The physics on your marching tenor really aren't too much different than on a drum set tom. After all, they're both simple cylinders with a membrane at each end. A single head will sound loud and open with a relatively simple tone. Adding a resonant head won't make the drum any louder, but it allows you to produce a more complex tone. Tune the tom and bottom heads to a consonant pitch and you can get a warm resonance. Tuning them to less consonant pitches can draw different timbres from the drum and attenuate resonance.

Thanks SkyDog...that helped!