In terms of chords and melody, Mary had a little lamb is more complex than the typical song, having above average scores in Chord Complexity, Melodic Complexity, Chord Progression Novelty and Chord-Bass Melody.
Mary had a little lamb is written in the key of F♯ Phrygian. According to the Theorytab database, it is the 8th most popular key among Phrygian keys and the 58th most popular among all keys. The F♯ Phrygian scale is similar to the F♯ Minor scale except that its 2nd note (G) is a half step lower. Chord progressions in Phrygian often rely on the major chord built off of this 2nd scale degree (G major) which gives the key its distinctive sound. See the F♯ Phrygian Cheat Sheet for popular chords, chord progressions, downloadable midi files and more!