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The frequency of a drum depends on the size and tightness of the skin and the volume of the resonating chamber. So, a smaller skin, a tighter skin and a smaller volume will each contribute to a higher pitched drum.

The reasons for this have to do with

(a)the speed of sound waves across the skin, which rises when the skin is tighter,

(b) the speed of sound in air inside the drum which means higher resonances will happen when the drum walls are closer together and

(c) the distance from the point you strike the skin and the edge of the skin, which means reflections from the edge happen sooner on small skins.

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