In Search of the Missing Fundamental: by Richard K. Jones
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Frequency, Pitch and Colour

If an oboe plays a middle C (C4 261.63 Hz) and then a clarinet plays the same note at the same loudness as the oboe, it is still easy to tell the two notes apart, because an oboe sounds different from a clarinet. This difference in the sound of the two instruments is the colour, or timbre, of the notes, which is based on each instrument’s own unique harmonic recipe. A note’s harmonic recipe is its number of overtones or partials (harmonic and non-harmonic) and their amplitude proportion relative to the fundamental. Along with their individual attack characteristics, it is these overtones (harmonic and non-harmonic) that give instruments their tone colour and without them, we could not tell one instrument from another.

The chart below graphs the first sixteen harmonic partials (with amplitude proportions) of a clarinet and oboe playing same pitch or frequency. The clarinet projects a strong fundamental and mostly odd harmonics while the oboe projects a strong fourth, fifth and sixth partial and a relatively weak or non-existent fundamental.

The oboe has almost no sound at the actual fundamental frequency, even though it is that pitch you hear when listening to it. The same is true of the bassoon sound. In fact, even if the fundamental frequency is omitted altogether, the ear still hears the same pitch as if the fundamental were. This missing fundamental effect is often referred to as virtual pitch or “reconstruction” of the fundamental. 2

A similar phenomenon also plays an important role in how we perceive timpani pitch. In the case of timpani, the pitch we perceive as being the “fundamental” is actually the second partial of a non-harmonic overtone series. It is the “construction” of a non-existent harmonic fundamental which is the objective when a timpanist tempers or “clears” timpani heads.

Chapter 2 of this book will introduce the theory of how circular vibrating membranes function and how the various modes of vibration contribute to the sound of timpani. However, as with any new discipline, there is usually a certain amount of new vocabulary, which needs to be learned and understood so the next section will be devoted to a short review of the concepts and terms introduced in Chapter 1. A stronger understanding of these terms and concepts may aid the reader in developing his/her own ability to listen to and better understand timpani tone.

Chapter 1 Review

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1) Chapter 1 Selected Bibliography and WWW Links

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