Zinman pauses when I ask whether he will be giving us Mozart's music as the audiences of 1787 might have heard it. "I do take into account what we know about authentic performance styles," he explains. "But I'm not one of those non-vibrato nuts."
After a distinguished career in his native United States, Zinman cemented an international reputation with Zurich's Tonhalle Orchestra. He has been its music director since 1995, with his contract now extended until 2015. "I'll be almost 80 then, so I can retire."
Zurich has been "a place that was about moving forward," he says. "I have an orchestra that doesn't have to worry whether it will be there next year and we don't have to negotiate salaries every three years."
Of Zinman's many critically praised recordings with this orchestra, the most celebrated is his complete cycle of Beethoven symphonies which "were recorded using the ideas I had already tried out with many other orchestras".
In 2006 there was a boxed set of the complete Strauss symphonic poems, along with the later Oboe Concerto and Four Last Songs, "beautiful pieces that sum up what Strauss had to say".
But don't ask this genial American to conduct Strauss' ballet, Joseph's Legend. He positively dislikes it and "could only do it if I wanted to punish an orchestra".
Which brings up the issue of what does a conductor do when he has to tackle a score for which he has little sympathy. "Every once in a while you have to," he cautions. "It happens more with concertos than symphonic pieces. You just fake it or try to find a way to love it - and sometimes you do end up loving it."
From his European vantage point, Zinman does worry about the health of the American music scene. "We're facing a crisis. When I was growing up, classical music was something that immigrants brought to America; they wanted to have it.
"That's changed now and their children are less interested, their children's children even less so. And when I worked in Baltimore there were four newspapers, each with a music critic. Now there's only one writer, coming up with two inches a week. There isn't someone creating the desire to go to a concert, which a good music critic does."
What: New Zealand Symphony Orchestra
Where and when: Auckland Town Hall, tonight at 8pm