Kantor's quick thinking and ability to play songs from multiple eras and genres has made him a fan favorite since becoming the organist in 2003. He's yet to miss a home game, playing a total of 1,226 straight games.
"I'm my own worst critic, but I would say it took me about eight years before I felt like I could say to people, 'I'm good at this,'" Kantor said. "It was very gradual. It's not unlike a ballplayer and it taking years from the time they are drafted to the time they make it to the Majors."
About half of all Major League teams have an organist. It has come back into favor with many fans as organists have tried to modernize what they play and how they take requests.
Kantor carries around a notebook that becomes thicker and thicker each year, with roughly 1,000 songs in it.
"When I think of a good one -- sometimes walking down the street in the middle of winter -- I try to find the notebook and write it down," said Kantor.
The notebook has become less necessary over the past few seasons since Kantor joined Twitter in late 2011, asking fans to tweet requests at him before and during games.
"I've been doing it for so long that I can listen to it once or twice and then mimic it back," Kantor said. "I try to pick the most interesting part of the song. Does it have a good melody? I want the most effective piece of the song."
Red Sox DJ TJ Connelly, who's been working with Kantor since 2005 and is also the DJ for the New England Patriots at Gillette Stadium, said he can't imagine Fenway without Kantor.
"I miss Josh considerably while DJing at Gillette," Connelly said. "It is an important part of the overall experience to have Josh at Fenway."
Before Kantor gets behind the organ and plays any tune, he arrives at the ballpark about two hours before first pitch to talk with the rotating Red Sox technical director (the club has three: Steve Roman, P.J. Huot and Mike Testa) and Connelly about how things went the previous game and how to coordinate things that are happening that game.
As fans begin to stream through the gates 90 minutes before first pitch, Kantor begins to play a 40-minute medley of songs. It's the only time the whole night he gets to play songs in their entirety.
"My predecessor identified Josh as a panic button," Connelly said. "If something is going wrong and you don't know what's up, just say 'Josh,' and he will play something and it will be OK."
Things weren't always this easy for Kantor. He still remembers that first game against the Orioles in 2003, when he walked into the men's restroom in the back of the press box before the game to splash cold water on his face as his heart pounded.
"As I walked in, [Red Sox announcer] Joe Castiglione was there, and he could tell that I was really pale," Kantor said. "We'd never met. He asked if I was OK and just sort of gave me a pep talk. He eased my nerves just enough where I could go and play."
While being the Red Sox's organist is a huge commitment, Kantor still finds time to play local shows and travel across the United States and to foreign countries.
Kantor played the keyboards for a festival in the Arctic Circle in Norway a few years ago, has jammed with John Paul Jones of Led Zeppelin and plays the keyboards for The Baseball Project, a band that includes Scott McCaughey (who played with R.E.M.) and Steve Wynn (of the Dream Syndicate). Kantor also helped form a band called The Spilt Squad, which includes Clem Burke from Blondie and Eddie Munoz from The Plimsouls.
When Kantor plays with local musicians, it's usually in Cambridge, Mass., performing in venues like Atwood's Tavern, Club Passim and Lizard Lounge.
One of those musicians is Lisa Bastoni, who's performed with Kantor for nearly 15 years. With Bastoni about to release a new album, Kantor has played on the album, worked out arrangements for songs and rehearsed with the rest of the band.
"When we perform together, there's a comfort level that has developed over time, that I think probably shows in our stage banter and also in Josh's ability to anticipate when I'll make an impromptu change, or forget the chords to one of my own songs," Bastoni said. "I know he's got my back and can help right the ship.
"When we load in to play some tiny rock club or folk venue, I never get the sense that he sees our shows any differently."
While he plays about 80 shows a year, Kantor's schedule centers around the baseball season. And if he has anything to say about it, Kantor will be the organist at Fenway for many more years to come.
"I hope I'm still doing this in 20 years and I look back on 2017 and think, 'Yeah, I was OK, but I'm not nearly as good as I was now,'" Kantor said. "I hope I keep getting better."