Corey Kilgannon/The New York Times Henry Grimes and Leo Lindberg with their reciprocal T-shirts.

They make an odd couple, these two jazzmen: The grizzled bass player with the roller-coaster life hauling his unwieldy instrument down the New York street, and the Nordic teenager from faraway with his jeans and sneakers and backpack filled with jazz songs scrawled on scraps of paper.

Henry Grimes, 73, is one of the foremost bass players in free jazz, having played on seminal records by Cecil Taylor, Albert Ayler, Don Cherry, Pharoah Sanders, and many others. After disappearing from the jazz scene and spending 35 years in obscurity, he made a heralded return to New York in 2003 and resumed his music career.

Leo Lindberg, 15, knows something about obscurity: he spent the first three years of his life without a jazz gig. By age four, his musical virtuosity was thrilling the musician friends of his father, Owe, a jazz bassist in Stockholm, and soon little Leo was playing nightclubs steadily, first with his father, and now with his own group. He plays bass, drums, keyboards, flute and saxophone.

His hair is mussed; his teeth have braces; his splotchy cheeks have peach-fuzz. He looks like he should be in Times Square with his parents, staring up at buildings and puzzling over a subway map. Technically, Leo is just another high school student on his first trip to New York City.

But it is hardly a typical visit. He is staying at the Grimes’s apartment walk-up building on York Avenue, above a pizza place. And he is playing a string of jazz gigs with Mr. Grimes.

“They see each other as bandmates, even though they might look very different,” said Mr. Grimes’s wife, Margaret Davis-Grimes.

Their relationship began in July 2003, when Mr. Grimes received a letter from this Swedish boy.

“Hallo Henry!” it began. “My name is Leo Lindberg and I am 9 years old. I listen to jazz music all the time … and play double-bass drums and trumpet.”

Leo wrote that he heard Mr. Grimes playing on a Don Cherry recording called “Complete Communion” and that, “I thought you were fantastic specially the bow solos and your sound.” He wrote that “I was very happy” that Mr. Grimes was playing again.

“Hope you feel good and starts playing again,” he wrote. “You are my bass hero.”

He included a photograph of himself with his double-bass and wearing a T-shirt with a photograph of Mr. Grimes.

Mr. Grimes wrote back and the two became pen pals.

“I figured I could use the stimulation,” Mr. Grimes said on Wednesday, as they both prepared to play with the guitarist Brandon Ross at the Issue Project Room, a performance space on Third Street in Brooklyn.

After 2003, Mr. Grimes toured several times in Scandinavia and each time, played with Leo at nightclubs.

“Some people may see lots of differences between them,” Ms. Davis-Grimes said. “But they just regard each other as bandmates.”

By the time Mr. Grimes became a prominent bassist in avant-garde jazz circles in the mid-1960s, he had already played with the likes of Charles Mingus, Thelonious Monk, Miles Davis, John Coltrane and Sonny Rollins. But in 1968, Mr. Grimes disappeared from the music scene. Broke and troubled, he sold his bass and was sometimes homeless and sometimes worked as a janitor and as a construction worker and lived in a furnished room in downtown Los Angeles.

Some jazz sources listed him as dead. Then, in 2002, a fan located him, and began playing his old recordings for him. With a bass donated by the bassist William Parker, he returned to New York in 2003 and has played more than 300 gigs since then around the world.

On Wednesday, Mr. Grimes unbuttoned his outer shirt to reveal a T-shirt he had made bearing the photograph of young Leo with his bass. Leo was warming up on the piano. He played note-for-note Wynton Kelly’s solo from “Freddie Freeloader,” a well-known blues number off the Miles Davis album “Kind of Blue.” Then he played Thelonious Monk’s “Bye-Ya,” and Mr. Grimes played along. Then he played “Old Devil Moon,” using the bass line Mr. Grimes played on a McCoy Tyner record “Reaching Fourth.”

Leo had transcribed and memorized Mr. Grimes’s bass solo from the song “Reaching Fourth,” on that album, and he began playing it on the piano. Mr. Grimes, who moves slowly when he is not playing, leaned forward abruptly, and said, “You know that?”

Accompanying Leo to New York is Fredrik Olsson, 35, a jazz guitarist from Stockholm who plays in Leo’s organ trio. Neither Leo nor Mr. Grimes could be described as verbose and Leo said he avoids asking many questions.

“I don’t want to be the boring guy to ask him, ‘What was it like to play with Sonny Rollins?’ and all this,” he said. “But of course, I do want to know.”

The way you learn from Mr. Grimes is by playing together.

“The one thing that Henry has taught me is swing,” said Leo, who has a reputation among older jazzmen of falling asleep before the gig is over. Ms. Davis-Grimes said they took Leo to see Roy Haynes perform in Brooklyn, and that, “We were going to meet Roy afterward, but of all of us old folks, guess who said he was too tired?”

Leo blushed and said, “Yes, looking back, I see this was the wrong decision.”