Physics of the 4th
If the “A” drum is struck first and is allowed to ring, the principal tone of that drum will begin to decay leaving mode 2,1 (e) to beat against the principal tone mode 1,1 of the “D” drum. A major second dissonance is heard as the two pitches ring together. One must also bear in mind that the principal tone of the the “D” drum will also fade quickly as well. If the head in not tempered well, the fifth of the spectrum on that drum will also dominate.
Partial Tones of a P4 on Timpani Struck Consecutively
The Principal Tone Decays Leaving a M2 Dissonance
It is interesting to note that from a voice leading perspective, this e is a tendency tone that wants to resolve downward and does in this case, which only reinforces the Common Practice Period dominant/tonic (tension/resolution) relationship. The use of timpani tuned to a perfect fourth in CPP literature only adds to the strength of the Dominant/Tonic cadential function, albeit in a very subtle manner when viewed from this perspective.
Due to the effect of the baffle created by the bowl, not only are the lower concentric modes damped (e.g. mode 0,1 the dissonant fundamental), but so also is the principal tone mode 1,1 to some degree. This can lead to what timpanists refer to as the overbearing fifth and pitch creep in the spectrum the longer the pitch sustains. When the frequency of the principal tone is not consistent from lug to lug, the overall strength of perceived pitch is severely diminished and permutations of the more audible mode 2,1 will tend to dominate the spectra. An overbearing fifth generates a pitch shift once the principal tone begins to decay. (see Pleading the Fifth)
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)
A harmonic P4 on timpani can be difficult to tune when the drums have the predominant fifth in the spectrum. When struck consecutively, the first overtone of the A drum, which is an E is beating against the principal tone D of your D drum. These two frequencies are only a major second apart. This is somewhat unavoidable with the harmonic interval of a P4. A way to make it less noticeable is to temper the heads so that fifth is not so strong. Spend some time tempering to where there is a strong presence of the tenth above the principal tone Mode (4,1).
When teaching timpani, it is best to teach the tuning of this interval as a melodic interval, and not a harmonic interval. Tune the interval quickly and efficiently; focus on the melodic skip, not the mix of the overtones. Learning to master your spectral and holistic listening skills will also help you hear, and focus on the melody of the sound rather than the harmony of the sound.
When tempering timpani heads, it is imperative to adjust the frequency of the principal tone at each tuning lug so that it includes many strong near-harmonic partials. When the tension of the head is adjusted in such a manner that the secondary preferred modes are focused on creating the virtual pitch of the principal tone (mode 1,1), mode 2,1 then becomes less pronounced/overbearing and the overall pitch will be perceived as being more harmonic in nature. On occasion, the missing fundamental can be perceived.
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