We have seen how wind and string instruments make sound. Most wind instruments (woodwinds or brass) are open or closed tubes in which air is set vibrating in standing waves within the tube, and these become traveling waves at the end of the tube. The vibrator in a violin or guitar is a string, under tension and fixed at both ends. By nature, all of a string's own vibrations are standing waves because its ends are fixed. Its vibrations cause the air to vibrate and sets up traveling vibrations. (All these systems are what physicists call harmonic oscillators.*)
In such oscillators, there is an inherent lowest frequency of vibration, called the fundamental. The oscillator might also be capable of vibrations of higher frequencies, which are called overtones, and they usually have simple frequency relationships with the fundamental. (Think C, C, G, C, E, G, Bb)
Drum heads are simple harmonic oscillators. But we don't associate pitch with the sound of most drums. Why not?
Watch the following videos (at least the first two) about the vibration characteristics of drum heads. Think about why these harmonic oscillators are, for the most part, "pitch-less".
https://youtu.be/v4ELxKKT5Rw harmonics of a latex drum head. Note that frequencies are not simple ratios of each other.
https://youtu.be/QksHbCwYngw (no sound) more about the simplest harmonics, with graphs of each mode, and red lines to show nodes, or non-moving parts of the surface. Note that the higher harmonics have more nodes.
https://youtu.be/DZ8VGAx4178 mathematical simulation of drum-head harmonics. Note how many ways a drum head can vibrate.
https://youtu.be/Stf7pOvxsM4 Watch how small particles (poppy seeds) settle onto the nodes (non-moving lines) of a timpani under controlled vibrations. (Now where did I put that broom?)
What's your answer? Are drum heads really pitch-less?
In what situations, and why, is the piano often classified as a percussion instrument?
Playing Melody on a Drum
Striking timpani** about halfway towards towards their centers will strongly activate the 1,1 mode, to the exclusion of most others. This is the mode that to which timpani can be "tuned" to produce distinct pitch. Listen to the timpani in this music, and notice where the player is striking them. (Concerto for Six Timpani and Orchestra by Georg Druschetzky (1745-1819) - First Movement)
* A harmonic oscillator is an object (string or spring or pendulum) or substance (water or air) that has an equilibrium situation (string: at rest; air: at uniform pressure), and when the object of substance is displaced from that situation, it provides a resisting force, proportional to the displacement, that tends to restore equilibrium. For example, plucking a string from its rest position stretches it, putting it under tension, and it then tends to pull itself back toward equilibrium; of course, once it returns, it is moving, and overshoots the equilibrium position, and you can see where that leads: to a continuing vibration.
** Note for word lovers: The word timpani is plural. The singular form of timpani is timpano, but it is rarely used (except perhaps by timpanists). In common parlance, one timpano is called a timpani. Timpanis is just plain wrong.
