Membrane Vibrational Modes

Stretched membranes have many vibrational modes, some of which are harmonically related to the lowest pitch and some not. The theoretical case of a rectangular membrane begins to show the complexity of membranes.

The musically more useful circular membranes have even greater complexity.

Rectangular Membrane

The resonant vibrational modes of an ideal membrane with length equal to 1.41 times its width are shown. The membrane produces harmonics, but also produces non-harmonic overtones. Where there are multiple segments, adjacent segments are moving in opposite directions during vibration.

No, I haven't seen a rectangular drum either, but it is a useful mathematical model to show that resonant systems often have overtones which are not harmonics. This is true also in the more useful circular membranes used in drum heads, but the overtones are much more complex there.