Course:PHYS341/Archive/2016wTerm2/KalimbaResonator

The Resonator of a Mbira

The mbira (also known as the kalimba) is a lamellophone instrument that is sometimes used with a resonator for amplification and resonance. In some cases, the mbira is placed into an external resonator, and in other cases the resonator is built into the mbira's box.

Fig.1 - Mbira with a gourd resonant box.

Structure of a Mbira

Like all lamellophone instruments, the mbira is constructed with multiple thin plates, each fixed at one end. These plates are set into vibration by an instrumentalist plucking the plate(s) with his or her thumbs. The plates of the mbira are made from a variety of different materials, including iron ore from rocks (which is how they were traditionally made), sofa springs, bicycle spokes and car seat springs . Traditionally Mbiras have been equipped with "buzzers" (beads attached to the instrument's tines) to accompany the notes defined by the plates themselves, however, many Western manufacturers have opted for a "cleaner" sound, thus eliminating the use of buzzers in some cases. On Hugh Tracey Kalimbas (the first mbiras to be sold in the Western world), removable beads are attached to create the distorted effect.

Aside from the tines and the buzzers, which provide the instrument's notes and distortion, respectively, it is common for Mbiras to be used with resonators to amplify the instrument's relatively quiet sound and add resonance to its fundamental frequencies. Resonators can be built into the instrument or added externally, often depending on the material that the plates are mounted upon. There are a wide variety of body materials that the plates can be mounted on, including boxes, boards, and hollowed gourds . See figure 1 for an example of a mbira with gourd mounting as a resonant box. In the case of the board mountings, it is common for the lack of a built-in sound hole resonator to be compensated for by attaching the instrument to an external resonator made from a calabash gourd (or another type of bowl) . In most cases, built-in resonators are simply holes in the hollowed-out body which can be used to manipulate the resonant properties of the cavity when someone covers it with their hand. .

How Mbira Resonant Boxes Work

When a Mbira is plucked on its own, the tines of the instrument vibrate, but if the mbira has a resonant box (i.e. has a sound hole), the vibration is resonated through it as well. For around 0.05 seconds, discordant frequencies known as the note's "attack phase" can be heard as the tines initially vibrate. After the attack phase, the energy in the vibration organizes itself so that the resonant frequency of the tine is heard by the human ear, and the vibration energy begins to move back and forth between the the bridge mechanism holding the tines in place and the end of the tine. In most cases, these vibrations decay as they bounce back and forth.

Along with the tines themselves, mbira resonant boxes have their own resonant frequencies. The resonant frequency of a box is largely dependant its size; larger boxes have lower frequencies and smaller boxes have higher frequencies, and as such alto boxes often have a fundamental frequency of around 440 Hz [A] while treble boxes often have a fundamental frequency of around 490-520 Hz [B - C]). A vibration's frequency is inversely related to the vibration's wavelength, and if the wavelength is doubled, the frequency is divided half, and ultimately a lower pitch is perceived.

Fig. 2 - Diagram of Helmholtz Resonance in a mbira

The resonant boxes of a mbira also have a sound hole to increase perceived the loudness of what's being played on the instrument. As with other instruments that use sound holes for resonance (guitars, for example), the sound hole is used to lower the lowest frequency of the instrument without having to thin out the resonant box to an extreme extent. The sound at lower frequencies is radiated from the air vibrating in the hole opening. This process is known as Helmholtz resonance, as can be seen in Fig. 2. The sound hole of the mbira (as with other instruments) is able to make lower frequencies seem louder due to the fact that the air inside the instrument's body and the sound hole are moving in opposite directions. This causes low-frequency oscillations in the sound that would not occur if it weren't for the sound hole. The lower the position of the air mode, the deeper the resonance. This eliminates the need to thin out the mbira's wood to an extreme extent, as thinning the wood creates a deeper resonance, but can eventually crack the wood.

External Resonators

Traditionally, mbiras have not been equipped with resonant boxes, but instead simply have a solid flat board mounting with no sound hole. Because of the lack of a resonant box, these sorts of mbiras tend to be quieter than those with resonant boxes. Despite this, the vibrations created from the plucking of the instrument's tines are still transferred into these solid mountings (these vibrations can be felt by the human hand). This vibrational energy can be transferred into other systems, thus making the sound louder and making lower frequencies more prominent. This is usually done by placing the mbira into a bowl-shaped container, traditionally a calabash gourd.

The process by which a bowl resonator causes a mbira to be perceived as louder is similar to the way in which a tuning fork can be amplified (to the human ear) with a resonance tube. When the tuning fork is struck, the tines vibrate at their own natural frequency, impinging upon the opening of the resonance tube. As a result the air inside the resonance tube vibrates at the same frequency as the tuning fork, causing the perceived loudness to increase when the water level in the tube is adjusted to an appropriate air column length that matches the vibration frequency. A similar process is used in the case of a mbira is a resonator bowl: when the tines of the instrument are plucked, the vibrations force the bowl to vibrate at that frequency as well, creating what seems to be a louder resonance.

To summarize, the hole in a mbira's resonant box makes lower frequencies appear louder by causing sound oscillations at the cavity that would not have occurred otherwise. External resonators make the sound appear louder by receiving the vibrations from the plucked instrument and amplifying them to the human ear.