When asked the question, “does the bowl shape contribute to the sound timpani produce?” most timpanists will give you a definitive YES! Bowl shapes and bowl materials are hotly contested issues among timpanists. Entire schools of playing have evolved around bowl shapes and general timpani design. Generations of timpanists have been taught to believe that the bowl shape has a profound influence on the path of the sound-wave on the inside of the drum.
Erroneous information about bowl shape and the
path of the sound-wave by English timpanist Henry W. Taylor 43
But, what are the scientific facts? Recent studies (see Significant Studies) have concluded that the harmonic sound spectra of timpani rely weakly on the shape of the bowl and does so only with respect to how the geometry of the bowl determines the volume of air the bowl can contain.
However, there are timpanists that desire a sound that is not based completely on the harmonicity of the pitch the drum can create. They are interested in producing a colored sound that will project and be more percussive or drum like by nature, rather than pitch centered. A sound that will have enough of an edge to be heard in a large orchestra, yet without too much distortion of the pitch. A sound that will actually add some harmonic distortion to the music. Can the bowl shape help achieve this or these desired characteristics due to other factors?
The primary focus of the significant scientific studies has been on how the bowl contributes to the harmonicity of the preferred modes, and not on the overall envelope of the timpani sound, especially the first few hundred milliseconds of the envelope known as the attack. Timpani have a wide dynamic range and the color varies dramatically depending on the actual amplitude of the sound. Consequently, timpani sound spectra change significantly as dynamic levels vary. Potential vibrations from the bowl and frame can be a desired trait, and an integral part of this color change. They do not contribute constructively to the pitch of the instrument, but they do have the potential to color the sound of the attack portion of the envelope, or when the head is in a steady state of motion at high dB levels. Even when one is in close proximity to the instrument, it is debatable whether this collateral color is actually heard due to its low dB level compared to that of the vibrating head. It should however, not be overlooked when discussing timpani sound.
When timpanists talk about “the sound” of the bowl shapes, the aural differences they hear are based on:
1) how the frequencies of the internal air modes (determined by the volume of the internal air mass) interact with the vibrational modes of the head
2) the viscothermal characteristics (viscosity and thermal conduction) of the volume of the air mass enclosed in the bowl
3) the amount of mechanical energy loss through the bowl walls
4) how efficient the bowl is as a thermal conductor
5) potentially, how well the bowl itself is free and able to vibrate (thickness/mass) which is determined by #3
Figure 3r simulates the first ten milliseconds of vibration of mode (1,1) as the pressure inside of the bowl jumps across the nodal boundary. In as much as the bowl itself is vibratory, this can/will set into motion specific resonant frequencies of the bowl, which (if strong enough) will contribute to the spectrum and can have some effect on the color of the sound for up to 500 milliseconds.
Fig. 3r
Simulation of pressure jump across boundary during first 10 ms 26
The motion of the volume of air (subject to air density), which is trapped inside of the bowl can cause the bowl to vibrate to a small degree (<1 dB) producing inharmonic partials. These inharmonic partials can become an integral participant in the color of the attack.Fleischer and Fast The attack transients of an instrument’s sound are crucial in determining its personality or character. Attack transients are essentially patterns of noise, which accompany the spectrum of a sound when it is being initiated. The brain primarily uses the attack transients of the envelope to identify an instrument. The attack transients of timpani spectra can vary widely. The bowl and frame play a subtle, but integral part in determining the attack transients of a timpano’s sound.
Bowl vibrations are also transmitted to the frame, which in turn can contribute audible inharmonic partials as well. This added hyper-resonance is also heard when the bowl and frame are vibratory while playing at loud dynamics, e.g., a sustained fortissimo passage or an extended fortissimo roll. Since these partials are inharmonic, and are not generated by the vibrating membrane, they are referred to as collateral color or parasitic pitch. More often than not, this collateral color or parasitic pitch degrades the harmonicity of the pitch producing partials, and shortens the sustain of the preferred modes of vibrating head.
The significant studies have shown that the sound being emitted from a timpano is a result of the bowl functioning as a baffled radiator, the volume and density of the air contained within the bowl interacting with the vibrations of the head, and not the shape, or the vibrations of the bowl or frame at all. The studies have focused on those partials in the spectrum which provide the instrument’s sound with a sense of harmonicity and not necessarily with the overall sound of the instrument. This concept of overall timpani sound varies from timpanist to timpanist just as the overall sound of timpani varies from drum to drum. Nonetheless, each timpanist has his/her own personal preferences as to what constitutes color in timpani sound.
In the material contained in the pages below, the concept of timpani sound is based on the harmonicity of a select group of partials in the overall spectrum of audible partials. This select group is referred to as the preferred modes.
In speaking of the bowl Benade states:
The varying degree in perfection in preserving the correct air-to-membrane relationship is what explains the observation by musicians that every drum plays best at one particular frequency in its range of usability. 20
In 1984, perhaps some hope was given to the timpanists’ belief of “the bowl shaping the sound” with the publication of the paper, Effects of air loading on timpani membrane vibrations by Richard S. Christian, Robert E. Davis, Arnold Tubis, Craig A. Anderson, Ronald I. Mills, and Thomas D. Rossing. This paper dealt with theoretical calculations (Green function method) of timpani modal frequencies and decay times of timpano bowl enclosures with varying volume. Their conclusion:
Although the timpani-membrane frequency shifts are more sensitive to total kettle volume than they are to the details of kettle geometry, the specifics of kettle shape may be important for the fine details of the timpani spectrum (e.g., the frequencies and relative strength of the partials other than the fm1), for the instrument response times, etc. This may well account for the various preferences timpani players have concerning kettle geometries. 21 (Here “fm1” refers to the principal tone frequency associated with mode (1,1).)
In 1988, Robert Eugene Davis in his Ph.D. dissertation Mathematical modeling of the orchestral timpani, used Green function and boundary integral methods to investigate the effects of air loading and kettle shape on the vibrational spectrum. He mathematically calculated timpani modal frequencies for five different kettle shapes and concluded:
The timpani spectrum depends weakly on the detailed kettle shape as long as the correct volume of the kettle with regard to the size of the membrane has been met. 22
Rossing’s analysis is simple and to the point:
Is kettle shape important in determining timpani sound? No. Careful studies indicate that the shape of the timpani kettle is quite unimportant in determining timpani sound provided that the volume is kept in correct range. 23
One must bear in mind that Rossing’s definition of timpani sound is based on the harmonicity of the preferred modes and not the overall sound of the timpani, which may include inharmonic partials (collateral color) for the purpose of color and projection.
Fleischer and Fastl investigated the influence of bowl vibrations, and bowl shape by using a single 73cm timpano frame and interchanging three different bowl shapes with different finishes. Their study showed:
In comparing the determined oscillation frequencies with the results of harmonic frequencies in the audible range of the timpani sound, there is no indication that the bowl actively contributes to the sound radiation. There are no components with the same frequencies of sound as that of the bowl. A constructive interference of sound is therefore excluded.
The volume of the air enclosed influences the intervals of the partial tones, to an especially high extent the frequency of the 01 tone. To keep this inharmonic tone inaudible, the kettle should be small. With respect to the intervals of main tone, quint and octave, however, there is an optimum volume. 24
Why does bowl shape not affect the sound with respect to the near-harmonic partials of the preferred modes? Is there an explanation? Rossing explains.
These results may surprise some timpanists, since articles in the literature frequently refer to “shaping” the sound by using kettles with hemispherical, parabolic or other shapes. A simple fact that helps explain why kettle shape is unimportant is that the sound wavelengths are so much larger than the kettle dimensions. (At 140 Hz, for example the wavelength is 2.5 meters, and even at 440 it is about 0.8 m). Thus the mode frequencies of the enclosed air, which depend on kettle volume are virtually unaffected by the shape of the kettle. 25
The volume of air inside of the bowl effectively fine tunes the partials created by the preferred modes helping to bring them into a near-harmonic relationship. Most modern timpani bowls seem to have the right volume to optimize the harmonicity of the principal partials, but Fleischer and Fastl believe that there is an optimum volume based on the diameter of the head.
To date, partials other than that of the preferred modes (collateral color) have not been a subject of scientific investigation with respect to exactly what is the overall sound of the timpani spectrum; the complete timpani sound that timpanists hear. More studies in this area are certainly needed.