Thomas D. Rossing of Northern Illinois University, and a number of his colleagues and associates: Craig A. Anderson, Richard S. Christian, Robert E. Davis, Garry Kvistad, Ronald I. Mills and Arnold Tubis published the results of numerous studies on timpani acoustics between 1976 and 2000. Rossing et al. conducted extensive research on the vibrational modes of timpani, how the bowl influences the sound and how the sound radiates from the instrument. 18
Ideally, a timpano bowl should not directly affect the vibrating head itself in as much as it should affect the air inside of the bowl that the head displaces when it vibrates. Rossing’s et al. research in this area provided much data on the subject of comparing the vibrational frequencies of a timpano, a timpano head without a bowl and ideal membrane. The charts in this section have been extracted from the article Acoustics of Timpani which Rossing published in the Percussionist [Percussive Notes Research Edition] (vol. 19, no. 3) (Fall 1982): 18-31. The timpani used in this particular study were two identical 26 inch (65cm) drums, one with a bowl and one without. Rossing does not give an exact model of the timpani, but it may be that these were Ludwig Professional Symphonic timpani with suspended bowls and external spider: the model which he used in his Acoustics of Timpani: Preliminary Studies as well as his article The Physics of Kettledrums, which was published in Scientific American, November 1982. In the Endnotes, Rossing gives credit to the Ludwig Drum Company for furnishing the drums.
One of Rossing’s conclusions was that the frequencies of the preferred modes are only somewhat influenced by the bowl; even without the bowl, an air loaded timpano membrane conveys a fairly definite sense of pitch. The preferred ratios 1.00, 1.48, 1.92, 2.36 and 2.78 (relative to mode (1,1)) are not quite as harmonic as those preferred mode frequencies with a bowl, but still tolerable.
Timpani without bowls are not a new phenomenon. In 1860 Adolphe Sax patented his timpani without a shell 19 and more recently Marcus de Mowbray of London England marketed a Tour Timp which is essentially a timpani without a bowl. Currently the DrumTone corporation offers a timpani surrogate, which they call DrumTone Timpani. There are probably a number of reasons why this type of timpani surrogate is not preferred by most professional timpanists. Perhaps it is due to the overall sound quality and lack of projection since the bowl contributes significantly to both.
Fig. 3i
Figure 3i is Rossing’s comparative data of a normal timpano, a timpano without a bowl and an ideal membrane. It is interesting to note that in this particular data, the frequency of mode (1,1), or the principal tone for the two drums, differs slightly. The pitch for the drum with a bowl is 150 Hz which is between a D3 and an Eb3 while the indicated pitch for the drum without a bowl is 155 Hz which is a Eb3. Both pitches are just about mid-range on a 26 inch Ludwig timpano and would yield a strong spectrum.
For the purpose of testing, it is the ratios that are important so the actual pitch doesn’t matter. However, it would be interesting to see the results of an experiment on the effects of air loading done on the same drum and just remove the bowl while keeping the same tension on the head. Critical to measurements of this type is a consistent baseline. In this case with two different timpanos, there may have been some uncontrolled variables which would be difficult to factor in, e.g. mechanical tolerances of the instruments as well as different membranes and membrane tensions. In fact, Rossing makes mention that measuring the tension of the membranes presented some difficulties in the studies.
Note: the same data from chart (fig. 3i) appear in other Rossing’s articles on timpani acoustics as well as in his most recent book Science of Percussion Instruments (World Scientific, 2000: page 8 ) so one might conclude that these figures are considered definitive by Rossing.
Figures 3j and 3k are pitch-class equivalent charts showing the preferred modes from Rossing’s data. Since Rossing’s principal tones differed slightly, they have been transposed to C3 130.8 Hz for consistency but mode ratios remain the same. The sound files are also based on a principal tone of C3 130.8 Hz. The frequency C3 130.8 Hz will be used as a baseline for all charts and sound files in this chapter.
Figure 3j charts the preferred modes without a bowl. All modes/partials deviate substantially from what is harmonic. The upper three modes/partials are in fact different pitch-classes all together. The triangle shaped notes approximate the nearest pitch-class of the higher modes/partials. Bear in mind that the accompanying sound file is at best only an approximation, and even with severely diminishing the amplitude proportions of modes (3,1), (4,1), (5,1), and (6,1), it is clear that the spectrum may be tolerable as Rossing states but clearly not approaching harmonicity.
Fig. 3j
Figure 3k charts the preferred modes with a bowl. The modes/partials are considerably closer to being harmonic, but the higher modes/partials still show significant deviation from true harmonicity.
Fig. 3k
The correction of mode (2,1) by forty-three cents, mode (3,1) by sixty-one cents and the others significantly as well, indicates that the bowl does affect the harmonicity of the instrument to some extent. The more the lower preferred modes can be adjusted to near harmonicity, the more clear the perceived pitch will be.
Rossing also observed that perhaps the most significant contribution of the bowl is to act as a baffle, which acoustically separates the top and bottom sides of the head. This increases the radiation efficiency, which decreases the decay times, especially the modes of the lower frequencies. This may seem counter intuitive to want to decrease the decay times of the lower modes (especially the preferred modes), but when some of those lower modes detract from the harmonicity, this can be a desirable trait.
Fig. 3l
Figure 3l charts the decay times of the lower mode frequencies of a timpano both with and without the bowl. Without the bowl, all of the modes are not very efficient at radiating their energy; therefore they have longer decay times, which seems desirable. However, this includes the inharmonic lower concentric modes as well as the more harmonic preferred modes. With a bowl, most of the lower modes radiate energy more efficiently and consequently they decay much faster. When a timpano is struck a quarter of the distance between the edge and the center, in many practical cases the inharmonic modes will radiate their energy much more efficiently and decay faster leaving the more harmonic preferred modes to dominate the sound spectrum.
Fig. 3m
Figure 3m is a sound spectrum graphing the amplitude, frequency and decay time of a 26 inch Ludwig Professional Series timpano (with a bowl). The more inharmonic concentric modes have less amplitude and faster decay time than do the diametric preferred modes (1,1), (2,1), (3,1), (4,1) and (5,1). Note the quick decay time of the principal tone mode (1,1) leaving modes (2,1), (3.1) and (4,1) to carry the pitch.8
Fig. 3n
Figure 3n (courtesy of Fleischer & Fastl) is a sound spectrum graphing the amplitude, frequency and decay time of a 73.66 cm Kolberg timpano. Again, the principal tone mode (1,1) decays much faster than the secondary modes (2,1), (3,1), (4,1).
Due to the effect of the baffle created by the bowl, not only are the lower concentric modes damped, but so also is the principal tone somewhat. This can lead to what timpanists refer to as the overbearing fifth and pitch creep in the spectrum. When tempering timpani heads, it is imperative to adjust the frequency of the principal tone at each tuning lug so that it includes many strong near-harmonic partials. When the frequency of the principal tone is not consistent from lug to lug, the overall strength of perceived pitch is severely diminished and permutations of the more audible mode 2,1 will tend to dominate the spectra. An overbearing fifth as well as a perceived pitch shift is likely to occur once the principal tone begins to decay. When the tension of the head is adjusted in such a manner that the secondary preferred modes are focused on creating the virtual pitch of the principal tone (mode 1,1), mode 2,1 then becomes less pronounced/overbearing and the overall pitch will be perceived as being more harmonic in nature. On occasion, the missing fundamental can be perceived. See Pleading the Fifth.