5.13.4 Pitches of notes produced by percussion instruments
We have seen that none of the rectangular bar, the circular membrane and the circular plate have harmonically related natural frequencies. It may not surprise you to learn, therefore, that instruments containing these primary vibrators tend to produce notes that don't have a very well-defined sense of pitch.
This is certainly true in the case of the cymbal, which has a circular plate as its primary vibrator. Whether a single cymbal is struck with a drumstick or two cymbals are crashed together, the note produced is essentially unpitched. It is also true of the snare drum, which has a circular membrane as the primary vibrator. You would be hard pushed to say that the sound produced when the drum is hit can be assigned a pitch.
But hang on! What about timpani (also known as kettledrums)? A kettledrum has a circular membrane as the primary vibrator but it produces a pitched note. Indeed, a timpanist can tune the drum by altering the tension of the membrane. So, why does a kettledrum produce a note of definite pitch when the natural frequencies of a circular membrane are not harmonically related? Well, in my analysis of the vibrational modes of a circular membrane I failed to take into account the effects of air damping. When the tension of the membrane is relatively low, the air-damping force has the effect of shifting the frequency of those modes of vibration that radiate a significant amount of sound, so that they do become approximately harmonically related.
You may also raise the same question regarding xylophones and glockenspiels. These instruments have rectangular bars as primary vibrators. We have already seen that a rectangular bar has natural frequencies that do not form a harmonic series. So, on the face of it one would expect that a xylophone or glockenspiel should produce unpitched notes. Of course, nothing could be further from the truth. In this case, I failed to take into account the effect of the supports on which the rectangular bars rest. The reason why these instruments actually produce pitched notes is beyond the scope of this unit.