In Search of the Missing Fundamental: by Richard K. Jones
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Electronic Tuners

Can electronic tuners be used when adjusting timpani heads? The response of most electronic tuners depends on the amount and strength of overtones present in the spectrum that correspond to those of the harmonic series. For use with timpani, the variables that determine this response not only include the physical integrity of the head and the mechanical integrity drum itself, but most of all, the accuracy by which the person tempering the head is able to adjust the tension and coax the harmonic partials out of the quagmire of inharmonic partials. After you develop an understanding for what timpani pitch is and isn’t (with respect to true harmonic pitch), what you can and can’t do with electronic tuners quickly becomes apparent. The paradox is, once the head has been well-tempered or cleared, most electronic tuners can register the pitch extremely well. Perhaps a better question might be, how can electronic tuners be used in the process of  adjusting timpani heads?

There are some schools of thought that believe the majority of timpani sound need only contain the principal tone, the fifth and maybe some octave in the spectrum; this was the standard for many centuries because that is about all the heads/instruments could produce. A spectrum with just the fifth and octave above the principal tone can yield a short-term sense of pitch, and this certainly is a functional timpani sound, however, since the principal tone decays faster than the other harmonic overtones (a common occurrence on most contemporary membrane materials), the fifth often takes over the sound creating a pitch shift. This is still a functional timpani sound because it does convey some sense of pitch, but it is generally not strong enough to register on electronic tuners since they like detectable patterns that conform to the harmonic series. Two or three weak harmonic partials are generally not enough to register a consistent pattern. The noise of the inharmonic partials tends to prevail.

Modern timpani can produce a sound rich with quasi-harmonic overtones, so  settling for only a principal tone and the fifth in the spectrum is not always a option. Tempering the upper partials to some degree will be necessary. Many of the early practitioners of the art who have written about timpani pitch, including Kirby, White, Taylor, Blades* all spoke of being able to hear the intervals of the octave, the tenth, the twelfth and sometimes even the fifteenth above the principal tone. It is a safe bet to say that all of these gentlemen did not have electronic tuners to assist them, but they did know what constitutes good timpani pitch and were able to achieve it with just their ears.

Interestingly enough, when a person is able to temper where, at each lug point, the tenth and twelfth are strong and aligned correctly in the spectrum, a phenomenon called virtual pitch is produced. Virtual pitch then begins to fill in the missing harmonic partials of the spectrum including the fundamental so that the human ear perceives a pitch with a complete harmonic series. Ironically, many electronic tuners are designed to be able to do the same thing. When a timpano head is cleared to the point that the higher harmonic partials are present and aligned correctly, an electronic tuner can detect the pitch as being that of the actual fundamental, which is an octave below that of the audible principal tone. The stronger the virtual pitch, the quicker the device responds and the longer the response lasts. Bear in mind that the alignment of these partials is also subject to the influence of the volume of air in the bowl relative to tension of the head as well as the influence of the prevailing air density when the head is being tempered.

The graphics below illustrate this phenomenon. A notated C3 was played on a 72cm Fiedler Timpano and measured with the Cleartune – Chromatic Tuner for iPhone & Android. The pitch that registered on the Cleartune App was a C2, which is one octave below notated and sounding pitch C3.

A written/notated C3 was registered as a C2 indicating that the tempering was such that the overtones produced enough harmonicity to create a spectrum where the virtual pitch of the missing fundamental C2 was strong enough to be detected by the Cleartune App.

Tempering a Head

Using a different electronic tuner app on an iPhone (insTuner), on the same 72cm Fiedler timpano, when the head was tempered at a low C2, the insTuner registered the pitch as being that of C1.


Virtual Pitch-Missing Fundamental Spectogram

When sounding a C3 @130 Hz on a 72cm Fiedler timpano, the Spectogram below (click to enlarge) shows the relative frequencies for modes 1,1 through 6,1 as well as activity for the missing fundamental, which would be C2 65.41 Hz. This frequency (C2 65.41) is not a vibration that occurs in the head, but is visible in the spectrum because of the virtual pitch created by the near harmonic partials. This spectogram was generated with the SpectrumView Frequency Analysis iOS App on an iPad2.

Missing Fundamental Spectogram

Many electronic pitch measuring devices can be used to test accuracy of timpani pitch, provided you want the timpani pitch to be as close to harmonic as possible.

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