The main harmonizing element has been a list by which the musicians have agreed to abide. It is an hour-by-hour performance rotation each day from 10 a.m. to 7 p.m. that Mr. Muniz creates every morning and texts to five regular musicians.
A vital consideration in making the lineup is keeping certain musicians apart, to avoid confrontations.
“Imagine that — grown men,” said Mr. Muniz, who despite a gruff edge and a low tolerance for people who do not tip was seen as fair and tough enough to be keeper of the list.
“Some days, I’ll get 10,000 texts that someone took an extra hour, and I’ll have to come here and solve it,” he said. “But for now, it’s working.”
“The cops were here every day,” Mr. Muniz added. “They ain’t coming anymore.”
Contentiousness has always been part of performing here, said Randy DeLuca, 67, who remembers when the spot was ruled by Gary dos Santos, who called himself the mayor of Strawberry Fields.
For nearly two decades, Mr. dos Santos arranged flowers on the mosaic and used his overbearing presence to select who would be allowed to play.
“He annoyed people, but he provided structure,” Mr. DeLuca said of Mr. dos Santos, who died in 2013 at age 49 from leukemia, leaving the musicians to battle it out for themselves.
“After Gary died, it went into chaos,” Mr. DeLuca said.
But the list has helped reduce the daily haggling over how long and often each musician gets to play, said Jimmy Dalton Baker, 28, another regular, who called live renditions of songs by Mr. Lennon and the Beatles an integral part of visiting Strawberry Fields.
“The tourists don’t come here to see us arguing,” he said. “They come for the John Lennon experience, and we’re the soundtrack for that experience.”
This was apparent on a recent weekday when Ryan Hagen got on one knee and extended an engagement ring to his girlfriend, Leann Harber-Crosno, as one performer, Billy Oganasanti, 59, indulged the couple’s request to play “Imagine.”
“I play to get everyone in a good mood,” said Mr. Oganasanti, who invites listeners to sing and offers them a tambourine.
To tourists, he is an engaging performer with a wide repertoire and witty banter, but to his musician colleagues he is overly zealous in claiming open slots.
He called the new organization system a good solution and defended his right to more playing time, citing his devotion to the Beatles and Mr. Lennon, both of whom he said he had seen perform live.
“They’re not real Beatles fans — they’re just playing here for the money,” Mr. Oganasanti said of the competing musicians. “This is not a place you should be playing just for money.’’
Like many of the current musicians, Mr. dos Santos adhered to the view that authority over Strawberry Fields came from Mr. Lennon’s spirit channeled through his widow, Yoko Ono, who helped create the memorial. She still lives in the Dakota.
Most of the musicians have stories about Ms. Ono visiting the park and, they said, tacitly blessing their right to play there by enjoying their songs. José Feliciano, the singer and guitar player, who has given impromptu performances at Strawberry Fields, said continuing the busking tradition there was “the way John Lennon would have wanted it if he were alive,” and that, perhaps, Ms. Ono could help things run smoothly. A representative for Ms. Ono said she would not comment on what happens in Strawberry Fields.
Some buskers have bragged about banner days on which they have brought in well over $50 an hour. But more often, they can be heard grousing about the smattering of crumpled dollar bills in their guitar cases after performing one heartfelt Beatles song after another.
Still, the musicians said they supported themselves with the tips they earned there, and several, including Mr. Muniz and Mr. Baker, said the money enabled them to escape homelessness.
Mr. Muniz, a Queens native, said he left home as a teenager to live on the streets. He learned to play the guitar from an instruction book.
Recently, Mr. Baker took Mr. Muniz’s place at the bench and laid his guitar case at his feet and planted a dollar bill in it to give tourists a hint. As a high school group from Ottawa filed by, he strummed the chords to “Imagine” and began his usual polite patter.
“Welcome to John Lennon’s second home,” Mr. Baker said. “It’s so nice to see so many beautiful faces out there. You guys are keeping us alive.”
And the new code of conduct is keeping the musicians in line. As another regular, Charlie Clementz, 50, said: “We’re policing ourselves now. It’s definitely better.”