Sophie Taeuber-Arp’s first foray into architecture was close to home: a new studio-home for her and her husband, the German-French sculptor Jean (Hans) Arp, on the fringes of the Meudon forest southwest of Paris. Designed in 1928, the cubed building is simple, functional and exact – much like her paintings and textiles. A long overdue retrospective at Tate Modern, which opened first at the Kunstmuseum Basel and will later travel to MoMA in New York, explores the wide-ranging work and enduring influence of this multidisciplinary artist.

Born in the Swiss Alps in 1889, Taeuber-Arp grew up in a region associated with textile manufacturing and went on to train as an artist, textile designer and dancer. In 1916, she became a teacher at the School of Applied Arts in Zürich, as well as a member of the revolutionary cultural movement that briefly flourished in the Swiss capital during the First World War: dada. Resisting rationality and the senselessness of war, dada artists used unfamiliar materials and methods to create spontaneous and subversive art, poetry and performances.

Taeuber-Arp, who had already established her distinctive geometric abstractions by the time dada was founded at the Cabaret Voltaire in 1917, produced her first mature works during this period of political and cultural upheaval. In 1918, she designed a series of striking polychrome puppets and geometric stage sets for an avant-garde interpretation of King Stag (1762) at the Swiss Marionette Theatre. Later that year she participated in a string of exhibitions organised by The New Life, a group founded by the Swiss artist Fritz Baumann to dismantle the barriers between everyday crafts and fine art. In the 1920s she began to experiment with architecture and interior design, while in the 1930s she produced primary-coloured paintings and wood reliefs. At the outbreak of the Second World War, she fled Paris and turned to drawing.

Unfazed by traditional art historical categories, Taeuber-Arp applied the formal language of abstraction to beadwork, bedding, furniture and interiors. Like those of her dada contemporaries, her creations are spontaneous and subversive. Rather than angry, though, her abstractions are joyful. There’s something liberating about the sense of movement, the rhythmic patterns and the playful blocks of colour. Her version of abstract art is life-affirming rather than cynical; real rather than spiritual.

Despite her genre-bending contribution to modern art and design, Taeuber-Arp remains relatively unknown, even in her native Switzerland. Bringing together more than 200 key works from collections across Europe and the US, this touring exhibition hopes to change that. As the studio-home now managed by the Fondation Arp shows, she moved between different disciplines with wit and grace. It’s time to reposition her as one of the most radical and innovative figures of the 20th-century avant-garde.

Sophie Taeuber-Arp is at Tate Modern from 15 July until 17 October 2021