Beethoven’s Allegro vivace opens the Sonata No. 2 in A major with quick exchanges, sudden changes of weight, and a restless sense of movement. Short, detached gestures sit beside flowing melodic lines, while rapid scales and broken chords carry the music across the keyboard. The movement follows a sonata-form design: an opening group of contrasting themes leads into a development, followed by their return in a reshaped setting.

Measures 1–20 introduce the opening theme, beginning quietly with octave-spaced right-hand notes and a single bass line moving in the same rhythm. Tiny descending runs interrupt the detached notes, giving the theme its stop-and-start character. The texture soon becomes less predictable: one hand falls silent while the other continues, rising figures pass between the hands, and brief chords punctuate the line. A softer passage places a singing upper voice over a moving bass, with inner notes filling out the harmony. These changes make the opening much more varied than its compact first idea suggests.

Measures 21–57 expand the movement’s scale through the transition. Triplet figures climb through successive registers, followed by descending detached notes and exchanges between the hands. At measure 58, the contrasting theme enters, marked espressivo. Its comparatively spacious right-hand melody unfolds above a much busier left hand, whose repeated sixteenth-note patterns often contain two notes at once. Chromatic changes and rising sequences gradually intensify this texture. The closing material brings back brilliant passagework before the music settles into a quieter cadence and the printed alternative endings.

In the development, the opening gesture returns in a new harmonic setting. A sustained stretch combines short bass motives with continuous chordal figures, and the melodic outline moves between different registers. Later, fragments of the gentler opening material are traded between the hands and threaded through changing harmonies. Held chords, rests, and softer dynamics interrupt the momentum before the main theme returns. The recapitulation revisits the earlier contrasts with altered transitions and registers; its closing pages move from forceful runs toward a restrained, quiet finish.

The supplied edition offers an interesting glimpse of its teaching purpose: it labels the main theme, sub-theme, closing theme, and development directly in the score, with an abbreviation key above the first system. These printed signposts make the movement’s large-scale organization visible alongside the notes.