The song Cool is important to the character development of the Jets. Riff sings Cool, with lines from Action, A-Rab, and Baby John. In the song Riff is trying to maintain control of the jets and is advising them to constrain and direct their anger and tension towards the Sharks. This reveals Riff's control of the Jets and their respect for him.
This can be seen by the way the characters are instantly responsive to his directions, for example when he tells Action to “get cool”, A-Rab to “bust cool”, and Baby John “go cool”, they listen to him and seem to be attentive. This reveals that Riff is a strategist and leader.
This song also features a number of the other Jets and reveals through dance and their chants of "go, crazy, go" their pent up anger towards the Sharks, or perhaps pent up anger towards a society which has failed them.
Cool is significant to the structure of West Side Story in that it occurs after the dance at the gym and right before the war counsel at Doc's. At this point, tension and anger towards the Sharks is at an all-time high. The song is in sharp contrast to the energetic and exuberant America which precedes it, and symbolizes the passion and cool detachment that is felt by the Jets. The song also exhibits the anger being felt by the Jets and adds tension to the play by making it very clear that explosive conflict is inevitable.
Cool is much less aggressive and intense than America. Instead of bold, loud instruments, the arrangement of Cool is centered on jazz percussion, bass, and saxophone. This gives the song a smooth, jazzy feel.
Cool features long periods of instrumental music, leaving room for a frenetic dance in which the boys and girls release their emotions and “get cool". The musical interlude is interrupted only by the Jet chorus chants of "cool", "go", and "crazy" which adds to the frenetic energy, passion, and tension of the scene.
To produce a feeling of cool detachment Bernstein uses a cool jazz idiom, a subspecies of bebop from the 1940's. The song employs a twelve-tone system – a highly modernist musical technique. The use of twelve-tone can be seen most clearly in the central fugue, which uses all twelve pitches exactly once. This gives the song an edgy, abstract effect; which is incredibly important at this point in the play where the Jets are trying to take control of their situation.
Cool also uses tritones, which have been called “the devil’s interval”. This produces an eerie effect that adds to the tension of the situation and perhaps even foreshadows the violence and death that is to come.
Rhythmically, Cool is jazzy and smooth. Bernstein uses dotted rhythms and off beats throughout the song to produce a swung effect. The rhythmic, and subtle but consistent percussion provides an interesting background to the other instruments and vocal work; and keeps the song moving forward despite varied and inconsistent vocal and instrumental lines.
Cool uses imagery to strengthen the song. The lyrics implicitly reference childhood. For example, Riff calls the other characters "boy", and at one point "school boy". Toy imagery is also used when Riff mentions rockets and yo-yos. This reminds the audience of the characters youth and relative innocence directly before they are about to enter a war counsel for a rumble. This produces a feeling off compassion for the Jets and disappointment and regret that society has failed these boys.