“Whenever I want to hear something new,” Miles Davis once said, “I listen to Dizzy.” That might have surprised many of Davis’s fans. By the 1960s, Dizzy Gillespie was dismissed as old hat by many younger jazz listeners. They bought into Davis’s anti-showmanship, the way he turned his back on his audiences (often literally) and treated authority figures (especially white ones) with contempt. Gillespie, like Louis Armstrong, was regarded as a former firebrand who had turned into a smiling, singing clown. In both cases, nothing could have been further from the truth.

John Birks Gillespie will ultimately be best remembered for his role in two remarkable achievements that were largely completed by the time he turned 30: the birth of bebop, or modern jazz, and the forging of the various elements that became Latin jazz. Yet these were merely the two most significant accomplishments in a lifelong artistic evolution. Donald Maggin’s solid new biography of the trumpet player, “Dizzy: The Life and Times of John Birks Gillespie” (HarperEntertainment, 432 pages, $26.95), shows that Miles Davis was indeed right – Dizzy was always into something new. Indeed, Gillespie’s pattern of continual artistic renewal very likely inspired Davis, one of his earliest acolytes, to do the same.

Gillespie’s explorations began modestly, with a desire to compete with his first trumpet hero, Roy Eldridge. He was a product of the swing era, and even though bop was blamed for helping to exacerbate the demise of the big bands, Gillespie’s no. 1 priority was always to lead a big band that would play the modern harmonies and rhythms that he loved.

His early big band of 1946-48 came close, producing some of the most amazing orchestral jazz ever recorded. But Gillespie consistently reconvened his large-format ensembles every time fate and funding allowed. By the 1950s, he was working in every conceivable setting, playing all kinds of jazz (and even non-jazz), and collaborating with virtually every major musician up to the challenge of sharing a microphone with him.

Still, the central event in “Dizzy,” as it must be, is Mr. Maggin’s recounting of the creation of modern jazz. Saxophonist Paquito D’Rivera, who worked in Gillespie’s later bands, remembered that the trumpeter vehemently denied being the sole creator of bebop – or, as he put it, “I didn’t invent s-.” Mr. Maggin takes us through the process, step by step, through which bebop actually was born.

Drawing on Dizzy’s own book, “To Be or Not To Bop,” Ira Gitler’s essential “Swing To Bop,” and other sources, Mr. Maggin has fashioned a very readable narrative that charts the genesis of the new music from the meeting of Gillespie and drummer Kenny Clarke in 1938. Gillespie was already hearing a new music in his head, a new kind of jazz based on a different approach to harmony and rhythm. Over the next five years, he and a small group of like-minded colleagues put the pieces together.

Mr. Maggin well describes the collaborations between Gillespie, Clarke, guitarist Charlie Christian, pianist Thelonious Monk and, especially, alto saxophonist Charlie Parker. All were inspired by “advanced” swing musicians like Coleman Hawkins and Art Tatum, and each independently, at first separately in different parts of the country, had conceived of a new music. He shows that all these men were invaluable in the founding of bop, but he also makes convincing argument for Gillespie’s primary role.

This was as much because of personality as anything else: Gillespie was the only one of bop’s forefathers who was a born star (and who, unlike Monk or Parker, had no mental or addiction issues). In addition to prodigious talent, he supplied a face to put on the music. Modern jazz would soon become the province of super-serious types who felt that great jazz soloists, much like great classical musicians, didn’t need to crack jokes or sing silly songs. Dizzy was an irrepressible cutup. He was also the genre’s first celebrity, and the designated scapegoat for musical reactionaries who came to criticize the music.

One thing Gillepsie was not was a superior blues player. By the end of his career, he was able to craft respectable improvisations in blues form, but the idiom did not come naturally to him; it was thanks to Parker that bebop was built on a firm foundation of the blues. Gillespie’s strength was rhythm: He alone could have had the vision and know-how to create orchestral music as dependent on African-Cuban polyrhythms as it was on the advanced harmonies and rhythms of bebop.

If Gillespie had died at the same age as Parker, 35, his place in music history would have been assured. But how fortunate we are that he lived another four decades. He continually refined and consolidated his bebop and Afro-Latin innovations, and he consistently found new mountains to climb. Dizzy was a star in a series of Norman Granz jam sessions, he was at the forefront of three amazing, long-form works composed by Lalo Schifrin and J.J. Johnson in the early 1960s, he explored bossa nova and calypso rhythms, and he headlined on the jazz festival circuit pioneered by George Wein.

Finally, Gillespie was around for the beginnings of the jazz repertory movement and the founding of the New York Jazz Repertory Company, the American Jazz Orchestra, and Jazz at Lincoln Center. Even his comparative failures – such as his ill-advised funk and fusion albums, and “Something in Your Smile” a 1967 track (from the album “Swing Low, Sweet Cadillac”), which, as far as I know, amounts to his only attempt at “serious” ballad singing – are instructive and interesting.

Mr. Maggin is not a scintillating music writer, but he has fashioned Gillespie’s career into an exciting narrative. He is particularly strong on the early years, with a lot of details about the background of the Gillespie family in Cheraw, S.C., tracing its ancestors back to their Yoruba roots. He is also informative on Dizzy’s relationship with his father, who was loving but somewhat cruel and quick to punish.

The Dizzy I remember was a proselytizer and teacher. When he was a newcomer, many established musicians had been hostile to him. Gillespie resolved to help as many young musicians as he could. According to Mr. Maggin, he even had a special phone line put in his house in Englewood, N.J., so they could call him with questions. He brought the same spirit to his religious beliefs after he converted to the Bahai faith at age 50; to him, preaching a new way to phrase a chord or explaining a new way to look at God were essentially the same thing.

By the time Dizzy died in 1993, at the age of 75, he was hailed – as he jokingly yet accurately put it – as “the Elder Statesman of Bebop.” Mr. Maggin makes the strong case that he was its godfather as well. Gillespie often thanked Louis Armstrong for what he said was his “employment” – what he meant was that no jazzman could have had a career had not Armstrong been there first. “No him, no me,” he said. I shudder to think what postwar jazz would have been like without John Birks Gillespie: No him, no anybody.