What is the frequency of the note nine half-steps below middle A (which has a frequency of $437 \mathrm{cps}$ )? eleven half-steps below middle A?
The frequency nine half-steps below middle $A$ is $\square$ cps. (Round to the nearest integer as needed.)

Step 1 ：Given that the frequency of middle A is 437 cps, we are asked to find the frequency of the note nine half-steps below middle A.

Step 2 ：We use the formula for the frequency of a note n half-steps from a given note, which is \(f = f0 * (2^{n/12})\), where \(f0\) is the frequency of the given note and \(n\) is the number of half-steps.

Step 3 ：In this case, \(f0 = 437\) and \(n = -9\) because we are looking for the frequency of the note nine half-steps below middle A.

Step 4 ：Substituting these values into the formula, we get \(f = 437 * (2^{-9/12})\).

Step 5 ：Calculating the above expression, we get \(f = 259.8417546280945\).

Step 6 ：Rounding to the nearest integer, we get \(f = 260\).

Step 7 ：Final Answer: The frequency nine half-steps below middle A is \(\boxed{260}\) cps.