What physical properties determine the sound of a drum head?

I am working on a rubber substitute for a leather-membrane drum. The objective is to replicate to reasonable extent the "sound" or timbre that the leather drum head makes with a rubber drum head as compared to frequency, which can be replicated in any material.

Aware that an inertial element is important, density is one of my parameters in comparing various samples of rubber to the leather. Also I consider an elastic component, the modulus of elasticity for ease of testing.

Are these parameters sufficient and correct in achieving the objective ?

• yes, tension and density are the only parameters that matter. Just replace linear density by areal density in the wikipedia article.
– Mary
Aug 2, 2018 at 13:03
• actually, what I said is not entirely true, it is correct if we only consider the frequency but the timbre also depends on the harmonics and the envelope of the sound. The elasticity effectively seems relevant there. I doubt you can make the rubber sound as leather but you might find the right material. That's an interesting topic, if you find more about that, I would be interested if you could follow-up.
– Mary
Aug 2, 2018 at 13:12
• @Mary thanks Mary. Interesting point about the harmonic element, although that might take a more comprehensive analysis. There is also an element of the surface, especially in the tabla where part of the timbre is the sound of the palm striking the surface, a clapping-like sound. Aug 2, 2018 at 16:55

here are the parameters you'll need to control in your investigation:

1) the elastic modulus of the material,

2) the thickness of the material,

3) its mass per unit area,

4) the damping coefficient (internal friction) of the material, and

5) the roughness or "tooth" of the surface.

if you go shopping for drumheads at a well-equipped drum store you will find a number of synthetic substitute heads for natural (skin or leather) heads. in this sense, this is (to first order) a solved problem.

• Thanks Niels for the excellent answer. This is in fact an effort to replicate the very specific sound that a tabla makes, to manufacture which is a very fine and complex practice. For level one, replicating the properties of leather is sufficient. Further refinements would probably involve analysis of the surface. I'll check out drum stores and pick up some drumheads as you suggest. Aug 2, 2018 at 18:10