Solomon R. Guggenheim bought artworks from Europe’s avant-garde abstractionists during the 1930s, building a collection that now forms the heart of the Guggenheim Museum’s holdings. Two current exhibitions culled from the Guggenheim’s permanent collection disclose a creative exchange between artists in Europe during some of the most difficult years in that continent’s history.

New Harmony: Abstraction between the Wars, 1919–1939 complements the 2010-11 Guggenheim exhibit Chaos and Classicism: Art in France, Italy and Germany, 1918-1936. Chaos and Classicism displayed a selection of figurative artworks from Europe’s interwar period to make the case that the impulse among certain artists for classical themes revealed a longing for a return to order after the devastation of World War I, a social dynamic exploited by the Nazis. New Harmony, curated by Tracey Bashkoff, completes that story by exhibiting works by artists who resisted that impulse for classicism, instead embracing “the avant-garde practices of abstraction in artistic nexuses across Europe.”

The exhibition title comes from a canvas in the show by Swiss-German artist Paul Klee, “New Harmony (Neue Harmonie),” 1936, a painting of a loosely drawn grid. In this work the lines of a grid swerve, with rhythmic dark boxes everywhere except two vermillion squares glowing with light. Bashkoff says Klee (1879-1940), a Bauhaus instructor from a family of musicians, “evokes the structure of Arnold Schoenberg’s unconventional compositions” with this work. Josef Albers, Vasily Kandinsky and László Moholy-Nagy, all represented here, also taught at the Bauhaus, exploring abstract design principles and color theory in class and in their artworks.

Vasily Kandinsky (1866-1944) shared Klee’s interest in expressing musical concepts in paintings. Downstairs Kandinsky in Paris, 1934-1944 explores the influence of avant-garde art in France on the Russian during his last decade. In the 11 paintings here, half of them made as World War Two raged, the abstract forms in Kandinky’s works become increasingly biomorphic, perhaps an influence of Surrealism.

“Capricious Forms,” 1937, a canvas made with pastel colored lines looks like a petri dish under a microscope, organisms swimming around the canvas, decorative dots throughout the design. “Dominant Curve (Courbe dominante),” 1936, the largest canvas in this show, is also the most resolved, a sickle-like form working as an architectural element, balancing and supporting the composition. Here the palette is both vivid and harmonious.

Since James Turrell’s light installation opened, there has been a line along 5th Avenue of museumgoers waiting to enter the Guggenheim. And once inside, the wait to see the rest of Turrell’s retrospective can be over an hour. But tiptoe through the people laid out on the atrium floor gazing at Turrell’s light show and make your way over to these two thought-provoking exhibitions; they provide added reasons to visit the Guggenheim and, once inside the museum, the only lines here are in the artworks.

New Harmony: Abstraction between the Wars, 1919-1939, through September 8, 2013 and Kandinsky in Paris, 1934–1944, ongoing, Solomon R. Guggenheim Museum, 1071 Fifth Avenue, New York, NY, 212.423.3587, www.guggenheim.org

More information about Xico Greenwald’s work can be found at xicogreenwald.com