What are you using for a schematic to connect the sensor to the Arduino?
Yes this sort of thing will happen because the sensor output rings and it will pass through the threshold value many times. You can try making this threshold value higher, or add a small delay just after you detect a hit ( send out a MIDI message ) or address the problem in hardware with a capacitor.
This is the sort of signal you are seeing from your sensor.
Notice the multiple edges on the signal as the sensor rings above and below the threshold. Note here the logic low indicates a hit on the sensor.
Note from that site that what he calls a zinner diode is in fact a zener diode. The code is very naive and many times longer than it should be.