The Caribbean Steel Pan: Marriage of Science and Art
Dr. Uwe J. Hansen, Professor Emeritus of Physics, Indiana State UniversitySound travels as waves which cause compression and rarefaction in the ear. To cause a rise in frequency of sound, the vibrating instrument must be either less massive or under greater tension.
Music depends on certain relationships of sound which cause it to be harmoneous. Illustrating with a spring, we can see moving one end up and down while holding the other anchored, the wave generated will be reflected back upon reaching the anchored end. If the free end is moved in sync with this reflected wave we can achieve a single arc which alternates between center rise and center fall. This is the fundamental frequency for our spring. If we raise and lower the free end twice as fast, we create two standing arcs with a still point (or node) at the center between the active and anchored ends of the spring. When this occurs we have a frequency relationship of 2:1 which is known musically as an "octave". If we increase the action to get three arcs in the spring with two evenly spaced nodes (as opposed to two arcs with one node) we then have the ratio of 3:2 in frequency which is the musical 5th. We can continue upward with standing wave forms of the same spring increasing the number of nodes by one to get the 4:3 relation (a musical 4th), the 5:4 relation (a musical 3rd), and the 6:5 relation (a musical minor 3rd). These are all naturally occurring harmonics for instruments wheather they be string, springs, air columns, of whatever; and are based on the naturally occurring one-dimensional relationships (ie. increasing by integers the number nodes in a linear standing wave).
What makes the steel pan very interesting is that it is not one-dimensional (like a vibrating string or air column) but it is two dimensional, since the vibrational points are areas of steel on the pan head. Instead of having nodal points to define harmonics, you now have nodal lines (or rings) within the sound producing areas, and the vibration of one area (or note) on the pan induces vibration to all other areas of the pan with associated harmonics. The main trick to producing pleasing musical sounds with such an instrument is to keep high pressure points on the sound surface from short circuiting to low pressure points and get the nodal lines properly placed to produce harmonic overtones.
The balance of Dr. Hansens talk is quite technical and involves studies of just how the complex coupling of the pan head can be studied using laser light, and how this leads to an understanding and improvement of the sound quality of the steel pan as a musical instrument. This is based on a well illustrated paper he gave which is available as a "pdf" file (CLICK for a copy) from his web site http://newton.indstate.edu/phhanse.