The difficulty lies in what Gjelsten describes as "their unusual play of opposites and contradictions.
"It's the reality of life. Life's not all pretty; it's not like in earlier classical music where you might have a whole movement that's happy and another that's sad. In late Beethoven, every phrase is full of our daily life experiences."
Gjelsten's own phrases sometimes trail off, but you sense the man draws an almost holistic strength from both the scores and the playing of them.
As for audiences, "it's a kind of marathon," he warns. "People need to be psyched-in as if they were experiencing three Shakespeare plays in one evening."
Yet the concerts seem far less daunting when he starts to outline the basic musical ingredients that go into them, from song and dance to an element of high drama.
"There's humour as well. There's also the discourse between the four of us; so animated at times that it almost threatens to break down into some kind of argument."
In fact, one could not hope for a more collegial crew than these four musicians who will celebrate the group's 25th anniversary next month.
"When we find ourselves in an argument during rehearsal, there's a definite sense that we've been there before," he laughs.
For some years, the quartet has been looking for a venue that catches the soul of Auckland, and St Matthew-in-the-City is as close as it comes.
"We love these smaller venues as the audiences are a little closer to us," Gjelsten explains. "Rather than just listen to the beauty of the sound or the excitement of the virtuosity, they can be a part of our conversation. Just as if we were in their sitting-room hearing everything from who's going to do the dishes to what country has just been invaded."
Neither of us is worried if such conversational topics sound rather menial in the presence of the monumental Beethoven.
Like Mahler, Beethoven happily embraced both high and low culture in his music and Gjelsten cannot resist giving me an instance. In Opus 127, after the cellist's favourite slow movement, "ending in an epiphany where you're riding on this E flat major wave and don't want the music to ever stop", Beethoven decides otherwise.
"The scherzo takes you out of your reveries and almost slaps you in the face for being so deeply engrossed," he laughs. "It's time for other experiences."
Where and when: St Matthew-in-the-City, Saturday September 1 at 6pm, Sunday September 2 at 2.30pm