Reducing the ringiness (overtones/harmonics) on a snare drum
Taking the time to choose the right head and properly tune a drum is always the best way to get the pitch, resonance, overtones, muffling and response just
right. Some heads even have built-in dampening or muffling that will reduce the snare’s tendency to “ring.” Remo's website has some great tips on snare drum tuning:
In addition to tuning, drumhead manufacturers usually make at least a couple of different dampening products such as adhesive gels, dampening rings of
different thicknesses and patches that “anchor” the head to the shell to help reduce resonance/overtones. All of these will produce different effects on the
overtones/harmonics in the higher registers.
For a quick and dirty fix, try putting a little (or a lot depending on the case) masking tape near the edge of the head (where it meets the hoop). That will deaden the overtones little by little. Experiment with placement (middle, against the batter head, against the resonant head) for different effects.