What musical term denotes a very fast tempo?

The term that denotes a very fast tempo is "Presto." In musical terminology, Presto indicates a tempo that is typically faster than Allegro, often around 168 to 177 beats per minute. It conveys a sense of urgency and excitement in the music, making it suitable for lively and energetic pieces.

To provide context, Allegro signifies a fast tempo but is not as quick as Presto, generally ranging from about 120 to 168 beats per minute. Vivace also indicates a lively and brisk tempo, similar to Allegro, but it is typically understood to be slightly faster, though still not reaching the extreme pace that Presto conveys. Adagio, on the other hand, denotes a slow tempo, often around 66 to 76 beats per minute, which is the opposite of what is being asked in this question. Therefore, Presto is indeed the term that accurately reflects a very fast tempo in music.