Which term refers to a gradual broadening and slowing in a piece of music?

The term that refers to a gradual broadening and slowing in a piece of music is "allargando." This term indicates a technique in performance where the tempo not only slows down but also allows for a more expansive, expressive delivery of the music. It suggests a feeling of relaxation and stretching the phrases as they unfold, often contributing to the emotional impact of the piece.

Understanding "allargando" is essential in interpreting musical scores, particularly in sections that require a more dramatic or lyrical approach. Musicians use this term to signal a shift in the music's pace and character, allowing for dynamic expression.

In contrast, "adagio" refers to a slow tempo, but it does not inherently imply a gradual broadening or slowing. "Accelerando" indicates a gradual speeding up of the music, while "agitato" suggests a restless or agitated character, which is quite the opposite of a broadening and slowing effect. Therefore, "allargando" stands out as the correct answer for describing a gradual broadening and slowing in music.