In Search of the Missing Fundamental: by Richard K. Jones
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Fleisher & Fastl

Physikalische und gehörbezogene Analyse von Paukenklängen *


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 11 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 21 and 31 mode, respectively. The 01 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 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. 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


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