In Search of the Missing Fundamental: by Richard K. Jones
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The Bearing Edge

Since this bearing edge also acts as the first nodal point for the membrane (concentric mode 0,1, the actual inharmonic fundamental of the head) a wider (5mm >), more rounded lip  (especially one that is rolled to the inside of the bowl) has the potential of damping this mode to some extent, and the subsequent concentric modes as well.

weak-Boundary

Fat Lip-Final

The timpano bowl is a system modifier. The primary function of the bowl is to act as a baffle (not as a Helmholtz resonator), limiting the amount of sound that is being radiated from the underside of the membrane. The baffle causes (mode 0,1) to become a monopole source, which radiates its energy efficiently so the sound radiated from this mode will die away quickly. However, since (mode 0,1) is the first vibrating mode, it has the potential of oscillating with the most motion because it would have the most energy, if excited. This mode is also present in all of the preferred modes that do create the sense of pitch, so it is impossible to mute this mode completely.

The objective in achieving timpani harmonicity is to suppress the inharmonic partials as much as possible so that the preferred modes can dominate the spectrum. If the volume of air in the bowl is such that it doesn’t dampen (mode 0,1) to any significant extent (see Fleisher & Fastl), a rounder lip can help diminish the energy from this mode. As the head moves up and down physically touching the lip as it reverses direction during its negative cycle, some of the mechanical energy of the head dissipates (conversion to heat) with each cycle each time it touches the lip.


Oscillation of Mode 0,1 (Ideal Circular Membrane)

Since they radiate their energy quickly, none of the concentric modes contribute significantly to the perceived pitch so when these modes are less prominent, the sound of the drum is often characterized as being darker and more dry or dull in color and with somewhat less sustain, yet with a prominent fundamental tone. However, it should be duly noted that the preferred diametric modes also us the lip of the bowl as one of their nodal points. If the concentric modes are dampened too much at the lip, so will be the diametric modes. Too much damping at the lip will jeopardize the drum’s natural sustain, volume, projection (cutting power), and resonance because of the rapid loss of energy from the vibrating head. Full of fundamental perhaps, but not necessarily overtly loud, or resonant. A darker sounding drum, one with a round lip would work well with a smaller ensemble in a live or bright hall where the natural acoustics of the room project the sound and brighten the color. (See Why Copper?:Dresdner Apparatebau)

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