"It's a tradition that goes back to Monteverdi," he explains. "Then there are the Vivaldi concertos, with those wonderful melodies that must be part of our Italian DNA."
We won't hear Vivaldi on this tour but Anselmi considers him "one of the greatest melody-writers".
Not all the tunes are imbued with the clear skies and abundant vino we associate with the Mediterranean.
"Vivaldi wrote so many adagios that are so very, very touching. But their emotions relate to times which were more positive than our own."
Anselmi points to a Respighi aria, on the upcoming programme, as "very much looking back to that tradition and those times".
What could be more Italian than the concert's opening work, Rossini's G major Sonata a Quattro?
"It's very beautiful and very funny. Rossini was a close friend of Paganini, who influenced some of his string writing."
Anselmi says cellist Pietro Bosna will be playing Une Larme, a set of variations written when Rossini had put his operas behind him and worked on smaller-scale gems that he described as "the sins of my old age".
Another offering from an operatic composer is an allegro by Donizetti that is "a little like Mozart and perhaps a little deeper than Rossini", Anselmi says.
Two pieces in I Musici's programme reflect the world of Italian cinema. Nino Rota's Concerto for Strings was commissioned by the group in 1964, when the composer was established as the man whose music provided haunting backgrounds in the films of Federico Fellini.
"Rota knows how to create atmosphere. There's so much of it here, even a touch of Viennese. But there's also a lot that could easily have come from a Fellini movie."
Luis Bacalov's Concerto Grosso was written for I Musici's 60th anniversary. Bacalov, 80 this year, is known for film scores such as Il Postino but, in the 70s, he collaborated with some of Italy's top progressive rockers.
"You can hear it in the new work," says Anselmi. "It's very difficult," is his first assessment, and then he comes up with a second which suggests I Musici will be delivering a lively concert.
"You could say it was a little like baroque rock."
Performance
What: I Musici di Roma
Where and when: Gallagher Academy of Performing Arts, Hamilton, tomorrow at 5pm; Auckland Town Hall, Monday at 8pm.