This is a concession to chord-scale devotees. It's meant to be soloed emphasizing the chords.
It has no key center. It cycles through the major 7's and dominant 7's of all twelve keys. Thus, 24 chords in 24 measures. Hence the title.
The melody contains a lot of flat 5's, which mostly resolve. It's consonant until near the end, when it departs more from the chord tones.
The lead sheet differs slightly from the arrangement. Alto, tenor, and trombone play the lead in unison, the alto an octave above the others. Three trumpets provide a counter-melody. The rhythm section has guitar but no piano.