This is Souls in the Great Machine, by Sean McMullen (first in the GreatWinter trilogy). From this review
Low-tech:
Many years after a disaster called Greatwinter destroyed human civilization, people in what was once Australia live in smallish city states. Technology includes fairly ingenious mechanical devices, and guns, but no electricity or electronics.
Human-powered Computer:
Into this mix Sean McMullen throws Lemorel, a young provincial woman and a talented mathematician, whose ambition has led her into several duels. She ends up at Libris, with many other talented mathematicians, supporting the Calculor.
For example, Zarvora, perhaps the closest thing to an overall heroine in the book, kidnaps and imprisons people for years to make the Calculor work.
Hypnotizing cetaceans:
And one more odd feature -- a mysterious Call, to which every animal larger than a cat, including humans, is subject. When the Call happens, once every several days, all these higher animals are compelled to head in one direction, until the Call ceases. Humans have devised tethers, to keep them in place until the Call frees them, and "Mercy Walls", which they run into and push against until set free of the compulsion. If human are careless enough to forget their tether, or to be outside or away from a Mercy Wall, they will head in the direction of the Call, even if it takes them into a river, or over a cliff, or into somebody else's territory.