Kudos for pointing out that this is a classic example of menu costs, but price changes occur for many reasons besides the Fed. Even if you had a fixed supply of gold coins and nobody could ever mine new coins, the value of those coins would change in proportion to the value of the overall economy, and that will tend to change for all sorts of reasons such as population growth.
But there isn't a fixed amount of gold. More gold gets mined when the demand for currency rises relative to the price of energy. The price of oil roughly tracks the price of gold not because gold is a magical denominator, but because an ounce of gold represents a certain amount of sunk energy that mined it.