The appearance at Ryles on June 17 of highly touted piano trio the Bad Plus raised issues dear to every jazz fan’s heart. You can have your Avrils and your Hives and your Strokes — name your favorite current soundtrack of your life — but nowhere is the phenomenon of "the next big thing" more closely scrutinized than in jazz. Jazz has its own strict rules of authenticity, just as rock and roll does. For one, there’s the tradition itself. People were asking "Is it jazz?" long before they were asking "Is it punk?" And I don’t mean just Ornette Coleman or jazz rock. Cab Calloway famously dismissed bebop as "Chinese music." The criteria for punk rock is as often social as musical, and just as specious either way. Hey, Billie Joe’s mommy may have driven him to band practice, but Joe Strummer was by no means blue collar. And while we’re at it, Miles Davis’s daddy was a well-to-do dentist. Was Miles not an authentic blues player because he never picked cotton? Or was being black credential enough?

But the bottom-line criteria for authenticity in jazz is chops. As Miles might have asked: can the motherfucker play? That’s an argument that’s driven jazz musicians, fans, and critics since the beginning. In the case of a Louis Armstrong, no one could question his ability — no one in any genre was playing those high C’s (and later, F’s) on trumpet before Louis came along. But as a music that values innovation, jazz begs questions of technical proficiency. Aside from Miles’s curt dismissal of Ornette’s music, the otherwise good-natured swing trumpeter Roy Eldridge said, "I listened to him all kind of ways. I listened to him high and I listened to him cold sober. I even played with him. I think he’s jivin’, baby. He’s putting everybody on."

The jive player. The player who can’t — or won’t — play. Hardly an issue in rock, but in jazz it’s the bottom line. Musicians themselves have been beating one another up over it for years. And if someone is playing a new music, subject to its own rules, then how do you measure the player’s ability? "In the course of the proceedings, he occasionally wanders off from his ‘changes’ — whether on purpose or not I cannot say," wrote Gunther Schuller about bassist Buell Neidlinger’s playing on an early Cecil Taylor recording, summing up the problem in a nutshell.

So we have recorded evidence of Coleman Hawkins bragging about how he bullied trombonist Jimmy Harrison for not knowing his changes. (Hawkins was the acknowledged early dean of jazz harmony — having him dis your knowledge of chord changes would be the equivalent of Bach knocking your knowledge of counterpoint.) And so the complaints go on — does this or that musician "swing," have proficiency on his instrument (is Anthony Braxton a good saxophonist?), play credible blues? There’s a competitive edge to these arguments too. Recently I heard of an esteemed jazz musician knocking pianist Brad Mehldau — a musician of unassailable technique, one would think, no matter how you feel about his music — because at a session someone called "How High the Moon" and Mehldau didn’t know it.

Jazz is the opposite of rock in that performers are often judged by the how of their playing rather than the what — a fallacy that Schuller has also written about. Which brings me to my problem with the Bad Plus. In their debut Boston appearance, the band drew about 200 twenty- and thirtysomethings who stayed through two shows. I haven’t seen expectations like this since guitarist James "Blood" Ulmer played the Channel back in the late ’70s.

The Bad Plus come from New York with similar endorsements, but my problem with them is more what than how. I don’t think anyone would doubt they can play. Pianist Ethan Iverson is a former musical director for the Mark Morris Dance Group. Bassist Reid Anderson and David King are equally credentialed. Their book includes the by-now requisite nods to contemporary pop and rock: Blondie’s "Heart of Glass," Aphex Twin’s "Flim," and of course, Nirvana’s "Smells like Teen Spirit." At Ryles, they played Neil Young’s "Heart of Gold" (replete with the band singing an a cappella chorus), Abba’s "Knowing Me Knowing You," and, as an encore, Gloria Gaynor’s "I Will Survive."

The band also have a flair for deadpan-humorous theatrics. Iverson introduced his "Cheney Piñata" by saying, "It does have some genuine piñata feeling, I think . . . and it does have a tragic ending." Anderson and King wore short-sleeve shirts; the shaven-headed, goateed, and bespectacled Iverson wore a dark suit. During a recurring bass-drums sequence in one tune, Iverson stood and faced the audience. And though I couldn’t see it from my seat at the back of the room, King apparently played one piece with the help of a pair of walkie-talkies.

What do they sound like? The covers give you an idea, but these are carefully arranged pieces full of cued ensemble dynamic shifts and surprise unison passages between Iverson’s left hand and Anderson’s bass. In other words, if you’re a musician, you can’t just sit in with the Bad Plus, even if you know "Smells like Teen Spirit" and "How High the Moon." The band avoid the dreaded (by non-jazz audiences) ching-chinga-ching beat and walking bass of straight jazz, and they like odd meters, but not exclusively. Instead, they’ll assert 4/4 with big slamming staccato chords (power chords?). Sometimes it’s Iverson who sustains an uninflected on-the-beat four in his left hand while Anderson and King play "jazz" — free or loose tempos. And Anderson’s solos in particular, with their more conventional jazz-horn-like phrasing, often came as a relief.

The Bad Plus’s music can be a tonic. Anderson’s "Big Eater," the opening track of their current These Are the Vistas (Columbia), with the odd, out-of-phase shifting accents of its repeated opening chords (stated in unison by Anderson and Iverson over King’s free beat), has a tickling airiness. The foursquare martial rhythm of King’s "1972 Bronze Medalist" (also played at Ryles) makes it an anti-jazz comedy. And there were other little revelatory moments — Iverson’s skill with Chopinesque harmonies, his very jazz-like chromatic right-hand runs. When Anderson plucked the melody of "Every Breath You Take," there was another revelation. As my wife put it, "I never realized: Sting’s voice really does sound like a bass." And in general, there was the band’s pop-song concision.

But there were also a lot of schlocky big major-chord climaxes. I’m not one to complain that music "isn’t jazz" as long as it’s something. The Bad Plus have a unique ensemble sound, which is rare enough in jazz. And they can play. But the "jive player" syndrome has a flipside: for a lot of us, half the fun of discovering new vistas is figuring out whether indeed they are putting everyone on. There’s something in the jazz fan — or at least in this jazz fan — that hungers for the renewing experience of "What the hell IS this?" That ongoing argument about what jazz is is part of what makes it intellectually and emotionally compelling. It’s the excitement of encountering something we can’t quite name, what Ellington called "beyond category." With the Bad Plus, unfortunately, that question doesn’t linger for long. At Ryles, when they settled into a loose, folk-based theme, I thought that finally they were living up to those expectations. The tune turned out to be Ornette Coleman’s "Street Woman," from Science Fiction (Columbia, 1972) — "one of our favorite albums," Iverson said.

I WASN’T ABLE TO CATCH much of the Boston Globe Jazz & Blues Festival this year, six out of nine of whose events were free. I did want to see Roy Hargrove’s RH Factor at Copley Square a week ago Thursday. Mostly I wanted to see whether live they’d catch fire with a looseness and aggression they don’t show on Hargrove’s new Hard Groove (Verve). Hargrove came armed: two keyboard players, two drummers, guitar, bass, drums, and two saxophonists. They started with Joe Zawinul’s "In a Silent Way," Hargrove, in a red-white-and-blue track outfit, floating long held notes over Jason Thomas’s motoric hi-hat. There were some good fireworks — Hargrove sustaining some high-note trilling with circular breathing and doctoring his trumpet sound with guitar effects, alto-saxophonist Keith Anderson working the crowd with R&B licks, tenor-sax Jacques Schwarz-Bart having Coltrane moments with rushes of scales and arpeggios and, during "Forget Regret," varying his solo with double-timing and an extended passage in the altissimo register. It was a solid performance — Hargrove even sang a little, on P-Funk’s "I’ll Stay," in a credible R&B baritone with a touch of falsetto. He paraphrased the melody on his horn, worried it with repeated phrases, slowed it down.

But it was still a low-key affair. (The drummers, except for some hip-hop fours, played in unison all afternoon.) The high point may actually have been second-keyboardist Renee Neufville’s singing of "Forget Regret," a Schwarz-Bart composition from the album. The simple lover’s catalogue ("Your sugar, your feel, your touch, your hair"), sung on a varied rising open interval, could be the pop hit Hargrove is looking for.

The fest’s grand finale on Sunday took place in a near-constant downpour. With no crowd to speak of, and the steady deluge, the organizers cancelled the scheduled 2 p.m. opener, Me’Shell Ndegéocello. But Arturo Sandoval and Herbie Hancock went on as planned in front of a few hundred umbrella’d diehards.

Sandoval, in a green blazer and dark shirt, led a sextet unwilted, rocking with a mix of high-powered Afro-Cuban rhythms and bebop. He played both flügelhorn and trumpet, the latter with stunning high notes. He played a hyperkinetic piano solo. On another tune he scatted, mixing clearly enunciated 32nd-note velocity with a more-or-less pitch-accurate impersonation of a bowed bass. On another day I might have resented showboating like this, but in the pouring rain I was grateful.

Herbie Hancock’s set — with Scott Colley on bass, Terri Lyne Carrington on drums, and Gary Thomas on tenor sax — was by contrast loose and ruminative. It was thoroughly compelling at first — the free tempos and overall elastic sense of time created a dreamy expectancy. Sandoval’s tenor-saxophonist, Felipe Lamoglia, created excitement with hyperactive Coltrane-like outbursts of shrieks and note clusters. Thomas played uncluttered lines of eighth notes. In this relaxed atmosphere, the rhythmic interaction among band members unfolded transparently before one’s ears. But it’s difficult to dream when the rain is falling and the wind is blowing, and in the set’s penultimate tune, Hancock rewarded the patient crowd with one of his typically explosive solos, rocking with syncopated chording and breathtaking runs.