Between 2005 and 2008, Helmut Fleischer and Hugo Fastl (Institut für Mechanik, Universität der Bundeswehr München) contributed to their ongoing series Beiträge zur Vibro- und Psychoakustik by conducting three studies on timpani. The trilogy Vibroakustische Untersuchungen an Paukenfellen – Fell, Kessel und Gestell der Orchesterpauke, and Physikalische und gehörbezogene Analyse von Paukenklängen is consistent with the findings of the earlier studies done on timpani acoustics plus added much new and intriguing data to the field. The following is an English translation of the summary from each study. These translations are lightly edited for readability.
Vibroakustische Untersuchungen an Paukenfellen Fleischer & Fast
VIBRO-ACOUSTIC INVESTIGATIONS ON KETTLEDRUM HEADS
Calculations and experiments are described towards better understanding the generation and radiation of sound by the kettledrum (timpani). The vibrational behavior of the heads of various kettledrums is studied using various approaches.
After a short review of the theory of the ideal membrane, the classical Chladni method is used to visualize nodal lines. Thereafter, acoustic experiments on kettledrums are depicted. Measuring the directional characteristics in the far field gives hints on the number of nodal diameters. The sound pressure or velocity in the near field can be exploited to reconstruct the radial distribution of the velocity of the head vibration and thus to identify nodal circles. The driving point impedance or admittance give insight into the vibration willingness of the head at a specific location. Non-contact approaches (Laser triangulation and Laser velocimetry) yield the bases for the Modal Analysis of kettledrum heads. Comprehensive experimental data are compiled by means of a Laser Scanning Vibrometer. Operating deflection shapes as well as eigenmodes of various heads in different tunings are presented.
The majority of the results is displayed as red-green colour maps in the appendix. These investigations are to assemble a multitude of experimental data to create an idea of the head’s vibrational characteristics. The aim is to improve modeling of the head with respect to the function of the kettledrum as a musical instrument.
Fig. 3o (click graphic to enlarge)
Fell, Kessel und Gestell der Orchesterpauke Fleischer & Fastl
HEAD, KETTLE AND STAND OF THE ORCHESTRAL TIMPANI
Beside the head of the timpani, its non-active components such as the kettle, stand and additional parts are in the focus of the considerations. In continuation of former studies the mechanical vibrations of these parts of the timpani were investigated. First of all, the actual source of the timpani sound was identified. It was found that the sound originates exclusively from the head and not from the kettle of the timpani. This finding is based on intensity measurements and numerical computations. Nevertheless, it has to be kept in mind that the kettle plays an important passive role. It acts on the acoustic radiation and on the fine-tuning of the intervals of the head’s vibration frequencies.
Experiments as well as computer simulations using Finite Elements and coupled Finite Elements/Boundary Elements have shown that the kettle is vibratory, but to a much less extent than the head. Further experiments have confirmed that the same holds for the stand and the remaining components of the instrument. The vibrations of these parts do not constructively contribute to the generation of the timpani sound. On the contrary, there are indications that they can downgrade the acoustic signal by shortening the sustain of partial tones. Within narrow frequency regions, the main tone, quint or octave happen to decay much faster than defined by the radiation resistance as the only damping mechanism.
It is suspected that resonances of distinct parts of the instrument stand can convert vibration energy into heat which, in consequence, is no longer available to the generation of sound. It could be detected that the quint and octave decay irregularly fast when a resonance of the kettle edge is excited by the vibrating head. Future experiments are to show if the timpani sound sustains longer and more uniformly when resonance effects of non-active components of the timpani are avoided.
Fig. 3p (click graphic to enlarge)
Physikalische und gehörbezogene Analyse von Paukenklängen Fleischer & Fastl
PHYSICAL AND AURALLY RELATED ANALYSIS OF TIMPANI SOUNDS
Comprehensive material is compiled based on experiments related to the acoustic signal of kettledrums (timpani). Sounds of professional orchestral instruments of sizes No. 2 (large timpani) and No. 4 (small timpani) were investigated. Psychoacoustic tests and an aurally- related analysis have revealed that the main tone, generated by the 1,1 mode of the head, plays the most important role. Its spectral pitch defines the musical pitch of the timpani note. Further sound-constitutive tones are the quint, which is characteristic for the timpani, and the octave, which strengthens the musical pitch. They originate from the 2,1 and 3,1 mode, respectively. The 0,1 tone arising from the first axi-symmetric mode does not fit into this approximately harmonic structure.
The further considerations focus on these four partial tones. FFT analysis was used for visualizing the temporal history and spectral content of the acoustic signals. Two types of “water- fall” diagrams are presented for a wide variety of timpani with different kettles, plastic or natural heads and in varying tunings. In the whole tuning range, which covers up to an octave, the frequencies of the four first partial tones were ascertained and displayed as a function of the main tone frequency. As a rule, the frequency of the quint is close to 1.5 times the main tone frequency, and the frequency of the octave is close to twice the main tone frequency. In terms of the intervals, the No. 2 instruments prove to be of a very high quality level. The No 4 timpani shows up to be a little bit inferior to the No. 2 items.
In order to clarify its role, the kettle was removed. The partial frequencies were ascertained and compared to those of a complete timpani with kettle. The kettle proves as essential for the decay and the intervals of the partial tones. In a further experiment, kettles were partially filled with water (or with damping material) and the frequencies measured. The volume of the air enclosed influences the intervals of the partial tones, to an especially high extent the frequency of the 0,1 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. This is in the region of 128 l up to 143 l for the No. 2 and of 60 l up to 75 l for the No. 4 timpani.
Fig. 3q (click graphic to enlarge)
