Alvar Aalto, the great Finnish architect, was as famous for the chairs and tables he designed as for his buildings. An exhibition of his furniture and glass products, on view at the Museum of Modern Art through Nov. 27, reminds us most emphatically why this was so.

The exhibition gives great pleasure to the eyes: The purity of lean design is in the very air of the large room in which the pieces have been beautifully installed. It is not as if Aalto's designs are unfamiliar. They are, indeed, known round the world -- they had an incredible influence on the look of the modern living room in the two decades following the end of World War II, and many are still being produced. But seeing the originals together has a very special impact, perhaps because 27 of the 33 pieces of furniture on view were designed between 1929 and 1939, a decade during which Aalto was working at a peak of inspiration and ingenuity.

Aalto, who turned 33 in 1929 (and who died in 1976), had seized upon a fresh wind of the times defined by Frank Lloyd Wright in 1930 when he observed that "today, it seems to me, we hear this cry, 'Be Clean,' from the depths of our own need. It is almost as though the Machine itself had, by force, issued an edict similar to Shinto -- 'Be Clean.' Clean lines . . . clean purposes." Aalto's designs are clean and then some: Unornamented and structurally clear, his furniture has a pristine quality, as if it aspired to become a platonic definition of the modernist code, "form follows function."

But although he believed in the necessity of standardization, and although his furniture from the beginning was conceived with large-scale production in mind, it does not seem so readily identified with the "machine esthetic" as the renowned pieces designed in the 1920s by Marcel Breuer, Ludwig Mies van der Rohe and Le Corbusier. This is primarily because, except for a brief flirtation with tubular metal supports in the early 1930s, Aalto worked almost exclusively with wood, which he respectfully called "the form-inspiring, deeply human material."

Two large architectural commissions in Finland in the late 1920s -- a tuberculosis sanatorium in Paimio and a municipal library in Viipuri -- brought Aalto almost instant international recognition. He designed most of the furniture for these buildings: armchairs, stacking chairs, tables and stools that have become synonymous with his name. Working with Otto Korhonen, the technical manager of a furniture factory near Turku, he was able to push the craft of bending plywood to new limits, producing pieces such as the Paimio lounge chair, whose resilient bent seat and graceful curvilinear supports helped to create a new look in furniture that would last for three decades.

As all furniture designers must, Aalto paid particular attention to the design of chair and table legs, and he was able to contribute two definitively new solutions to the age-old problem of how to attach the vertical to the horizontal members. The first came in the 1930s, when, with Korhonen's assistance, he perfected an ingenious design for a solid wooden leg that, as a result of thin layers of wood inserted at the point of the angle, could be bent a full 90 degrees. This "L-leg," as curator J. Stewart Johnson points out in the catalogue, "made possible the easiest and most economical assembly of furniture," obviating the need for secondary supports such as stretchers, frames or wedges. The most famous examples of this design are the stacking chairs made for the Viipuri library in 1932-33, but it has been widely employed. Then, in 1954, Aalto invented the most elegant of his leg designs, the five-piece "fan leg" that fits flush into the corners of flat-topped furniture pieces. "The fluid transition from horizontal top to vertical leg has much of the strength and grace of Gothic fan vaulting," Johnson observes, without exaggeration.

Aalto was also a pioneer in the design and manufacture of utilitarian, free-form glass vessels of the sort that would become nearly ubiquitous during the 1950s. His designs in this mold are beautiful, but I prefer his very first glass pieces, such as the so-called "Flower of Riihimaki," a nest of five thin-walled vessels that are at once sophisticated and utterly straightforward. Come to think of it, these characteristics typify Aalto's best furniture designs, which are what makes this exhibition truly memorable.