With a round shape, you can maintain consistent tension in all directions from the centre at the same time as consistent distance from the center. This will make the residence frequency of the shape clear. For objects under tension, like a drum head or a guitar string the residence. Frequency formula is dictated by length, tension and properties of the material. Assuming that you were comparing equivalent, drum head materials from a round drum to a square drum the round drum resonance frequency will be dictated by its diameter and tension. With a square drum head, you would not have the same distance in all directions therefore the residence frequency may not ring as clear.
That’s what the theory suggests. I have not actually tested a square drum head with a frequency analyzer yet.
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