Between 1915 and the early 1920s, when he virtually ceased performing in public, Ornstein was one of the best known (by some lights, notorious) figures in American classical music. In the description of Broyles and Denise Von Glahn, his "draw was immense. He constantly performed before packed halls, often more than two thousand, in many places the 'largest audience of the season. His solo piano pieces such as "Wild Men's Dance" (aka "Danse Sauvage"; ca. 1913–14) and "Impressions of the Thames" (ca. 1913–14) pioneered the integrated use of the tone cluster in classical music composition, which Henry Cowell, three years Ornstein's junior, would do even more to popularize. In the description of scholar Gordon Rumson, "Wild Men's Dance" is a "work of vehement, unruly rhythm, compounded of dense chord clusters ... and brutal accents. Complex rhythms and gigantic crashing chords traverse the whole range of the piano. This remains a work for a great virtuoso able to imbue it with a burning, ferocious energy." Aaron Copland recalled a performance of it as the most controversial moment of his later teen years. In 2002, a "New York Times" reviewer declared that it "remains a shocker." According to critic Kyle Gann, "Impressions of the Thames", "if Debussyan in its textures, used more prickly chords than Debussy ever dared, and also clusters in the treble range and a low pounding that foreshadowed Charlemagne Palestine, yet modulated ... with a compelling sense of unity."