That's accomplished by deduction based on exhaustive research, and by playing on instruments that are old (at least one in this room was already in service when Vivaldi and Bach sat down to write) or are made new-old: the designs, woods, resins, glues and techniques are those in use 300 years ago and the strings are made of sheep gut rather than synthetic or steel.
Some differences are subtle: the angle of a violin's neck changed to increase volume when performances moved from salons to concert halls. But some are more obvious: the so-called "swan-bill" bows, typically made of snakewood, look more like an archer's weapon than the modern axe-head bow and, by tapering towards the tip, have a built-in volume control. More noticeably still, violins and violas don't have chin rests and the cellists, without a spike, clasp their instruments between their thighs to hold them at the right height.
"Sometimes, I think we deserve danger money," says the orchestra's co-director Miranda Hutton, as she shows me how hard it is to slide the hand down the instrument's neck when it is not anchored under the chin.
The cumulative effect of all these differences is striking. Hutton tells me that, in contrast to its singing classical counterpart, the baroque violin has a speaking voice.
It's not a metaphor that suggested itself to me.
The sound filling the room seemed richer than that of string orchestras I've heard, and had a freshness and exuberance about it, as of something newly made.
"It's a real passion for us, to play the music as the composer intended it and would have heard it," says Hutton. "When you really get into it you hear this wonderful lightness and dance sound. The instruments really bring it to life."
The concertmaster, Ryo Terakado, explains during a tea break that a violin is always a violin. "Of all the instruments the violin is the least changed, because it was already perfect when they invented it.
"But playing baroque violin is like starting again. The gut strings react so differently. It's like you have learned to walk, now do a tightrope."
Now in its 11th year, NZ Barok (the spelling reflects the fact that many of the players have trained in the Netherlands, a mecca of the early-music revival last century) is the country's only baroque orchestra.
One of the world's leading baroque violinists, Brussels-based Terakado is in the country to lead the orchestra in concerts this weekend. But don't call him a conductor: the ensemble has no one in that new-fangled role because, as Hutton explains, that's how it was in Bach's day.
Instead, the group works collectively, cueing and watching each other, often with what seems like a sixth sense.
"In a symphony orchestra," says Hutton, "you are not allowed to speak.
"You have to shut up, do as you're told and have no thoughts of your own. In this, every person thinks independently and can contribute."
This collegial approach creates a light-hearted atmosphere.
When Terakado gently suggests a change in one violinist's technique, she winces self-deprecatingly.
"I know," she wails. "It sounds like a dog."
"What kind of dog?" a colleague asks.
"A dog that barks," deadpans Terakado.
• NZ Barok plays in Hamilton on Friday and Auckland on Saturday and Sunday. www.nzbarok.org.nz