Every harmonic produced by a vibrating string includes specific nodal points, positions along the string that remain stationary while the rest of the string vibrates. These nodes are a key feature of standing wave patterns. 5 6 17
Figure 1f shows the first six harmonic partials of an open string and the locations of their nodal points.
When a string vibrates freely (i.e., as an open string), it vibrates in a superposition of multiple harmonic modes simultaneously. Each of these modes, the fundamental and its overtones. contributes to the total sound. The result is a complex tone that the ear interprets as a single pitch, with the fundamental being the most prominent.
Touching Nodes to Isolate Harmonics
If you lightly touch the string at one of its nodal points (without pressing it fully down), you selectively suppress harmonics that do not have a node at that point, allowing only certain harmonics to vibrate.
Figure 1g demonstrates how touching the string at various nodal points excites specific overtones.
For example, touching the string exactly at its midpoint activates only the second harmonic, which divides the string in half. The resulting tone sounds one octave above the fundamental and has a clearer but less full sound, since many other harmonics have been suppressed. The specific harmonic you isolate depends on where along the string you place your finger.
Linking to Timpani: A Different Kind of Vibration
Although timpani do not use strings, a similar principle applies to how they produce pitch. Timpani do not vibrate primarily at their fundamental frequency. Instead, when struck correctly, they excite a secondary vibrational mode, specifically, mode (1,1).
- This (1,1) mode involves one nodal diameter and one nodal circle, and is the first mode with enough harmonic character and acoustic strength to be perceived as pitch. The actual fundamental mode of the timpani (the (0,1) mode) is heavily damped and does not contribute significantly to pitch perception. It produces a sound that is lower and acoustically dull, often described as lacking tonal clarity.
Thus, the pitch we associate with timpani arises from this principal tone, which is not the true fundamental, but a higher, more musically useful partial.