Selecting different materials would not change much. Call the frequencies \lambda_1, \lambda_2, \lambda_3...

You can prove that changing the material has no effect on the relative frequencies: \lambda_2 / \lambda_1, \lambda_3 / \lambda_1, etc. are completely independent of the material.

The shape is the determining factor; changing the materials (and hence the wave speed) just dilates the whole spectrum.