Webster defines the word "exultation" as "the act of exulting; rejoicing; jubilation; triumph" which makes it a perfect description for the character of Exultations. The piece can be seen as a series of jubilations, both thematically (the 16th note opening of the first theme being one), and in general mood. The tempo throughout is fairly fast (beginning with quarter=130) and slows down in only few places when it immediately picks up again. I feel that the nature of these "exultations" are almost religious and result, perhaps, from some sort of joyful ceremony.

Formally, the work can be thought of in three large sections. The first section consists of an upbeat, rhythmic first theme idea followed by a more lyrical one, which could be termed a second theme. The middle section opens contrapuntally based on the lyrical, second theme material. This reaches a huge climax which is followed by hints of the opening, rhythmic idea. Eventually, another climax is reached which leads directly into the final section, a quasi recapitulation, where the first theme is presented again and then is briefly superimposed over the second theme idea. Everything quickly dies away, except for a short, soft horn note, after which the entire ensemble rejoices in their final exultation.