Exultation, written in 1925, was once described by Henry Cowell as an "Irish walking tune." The piece is one of many Cowell wrote in the late 1910s and early 1920s based on his interest in Irish mythology. It also employs some of the adventuresome playing techniques that Cowell developed during the same period. Specifically, in Exultation he calls for the use of "arm-sized" tone clusters, or large groups of adjacent notes on the piano keyboard played simultaneously, using the palm or side of the hand or the forearm. That distinctive sound is just one feature of what is otherwise a sprightly, Irish-inflected tune over a stomping chordal accompaniment. Cowell returned to the composition twice in later years. He arranged it for string orchestra in 1930, and ten years after that used it once again as the second movement of his Four Irish Tales for piano and orchestra, assembled from various examples of his solo piano work.

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