Even with a fixed money supply, prices are still set by a formula that accounts for the velocity of money, or how often any particular unit of money is spent (I spend a dollar at the store, who spends the dollar with a supplier, who spends the dollar by paying a worker, who spends the dollar and so on and so forth). It also accounts for the total economic production.
Peg the whole thing to a semi fixed supply of gold and the prices can still change drastically with shifts in the velocity of money or total aggregate production. That's why fiat currency is good, so that the central bank can pull on different levers to try to keep prices stable, even as different things are happening.