Joe Dickey - dickey@jhu.edu
Center for Non Destructive Evaluation
The Johns Hopkins University
810 Wyman Park Drive, Suite G010
Baltimore, MD 21211
(410) 266-6832
Ray Wakeland
The Pennsylvania State University
State College, PA 16804
Popular version of paper 4pSA3
Presented Thursday afternoon, May 1, 2003
145th ASA Meeting, Nashville, TN
As banjo players, Joe Dickey and Ray Wakeland were well aware of all the folklore, homespun theories, players' tips and preferences and "black magic" that go into setting up and tuning a banjo to get just the right sound. As a Johns Hopkins University research scientist specializing in structural acoustics and a Penn State graduate student in acoustics, respectively, they were amazed to discover that search as they might they could find no scientific papers breaking down the acoustics of the banjo. They found thousands of papers analyzing violins and guitars and some about unusual stringed instruments like the Ethiopian bagana and the Chinese yangqin, but none on the ever-popular American five-string banjo, even though its simple strings-and-membrane construction makes it an ideal candidate for mathematical modeling.
Dickey has now devised a computer-based model that's sure to strike a chord with banjo makers and players everywhere as they strive for the perfect tone, and Wakeland has made measurements of actual banjo sounds to help verify the model.
The sound of a banjo is created by plucking a string connected to two support points, one of which is attached to a stretched membrane called a "head." The plucked string reverberates and then settles into a vibration at a frequency, or note, determined by the string's tension and mass. The banjo's head picks up the vibration from the string through the connecting bridge and radiates it, making it louder and adding its own tonal qualities to the note.
The schematic in Figure 1 shows how these banjo basics are broken down into dynamic systems that can then be modeled mathematically. Of course, this is complicated by the fact that there are five strings rather than one. The modeling process is further complicated by the fact that setting up and tuning a banjo involves a large number of adjustable elements. This is why Dickey's modeling technique has such potential value.
Figure 1: The banjo, simplified, showing a) an actual banjo, b) a schematic
representation of a one-string banjo, and c) a schematic of the wave-bearing
systems 1 & 2 with their connections and terminations. The model for the five-string
banjo has six systems, five for the strings and one for the head.
The factors that affect banjo tone include how quickly the initial string vibration settles into a note, what tension is applied to strings and head, how the components are configured, what they're made of, and so on.
Using the mathematical model, selected parameters can be studied thoroughly to determine their impact on tone. Three aspects of tone have been identified for study. The first is brightness, determined by the amount of higher-frequency sound superimposed on the fundamental note. The second is loudness. And the third is decay, referring to how quickly the tone fades after a standard pluck. The mathematical model is used to analyze banjo set-up variations in terms of these three parameters. For example, the tension of the head membrane is known to have a major influence on banjo tone. With the mathematical model, Dickey can predict the effect of any head tension on brightness, loudness and decay, as shown in Figure 2. His analysis shows that as head tension decreases, brightness decreases to generate a warmer sound with fewer overtones. It also shows that decay will not change much and loudness will be decrease slightly.
Figure 2: Model results showing the effects on banjo tone of increasing head membrane tension.
Other findings so far demonstrate how increasing the mass of the bridge connecting the strings with the head decreases the brightness and loudness, and how the position of the pluck on the string can result in interestingly complex brightness behavior.
Dickey and Wakeland hope that by putting this kind of scientific data into the hands of banjo makers and players, they can help banjos evolve and make banjo music more distinctive and more enjoyable than ever.