In Search of the Missing Fundamental: by Richard K. Jones
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Membrane Modes

The (5,1) Mode
The tenth mode of a circular membrane is the (5,1) mode which has five nodal diameters and one nodal circles at the fixed outer rim. Like the (1,1), (2,1), (3,1) (4,1) modes, this pattern is a poor radiator or sound and therefore takes longer to decay, and contributes to the sustained harmonicity and sense of pitch of a timpano. It is the fifth of the  preferred modes.

Note that none of the modal frequencies above the fundamental (1.593, 2.135, 2.295, 2.917, 3.598, 3.65 etc.) consist of multiples of the fundamental (i.e., 1, 2, 3, 4 etc), and thus do not constitute a harmonic series. In theory, the sound of the timpani should not have any more pitch than that of any other drum if the partials are not harmonic.

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