allegro assai

very adverb. as·​sai ä-ˈsī : very. used with tempo direction in music.

A word used in musical directions such as allegro assai, "very fast." ( in other words, closer to the 182 quarter notes a minute than to the 154 quarter notes a minute)

A slow movt. is often called 'an Adagio'. adagissimo, extremely slow. adagio assai, very slow. From: adagio in The Concise Oxford Dictionary of Music »

It is all somewhat subjective however on how much it means. Adding Assai to the tempo, or "very much" would be play at the faster end of the Andante spectrum. Adding Non Troppo or "not too much" would be at the slower end.

pai·​sa pī-ˈsä 1. plural paisa a monetary subunit of the rupee (Nepal, Pakistan) and taka see rupee, taka at Money Table. 2. plural paise pī-ˈsā a monetary subunit of the rupee (India) see rupee at Money Table.

fast, but not overly so In music, an instruction of "allegro ma non troppo" means to play "fast, but not overly so".

vivace. / (vɪˈvɑːtʃɪ) / adjective, adverb. music to be performed in a brisk lively manner.

a brisk, lively tempo vivace (plural vivaces) (music) A piece to be played at a brisk, lively tempo.

Larghissimo – extremely slow, slowest type of tempo (24 bpm and under) Adagissimo and Grave – very slow, very slow and solemn (24-40 bpm) Largo – slow and broad (40–66 bpm) Larghetto – rather slow and broad (44–66 bpm)

: moderately slow. usually used as a direction in music.

Andante (Italian: 'walking'). Meaning the music should be played at a walking pace. Not too fast or slow.

a moderately slow tempo andante (plural andantes) (music) A tempo mark directing that a passage is to be played in a moderately slow tempo; faster than adagio but slower than moderato.