Oscillation of Mode 0,1 (Ideal Circular Membrane)
The amplitude of sound will diminish over time due to resistance. The decay of amplitude over time is called damping. For timpani, there are five possible reasons for energy loss resulting in the damping of the sound emitted from the instrument. 47 48 50
1) radiation of sound
2) mechanical loss in the membrane
3) viscothermal loss in the confined air [inside of the bowl]
4) mechanical loss in the kettle [bowl] walls
5) mechanical loss in the frame and external parts
The lip of the timpano bowl, also known as the bearing edge, dictates the boundary conditions for the vibrating membrane. For timpani, this is a fixed or rigid boundary condition. This means that energy from the part of the membrane that creates the perceived pitch does not freely propagate past this point; it is strongly constrained at the boundary. This boundary condition also defines the first nodal point (a point of minimal vibration) of the membrane, and it is the only point of physical contact between the head and the bowl. It is at this point where the vibrating portion of the head has the least amount of physical motion. A bowl with a wider, more rounded lip will have much more of the vibrating head in contact with the bowl for a longer period of time. This contact produces a stronger coupling with the bowl, potentially increasing the transmission of energy to the bowl and external parts and decreasing the amount of energy that can be used by the head to produce sound. A sharper lip, or stronger point on which the head can rest, will cause less coupling adding the potential for less damping because more energy can be used by the vibrating head. The strong pointed lip enforces the required boundary conditions for an ideal circular vibrating membrane, where the rounded lip does not hold to them as rigidly (see Fleisher & Fastl).
One must bear in mind, however, that this energy is minimal compared to the energy created by the motion of the mass of air trapped inside of the bowl as the head vibrates (internal air motion driven largely by the head’s lower-order motion). The motion of the trapped internal air modes has the most impact on how the bowl will vibrate, not how much of the lip is in contact with the head. However, how much of the lip that comes in contact with the head does contribute substantially to the mechanical energy loss through the membrane. (see #2 above)
JAES Volume 61 Issue 10 pp. 737-748; October 2013
Snapshots of the cross section of the pressure field for a timpano at times as indicated. The “resonant” qualities (collateral color) of the bowl are a result of the pressure of the internal air mass coupling with the mass of the bowl, in as much as the bowl is allowed to vibrate.
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.
The timpano bowl is a system modifier. The primary function of the bowl is to act as a baffle, not as a Helmholtz resonator. This limits 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 damp (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)
Concentric modes radiate their energy quickly and do not contribute significantly to the perceived pitch. 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 damped too much at the lip, so will be the diametric modes. In other words, extra damping at the edge does not selectively target only mode (0,1); it can also sap energy from the preferred 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. The result may be a drum that is full of fundamental, 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)
A thinner (< 2mm) , or more pointed lip (especially one which is rolled to the outside of the bowl) will not damp the concentric modes (and diametric modes) as much because the head will have less contact with it during its negative cycle (weaker coupling) causing less mechanical energy loss through the head. With less damping, more of the inharmonic partials will also be prominent in the spectrum. This gives the drum a brighter color. When more of the inharmonic concentric modes are in the spectrum, the drum may be perceived as having greater volume, projection and resonance, simply because the head can generate and sustain energy (both harmonic and inharmonic) more easily.
If the volume of air inside the bowl is such that it doesn’t suppress mode 0,1 (and the subsequent concentric modes), too much of this concentric motion can and will dilute the principal tone. The result will be a loud, sustained and percussive sound that lacks a strong pitch center in both the attack and decay. Very percussive perhaps, but not necessarily full of pitch or the weight of the principal tone.
A brighter sounding drum, one with minimal internal air volume, and a thin lip would work well in a very dry hall where the natural acoustics of the room absorb the sound and darken the color or when extreme projection of the sound is needed to fill a big hall or drive a large ensemble.
Perhaps the best of both worlds is a bowl with a medium flat lip (circa 2.5-3 mm). This style of lip combines the tonal characteristics of the round lip with the projection and sustaining power of the thin lip. Bear in mind that the bearing edge is only one ingredient in the recipe for the voice of a timpano. How the lip interacts with different types of heads, the volume of internal air in the bowl, and the materials and the process of how the bowl is made must also be factored into the equation.
No matter what type of bearing edge (lip) your drum has, it is imperative that the lip is of a consistent width around the circumference of the drum, it is in plane (flat), and is completely smooth. There is a considerable amount of pressure applied to the lip by the tension of the head as it moves across the lip and in order for it to move smoothly without binding or squeaking, some sort of lubrication is usually necessary. Over the years players have used graphite, paraffin, oil soap, curd soap, ox gall soap, ChapStickTM, lanolin and cork grease, and a host of other substances to lubricate the bearing edge, but more recently various products made from the synthetic compound PTFE (polytetrafluoroethylene) have come into vogue. Among them are PTFE tape, PTFE spray and dry PTFE powder.
The PTFE tape (Teflon tape, 3 mil thickness, 5/8″ wide) is probably the most widely used by manufacturers, but the PTFE spray comes highly recommended as well. Both have their advantages and disadvantages. The PTFE tape is relatively expensive and can wear-out over time. The PTFE spray is messy and often difficult to apply evenly to the lip, plus it is detrimental to your health if inhaled. Teflon is inert so no chemical will will completely dissolve it. If it has highly impregnated the lip of the bowl, you will likely have to remove it by mechanical means. There are no commercially available solvents for PTFE and the only way to remove it is by mechanical removal. When using the aerosol PTFE spray, take extreme caution and use in a well-ventilated area only.
The author has used 1 inch Rulon tape (a PTFE derivative) as a lip surface on drums with wide rounded lips with great success. Rulon tape is a few mils thicker than the traditional Teflon tape used by some professional timpanists. Because of the wider lip, the drums are excellent for producing a period sound with slightly less resonance and sustain, yet yield a prominent principal tone.