Our objectives for this project include an in depth analysis of the properties of stringed instruments. We strived to understand how different stringed instruments function individually, and how instruments differ in their sound and function. Stringed instruments create the sound in three phases: (i) the source or string, (ii) the medium or body and (iii) the interface, which is the oscillation of the air around the body. These elements interact to create the sound we hear in each instrument. In this research, we gathered string oscillation data, vibrating the strings at different locations with different methods of excitement. We studied body vibrations by looking at the sand patterns that form when the instrument is excited at different frequencies. We also analyzed high-speed videos of the strings to better observe the oscillations produced. We performed comparisons of the instruments that revealed each instrument’s unique characteristics.
Musical instruments create sounds at their natural vibrational frequencies, which depend upon their size and structure. The natural frequencies of a musical instrument are called the harmonics of the instrument. The parts of an instrument interact and force each other into vibrating at their harmonics (standing wave patterns). This is known as resonance. A string fixed at both ends can oscillate in many modes, called harmonics. These must keep the string fixed at the ends. These harmonics are shown in Figure 1.
The sound of each instrument is unique because it exhibits characteristic frequencies that set it apart from other instruments. We gathered sound data using a computer interface that captured the sound through a microphone and turned it into a raw waveform. The experimental setup is shown in the next three figures:
The resonances seen above occur at frequencies of 0 Hz (no excitement), 80 Hz, 110 Hz, 236 Hz, 362 Hz and 408 Hz, respectively. The bare locations are where the body oscillations occur and contribute to the overall sound of the instrument.
The harmonic structure of stringed instruments is reflected in the string resonances, since they initiate the sound. High-speed videos of the string were taken to portray the real time oscillations. We created mathematical models of the strings from the harmonics, and compared the visual representations in the high-speed videos to them. A high-speed camera and a bright light source were used.
When the waveform is reconstructed from the harmonics, it looks like [Figure 9] below. This compares favorably with the actual waveform. The video shows the intermediate oscillations as a hesitation between the extremes.
To understand the differences amongst instruments, we correlated the string and body oscillations. The instruments were separated into their corresponding body shapes to see the differences. The results for the lesser-known instruments follow here.
The figure eight and triangular shaped instruments produced a significantly larger amount of harmonics with the pick as compared to the peanut or teardrop shaped instruments. The circular shaped banjo body excited the highest amount of harmonics, yielding its “tinny” sound.
The body oscillations mainly affected the fundamental and second harmonics. For the mandolin and the acoustic guitar, the body oscillations only affected the fundamental harmonics. The strummer data indicated that the notes excited with the thumb had a much larger correspondence with the body oscillations.
The following figures show the relations between the string and body resonances for the dulcimer, strummer and banjo that work together to form the unique sound of the instrument. The dulcimer and strummer have a wooden body, while the banjo’s body is a membrane. The colored numbers indicate different body resonance frequencies and the percents represent the fraction of the sound that is due to the body resonance. The dulcimer has a peanut shape and is comparatively much larger than the strummer, which is triangular. The strummer excited fewer harmonics than the dulcimer did.
Figure 15. Correlations of string resonances with body shape – seven of twelve instruments
Studies like this allow us to understand instruments better, so that artists can make best use of their characteristics and instrument designers can build more innovative instruments.
D. Hall, Musical Acoustics, 3rd Ed.
Rossing, The Science of Sound, 3rd Ed.