Interest rate determination in the real world I have just learnt about the demand and supply framework for money and how the equilibrium interest rate in an economy can be determined. In theory, based on that framework, an increase in nominal incomes would lead to an increase in the demand for money, causing interest rates to rise. However, in reality, I don't see that occurring. In fact, in reality, say in the United States, rates are often set by the Federal Reserve through manipulation of the money supply. To me, rates don't seem to change as a result of changes in nominal incomes. Why is this so?
There is one more element to take into account into this demand and supply schedule: how does the central bank conduct it's (traditional) monetary policy? There are two options:

decide on base money supplied and let the money market interest rate be determined endogenously as the money market equilibrium. In this case, for a given money multiplier, the supply of money is vertical and the interest rate adjusts to clear the market. In this case: an increase in money demand does affect money market rates;
decide on the appropriate interest rate and let the amount of base money supplied to the market be endogenously determined by the money market equilibrium. In this case, supply of money is horizontal and, at the central bank will supply all the base money that is demanded by the financial sector at the chosen interest rate. An increase in money demand is now completely accommodated by increased money supply.

The role of nominal incomes in shifting money demand seems, at least to me, mostly related to periods of volatile inflation rates: if prices suddenly increase by 5% you'll need 5% more money to finance all transactions. So, households, firms, banks, ... will want to keep a slightly higher cash balance.
So, two reasons why rates may not respond to nominal income:

nominal income affects money demand, but increases in money demand may be, depending on the policy instrument, completely accommodated by increased supply;
fluctuations in nominal income may not be a dominant driver of changes in money demand. In this case there may still be a causal effect, but it's just of crazy small importance compared to other factors that shift money demand.