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Chicago had long since made its name as a swinging jazz-rock outfit when Foster came onboard for a creative and commercial reboot led by him and the band’s singer, Peter Cetera.

Backed by a five-piece band, he danced in and out of funk, jazz-rock fusion and a kind of futuristic gospel.

She wrote elegant, drifting songs that became jazz standards, such as “Ida Lupino” and “Lawns”; yearning, cinematic big-band pieces, such as “Fleur Carnivore”; iconoclastic rearrangements of national anthems and classical fare; and unwieldy, uncategorizable projects such as her jazz-rock opera “Escalator Over the Hill.”

Since the trumpeter’s shape-shifting career encompassed so many phases and styles, we’ve decided to focus on just one: the era known as “Electric Miles,” starting in 1968 and continuing for more than 20 years, when he embraced electric instruments and stubborn, snaky grooves, in the process basically drawing up a blueprint for the genre now known as jazz-rock fusion.

In the 1970s, when the electric bass became an instrument of choice in many jazz ensembles because its thumping tones suited the commercial sounds of jazz-rock fusion, Mr. Lee, an acoustic bass purist, refused to go along and lost work as a result.