As a student at the Royal Danish Academy of Music, young Giordano Bellincampi was constantly reminded of his institution's heritage.

Paintings and sculptures of Denmark's musical great and good covered the place. Here's composer Niels Gade, the school's founder, and the person who conducted the first performance of Mendelssohn's Violin Concerto. There's JPE Hartmann, friend to Chopin, Rossini and Spohr, and the head of a great Danish artistic family that continues to this day (director Lar von Trier is a direct descendant).

Looming over them all, though, was Carl Nielsen, then and now the most important of all Danish musical figures.

"Nielsen was an innovator," says Bellincampi, who conducts Auckland Philharmonia Orchestra in the composer's Symphony No.5 tomorrow. "He had such incredible ideas about harmonies and instrumentation. There are contemporary Danish composers with fantastic international careers but Nielsen is still definitely the big one."

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Before Bellincampi took over as APO music director four years ago, Nielsen was an oddity in our concert halls but the conductor is steadily working his way through the complete set of symphonies. What's the key to Nielsen?

"He challenges the instruments a lot," says Bellincampi. "Sometimes he writes passages that are illogical for that instrument, but they're inspiring for the musician. In the fifth symphony there are long, long lines where the strings never stop - it's really tough - but the important thing is that you sense the urge within humans to express music. It's a spontaneous way of writing that doesn't go through a lot of filters."

With the APO Bellincampi has focused on the core repertoire, but as a young man he was a new-music tyro. From 1997 to 2000 he led the Athelas Sinfonietta, a chamber orchestra dedicated to the works of living Danish composers.

"It was a fantastic period," Bellincampi recalls, "really getting into the process of collaborating with composers about new works."

One of those he worked with was Hans Abrahamsen and in 2020 the APO will play a new horn concerto from the composer. It's a big deal for two reasons. First, Abrahamsen – who, like Bellincampi, is now a professor at the Royal Danish Academy – is a winner of the Grawemeyer Award, essentially the Nobel Prize for composition. Winners comprise a who's who of contemporary music, and include the likes of Lutosławski, Ligeti, John Adams, Tan Dun, Boulez, Takemitsu and Thomas Adès.

Second, the APO co-commissioned the work with several international orchestras, including the most revered band in classical music, the Berlin Philharmonic. The Berlin Phil's Stefan Dohr will play the solo part.

"We are extremely proud of the commission," says Bellincampi, who, when we speak, has just booked tickets to see the piece performed in Germany. Bellincampi will conduct the concerto three weeks after his trip for the opening night of the APO's 2020 season. Despite his history, Bellincampi rarely presents contemporary music with the APO. He says it's a matter of practicality.

"The challenge is that I have a limited number of weeks in New Zealand, and we have an urge to develop the orchestra's core sound. I see it as an important part of the music director's job to be there for Brahms, Mendelssohn and Beethoven, where things are really grounded in the way we are playing."

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As well as Nielsen, this week's concert gives Bellincampi an opportunity to delve into the grounded orchestral meat and drink of Beethoven, with Ning Feng playing the composer's violin concerto. But the conductor also gets to exercise his contemporary chops, when he gives the world premiere of Salina Fisher's Murmuring Light.

"The score has beautiful qualities," says Bellincampi. "The aesthetics seem really clear."

Bellincampi says he hasn't discussed the piece with Fisher and that unlike his days with Athelas, he now prefers not to have long conversations about the details of a new work.

"Over the years I've sensed it's better not to use words because the composer has put all the work into the score. As soon as we start talking about it, it loses some magic, so I've moved towards almost not talking at all before the first reading at a rehearsal. After the first reading and some work we can have a good conversation."

According to Bellincampi, there's nothing like playing a piece of music for the first time.

"I love the point where I give the preparation for the down beat of a new score. Although I have a vision of what it's going to be, and all the musicians are prepared, no one really knows how it will actually sound. That's a gorgeous moment."

Lowdown
What: APO – Conflict & Triumph
Where & when: Auckland Town Hall, Thursday