Architect Rafael Viñoly is losing count of his pianos. It’s out of control.

Three in the city, two on Long Island, one in London, another in South America, one in Miami, another lent to his son, maybe one in Los Angeles. He’s about to bump up the tally with a Fazioli from Venice. Will it go into the new office he’s about to set up in Dubai?

“It’s embarrassing. This becomes a fanaticism,” Mr. Viñoly said recently at his TriBeCa headquarters, which are furnished with not one, but two Steinway concert grands yin-yanging.

“One of these belongs to Mitsuko [Uchida], bought for the Marlboro Festival,” he said. “I keep it for her. She’ll probably show up tomorrow to practice. Sometimes we play together.”

This was two days before Ms. Uchida’s Carnegie recital. In the past, Rostropovich visited him; Martha Argerich is a regular when she doesn’t cancel. Maurizio Pollini, however, always travels with his own piano, so the two meet elsewhere.

The Uruguayan-born Mr. Viñoly is no mere collector. He is a bona fide musician who once contemplated a career as a pianist; he attended a music conservatory before switching fields, and knows how to finger those 88 ivories.

“Amazingly, I should confess that I still do consider sitting down to work out something as it deserves to work out,” he said. Scores by Beethoven, Mozart, Chopin, and Schumann clutter his pianos.

It’s hard to believe that someone as globally busy as Mr. Viñoly, with 250 employees to manage around the world, still has time for practice, practice, practice in addition to attending concerts at Carnegie Hall.

“I spend more time there than here,” he said. “It’s really a spectacular place.” And although he is among the world’s most knowledgeable architects in music, he’s not one to pay glib lip service to oft-recited similarities between the two disciplines. For him, architecture isn’t frozen music.

“There is no piece of music that could relate to anything else but itself and its world,” he asserted. “It is truly an independent. The one thing coplanar with music is the compositional aspect, the fact that you are composing something. Architecture is essentially a score, and what happens with it depends on the people who play it, enjoy it, use it, or hate it.”

That said, his design for Verizon Hall, the Philadelphia Orchestra’s home in the Kimmel Center for the Performing Arts, resembles the curvaceous interior of a big stringed instrument.

Mr. Viñoly’s own performance hall is his small private theater, a charming piano pavilion he designed and built eight years ago on his 5-acre property in Water Mill, Long Island.

“It’s better than a swimming pool, better than a tennis court,” he said.

The charming retreat on Mill Pond, which he shares with his Argentinean wife, Diana, features a big white house whose main section dates from 1790. There’s a little teahouse near the lake, and a swimming pool. Instead of a tennis court, there’s a 2,500-square-foot, freestanding, wooden-and-glass structure, situated on a small slope, with wraparound patio. Visible through the windows are a gorgeous Hamburg Steinway on a small proscenium, in front of which are 24 seats, with some more on a mezzanine. On the lower level is a guest room.

It’s rare that an architect is his own client.

“It’s the most horrible thing you could ever wish,” he said. “It’s very difficult to understand, as tiny as this is, it takes exactly the same amount of work as doing the Tokyo International Forum,” one of his most famous buildings. “There’s no distinction between the levels of responsibility and intricacy. The one thing that I chose to do, which is usually something you cannot do, is to forget the budget. To put it another way, it was four times over budget. I should have fired myself.”

But the little theater is the icing on the cake of Mr. Viñoly’s passion. Daniel Barenboim has stayed in the house and played there. Unlike Mr. Barenboim, Mr. Viñoly is too shy to perform in public, in spite of a recent invitation to play at Royal Albert Hall in London.

“Battling the mysteries of performance is a lifelong problem for most of us,” he mused. He said he was astounded when legendary piano virtuoso Alfred Brendel told him before retiring several years ago that he was going to “try to understand Mozart.” That someone at such a level of accomplishment still felt he had to come to terms with that music boggles the mind but beautifully demonstrates the bottomless depths music presents to a serious, probing musician.

Mr. Viñoly would like to delve deeper into his Mozart, too. That’s why he’s taken up piano lessons again at age 63.

“‘You want to play Mozart?'” he said, quoting his teacher. “‘This is like walking naked on Fifth Avenue, so you have to be in good shape. Because you can’t hide anything.'” He’s also learning Chopin’s G minor Ballade; Beethoven’s Piano Sonata in A Major, Op. 101; Six Little Piano Pieces by Schoenberg, and Schumann’s “Kreisleriana,” which he says is “one of the most difficult pieces on the face of the earth.”

Mr. Viñoly is no show-off. Though a mean sight reader, he comprehends that musical performance not only requires understanding and technique, but an ability to project a compelling interpretation in front of an audience, usually by memory.

“Greatness is so rare, and so fundamental in music,” he said. “That’s the reason I don’t play, because you really need to be at the level of Mitsuko.” He laughed. “Mitsuko told me once that she’s not a great pianist but a great piano chooser, and I’m looking forward for her to choose one for me.”

So there might be yet another piano to add to the collection.

“I never thought this was a hobby,” Mr. Viñoly said. “It’s not an entertainment. It’s a rare combination of pleasure and suffering.”