used the ancient process of sand-casting. The couple also designed most of the furniture, handrails, and even the music stands used during performances.

Walking through the house, you notice Mies’s influence in the architects’ way of abstracting nature in orthogonal elements such as the swimming pool, and Aalto’s spirit in the organic, fluid form of the living spaces. The tension between these different approaches helps animate the architecture while demonstrating the skillful calibration of opposites.