The same can be said of Mr. Coleman’s music, and it’s a serendipitous convergence that brings the two together. A major exhibition of Pollock’s works on paper is going on at the Guggenheim Museum. A rare concert by Mr. Coleman’s quartet takes place this Friday at Carnegie Hall, as part of the JVC Jazz Festival.

Mr. Coleman has often been called the Jackson Pollock of the alto saxophone, and he smiles at the comparison. In the liner notes on his 1959 album, Change of the Century, he described his music as “something like the paintings of Jackson Pollock.” The cover of Free Jazz (1960) featured a reproduction of Pollock’s White Light.

In the late 40’s, Pollock shattered the barriers of modern art, abandoning figures, conventional color schemes, even the boundaries of a canvas. A decade later, Mr. Coleman did the same to modern jazz, abandoning chord changes, standard rhythms and the divide between the soloist and the band; in his music, everybody improvises all at once, yet it somehow holds together.

So it’s a tingling sensation to follow this modern icon, now 76, wearing a porkpie hat and a self-designed suit that Jasper Johns might have painted, as he shuffles through the Guggenheim, musing on Pollock’s works.

Gazing at Green Silver, another 1949 “all-over” masterpiece, he says, “See? There’s the top of the painting, there’s the bottom. But as far as the activity going on all over, it’s equal.” He pauses and shakes his head, impressed. “It’s not random. He knows what he’s doing. He knows when he’s finished. But still, it’s free-form.”

Sort of like your music?

“Well, like music, not just my music.”

But most musicians put the melody up front, the chords in the background.

“But that’s only because somebody told them that’s how it should be.”

Mr. Coleman has long found abstract art a congenial setting. He made his New York debut at a Bowery bar called the Five Spot in November 1959 (one month after the first Guggenheim opened). A group of neighborhood artists—Larry Rivers, Franz Kline, Robert Rauschenberg, Willem de Kooning—had persuaded the bar’s owner to bring in progressive-jazz musicians.

Thelonious Monk and John Coltrane played there for months on end. But it was Mr. Coleman who set off a storm. The city’s cultural denizens divided into factions. Fistfights broke out over whether Ornette was a trailblazing genius or an eccentric fake. The same reception, of course, had greeted Pollock at the start of his earlier revolution, some gasping that he’d unlocked the future, others scoffing that he just couldn’t paint.

“I paint sometimes myself,” Mr. Coleman said. “I know what’s behind wanting to paint. You want to touch something you can’t see. This term ‘abstract art’—what it means is something that causes you to see more than what you’re looking at.”

He pauses to focus on a drawing from 1946, looking at it intently from one side, then from the other side. “Mmm, mmm, mmm. Man, that’s good!” he says. “What’s the title of this?”

The placard says Untitled.

“Ah,” he replies with a smile. “That’s a good title.”

Fred Kaplan is a columnist for Slate.

The same can be said of Mr. Coleman’s music, and it’s a serendipitous convergence that brings the two together. A major exhibition of Pollock’s works on paper is going on at the Guggenheim Museum. A rare concert by Mr. Coleman’s quartet takes place this Friday at Carnegie Hall, as part of the JVC Jazz Festival.

Mr. Coleman has often been called the Jackson Pollock of the alto saxophone, and he smiles at the comparison. In the liner notes on his 1959 album, Change of the Century, he described his music as “something like the paintings of Jackson Pollock.” The cover of Free Jazz (1960) featured a reproduction of Pollock’s White Light.

In the late 40’s, Pollock shattered the barriers of modern art, abandoning figures, conventional color schemes, even the boundaries of a canvas. A decade later, Mr. Coleman did the same to modern jazz, abandoning chord changes, standard rhythms and the divide between the soloist and the band; in his music, everybody improvises all at once, yet it somehow holds together.

So it’s a tingling sensation to follow this modern icon, now 76, wearing a porkpie hat and a self-designed suit that Jasper Johns might have painted, as he shuffles through the Guggenheim, musing on Pollock’s works.

Gazing at Green Silver, another 1949 “all-over” masterpiece, he says, “See? There’s the top of the painting, there’s the bottom. But as far as the activity going on all over, it’s equal.” He pauses and shakes his head, impressed. “It’s not random. He knows what he’s doing. He knows when he’s finished. But still, it’s free-form.”

Sort of like your music?

“Well, like music, not just my music.”

But most musicians put the melody up front, the chords in the background.

“But that’s only because somebody told them that’s how it should be.”

Mr. Coleman has long found abstract art a congenial setting. He made his New York debut at a Bowery bar called the Five Spot in November 1959 (one month after the first Guggenheim opened). A group of neighborhood artists—Larry Rivers, Franz Kline, Robert Rauschenberg, Willem de Kooning—had persuaded the bar’s owner to bring in progressive-jazz musicians.

Thelonious Monk and John Coltrane played there for months on end. But it was Mr. Coleman who set off a storm. The city’s cultural denizens divided into factions. Fistfights broke out over whether Ornette was a trailblazing genius or an eccentric fake. The same reception, of course, had greeted Pollock at the start of his earlier revolution, some gasping that he’d unlocked the future, others scoffing that he just couldn’t paint.

“I paint sometimes myself,” Mr. Coleman said. “I know what’s behind wanting to paint. You want to touch something you can’t see. This term ‘abstract art’—what it means is something that causes you to see more than what you’re looking at.”

He pauses to focus on a drawing from 1946, looking at it intently from one side, then from the other side. “Mmm, mmm, mmm. Man, that’s good!” he says. “What’s the title of this?”

The placard says Untitled.

“Ah,” he replies with a smile. “That’s a good title.”

Fred Kaplan is a columnist for Slate.

Maybe the biggest jaw-dropper comes in Chapter 4, “The Hunt for WMD.” It’s about Dr. Sawsan Alhaddad, a woman in her 50’s, now living in Cleveland, Ohio, who escaped Saddam’s Iraq 27 years ago. In May 2002, a C.I.A. agent tracked her down and asked her to go back to Baghdad and do a little espionage. Her brother, who still lived there, had worked in Saddam’s nuclear-weapons program in the 1980’s and early 90’s. The C.I.A. wanted her to ask him a series of questions about the program’s current status and to offer him refuge in the United States. Bravely, she made the trip, asked the questions (usually on long walks, at night) and learned that the program had been dead for a decade. She went back to the States and told her case officers the news. But the C.I.A. waved it off; her brother, they said, was obviously lying.

Then Mr. Risen adds the kicker. The C.I.A. had persuaded the exiled relatives of 30 Iraqi weapons scientists to make the risky trip back to their homeland. All of them came back with the same story: Iraq had no nuclear program. This was an amazing treasure trove of intelligence at a time when the C.I.A., which had no spies on the ground, was straining to learn all it could about Iraqi weapons of mass destruction. And yet the information was dismissed, ignored. Nothing about the 30 relatives was ever passed on to the State Department, the Pentagon or the White House. Nor were their findings incorporated into the C.I.A.’s own National Intelligence Estimate on Iraq’s W.M.D., written a mere month later, which concluded, on nothing particularly solid, that Iraq “is reconstituting its nuclear program.”

Mr. Risen lays out a dozen similar instances of reality slamming into Team Bush’s assumptions—and the assumptions emerging unruffled. Time and again, officials who raised doubts were flung to the sidelines, while those who got with the program and clamped on their blinders won promotions.

Another amazing story along these lines dates from June 2003, after U.S. forces in Iraq captured Abid Hamid Mahmud al-Tikriti, Saddam Hussein’s personal secretary. This was such a huge find—Mr. Hamid had been designated the “Ace of Diamonds” in U.S. Central Command’s deck of 52 most-wanted Saddamites—that the C.I.A. assigned its best Arabic speaker to conduct the interrogation. Mr. Hamid revealed two key things: First, Saddam had not been at Dora Farms the night that President Bush, acting on Mr. Tenet’s urgings, launched a cruise-missile strike on the farm, starting the war a bit earlier than planned, in hopes of decapitating the regime from the get-go. Second, there was no W.M.D. program. The C.I.A. bosses concluded that Mr. Hamid was lying, blamed their top-notch interrogator for going too easy on him and replaced her.

Another episode: In November 2003, the Baghdad station chief sent a special cable to Langley, warning that an insurgency was stirring and that the U.S. was in danger of losing the war that the President had declared we’d already won. Headquarters started distributing inflammatory memos, accusing the station chief of personal misconduct. He quit the agency in disgust.

Mr. Risen blames George Tenet for the climate of incompetence, groupthink and political kowtowing that enshrouded Langley in those crucial months leading up to war. In Plan of Attack (2004), Bob Woodward revealed that the C.I.A. director had assured President George W. Bush that the intelligence on Iraq’s W.M.D. was a “slam dunk.” Mr. Risen provides the back-story: He notes that, after the 2000 election, Mr. Bush nearly replaced Mr. Tenet, who was after all a holdover from the Clinton administration; Mr. Tenet won him over through persistent ingratiation and some lobbying with the President’s father (who still had some influence over his boy). When, after 9/11, the President resisted widespread calls for a clean sweep at Langley, Mr. Tenet felt he owed him big time. Mr. Risen reveals that at two conferences of regional station chiefs—one in Rome in April 2002, another in London the following November—senior C.I.A. officials made it clear that the President was going to war, that the agency had to jump onboard, that the second-guessing and criticizing must come to an end.

All of this raises the question: How much did George W. Bush know, and when did he know it? In the extremely unlikely event that the President sat down and read this book, would any of it surprise or outrage him? Like countless other chronicles, this book tells of Vice President Dick Cheney and Secretary of Defense Donald Rumsfeld running rings around the entire bureaucracy. Were they also running rings around the Oval Office? Mr. Risen recounts one episode in which Mr. Rumsfeld simply ignored the President’s orders. (Mr. Bush, upset that the new Afghan government that he’d helped install might be turning into a “narco-state,” wanted to destroy the new Afghan government’s poppy fields; Mr. Rumsfeld brushed the directive aside.) It’s indisputable at this point that the intelligence community was responding to pressure from the White House throughout the year leading up to the war. But how much of that pressure came from Mr. Bush and how much from his sneering No. 2 down the hall? More to the point, if Mr. Bush had known everything that James Risen has subsequently discovered, would he have gone to war?

Probably he would have. Wars rarely have single causes, and everyone in Team Bush, the captain included, seems to have had his own reasons for toppling Saddam Hussein (and his own set of assurances that the war would be a cakewalk). Still, it’s stunning to realize that, nearly three years after the fact—and despite dozens of books and hundreds of incisive newspaper and magazine articles—we don’t yet know why this war took place. I suspect we may never fully know, unless Mr. Cheney, Mr. Rumsfeld or one of their secretaries was taking notes or running a dicta-belt during their many phone conversations from the summer of 2002 through the spring of 2003.

Mr. Risen doesn’t help us out on this score, either. Then again, he doesn’t pretend to. His sources (several of whom he names, by the way) tend not to rank high enough to be privy to such matters—and, on balance, that’s for the best, since those who are in the know wouldn’t tell him or any other reporter, anyway. (Mr. Woodward, for all his access, did no better on the big questions in his tome, and he got wind of almost nothing that State of War uncovers.)

That said, I do wish there were more to this book. It reads like a string of magazine articles rather than a cohesive work. The author’s just-the-facts-ma’am approach is refreshing, to a point (we’ve probably had enough color-for-its-own-sake accounts of what Dick Cheney was eating at a crucial lunch), but one yearns for a bit more flesh, a few scene-setters, some style. Still, one has little cause for complaint. The book, though dry, is at least short, lucid and ceaselessly revelatory. Mr. Risen constructs more—and more hair-raising—skeletons with his bare-bones stories than any number of meatier, you-are-there wind-wheezers.

Fred Kaplan is the national-security columnist for Slate.

Maybe the biggest jaw-dropper comes in Chapter 4, “The Hunt for WMD.” It’s about Dr. Sawsan Alhaddad, a woman in her 50’s, now living in Cleveland, Ohio, who escaped Saddam’s Iraq 27 years ago. In May 2002, a C.I.A. agent tracked her down and asked her to go back to Baghdad and do a little espionage. Her brother, who still lived there, had worked in Saddam’s nuclear-weapons program in the 1980’s and early 90’s. The C.I.A. wanted her to ask him a series of questions about the program’s current status and to offer him refuge in the United States. Bravely, she made the trip, asked the questions (usually on long walks, at night) and learned that the program had been dead for a decade. She went back to the States and told her case officers the news. But the C.I.A. waved it off; her brother, they said, was obviously lying.

Then Mr. Risen adds the kicker. The C.I.A. had persuaded the exiled relatives of 30 Iraqi weapons scientists to make the risky trip back to their homeland. All of them came back with the same story: Iraq had no nuclear program. This was an amazing treasure trove of intelligence at a time when the C.I.A., which had no spies on the ground, was straining to learn all it could about Iraqi weapons of mass destruction. And yet the information was dismissed, ignored. Nothing about the 30 relatives was ever passed on to the State Department, the Pentagon or the White House. Nor were their findings incorporated into the C.I.A.’s own National Intelligence Estimate on Iraq’s W.M.D., written a mere month later, which concluded, on nothing particularly solid, that Iraq “is reconstituting its nuclear program.”

Mr. Risen lays out a dozen similar instances of reality slamming into Team Bush’s assumptions—and the assumptions emerging unruffled. Time and again, officials who raised doubts were flung to the sidelines, while those who got with the program and clamped on their blinders won promotions.

Another amazing story along these lines dates from June 2003, after U.S. forces in Iraq captured Abid Hamid Mahmud al-Tikriti, Saddam Hussein’s personal secretary. This was such a huge find—Mr. Hamid had been designated the “Ace of Diamonds” in U.S. Central Command’s deck of 52 most-wanted Saddamites—that the C.I.A. assigned its best Arabic speaker to conduct the interrogation. Mr. Hamid revealed two key things: First, Saddam had not been at Dora Farms the night that President Bush, acting on Mr. Tenet’s urgings, launched a cruise-missile strike on the farm, starting the war a bit earlier than planned, in hopes of decapitating the regime from the get-go. Second, there was no W.M.D. program. The C.I.A. bosses concluded that Mr. Hamid was lying, blamed their top-notch interrogator for going too easy on him and replaced her.

Another episode: In November 2003, the Baghdad station chief sent a special cable to Langley, warning that an insurgency was stirring and that the U.S. was in danger of losing the war that the President had declared we’d already won. Headquarters started distributing inflammatory memos, accusing the station chief of personal misconduct. He quit the agency in disgust.

Mr. Risen blames George Tenet for the climate of incompetence, groupthink and political kowtowing that enshrouded Langley in those crucial months leading up to war. In Plan of Attack (2004), Bob Woodward revealed that the C.I.A. director had assured President George W. Bush that the intelligence on Iraq’s W.M.D. was a “slam dunk.” Mr. Risen provides the back-story: He notes that, after the 2000 election, Mr. Bush nearly replaced Mr. Tenet, who was after all a holdover from the Clinton administration; Mr. Tenet won him over through persistent ingratiation and some lobbying with the President’s father (who still had some influence over his boy). When, after 9/11, the President resisted widespread calls for a clean sweep at Langley, Mr. Tenet felt he owed him big time. Mr. Risen reveals that at two conferences of regional station chiefs—one in Rome in April 2002, another in London the following November—senior C.I.A. officials made it clear that the President was going to war, that the agency had to jump onboard, that the second-guessing and criticizing must come to an end.

All of this raises the question: How much did George W. Bush know, and when did he know it? In the extremely unlikely event that the President sat down and read this book, would any of it surprise or outrage him? Like countless other chronicles, this book tells of Vice President Dick Cheney and Secretary of Defense Donald Rumsfeld running rings around the entire bureaucracy. Were they also running rings around the Oval Office? Mr. Risen recounts one episode in which Mr. Rumsfeld simply ignored the President’s orders. (Mr. Bush, upset that the new Afghan government that he’d helped install might be turning into a “narco-state,” wanted to destroy the new Afghan government’s poppy fields; Mr. Rumsfeld brushed the directive aside.) It’s indisputable at this point that the intelligence community was responding to pressure from the White House throughout the year leading up to the war. But how much of that pressure came from Mr. Bush and how much from his sneering No. 2 down the hall? More to the point, if Mr. Bush had known everything that James Risen has subsequently discovered, would he have gone to war?

Probably he would have. Wars rarely have single causes, and everyone in Team Bush, the captain included, seems to have had his own reasons for toppling Saddam Hussein (and his own set of assurances that the war would be a cakewalk). Still, it’s stunning to realize that, nearly three years after the fact—and despite dozens of books and hundreds of incisive newspaper and magazine articles—we don’t yet know why this war took place. I suspect we may never fully know, unless Mr. Cheney, Mr. Rumsfeld or one of their secretaries was taking notes or running a dicta-belt during their many phone conversations from the summer of 2002 through the spring of 2003.

Mr. Risen doesn’t help us out on this score, either. Then again, he doesn’t pretend to. His sources (several of whom he names, by the way) tend not to rank high enough to be privy to such matters—and, on balance, that’s for the best, since those who are in the know wouldn’t tell him or any other reporter, anyway. (Mr. Woodward, for all his access, did no better on the big questions in his tome, and he got wind of almost nothing that State of War uncovers.)

That said, I do wish there were more to this book. It reads like a string of magazine articles rather than a cohesive work. The author’s just-the-facts-ma’am approach is refreshing, to a point (we’ve probably had enough color-for-its-own-sake accounts of what Dick Cheney was eating at a crucial lunch), but one yearns for a bit more flesh, a few scene-setters, some style. Still, one has little cause for complaint. The book, though dry, is at least short, lucid and ceaselessly revelatory. Mr. Risen constructs more—and more hair-raising—skeletons with his bare-bones stories than any number of meatier, you-are-there wind-wheezers.

Fred Kaplan is the national-security columnist for Slate.

It was an amazingly experimental time in jazz—in American culture generally—and Mr. Rollins’ probings were especially intense. Just a few years earlier, Miles Davis had broken free of his mentor Charlie Parker’s exquisite stranglehold on modern harmony; John Coltrane was taking Miles’ musings into a whole new orbit, feverishly scouring every crevice of a chord for some new spirit of expression; Ornette Coleman blew down structure altogether. There was an excitement about the new for its own sake. Mr. Coleman’s style of free jazz was called “the new thing.” A sudden craze for Latin rhythms was dubbed “bossa nova.” Even in politics, John Kennedy was heralding a “New Frontier.”

In this hothouse atmosphere, at the peak of his powers and popularity, Mr. Rollins—self-consciously lacking a new thing of his own—dropped out. A magazine writer saw him practicing his horn one night on the Williamsburg Bridge and published a short story about the spectacle; Mr. Rollins’ self-exile took on a mystique. As he prepared his return to the jazz scene, RCA offered him a record contract, on the condition that he call his debut album The Bridge.

That album starts off with a tune of the same title—as does this two-disc collection—and instantly we hear a new Rollins: fierce in tone, blowing fragments of melodies in staggered cadences with abrupt shifts of tempo. There’s a rebellious restlessness in his playing, sharpened by its contrast with the rhythm section, which included Jim Hall plucking skylark lines on guitar in place of someone pounding chords on a piano—at the time, a novel substitution. On a slow ballad like “God Bless the Child,” Mr. Rollins would bark abbreviations of the melody, then embellish it with dense, Pollock-like swirls and zigzags—yet, at each step, retain and deepen the song’s romance and lyricism.

Some regarded this new Rollins as conservative, even stodgy, compared with the rocket flares that Mr. Coleman and Coltrane were sending up. For one thing, he was still playing songs, mainly standard ballads. But heard in retrospect, on its own terms, Mr. Rollins’ music from this era sends a jolt. There’s a satisfying tension to it—a tension that serious jazz musicians have confronted and worked their way through ever since—between freedom and structure, improvisation and melody, innovation and form.

The magical thing about Sonny Rollins has always been his ability to stretch this tension to a point that would exhaust the imagination (not to mention the lungs) of most horn players—and then to stretch it even further. In live concerts, even now at the age of 75, he can improvise on a tune for chorus after chorus—first on its chords, then on its scale, then on its mood, then just on something about it that reminds him of some other tune—without repeating a single idea, sometimes veering wildly off-course but always touching base at the end of the phrase.

He’d developed this knack well before the RCA years (Gunther Schuller wrote his famous essay, “Sonny Rollins and the Art of Thematic Improvisation,” back in 1958), but it was on these recordings that he pushed the technique into new terrain, fused it with new forms of music and played it off against new musicians—sometimes, seemingly, just to see how the mix worked out.

Three months after the sessions for The Bridge, he recorded an album devoted entirely to bossa nova ( What’s New, the weakest of the bunch, and my only complaint about this compilation is that there’s too much from it). Three months after that, in July 1962, he formed a new piano-less, guitar-less band with two of Ornette Coleman’s bandmates—trumpeter Don Cherry and drummer Billy Higgins—and took them into the Village Gate to lay down a live album ( Our Man in Jazz) that’s still hair-raising. The following year, he fulfilled a fantasy of recording an album with his longtime idol on tenor sax, Coleman Hawkins ( Sonny Meets Hawk) and, in the process, gave no ground, flinging startlingly out-there phrases at his hero—even on “Lover Man,” Hawkins’ trademark tune—almost as a challenge, to see how he’d strike back. The album doesn’t quite jell, but it’s a fascinating clash, not least because Hawkins was one of the few swing-era veterans who embraced new sounds; several years before, he’d adapted fluently to Charlie Parker’s bebop, and gleefully played as both leader and sideman with the archly angular Thelonious Monk.

Mr. Rollins waited a half-year, until February 1964, before recording another album ( Now’s the Time) with a band that included pianist Herbie Hancock and bassist Ron Carter, just as they were also auditioning for Miles Davis (who was a closer match for them, it turned out), and then got back together with Jim Hall and bassist Bob Cranshaw (who’s still playing with Mr. Rollins) for the last RCA project ( The Standard Sonny Rollins).

After leaving RCA, he signed with the Impulse! label and recorded East Broadway Rundown, his freest album yet or since, with two members of Coltrane’s path-breaking quartet (drummer Elvin Jones and bassist Jimmy Garrison). In 1967, he took another sabbatical—this one lasting four years—before coming back for good.

The music of the subsequent three decades has been less turbulent and engrossing—for jazz and for Sonny Rollins. He has seemed less interested in formal experimentation and less keen to play with independent young musicians. With few exceptions, his studio albums have been drab compared with those from 40 or 50 years ago. But his live concerts—and the best tracks of his live albums, especially “G-Man” and, most recently, “Without a Song”—are riveting and adventurous, his solos streaming through the stratosphere yet locked onto some fundamental pulse.

Next time Sonny Rollins comes to the city, see him at all costs. Until then, this two-disc collection will do.

It was an amazingly experimental time in jazz—in American culture generally—and Mr. Rollins’ probings were especially intense. Just a few years earlier, Miles Davis had broken free of his mentor Charlie Parker’s exquisite stranglehold on modern harmony; John Coltrane was taking Miles’ musings into a whole new orbit, feverishly scouring every crevice of a chord for some new spirit of expression; Ornette Coleman blew down structure altogether. There was an excitement about the new for its own sake. Mr. Coleman’s style of free jazz was called “the new thing.” A sudden craze for Latin rhythms was dubbed “bossa nova.” Even in politics, John Kennedy was heralding a “New Frontier.”

In this hothouse atmosphere, at the peak of his powers and popularity, Mr. Rollins—self-consciously lacking a new thing of his own—dropped out. A magazine writer saw him practicing his horn one night on the Williamsburg Bridge and published a short story about the spectacle; Mr. Rollins’ self-exile took on a mystique. As he prepared his return to the jazz scene, RCA offered him a record contract, on the condition that he call his debut album The Bridge.

That album starts off with a tune of the same title—as does this two-disc collection—and instantly we hear a new Rollins: fierce in tone, blowing fragments of melodies in staggered cadences with abrupt shifts of tempo. There’s a rebellious restlessness in his playing, sharpened by its contrast with the rhythm section, which included Jim Hall plucking skylark lines on guitar in place of someone pounding chords on a piano—at the time, a novel substitution. On a slow ballad like “God Bless the Child,” Mr. Rollins would bark abbreviations of the melody, then embellish it with dense, Pollock-like swirls and zigzags—yet, at each step, retain and deepen the song’s romance and lyricism.

Some regarded this new Rollins as conservative, even stodgy, compared with the rocket flares that Mr. Coleman and Coltrane were sending up. For one thing, he was still playing songs, mainly standard ballads. But heard in retrospect, on its own terms, Mr. Rollins’ music from this era sends a jolt. There’s a satisfying tension to it—a tension that serious jazz musicians have confronted and worked their way through ever since—between freedom and structure, improvisation and melody, innovation and form.

The magical thing about Sonny Rollins has always been his ability to stretch this tension to a point that would exhaust the imagination (not to mention the lungs) of most horn players—and then to stretch it even further. In live concerts, even now at the age of 75, he can improvise on a tune for chorus after chorus—first on its chords, then on its scale, then on its mood, then just on something about it that reminds him of some other tune—without repeating a single idea, sometimes veering wildly off-course but always touching base at the end of the phrase.

He’d developed this knack well before the RCA years (Gunther Schuller wrote his famous essay, “Sonny Rollins and the Art of Thematic Improvisation,” back in 1958), but it was on these recordings that he pushed the technique into new terrain, fused it with new forms of music and played it off against new musicians—sometimes, seemingly, just to see how the mix worked out.

Three months after the sessions for The Bridge, he recorded an album devoted entirely to bossa nova (What’s New, the weakest of the bunch, and my only complaint about this compilation is that there’s too much from it). Three months after that, in July 1962, he formed a new piano-less, guitar-less band with two of Ornette Coleman’s bandmates—trumpeter Don Cherry and drummer Billy Higgins—and took them into the Village Gate to lay down a live album (Our Man in Jazz) that’s still hair-raising. The following year, he fulfilled a fantasy of recording an album with his longtime idol on tenor sax, Coleman Hawkins (Sonny Meets Hawk) and, in the process, gave no ground, flinging startlingly out-there phrases at his hero—even on “Lover Man,” Hawkins’ trademark tune—almost as a challenge, to see how he’d strike back. The album doesn’t quite jell, but it’s a fascinating clash, not least because Hawkins was one of the few swing-era veterans who embraced new sounds; several years before, he’d adapted fluently to Charlie Parker’s bebop, and gleefully played as both leader and sideman with the archly angular Thelonious Monk.

Mr. Rollins waited a half-year, until February 1964, before recording another album (Now’s the Time) with a band that included pianist Herbie Hancock and bassist Ron Carter, just as they were also auditioning for Miles Davis (who was a closer match for them, it turned out), and then got back together with Jim Hall and bassist Bob Cranshaw (who’s still playing with Mr. Rollins) for the last RCA project (The Standard Sonny Rollins).

After leaving RCA, he signed with the Impulse! label and recorded East Broadway Rundown, his freest album yet or since, with two members of Coltrane’s path-breaking quartet (drummer Elvin Jones and bassist Jimmy Garrison). In 1967, he took another sabbatical—this one lasting four years—before coming back for good.

The music of the subsequent three decades has been less turbulent and engrossing—for jazz and for Sonny Rollins. He has seemed less interested in formal experimentation and less keen to play with independent young musicians. With few exceptions, his studio albums have been drab compared with those from 40 or 50 years ago. But his live concerts—and the best tracks of his live albums, especially “G-Man” and, most recently, “Without a Song”—are riveting and adventurous, his solos streaming through the stratosphere yet locked onto some fundamental pulse.

Next time Sonny Rollins comes to the city, see him at all costs. Until then, this two-disc collection will do.

Yet Mr. Ehrlich—who plays mainly alto saxophone and clarinet—has never made much of a splash, even by the modest standards of modern jazz. The reason, I suspect, is that he doesn’t have a signature sound; you wouldn’t easily identify him in a blindfold test, as you would other top-notch horn players. For most jazz musicians, this would be a death knell—but not here. The central element in Marty Ehrlich’s music is not Marty Ehrlich but the music. His tone can be classically pure, sweetly romantic, growlingly dirty or piercingly insistent, depending on what he feels is appropriate for the music at hand. And while he’s a superb performer, it’s as a composer and arranger that he shines.

Listen to “Enough Enough,” the first track on News on the Rail—and one of the most boisterous album-openers in ages. It’s an up-tempo rouser, with the six musicians (three horns, piano, bass and drums) careening in what you might think are scattershot directions, until you realize that their crisscrossings are swaying perfectly in sync—thanks to a solid-anchor bass line, harmonies that are as lush as they are discordant and, above all, a crisp, clear melody.

This is what makes Mr. Ehrlich’s music so appealing and accessible: He comes out of an avant-garde tradition—he can lay down atonal scales, off-pitch chords and staggered tempos with the knottiest of them—but he also has a supreme feel for ensemble balance. You hear every line in his pieces, and there’s no confusing which line is the lead—the melody—even if it takes curves that melodies don’t often follow.

Unlike many jazz musicians, who jump at the first chance to lead their own bands (often before they’re ready), Mr. Ehrlich spent many years in happy tutelage, playing sideman to such masters as Julius Hemphill, Muhal Richard Abrams, Jaki Byard, Anthony Braxton, George Russell and Andrew Hill. (Mr. Hemphill, the original leader and most harmonically imaginative arranger of the World Saxophone Quartet, was a particularly strong influence and longtime friend; after his death in 1995, Mr. Ehrlich led the Julius Hemphill Sextet, which was—and, at occasional gatherings, still is—devoted to playing his music.) The common strand connecting these mentors is that they all devised novel ways of combining tight composition with free improvisation—an approach Mr. Ehrlich artfully emulates.

Classically trained before he immersed himself in jazz, Mr. Ehrlich wrote and arranged all eight songs on his new CD—a mix of straight-ahead, avant-blues, funk, Monkish ditties and stirring ballads. You can hear traces of his mentors in this music, as well as bits of Charles Mingus and Eric Dolphy. But he’s too original to be tagged as derivative. The band—James Zollar on trumpet and flugelhorn; Howard Johnson on tuba, baritone sax, and bass clarinet; James Weidman on piano and melodica; Greg Cohen on bass; and Allison Miller on drums—is the strongest he’s assembled to date: top-notch players in fine form.

The ballads on this album, especially the last tune, “Keeper of the Flame,” sound much like the mournful ballads that Mr. Ehrlich plays with his Dark Woods Ensemble, a clarinet-led trio with Erik Friedlander on cello and Mark Helias on bass. But the sextet’s three extra musicians allow him to weave in a subtle counterpoint, a denser layer of harmony, an emotional twist.

In the liner notes, Mr. Ehrlich refers to this particular sextet—which played at the Jazz Standard recently—as a “large small” ensemble (as opposed to a “small large” ensemble). I take this to mean that he arranged the music so that the group would sound like an expanded trio or quartet instead of a scaled-down octet or big band. The distinction isn’t semantic, or doesn’t have to be. A scaled-down big band, often the result of a financial pinch, can sound thin; you notice the missing parts. An expanded small band, if embellished with flair, can sound rich, even ravishing. That’s what this band and this album sound like.

Mr. Moran, not quite 30, is one of those musicians (the saxophonist James Carter is another) who can play everything, with complete authority, in any style, yet infuse it with his own touch. On his 2002 CD, Modernistic—probably the most riveting and pleasurable solo-piano jazz album in a decade—he plays standard ballads (one of the very few original takes of “Body and Soul” since Coleman Hawkins), stride (James P. Johnson’s “You’ve Got to Be Modernistic”), rap (a spirited take of Afrika Bambaataa’s “Planet Rock”), spirituals (his own composition, “Gentle Shifts South”) and classical (a quite respectable rendition of Schumann’s “Auf Einer Burg”). I have also heard him, in concerts, make music from the tonal cadences of a Chinese newscaster’s stock-market report and a Turkish housewife’s phone conversation.

His eclecticism stems in part from his background. He grew up in Texas, tutored in New York with two harmonically eccentric keyboard masters (Andrew Hill and Jaki Byard) and nurtured a passion for movies, for movie soundtracks, for modern art and for high-end design. He works all these influences into his music, not as some pomo elbow-nudge but as insouciantly natural elements. There’s also a generational impulse involved: With all the world’s sounds a mouse-click away, why not embrace whatever they might have to offer?

His new album, Same Mother, features his Bandwagon trio: Tarus Mateen on bass and Nasheet Waits on drums. I was disappointed with an earlier Bandwagon disc. The group was very good, but I felt that Mr. Moran played better in solo, that the trio—maybe the trio format generally—weighed him down.

Same Mother changed my mind. First, Mr. Mateen and Mr. Waits have grown as musicians. Second, Mr. Moran has devised a concept for trio music. (The group’s first album, called The Bandwagon, consisted mainly of tunes from Modernistic but played less well.) Finally, he’s added a fourth to the mix—Marvin Sewell, best known for playing with Cassandra Wilson, on acoustic and electric guitars—and the ensemble finally cooks as an ensemble, not merely as a leader backed by accompanists.

The augmented band hangs together because Mr. Moran’s new concept is the blues—specifically, the common roots of jazz and blues (hence the title: The two types of music have the “same mother”)—and Mr. Sewell’s twangy guitars tap into those roots. They also provide a second center of gravity to the music—sometimes running parallel to Mr. Moran’s, sometimes tearing against it—and thus an alternative lead that the bass and drums can follow or play off of, moving back and forth from one to the other, or finding some middle turf that links or builds tension with both.

Mr. Moran will be playing in Central Park with the trio version of Bandwagon. But, judging from the one time I’ve seen them since Same Mother was recorded, it’s a richer band even without Mr. Sewell: more cerebral yet also more emotional because it’s grounded in the blues, that most grinding of music.

Brad Mehldau will play his SummerStage set solo, though, ironically, he tends to sound better with a trio. He’s led a working trio for nearly a decade, featuring Larry Grenadier on bass and Jorge Rossy on drums. They’ve released five CD’s, titled—with a nod to Bach—The Art of the Trio, subtitled “Vol. 1,” “Vol. 2” and so forth.

Mr. Mehldau, 35, grew up in Connecticut, a child prodigy gifted at classical music who switched to jazz as a teenager after hearing Keith Jarrett’s Köln Concert album. Mr. Jarrett remains a central influence; you can hear it in Mr. Mehldau’s flair for extended improvisation, his tendency toward rhapsody, and—especially when playing standard ballads—his penchant for turning and twisting the chords and cadences every which way, like a latter-day Bach crafting variations on a fugue (with results that range from brilliantly rapturous to self-consciously clever).

His trio keeps him from bogging down in these excursions. (The same can sometimes be said of Mr. Jarrett’s trio.) The drums propel the rhythm forward, the bass anchors the beat in time; Mr. Mehldau must keep moving with them or, when he does stop to mull a passage or explore its angles and colors, a tension nicely sizzles, and when the tension resolves—when the musicians realign—you heave a satisfying sigh, until the players veer out of sync again and the pattern of tension and resolution repeats itself, over and over.

At his best, Mr. Mehldau weaves some of this suspense and relief into his solo playing. On Live in Tokyo, you can most potently hear—and feel—the effect in his improvisations on Nick Drake’s “River Man” and Gershwin’s “How Long Has This Been Going On.”

Mr. Mehldau has lately expanded his repertoire to include Radiohead—his Tokyo concert included a 19-minute “Paranoid Android”—but he takes a distinct approach to such fare. When Mr. Moran covers “Planet Rock,” you think this is how Afrika Bambaataa would play it if he were a jazz pianist. When Mr. Mehldau covers “Paranoid Android,” you think this is how Radiohead would play it if they were Brahms or Schumann. Then again, for Radiohead, this approach is just fine.

Friday’s SummerStage concert also showcases a third pianist, Eric Lewis, best known as a sideman to Wynton Marsalis. His playing was humdrum on Mr. Marsalis’ last CD, The Magic Hour (the worst album in the trumpeter’s 22-year career as a leader), but full of verve and sparkle on his forthcoming release (due out at the end of this month), Amongst the People. I’ve never heard Mr. Lewis play solo, so whatever happens will be a sound of surprise.

Mr. Moran, not quite 30, is one of those musicians (the saxophonist James Carter is another) who can play everything, with complete authority, in any style, yet infuse it with his own touch. On his 2002 CD, Modernistic—probably the most riveting and pleasurable solo-piano jazz album in a decade—he plays standard ballads (one of the very few original takes of “Body and Soul” since Coleman Hawkins), stride (James P. Johnson’s “You’ve Got to Be Modernistic”), rap (a spirited take of Afrika Bambaataa’s “Planet Rock”), spirituals (his own composition, “Gentle Shifts South”) and classical (a quite respectable rendition of Schumann’s “Auf Einer Burg”). I have also heard him, in concerts, make music from the tonal cadences of a Chinese newscaster’s stock-market report and a Turkish housewife’s phone conversation.

His eclecticism stems in part from his background. He grew up in Texas, tutored in New York with two harmonically eccentric keyboard masters (Andrew Hill and Jaki Byard) and nurtured a passion for movies, for movie soundtracks, for modern art and for high-end design. He works all these influences into his music, not as some pomo elbow-nudge but as insouciantly natural elements. There’s also a generational impulse involved: With all the world’s sounds a mouse-click away, why not embrace whatever they might have to offer?

His new album, Same Mother, features his Bandwagon trio: Tarus Mateen on bass and Nasheet Waits on drums. I was disappointed with an earlier Bandwagon disc. The group was very good, but I felt that Mr. Moran played better in solo, that the trio—maybe the trio format generally—weighed him down.

Same Mother changed my mind. First, Mr. Mateen and Mr. Waits have grown as musicians. Second, Mr. Moran has devised a concept for trio music. (The group’s first album, called The Bandwagon, consisted mainly of tunes from Modernistic but played less well.) Finally, he’s added a fourth to the mix—Marvin Sewell, best known for playing with Cassandra Wilson, on acoustic and electric guitars—and the ensemble finally cooks as an ensemble, not merely as a leader backed by accompanists.

The augmented band hangs together because Mr. Moran’s new concept is the blues—specifically, the common roots of jazz and blues (hence the title: The two types of music have the “same mother”)—and Mr. Sewell’s twangy guitars tap into those roots. They also provide a second center of gravity to the music—sometimes running parallel to Mr. Moran’s, sometimes tearing against it—and thus an alternative lead that the bass and drums can follow or play off of, moving back and forth from one to the other, or finding some middle turf that links or builds tension with both.

Mr. Moran will be playing in Central Park with the trio version of Bandwagon. But, judging from the one time I’ve seen them since Same Mother was recorded, it’s a richer band even without Mr. Sewell: more cerebral yet also more emotional because it’s grounded in the blues, that most grinding of music.

Brad Mehldau will play his SummerStage set solo, though, ironically, he tends to sound better with a trio. He’s led a working trio for nearly a decade, featuring Larry Grenadier on bass and Jorge Rossy on drums. They’ve released five CD’s, titled—with a nod to Bach—The Art of the Trio, subtitled “Vol. 1,” “Vol. 2” and so forth.

Mr. Mehldau, 35, grew up in Connecticut, a child prodigy gifted at classical music who switched to jazz as a teenager after hearing Keith Jarrett’s Köln Concert album. Mr. Jarrett remains a central influence; you can hear it in Mr. Mehldau’s flair for extended improvisation, his tendency toward rhapsody, and—especially when playing standard ballads—his penchant for turning and twisting the chords and cadences every which way, like a latter-day Bach crafting variations on a fugue (with results that range from brilliantly rapturous to self-consciously clever).

His trio keeps him from bogging down in these excursions. (The same can sometimes be said of Mr. Jarrett’s trio.) The drums propel the rhythm forward, the bass anchors the beat in time; Mr. Mehldau must keep moving with them or, when he does stop to mull a passage or explore its angles and colors, a tension nicely sizzles, and when the tension resolves—when the musicians realign—you heave a satisfying sigh, until the players veer out of sync again and the pattern of tension and resolution repeats itself, over and over.

At his best, Mr. Mehldau weaves some of this suspense and relief into his solo playing. On Live in Tokyo, you can most potently hear—and feel—the effect in his improvisations on Nick Drake’s “River Man” and Gershwin’s “How Long Has This Been Going On.”

Mr. Mehldau has lately expanded his repertoire to include Radiohead—his Tokyo concert included a 19-minute “Paranoid Android”—but he takes a distinct approach to such fare. When Mr. Moran covers “Planet Rock,” you think this is how Afrika Bambaataa would play it if he were a jazz pianist. When Mr. Mehldau covers “Paranoid Android,” you think this is how Radiohead would play it if they were Brahms or Schumann. Then again, for Radiohead, this approach is just fine.

Friday’s SummerStage concert also showcases a third pianist, Eric Lewis, best known as a sideman to Wynton Marsalis. His playing was humdrum on Mr. Marsalis’ last CD, The Magic Hour (the worst album in the trumpeter’s 22-year career as a leader), but full of verve and sparkle on his forthcoming release (due out at the end of this month), Amongst the People. I’ve never heard Mr. Lewis play solo, so whatever happens will be a sound of surprise.

Still, the most innovative acts, the ones that more sharply reflect what's fresh and exciting in modern jazz, are happening at the festival's side shows, in the city's jazz clubs-especially David Murray and the Gwo-Ka Masters at the Jazz Standard (June 17 to 19) and Don Byron heading four different bands over five nights at the Village Vanguard (June 21 to 25).

David Murray was a staple of the New York jazz scene in the 1980's and 90's, a galvanizing force among several saxophonists-including Arthur Blythe, Hamiet Bluiett, Chico Freeman and Julius Hemphill-who had immersed themselves in the avant-garde, found their own voices and then applied them to the "jazz tradition," breathing new life into old forms.

A decade ago, Mr. Murray moved to Paris, fell in with a community of Creole musicians-most notably the Gwo Ka percussion masters from Guadeloupe-and started exploring ways to fuse his brand of jazz with Afro-Caribbean rhythms. Several albums have come out of this fusion- Creole, Fo Deux Revue, Yonn-Dé and Gwotet-and, while I wouldn't count them among Mr. Murray's best, they are deeply satisfying.

On his best nights, a David Murray solo is an exhilarating thing, combining the improvisational zest of Sonny Rollins with the lush vibrato of Ben Webster. His horn seems locked onto some fundamental rhythm of the earth. The notes cascade and tumble with an unerring yet unpredictable flow, first with a volcanic fury, then with a breeze, a sigh. He blows in phrases, each sentence complete, yet his lines follow so jangled a path, radiate in so many directions, they seem impossible to resolve-until they are resolved, at which point, with scarcely a breath, a new sentence begins, feeding a stream of tension and resolution, firmly anchored to an undercurrent of harmony and melody. Combine this finely controlled frenzy with polyrhythmic hand-drumming and, when they click, it's just riveting.

Don Byron, one of the few full-time clarinetists in today's jazz, has always been engrossed with unlikely combinations. He played Stravinsky's Le Sacre du Printemps as his honors project at the New England Conservatory-then, after graduating, started a klezmer band, blew progressive R&B with Living Colour and joined a swarm of downtown jazz groups (including the David Murray Octet).

His five nights at the Vanguard will feature his sextet, Music for Six Musicians (Latin and Caribbean rhythms over flighty riffs and dark, Mingus-like harmonies); his big band (an expansion of the sextet with more horns, more drums and the great Malian singer Abdoulaye Diabate); his Adventurers Orchestra (a project that grew out of a five-year residency at Symphony Space, with a repertoire ranging from Stravinsky to Mancini to Earth, Wind and Fire); and, for two nights, his Ivey-Divey Trio (the group on his latest CD, with pianist Jason Moran and drummer Billy Hart, paying tribute to a Lester Young–Nat Cole–Buddy Rich trio from the late 40's).

If the festival lasted another week, Mr. Byron could add on his Bug Music big band (exploring the wilder side of early Ellington and the cartoon tunes of Raymond Scott), his Fine Line ensemble (playing songs by Sondheim, Chopin, Roy Orbison and Stevie Wonder), his Romance with the Unseen quartet (with guitarist Bill Frisell) or … the list could go on for a while.

The remarkable thing about Mr. Byron's eclecticism is that it's completely sincere. His music, while playful, is never campy; there are no ironic winks or nudges. Mr. Byron loves all this music. He infuses it with his own style, but treats it with respect. Another source of amazement is that he pulls it off. He can play with the pure, full-bodied tone of a classically trained clarinetist, but he can also get dirty in the blues. He has a special knack-nearly unique among jazz musicians-for manipulating rhythm: lagging behind the beat, then catching up, charging ahead, laying back again, all while swirling phrases, turning them inside out and every which way, as if he were tossing off the simplest tune in the world.

Mr. Murray, now 50, and Mr. Byron, 46, are no longer quite "young men," but their approach to music is more fresh and youthful-and more faithful to the radical impulses of the early jazz masters-than many younger musicians whose notion of jazz is restricted to 4/4 rhythm and standard ballads-and-blues chord changes.

"Fusion" earned a bad name in the early 70's, when desperate jazz musicians, suddenly eclipsed by rock 'n' roll, tried to retain commercial luster by adapting rock's most dumbed-down backbeat. Much of the resulting music was bad-not because it was fusion, but because it was bad fusion. Jazz has always been molded from a scattershot of musical influences. From the beginning, there was the fusion of African rhythms, slave call-and-response songs and Western European harmony. Jelly Roll Morton talked of jazz and its vital "Latin tinge." Dizzy Gillespie and George Russell fused Caribbean rhythms and bebop in "Cubano Be, Cubano Bop." Sonny Rollins fused jazz with the calypso. Even Duke Ellington-the patron saint of jazz traditionalists-injected a massive dose of funk in his 1966 masterpiece, The Far East Suite.

So, as the world grows smaller-in an era when you can buy records from all over the world with a click of a button-why shouldn't jazz musicians seek common ground with drummers from Guadeloupe or singers from Mali? And just as the jazz musicians of the 30's, 40's and 50's improvised on songs from Broadway and Tin Pan Alley, why shouldn't jazz musicians do the same with the popular tunes of their own time?

Most of today's best jazz musicians are also the most far-ranging. Jason Moran, the most original jazz pianist to emerge in the last few decades, traverses the standards (his solo album, Modernistic, contains one of the few novel twists on "Body and Soul" since Coleman Hawkins), but he also plays-and plays off-hip-hop, film soundtracks and the rhythms of a Turkish telephone conversation. Dave Douglas, the most inventive trumpeter of our time, has recorded tributes not only to Miles Davis and Wayne Shorter, but also to Joni Mitchell and Rufus Wainwright, and also plays variations on Balkan folk tunes, James Bond thrillers and themes inspired by Florentine architecture.

There will always be a place for standards. There's no equation between some Top 40 wonder and the glories of Kern and Gershwin. But jazz has always been less about what you play than how you play it. And there's so much out there to play.