I fixed the alarm sound. With the Senior Project clock, the buzzer and the buttons were connected to the same port. On the new clock, they were connected to different ports. I did not update the button reading routine correctly, so the buzzer output was not working at the moment a button was being read. This resulted in a little distortion being introduced into the signal going to the buzzer. This was easily fixed once I figured out what was causing the problem.
However, I made a discovery while troubleshooting this problem. While looking at the buzzer’s waveform on an oscilloscope, I saw voltage spikes being generated by the buzzer’s coil. I realized that I needed to add a diode to the circuit to protect the microcontroller from these spikes.