"Allegro moderato" means "moderately quick," and signifies that a song has a tempo between 112 and 124 beats per minute. Composed of the two Italian words "allegro" and "moderato," which means "fast" modified by "moderate". Allegro moderato is slower than allegro, but a bit faster than moderato. Another name used for allegro moderato is "allegretto."
Allegro moderato will be found on the top of the staff to enable the player to determine the speed and style of the piece before them. Allegro moderato is often used when the composer wishes to use a sonata form. Allegro moderato has a quick tempo, but resists having a marching tempo as an allegro tempo with no modifier is likely to have. Allegro moderato is not as broad of a term as other tempo markings; presto is between 168 and 200 beats per minute, allegro by itself is 120 to 168 beats per minute, moderato is 108 to 120 and andante is 76 to 108. The musician will often find the desired tempo for allegro moderato easily, and with a little help from a metronome or conductor, the collective will quickly be on beat. Notable classic songs with major parts marked with an allegro moderato tempo are the Symphony No. 3 from Tchaikovsky and the Symphony No. 29 by Mozart.