Air Loading
The frequencies of the vibrational modes of the volume of internal air enclosed within the bowl are higher than the frequencies of the membrane modes to which they couple.41 Since the motion of these air modes is dependent on the viscothermal characteristics (viscosity and thermal conduction) of the enclosed air, changes in air density can cause these modes to interact differently with upper partials of the vibrating membrane that have similar frequencies. Consequently, certain notes will tend to sing more on some days than others or the overtones will tend to be sound more in-tune depending on changes in environmental conditions.
With the head being the primary vibrating system, the weight of the air mass outside of the drum acts against the motion of the membrane, while the volume, mass and stiffness of the air modes enclosed inside of the bowl counter-acts against the motion of the membrane. This combined internal/external air interaction adjusts the vibrating modes of the head, in particular, a small group of partials called the preferred modes. When aligned just right, these preferred modes of the air-loaded head will vibrate as a harmonic system giving the drum its sense of pitch, harmonicity, and projection. Because our atmosphere does have mass and weight, it is air that in fact make it possible for timpani to produce pitch.
The bowl acts as a baffle (not as a resonator) separating these two air masses preventing them from interacting with each other, much like that of an enclosed speaker system.
The vibrating system is influenced by three factors:
1) the volume and viscothermal characteristics (viscosity and thermal conduction) of the air modes inside of the bowl
2) the density and the viscothermal characteristics of the air pressure outside of the bowl
3) the motion (vibrating modes) of the vibrating head
The three parts are of equal importance in determining the frequencies and overall vibrational shapes (preferred modes) that define the pitch, harmonicity, and to some degree, the color of the instrument. When the conditions of the internal and external air masses begin to differ, or differ significantly, the preferred modes of the vibrating head do not respond as they did when the head was originally tempered and the timbre, harmonicity and projection of the instrument’s voice is affected.
Graphic courtesy of Gordon Reid
Three Part System Defining
the “Harmonicity” of Timpani Pitch
1) internal air modes
2) external air pressure
3) vibrating membrane
Figure 3e shows the pitch-class equivalents of the harmonic preferred modes of an air loaded membrane notated on the Grand Staff with the damped fundamental (A2 110 Hz) included as a reference. Also included are the ratios and the number of cents for each of the preferred modes as calculated from the principal tone. (click fig. 3e to enlarge) The accompanying sound file includes just the air loaded harmonic preferred modes and does not include the damped fundamental referenced in figure 3e. N.B. The frequency of the inharmonic fundamental is raised somewhat by the air-loading of the head.
Fig. 3e
