Which term refers to a tempo that is fast but faster than allegro?

The term that refers to a tempo that is fast but faster than allegro is "presto." In musical terminology, tempo indications are used to describe how quickly a piece of music should be played. "Allegro" is already a lively tempo, typically indicating a speed between 120 to 168 beats per minute. "Presto," on the other hand, indicates a tempo that is even faster, often ranging from 168 beats per minute and up, making it a clear distinction as a quick tempo.

The other terms relate to different concepts in music. "Risoluto" means played resolutely or decisively, but it does not define a specific tempo. "Rallentando" indicates a gradual slowing down of the music, which is the opposite of what is being asked. Similarly, "ritardando" also means to slow down the tempo, especially as a piece approaches a conclusion, again not matching the request for a faster tempo. Thus, "presto" is the correct term for a tempo that is indeed faster than allegro.