Piano lessons and merit bonuses are key elements of two charter schools poised to receive approval this week to open in New York City in 2016.

The two schools, the New York City Charter School of the Arts and the Bronx Charter School for Excellence 2, have both had their applications recommended by officials at the SUNY Charter School Institute. If approved by the institute’s board of trustees on Oct. 15, the schools would bring the total number of city charter schools set to open next year to 26.

The City School of the Arts, whose three founders worked together on an arts education program in the Bronx, plans to open next August with about 100 sixth graders. The middle school will place a heavy emphasis on music, with new students spending nearly three hours on piano instruction and learning to read music every week, according to a summary of its application posted online.

The application also addresses some contentious enrollment issues. It notes that the school will “backfill all vacant seats at all grade levels” and that it will not require an audition or portfolio for admission — a given, since charter schools must enroll students through lotteries, but perhaps a nod to how the school will differ from the city’s many selective district middle schools.

Arthur Levine, former president of Teachers College, has agreed to join the school’s board. Levine said he had been impressed with the “tenacity” of founder Jamie Davidson to open her own school, since many prospective charters receive extra points for being replications.

“She is a person who dreamed of a school and then made it happen,” said Levine, now president of the Woodrow Wilson National Fellowship Foundation. “She didn’t make it happen through one of the charter chains.”

Davidson declined to comment before the Thursday vote.

The school wants to open in Lower Manhattan over the objections of local elected parent councils. The Community Education Council in District 1, which covers the Lower East Side and Chinatown, has written a 42-page opposition memo that says the application lacks specifics about its enrollment policies and argues there is not enough demand in the small district to justify its opening.

The parents are also asking questions about whether public notification rules were followed.

The city education department missed a deadline to hold a hearing on the proposal by three weeks. City officials held the hearing on Oct. 1 and comments were sent to SUNY four days later, a SUNY spokeswoman said.

The comments were not reflected in SUNY’s official recommendation.

“To invite public comment on the one hand but exclude it on the other really speaks to a broken process,” said Luke Henry, a District 1 council member.

SUNY spokeswoman Mahati Tonk said the comments would be available soon, but insisted that city officials were the ones who were late.

“The Institute always summarizes comments, even those received after requested deadlines,” Tonk said in a statement.

The city did not immediately respond to questions about the process.

The other school under consideration would replicate the Bronx Charter School for Excellence, an elementary school that is one of the highest performing in that borough. On last year’s state tests, 48 percent of students were proficient in English and 62 percent were proficient in math. The rates were double the averages of the Bronx’s District 11, where the school is located.

The application for Bronx Charter School for Excellence 2 notes that teachers and staff will receive bonuses based on student performance, but does not offer additional details. Representatives from the school did not respond to emails and calls on Tuesday.

The new schools would add to the growing number of charter schools in New York City, where 205 charter schools are open this year and another 24 are already preparing to open their doors in fall 2016.

That has posed a political challenge for Mayor Bill de Blasio, who has been cool to charter schools’ growth since taking office and believes district schools — which still serve the vast majority of the city’s student population — deserve more attention. Success Academy Charter Schools CEO Eva Moskowitz and allied groups like Families for Excellent Schools have countered that the district school system is incapable of dramatically improving public education and that the city should extend its support for an expansion of charter schools.

Still, de Blasio is on the hook to accommodate the space needs of new charter schools because of a state law passed in 2014.

The City School for the Arts plans to request space inside of a city-owned building in Manhattan’s districts 1 or 2. If denied, the city would have to reimburse the school for costs associated with operating in private space, which could reach $2,800 per student next year. (The Bronx school has already decided to open in private space, which disqualifies it from being eligible for rent reimbursement from the city, according to SUNY’s application summary.)

The two schools would be the first approved by SUNY in over a year. The Thursday meeting will also be SUNY’s first since its board chair Joseph Belluck vowed to block new charter schools from opening if the institute didn’t receive additional funding — comments he backed down from in an interview Tuesday.

“The process was sort of underway at the time I made the comments and I felt it was not appropriate to punish these two schools, which both seem very strong, because of our concerns with funding for the institute,” Belluck said.

The two schools would mark the fewest approved by SUNY since 2006 come just one year after the institute approved a record-high 24 charter applications, 14 of which were for new schools in the Success Academy network.

The small number of approvals underscores the uncertainty that has surrounded New York’s charter-school governance in the last year.

It wasn’t clear until June that SUNY would have any New York City charters left to approve, since it had neared its limit under the state’s charter-school cap. A last-minute legislative deal gave more charters to SUNY, but left little time for operators to prepare their applications.

Some operators previously applied through the state’s other charter authorizer, the State Education Department, which had more charters to approve for the city. The department abruptly rejected all applicants in March and although it is considering three charter applications for the city next year, some say their next try will be through SUNY.

“I applied through SED because it was the only option,” said Voice Charter School Principal Franklin Headley, who wants to open a second school. “I know more about SUNY’s process and I’ve heard positive things about their relationship with schools. Now that SUNY has charters, I think there’s an opportunity for us to apply through them.”