Virtual Pitch & Timpani

Even if the missing fundamental cannot be perceived by the human ear, the concept of virtual pitch is useful to the timpanist when using electronic tuners for tempering timpani. Electronic tuners that display the octave register as well as the frequency can be very useful for measuring the strength of mode 1,1 at each lug point. Since the spectrum of a well-adjusted timpano can approximate a harmonic series with a missing fundamental, when a tuner registers the actual pitch (at each lug point) as the one being an octave lower than the one actually being played, then the head has been balanced or tempered. e.g., when sounding a C3 @130 Hz on a 29” drum, and the tuner is registering C2 @65 Hz, this means that the upper partials are lined up well since the vibrations of the head are not producing that actual frequency. The virtual pitch of the spectrum is strong enough that the tuner detects a pitch with fundamental and harmonic series. In essence, the missing fundamental has been found.

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.

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.

How to Use Virtual Pitch When Tempering Timpani

For a detailed process on how to temper timpani, please read Chapter 5: Tempering Timpani. If your timpani heads are relatively clear, but just need some fine tuning, please read the section Step 6 Fine-Tuning. This step till guide you through the process of fine tuning timpani using an electronic tuner to define the Virtual Pitch of a timpano’s overtone series.

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