"Baroque music is among the most interesting music to play with other people," he says. "This whole social dimension of performing is very important for me."
Looking back, he acknowledges the influence of "those key recordings that were coming from England and Holland in the 1970s with names like Christopher Hogwood and Nikolaus Harnoncourt.
"They were the very first generation in Europe and their performances are still rewarding."
When I ask Alessandrini about his group encompassing more than a century of Italian music, he tells me that mere dates are immaterial.
"The distance between these composers and their music is not one of time, but the cities in which they worked," he says.
"You cannot approach music from Venice as you would pieces that come from Naples or Rome. At that time, Italy was not one unified country, and powerful cities, courts and churches would define themselves through the art and music that they sponsored and created."
Monteverdi's Vespers of 1610 was written during the composer's time in the court of Mantua, which Alessandrini describes as "one of the leading music centres in Northern Italy with Monteverdi working there".
The 90-minute score is a veritable monument, in the words of the conductor "consisting of absolutely new music, all in the latest concertato style that Monteverdi and his contemporaries used to explore the expressive potential of the words being sung.
"There are still moments of very strict counterpoint, but it's far from the Renaissance smoothness of Palestrina."
There is also a deeply personal dimension to this music, written when the composer was a young husband and father. "Surviving in the Mantua court was a financial struggle," Alessandrini tells me.
"Life was not easy for a musician in those days," he sighs. "Monteverdi would have better times when he moved to Venice as St Mark's was a prestigious chapel and his post well paid. He worried a lot about his young family, especially after his wife died in 1607.
The interpretation of this monumental piece is one of the most contested in all music ("a very complex story", as Alessandrini wryly comments), leading to many, sometimes startlingly diverse, recordings.
I'm told that the first performance of the Vespers was purely vocal, with instruments being added for its 1610 publication.
Next month the Michael Fowler Centre will resonate to an ensemble of two trumpet-like cornetti, three trombones, two violins and Alessandrini on keyboard continuo.
Concerto Italiano's 2004 recording of the Vespers is one of its finest available, and the perfect preview of the insights that this group will bring to Monteverdi.
And Alessandrini admits that, yes, CDs are very important: "Not only do they verify what is working in your performance, but they take your music all around the world, even to New Zealand."
