The strangest thing happened to me when I went to hear Cecil Taylor at the Iridium for his opening set on Wednesday night. I was suffering from a terrible cold and a splitting headache, which is hardly the ideal way to experience an intensely abstract pianist and composer whose music is notoriously difficult, even for those of us who have grown up with it. Mr. Taylor’s dense, prickly playing no doubt has caused some headaches in its time, yet I found that the more intensely I concentrated on the music, the better I felt.

Mr. Taylor’s AHA is a 15-piece group, but the only thing it has in common with traditional big bands is that the players work, for the most part, in sections: six saxophones (three altos, two tenors, one baritone), four trumpets, two trombones, tuba, bass, drums, and the leader’s piano. The bandstand at the Iridium was so crowded that bassist Albey Balgochian was playing a slender, Latin-style electric model.

Where most jazz bands, large and small, shift between ensemble and solo playing, the music of AHA is closer to the classical concerto form; indeed, the entire hour of Mr. Taylor’s opening set was a single work for piano and orchestra, in which the 76-year-old leader was essentially the only soloist.

You also expect a big band to work in terms of Count Basie-style calland-response riffs, in which the main soloist plays something and the rest of the band answers by playing something back. But AHA operates more like a large-format expansion of Mr. Taylor’s trio: When the leader begins playing one of his nervous, jittery phrases, the bass and drums will try to compliment it – and the rest of the band follows. The resulting dynamics and tonal colors are remarkable: the slithery sound of three altos sighing in unison, the whimsicality of three harmon-muted trumpets whimpering at once, the deep grunts of the trombones and tuba, and the surprisingly rich sound Mr. Balgochian coaxes out of his electric bass.

The set began with a long held note on the trumpets; at first I thought the brass section was merely tuning up, but it became clear they were playing a slow, dirge-like theme reminiscent of Ornette Coleman’s early work. Mr.Taylor entered cautiously, with just a single bass note, then another, gradually outlining a pattern with his left hand matched by the bassist’s skittering response. Mr. Taylor’s playing here was much more melodic than I expected, and the early part of the piece resembled a duel between the piano and the bass with the rest of the group choosing sides. Soon, though, the whole group was following Mr. Taylor like a single organism. When he got louder, they got louder; when he sped up, they sped up. Gradually, the piece built in volume and intensity until it sounded like a charging rhinoceros.

Did it ever become tedious? Mr.Taylor grabbed my attention from the start, and for the most part, he managed to hold it. But after slowly bringing the band up to a peak of excitement and eventually letting it decrescendo, he ended the piece with a climax of cacophony that outlasted my attention span. It never became boring, but he just seemed to keep the whole thing up in the air forever at full blast.

Cecil Taylor reminds me of a 15thcentury explorer unafraid to sail beyond the boundaries of the known world. The earth might turn out to be flat and he might fall off the edge, but so what? Mr. Taylor has been sailing off the edge of the world for 50 years now, and while jazz lovers disagree about whether he falls more than he flies, he was certainly flying Wednesday night at the Iridium.

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The only listeners who will be disappointed in singer Kevin Mahogany’s show at the Jazz Standard are those who come expecting what the club promised: a tribute to the great blues and jazz singer Joe Williams.

Mr. Mahogany, a Kansas City native, has spent most of his career digging into the canons of the great black male jazz and pop singers, and they populate his set. He opened Wednesday night’s late set with two tunes from Nat King Cole (the swinging “Route 66” and the sweet “When I Fall in Love”), and then moved on to a song made famous by Johnny Hartman, “Kiss and Run.” He also offered a medley that included JimmyWitherspoon’s signature “Times Getting Tougher Than Tough” and a Buddy Johnson number, “All Right, Okay,You Win.”

Mr. Mahogany hasn’t played New York in far too long, so it was a joy to witness his remarkable synergy with his backup band (pianist Benny Green, bassist Ray Drummond, and drummer Joe Farnsworth). As an added bonus, tenor saxophonist Eric Alexander was on hand to help Mr. Mahogany, a former saxophonist himself, recall such great voice-and-tenor combinations as Witherspoon and Ben Webster and Johnny Hartman and John Coltrane.

Unlike most jazz singers of the current generation, Mr. Mahogany isn’t afraid to get his hands dirty with the blues, and he wound up the set with Williams’s signature song, “Ev’ry Day I Have the Blues.” By juxtaposing the blues with the Great American Songbook, Mr. Mahogany, like the late Big Joe, reminds us that both forms will live forever.

Taylor until December 18 (1650 Broadway at 51st Street, 212-582-2121). Mahogany until December 18 (116 E. 27th Street, 212-576-2232).