Admittedly, the music of the Argentine pianist Guillermo Klein was a complete wild card to me until this week. I’ve seen his name on the bill at certain venues oriented toward downtown “experimental” composers, and that, combined with the knowledge that he was raised in Buenos Aires and currently resides in Barcelona, perhaps unconsciously led me to certain expectations. All I can say now is that I should have known better. When I learned that the Village Vanguard was giving a two-week run (something that happens maybe once a year) to Mr. Klein and an 11-piece ensemble, I figured the time had come to check out the young Argentine and his music.

How glad I am that I did. I had forgotten that Mr. Klein, who spent seven years in New York before moving to Spain, is part of the group of ambitious composer-arranger-bandleaders who congregated around the club Small’s, and included the equally prodigious Chris Byars, Jason Lindner, and Omer Avital. All of them, especially Mr. Klein, are more inside than outside, and write brilliantly tuneful compositions that offer rich melodies and stunning harmonies.

Mr. Klein’s band, which he calls “Los Gauchos,” consists of six horns who frequently double, a rhythm section consisting of guitar, bass, drums, and additional percussion, and Mr. Klein on piano.

If I describe Mr. Klein’s compositions as postmodernist, it’s only because that’s a more all-encompassing term than “swing” or “bebop,” even though there are probably more elements of those forms in his music. His tunes are solidly and swingingly rooted in the jazz tradition: For instance, nothing screeches or screams, and though he occasionally employs a note of discord for dramatic or music effect, he never tries to be shocking or jarring.

The second piece in Wednesday night’s set, “Brasil Adentro, Fugue X,” opened with the piano and the guitar playing carefully spaced notes designed to clash rather than complement each other in a deliberately disturbing sound. However, Mr. Klein reconciled the two instruments by gradually introducing the horns with notes that bridged the harmonic gap between the two extremes, resolving the discord into musical peace.

Unlike many contemporary, large-format jazz ensembles — Joe Lovano’s Nonet for instance — Mr. Klein uses the swing-era tradition of sectional writing, having all three saxes play together in an original three-part harmony, rather than working individually. The opening number, “Juana,” featured Chris Cheek on tenor sax, but not just soloing over the rhythm section, as most postwar big bands do, but playing a lot of call-and-response with a fully realized background complement of horns. In fact, his solo was so thoughtfully integrated into the overall composition that I wondered if he was playing a prewritten part, rather than improvising.

In spite of the name “Los Gauchos,” Mr. Klein’s music is no more Latin-specific than any other mainstream jazz composer writing today. His albums occasionally feature vocal interludes, which obviously make the music more Latin, but since his vocal microphone was apparently not working on Wednesday, he was unable to demonstrate this.

The centerpiece of the show was “Miula,” which is in the same vein as “Broken Web” from Mr. Klein’s 2002 album “Los Gauchos III” (Sunnyside). The two drummers begin by laying down a Pan-American polyrhythm. Over that go the saxists, alto and tenor, with a melody line that’s already catchy, but is made even more so when Mr. Klein has them phrase it in disjointed, fragmented form — something like the classical technique known as “hocket.” The ensemble seems to be continually falling apart and coming back together, constantly renewing itself in a self-perpetuating cycle.

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The highly decorated lyricist Alan Bergman (who, with his partner and wife Marilyn, have won more Oscars and Grammys than I want to sit around and count) has just released his first album, “Lyrically, Alan Bergman” (Verve). In celebration, he did a show Tuesday night at Joe’s Pub, accompanied by the virtuoso piano and bass duo of Mike Renzi and David Finck.

Mr. Bergman’s album is a curious but strangely compelling combination of an ordinary voice, extraordinary interpretive skills, and a superbly polished and sensitive orchestral backing. It sounds like the most elaborate demo ever produced, almost like a set of instructions for other, better-endowed vocalists: sing this phrase this way, this is where that emphasis should be, this is what that line is supposed to mean.

Take the way he starts “Windmills of Your Mind,” without a full line but just a single word — “Round” — that he makes into a statement all by itself. The album’s only drawback is that it doesn’t contain the as-yet-unpublished Bergman-Cy Coleman collaboration, “Travelin’ Music,” which was a highlight of the Joe’s show. Otherwise, Mr. Bergman was so completely convincing that I found myself shaking my head and wondering if my mind really does have windmills in it. He may not have chops enough to make all the notes, but he leaves nothing unsung.

wfriedwald@nysun.com