What musical term refers to a gradual broadening in tempo?

The term that refers to a gradual broadening in tempo is "allargando." This musical directive indicates that the performer should gradually slow down and often also emphasizes a more expansive and expressive sound. In a piece of music, when an allargando is applied, it encourages the musician to create a more dramatic effect by widening the tempo, typically at climactic moments, resulting in a more poignant or emotional delivery.

In contrast, other terms like "con fuoco," which means "with fire," indicates playing with passion and intensity, but does not pertain to the tempo itself. "Piu mosso," meaning "more movement," suggests a quicker tempo rather than a slowing down or broadening of tempo. "Rallentando," while also indicating a slowing down, does not specifically denote a broadening effect, focusing more on a gradual decrease in speed rather than an expansion in tempo. Therefore, "allargando" is the term that captures the essence of a gradual broadening in tempo effectively.