Although most indoor live performances have been banned in New York since the coronavirus began its deadly spread in March, about a dozen people turned up Wednesday night at Birdland, the jazz club near Times Square, for a 7 p.m. performance that was billed as dinner with live jazz. They had reservations.

Among them was Tricia Tait, 63, of Manhattan, who came for the band, led by the tuba player David Ostwald, which plays the music of Louis Armstrong. Until the pandemic hit, it had performed on most Wednesdays at Birdland. She admitted to health worries “in the back of my mind,” but said, “Sometimes you just have to take a chance and enjoy things.”

While the number of daily new coronavirus cases in New York City has been climbing to levels not seen since April, in-person learning has been suspended at public middle schools and high schools, and Gov. Andrew M. Cuomo warned this week that indoor dining in the city could soon be banned, Birdland and a number of other noted jazz clubs and piano bars across the city have been quietly offering live performances again, arguing that the music they are presenting is “incidental,” and therefore permitted by the pandemic-era guidelines set by the State Liquor Authority.

Those guidelines state that “only incidental music is permissible at this time” and that “advertised and/or ticketed shows are not permissible.” They continue: “Music should be incidental to the dining experience and not the draw itself.”

That has not prevented a number of New York venues that are better known for their performances than their cuisine — including Birdland, the Blue Note and Marie’s Crisis Cafe, a West Village piano bar that reopened Monday with a show tune singalong after declaring itself a dining establishment — from offering live music again.

“We think it’s incidental,” Ryan Paternite, the director of programming and media at Birdland, said of its calendar of performances that include a brass band and a jazz quartet. “It’s background music. That’s the rule.”

The rules have been challenged in court. After Michael Hund, a Buffalo guitarist, filed a lawsuit in August challenging them, a judge in the U.S. District Court in the Western District of New York issued a preliminary injunction last month preventing the state from enforcing its ban on advertised and ticketed shows. “The incidental-music rule prohibits one kind of live music and permits another,” the judge, John L. Sinatra Jr., wrote in his Nov. 13 decision. “This distinction is arbitrary.”

The state is appealing the ruling.

“The science is clear that mass gatherings can easily turn into superspreader events, and it is unconscionable that businesses would attempt to undermine proven public health rules like this as infections, hospitalizations and deaths continue to rise,” William Crowley, a spokesman for the liquor authority, said Thursday. He noted that a federal judge in New York City had ruled in another case that the restrictions were constitutional. He said that the state would “continue to vigorously defend our ability to fight this pandemic whenever it is challenged.”

But it is unclear what, exactly, “incidental” music means. Does that mean a guitar player in the corner? A six-person jazz band like the one that played at Birdland on Wednesday night? The Harlem Gospel Choir, which is set to perform at the Blue Note on Christmas Day? Mr. Crowley did not respond to questions seeking further clarity on Thursday, or about what enforcement actions the state has taken.

Robert Bookman, a lawyer who represents a number of New York’s live music venues, said venues interpreted the ruling as allowing them to advertise and sell tickets for incidental music performances during dinner.

So venues have chosen their words carefully. They are taking dinner reservations, and are announcing calendars of lineups for what Mr. Paternite, of Birdland, characterizes as “background music during dinner.” Unlike Mac’s Public House, the Staten Island bar that declared itself an autonomous zone and was recently lampooned on “Saturday Night Live,” they have no interest in openly flouting regulations.

Mr. Paternite said that Birdland, after laying off nearly all of its 60 employees in March, is now back to what he calls a “skeleton staff” of about 10 people.

“It’s a huge risk for us to be open,” he said. “And it only brings in a pittance. But it helps us out in our agreement with our landlord, because to pay our rent over time and stay current on our utilities and taxes, we need to stay open. But we’re losing massive amounts every day.”

If venues don’t reopen now, he fears, they may never do so. The Jazz Standard, a beloved 130-seat club on East 27th Street in Manhattan, announced last week that it would close permanently because of the pandemic. Arlene’s Grocery, a Lower East Side club that hosted the Strokes before they became well known, said it was “on life support” and, without aid, would have to close on Feb. 1.

Randy Taylor, the bartender and manager at Marie’s Crisis Cafe, said the last time the piano bar had served food was probably back in the 1970s — or perhaps earlier. “There’s a very old kitchen that’s totally disconnected upstairs,” he said. Its dining options are extremely limited: It currently offers $4 bowls of chips and salsa. “We are required to sell them,” he said. “We can’t just give them away.”

Steven Bensusan, the president of Blue Note Entertainment Group, said that he hopes the state does not move to shut down indoor dining.

“I know cases are spiking,” he said. “But we’re doing our best to keep people safe, and I hope we can continue to stay open. We’re not going to be profitable, but we have the ability to give some people work who’ve been with us for a long time.”

The clubs said that they were taking precautions. At the Blue Note, which reopened Nov. 27, the formerly shared tables are now six feet apart and separated by plexiglass barriers, and its two nightly dinner seatings are each capped at 25 percent capacity, or about 50 people. At Marie’s Crisis Cafe, where the masked pianist Alexander Barylski was ensconced behind clear shielding on Wednesday night as he led a jubilant group chorus of “Frosty the Snowman,” Mr. Taylor said that tables were separated by plastic barriers, and that the venue conducted temperature checks and collected contact tracing information at the door.

Marie’s Crisis Cafe had been livestreaming shows on Instagram and its Facebook group page, but Mr. Taylor said it wasn’t the same. On Wednesday night, 10 customers belted out holiday tunes through masks, some sipping their first drinks at a venue since March.

“There have been some tears,” Mr. Taylor said. “People really, really missed us. We can’t see their smiles through their masks, but their eyes say it all.”