Final answer:
To make an allegro marking indicate a very fast tempo, the modifier 'presto' should be added. 'Presto' signifies an even faster speed beyond the already brisk tempo of allegro.
Step-by-step explanation:
To indicate a very fast tempo when starting from an allegro marking, the modifier that should be added is presto. Allegro suggests a brisk tempo, but presto accelerates the pace even more, conveying a sense of urgency and swiftness in the music. In contrast, largo and adagio are terms associated with slow tempos, and vivace implies a tempo that is lively and brisk, but not necessarily to the extent of presto.
Vivace is an Italian musical term that translates to "lively" or "great vigor." It is often used as a modifier to indicate a fast and energetic tempo in music.
On the other hand, the modifiers Largo and Adagio would actually indicate slow tempos, while Presto would indicate a very fast tempo, but not as fast as Vivace.