In Search of the Missing Fundamental: by Richard K. Jones
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Strings and Harmonics

Each harmonic above a fundamental frequency also has what are called nodal points. Nodes or nodal points, are points that remain at rest while the other parts of the string are in a state of vibration. Figure 1f represents the first six partials of an open vibrating string and its various nodes.

 An open string vibrates with all of its harmonics and is stopped at all of its nodal points at the same time which means that the open string can vibrate simultaneously at all of these frequencies. The subsequent frequencies are not as loud as the fundamental and all blend together and so the human ear perceives it as being one pitch.
Fig. 1f
When this open string is touched lightly at certain nodal points, only the harmonics that have a node exactly at that point can still vibrate.
Fig. 1g

A string that is touched lightly exactly at its mid point can only vibrate at the frequencies that have a node there. Consequently, it will have a thinner sound than the open string. It will sound higher in pitch since only half of the string is vibrating. The harmonic that is excited depends on which nodal point is touched.

Interestingly enough, the actual sound of the timpani is not created by exciting the fundamental frequency of the drum but rather one of its partials, or to be more specific, one of its secondary modes of vibration, mode (1,1). Similar to exciting a harmonic partial on a vibrating string, the drum is struck in such a manner where the actual fundamental is virtually damped and the drum’s second mode of vibration, mode (1,1) is excited. It is this weaker mode of vibration that produces the pitch that we perceive. This mode of vibration is referred to as the principal tone of the timpani and not the fundamental. The actual fundamental does not have a pleasing sound.