Rossing Et al.
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 15o 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.
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.
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.