Figure 5a is a visualization of how the preferred modes that define timpani harmonicity interact with each other creating an amalgamation of pitch zones all vibrating together to create a single perceived pitch structure.
In Figure 5a, beginning with no modes of vibration, the first six preferred modes of a vibrating membrane are displayed as each mode from (1,1) to (6,1) is added. These six preferred modes pertain to the modes which contribute to timpani harmonicity. The modes are mode (1,1), mode (2,1), mode (3,1) mode (4,1), mode (5,1) and mode (6,1,). Notice how the interaction of the modes encompasses the entire circumference of the drum.
When tempering by ear alone, it can be extremely difficult to focus your listening on the principal tone only; it decays faster than the subsequent partials of the preferred modes (see Pleading the Fifth). In the initial stage of tempering by ear, it is helpful to develop a mode of listening where you focus on the initial attack only and disregard the sound of the sustain. Again, to reiterate, training your ear what not to listen for is as important as what to listen for with respect to the content of the spectrum. Once the principal tone has been isolated at each lug point, you can then begin listening to the content of the spectra of the sustained pitch.
Waterfall chart (frequency, time and amplitude) of a timpano sound spectrum
(single struck note) highlighting six preferred modes (1,1), (2,1), (3,1), (4,1), (5,1) and (6,1)
(Fleischer & Fastl)
Please read Chapter Five for a detailed process on how to temper timpani to achieve the most “harmonicity” possible.