"As you can tell ... it's only because he wants to (retire) and not because he has to that he's doing this," Cleve said.
He read a letter of congratulations from President Bill Clinton and asked Tuckwell to say a few words. But the musician wasn't ready to make a speech.
"We still have stuff to play yet. Let's get on with the music," Tuckwell said, to more applause.
And so he did, connecting the circle of his career with a contemporary horn concerto written for Tuckwell by Scottish composer Oliver Knussen. The piece seemed to make the horn sound even more dramatic and resulted in a standing ovation and three curtain calls for Tuckwell.
But it wasn't just fans who came to pay homage to Tuckwell.
"In a sense, one could say he was one of the most important horn players, if not the most important horn player, in the world," said Stephen Wigler, music critic for The (Baltimore) Sun.
For critics like Wigler, two things are remarkable about Barry Tuckwell: that he can play a notoriously difficult instrument so well; and that he has done it for so long.
First, the horn. It's approximately 20 feet of coiled brass tubing that requires the most subtle of moves to produce the right sound; one fingering can produce five different notes, greatly improving the chances of a "crack" between the notes.
"The tiniest drop of moisture in all that piping can produce the most unbelievable honk," Wigler said.
Then there's the longevity. Age and its effect on facial muscles, teeth, gums and the respiratory system can do terrible things to a hornist's ability to play. But Tuckwell, 65, is still going strong.
"He is still playing as well as ever, which is miraculous," Wigler said.
Jonathan Palevsky, program director of WBJC-FM (95.1), a classical radio station in Baltimore, called Tuckwell a ground-breaker who has brought renewed attention to the horn.
Tuckwell was the first horn player to give up a prestigious place in a symphony - once the first chair horn with the London Symphony Orchestra - and take a solo act on the road.
It turned out to be professionally rewarding for Tuckwell, but Palevsky said the real winners have been music fans across the globe.
"You need a guy who's just going to go around the world and wow people. And for the horn, that person was Barry Tuckwell," he said.
Tuckwell said earlier this week he was "overwhelmed" by the flood of written and spoken praise. But it has not inflated his ego, he said.
"It has just the opposite effect. It makes me feel really small," he said.
After the Thursday night performance, Tuckwell said he again was humbled.
"It comes as a shock when you get sustained applause at the beginning, because then you think, `I haven't done anything yet,'" he said.
He said he isn't ready to consider the bittersweet nature of the fans' and critics' reaction - that soon there will be no more concerts and no more standing ovations.
"I still have to concentrate. You can't think about all of that," he said.
Then he paused.
"I'll think about that at noon Saturday" after his final concert, he said.