The Bearing Edge
A thinner (< 2mm) , or more pointed lip (especially one which is rolled to the outside of the bowl) will not dampen the concentric modes (and diametric modes) as much because the head will have less contact with it during its negative cycle (weaker coupling) causing less mechanical energy loss through the head. With less damping, more of the inharmonic partials will also be prominent in the spectrum. This gives the drum a brighter color. When more of the inharmonic concentric modes are in the spectrum, the drum may be perceived as having greater volume, projection and resonance, simply because the head can generate and sustain energy (both harmonic and inharmonic) more easily.
If the volume of air inside the bowl is such that it doesn’t suppress mode 0,1 (and the subsequent concentric modes), too much of this concentric motion can and will dilute the principal tone. The result will be a loud, sustained and percussive sound that lacks a strong pitch center in both the attack and decay. Very percussive perhaps, but not necessarily full of pitch or the weight of the principal tone.
A brighter sounding drum, one with minimal internal air volume, and a thin lip would work well in a very dry hall where the natural acoustics of the room absorb the sound and darken the color or when extreme projection of the sound is needed to fill a big hall of drive a large ensemble.