Vivace means lively and indicates a fast, energetic tempo typically between 156 and 176 BPM. It sits between allegro and presto in the tempo hierarchy, and the word carries a sense of sparkle and vitality beyond mere speed — the music should feel animated and full of life.
Vivace appears frequently as a finale tempo, providing an exhilarating conclusion to a multi-movement work. It can also modify other markings: allegro vivace is faster and more energetic than plain allegro. The marking suits music that should feel joyful, spirited, and irrepressible — Mendelssohn's fairy music and Haydn's finales often capture the vivace spirit perfectly.
Mendelssohn could reportedly sight-read any piece of music at vivace tempo, even complex orchestral scores. His party trick was playing difficult passages while maintaining a conversation.