The original West End productions of Jesus Christ Superstar, Evita, Cats and Chicago have all fallen under his baton. As a session keyboard player he has served Hollywood composers John Williams, Jerry Goldsmith, and Marvin Hamlisch. He gets calls to MD for Victoria Wood, Bryn Terfel, Micahel Ball and Lesley Garrett.
This week he is on the road with Mickey Mouse, recreating a live musical experience of Disney's Fantasia that was a triumph at London's Royal Albert Hall in modern arenas in Manchester, Brimingham and kicking off on Friday at Glasgow's new SSE Hydro.
The show has been produced by Jonathan Heely, who has worked with Disney since 1981 when he helped recreate the score for the original classical animated film for a digital recording, a process he has continued through much of the classic Disney canon. The Fantasia show screens scenes from the 1940 Fantasia and its millennial revisitation, Fantasia 2000, with the music played live by the Royal Philharmonic Concert Orchestra. Its a process that demands much of Firman, but he is man who is absolutely across all the technology that keeping a big band synchronised with moving images requires.
Firman points out that Walt Disney did not ask Leopold Stokowski to perform the same trick. When Fantasia was made, the music was recorded first and the animators made Mickey move to the beat.
"There are times when I just look at the picture, and there is a click track from time to time, but more important are the 'punches' and 'streamers' that I can see on my screen, bursts of light and vertical lines that help me guage when a certain action or 'sync point' is going to arrive."
Firman illustrates what he means vocally over the phone, with the opening bars of Beethoven's Fifth Symphony. It is perfectly clear to me at the time, but the English language lacks the vocabulary to pass that intelligence on, so you will just have to take my word for it.
Firman's form in this discipline is bang up to date. He works a lot in Denmark, where he is Principal Guest Conductor with the Danish Radio Sinfonietta, and has performed the score of Pirates of the Caribbean there and in London with a screening of the film, a process he is about to repeat with the second film in the series, which has even better music, he says.
"And gosh, isn't Keira Knightley gorgeous in that one?" he adds, suggesting that the images are not entirely ignored.
"There's a lot more straightforward click track with that, because it is more modern music. Really with classical repertoire, it is counter-intuitive to stick so slavishly to the beat. You want to go faster or slower - tempi are so inate. But I think I enjoy it because of my history as a session player: I understand what the music is supposed to do."
The Fantasia live show restores some music, like Debussy's Claire de Lune, that failed to make the final cut of the film, and combines it with an edited version of the full film, which Stokowski, the celebrity conductor of his day, saw very much as an "art" project, working closely with the stories the animators illustrated.
Firman thinks that although there were already many serious composers at work in Hollywood, Fantasia helped give credibility to the music they were writing and introduced a new audience to the symphony orchestra.
"When the original film was released, Disney created a fancy new sound system for its screening, a sort of percursor of Dolby surround that Pirates of the Caribbean was written to make the most of, adding all those electronic effects and samples."
Working on such proven hits is a very different experience than working in the West End, says Firman, who was off to see Andrew Lloyd Webber's new Profumo musical, Stephen Ward, on the day we spoke.
"In musical theatre you can have no idea what will be a success or a failure. It is impossible to predict what will work. That is a story about a noble man with a great flaw and time of political revolution that threw up interesting characters. But do people still remember it?"
By contrast, the successful Pirates is "very effective and tuneful, but not a work of genius".
"It is a swashbuckling silly movie that leaves people time to take in the performance of the band too. Because people like seeing people doing live things."
As well as looking at Keira Knightley - and Mickey Mouse.
Disney Fantasia; Live in Concert is at SSE Hydro, Glasgow, on Friday.