Which tempo term indicates a gradual increase in speed?

The term that indicates a gradual increase in speed is "Accelerando," often abbreviated as "accel." This Italian word is derived from the root "accelerare," which means "to accelerate." In musical notation, when a composer wants the performer to gradually play faster, they will use this term. It signals that the tempo should gradually increase over a certain passage, enhancing the sense of momentum or urgency in the music.

In contrast, the other terms listed do not indicate an increase in speed. "Adagio" refers to a slow tempo, "Agitato" implies a restless or agitated character without specifying a change in speed, and "Allargando" suggests a broadening or slowing down of the tempo rather than an increase. Therefore, "Accelerando" is the term that most accurately conveys a gradual increase in speed.