Cartoons typically have music orchestrated for chase scenes. A fast tempo and repetitive beats are perfect for, say, running down the longest hallways, and past the same houseplant, again and again and again and again and…
For Roger Rabbit, even though half the characters were cartoons, Alan Silvestri created the kind of jazz real-life noir heroes Humphrey Bogart or Robert Mitchum would have listened to, especially if they were getting a drink with Betty Boop in the secret backroom of a speakeasy. The music creates a true noir atmosphere. It's a world of mystery and hard-boiled detectives. The Toons just happen to be there too.
Silvestri previously worked with Zemeckis on Romancing the Stone (1984) and Back to the Future (1985). With Roger Rabbit, he collaborated with the London Symphony Orchestra to create the iconic themes.
One stand-out musical moment in the film is Jessica's debut, when she shimmies around and sings the jazz classic "Why Don't You Do Right?" Even though Kathleen Turner provides the speaking voice for Jessica Rabbit, she doesn't do the singing. The sultry croon belongs to Amy Irving, then Steven Spielberg's wife.
It's a stunning performance, and what Amy Irving would be famous for were it not for one small thing. Or a hundred million small things. Irving became infamous in 1989 for one of the most expensive celebrity divorces ever, being awarded $100 million in her divorce with Spielberg. (Source)
But if you asked her, we imagine she'd say, "I'm not bad; I'm just a really rich divorcee."