Acoustic Aspects of the Balani of Mali

INTRODUCTION: The Balani

     This report is part of a larger project investigating acoustic features of two Bambara xylophones called balani, or balafon (French) from Southeastern Mali. They were constructed by Dugu Koro Diarra, a Bambara master balani player and craftsman, and by Brehman Malle, an accomplished Minianka bala player and former apprentice of Diarra. The results presented here concern the effect of gourd resonators on the acoustics of the instrument and the presence of a pitch which is not acoustically produced but which is clearly perceivable when two lamels (keys) are struck simultaneously.

     The physical structure of the balaniw consists of 17 wooden lamels mounted and tied with goatskin onto a wooden frame. The Bambara bala frame stands roughly 8" high from the ground at the left end, and gradually slants up to the other end, reaching approximately 13-14" . The keys at the left end have the lowest pitches, the largest being 25" long. On the right end are the smallest and highest pitched keys which measure about 12". Beneath each lamel a gourd is tied with string; each gourd contains from one to three holes over which spider egg-sacs (mirletons) are glued. The mallet sticks are made of light wood and the soft rubber heads are balls of melted and re-molded tree sap. Currents of air resulting from the impact of the mallet on the lamel pass through the gourds and over the mirletons, and produce the buzzing quality of the xylophone timbre.

     The results of intensive computer analyses of balani pitch measurements, actual performed music, and various other acoustic sound files, reveal the gourd resonators to have little impact on determining pitch quality. They do, however, produce most of the characteristic buzz-hum and resonance of the balani. In addition, my analyses show how it can be that the non-acoustically produced pitch, which I refer to as "hidden", is perceivable when there is no lamel to represent it. The presence of this pitch shows that the balani's pitch inventory is not pentatonic as many previous West African xylophone scholars have claimed. Because this "hidden" pitch is produced and perceived by the Bambara bala players in addition to the other five pitches, the pitch inventory contains at least six different pitches. I am not prepared to claim the type of scale or determine the pitch inventory at this time, but my data shows that it is not pentatonic.

     When the "hidden" pitch is not considered, the pitch inventory appears to be pentatonic. I measured the fixed intervals of both balaniw and recorded the approximate intervals charted below in figure 1. The inconsistency of the octaves' intervallic arrangements within each balani, and in comparison to each other, suggests that this tuning system is based on an equipentatonic model.

 

	Balani #1 (Malle)	Balani #2 (Diarra)
Octave1	M2 M2 m3 m3 M2	M2 M2 m3 M2 m3
Octave 2	M2 m3 m3 M2 m3	M2 m3 M2 m3 M2
Octave 3	M2 m3 M2 M2 m3	m3 M2 m3 M2 m3F

 Fig. 1: Comparison of intervals composing three octaves on two balafons.

Another remarkable feature of the perceived pitch of the instrument is that each lamel actually produces two pitches, a striking tone, when the mallet hits a key, and the sustained resonating tone of the key itself. The arrangement of pitches described above is illustrated in
figures 2 and 3.
 
 

Figure 2: Balani #1	Figure 3: Balani #2

 
 

     Duga Koro Diarra built balani #2 in 1992 at my request. I wanted to have a set of two balaniw which could be played together and with other balaniw from the region. Since I already had balani #1 in my posession, Duga used it as a model for tuning. I witnessed the construction and tuning process and based on my observations, it appeared that the balani's buzz-hum timbre is an acoustic feature which carries equally important--if not ultimate--weight as the pitch factor in Bambara appraisal of the balani's acoustic aesthetic.

     A brief description of the Bambara terminology used to describe the physical structure of the instrument is further evidence that pitch and scale are not the most important element of the acoustic aesthetic of the balani. During the construction of balani #2, Duga and Issah called the highest pitched keys "san fe" (towards the sky) and the lowest pitched keys "duguma fe" (towards the ground). Rather than identifying lamels according to pitch, musicians specify lamels by their relative physical location (remember that the balani frame is tallest or closest "towards the sky" at the bass key end and slopes down "towards the ground" as the keys get smaller and higher pitched). When I asked them to describe the sound of the high pitches, they defined them "fitini" (little) and the low pitches "bo" (big). Thus, pitch is recognized but not necessarily the most important feature of the total balani sound.

Effects of Gourd Resonators on Balani Pitch, Timbre, and Loudness

     In order to discover the effects of the gourd resonators on the sound of the instrument, I removed the gourds from Balani #1 and recorded every individual strike again making sure to maintain the manner and place of striking that I used on the first recording. To my ear, and that of a colleague who assisted me in recording, there was no difference in pitch and hardly any in amplitude. The most remarkable difference distinguishable to our ears was the absence of the buzz hum sound of the mirletons, and an attenuation of the striking tone on some of the lamels.

On keys where the striking and sustained tones are clear, spectra reveal the fundamentals and harmonics of both tones (figure 4).
 
 

Figure 4: Spectrum of tone from 5th lamel, showing primary and secondary pitches

     I hypothesize that there are two primary reasons that the two tones are heard distinct from each other, rather than blending into the timbre of the tone. First, the spectral envelops of the primary harmonics responsible for the sensations of strike and sustained tones are very different?that is, the strike tone reaches hearing threshhold and then decays much more quickly than the sustained tone, as seen in figure 5. Second, the sustained tone is inharmonic relative to the fundamental of the remainder of the tone, and is simultaneously prominent enough to stand out perceptually over the remainder of the balani tone.

Figure 5: Amplitudes (vertical axes) of sustained tone (top) and strike tone (bottom)
charted as function of time (horizontal axes). Strike tone reaches higher amplitude
sooner than sustained tone, but decays after approximately 300 ms, while sustained
tone lasts for approximately 1200 ms.

     A comparison of the tone of the balani with and without gourd resonators shows a difference in resonance. Figure 6 shows a tone produced without the gourd. Here, the amplitude drops dramatically and rapidly. Figure 7 represents a tone from the same lamel with its gourd. Here, the amplitude drops and then maintains it's level for a few milliseconds, before dropping off like the other. These figures show that the amplitude is in fact affected more than we had thought on listening. The difference in decay time of the tone with and without gourds revealed by the graphic data also suggests that the buzz-hum quality produced by the gourds may be the accumulation of resonant sound of many successive strikes played fast and loud. More investigation about this should be done, but I am presently inclined to view the gourds as creating the same acoustic effect that a large bathroom would. The balani gourds, like a closed bathroom, resonate onevoice just slightly, but if there are seventeen voices in the bathroom, all talking fast and loud simultaneously, each individual voice becomes blurred and the overall sound "hums". Similarly, the gourd allows a tone to resonate longer, well into the strike of the next tone, so that remnants of several tones are heard at once.
 
 

Figure 6: Rise and decay of balani tone without gourd.

 

Figure 7: Rise and decay of balai tone with gourd.

     For certain keys, the strike tone was perceived to be markedly diminished when a gourd was attached. Again, a comparison of tones from one such key with and without gourd, revealed that the gourd emphasizes the resonating tone, while dampening the strike tone. Figures 9 and 10 show pitch 5 from one of the balaniw struck with and without a gourd. The harmonics produced by the strike tone are clearly visible in the spectrum of the lamel with gourd, and equally clearly attenuated in the spectrum of the lamel without gourd. The physics of a coupled system of two resonators as represented by the xylophone with gourds is still to be investigated.
 
 

Figure 8: Lamel 5, with gourds

Figure 9: Lamel 5, without gourds

The "Hidden" Pitch

     During my apprenticeship with Brehman, I remarked one day that the balani was missing the minor third from the lowest A#; there was no C# lamel on the instrument. Brehman replied, "oh yes, it's here!" He played notes 3 (C) and 4 (D) together and asked me if I could hear it. When in the course of this analysis, I played the two notes together for two other people, they heard, like myself, the third very clearly. This hidden pitch seems to last as long or even longer than the two tones used to produce it. In an effort to discover an acoustic basis for this tone, I recorded simultaneous strikes of lamels 3 and 4 and ran the result through the computer for analysis. Figure 11 shows the waveform of the two tones played together. That the two tones are beating is clearly evident in the undulating shape of the wave. And that the minor third is heard in the beating of the two tones can be explained by the formula used to calculate the perceived pitch of two tones of slightly different frequencies played together: Fresultant = 1/2(F1+F2). Since the fundamental of lamel three is about 262 Hz and that of lamel four about 297 Hz, the resulting pitch of the two together must be 279.5 Hz, approximately C#. It should be noted, however, that the C# is not an inevitable percept given the two surrounding lamels. At frequencies of 262 and 297 Hz, approximately a major second apart, the frequency difference just borders the beating zone?the frequency region within which two tones will inevitably beat together. At 35 Hz difference, the two tones can be resolved separately into a second, or on the other hand, they can be heard as beating to produce the C# hidden "between" the two.

CONCLUSION
     This preliminary study into the Bambara balani's acoustic features revealed several interesting things. First, the data proved that the balani gourds function exclusively as resonating chambers and have very little effect on the instrument's pitch. From the pitch and interval analysis this study also opened up exciting research questions related to the phenomena of pitch perception and acoustic and non-acoustically produced sound. The discovery of the "hidden" pitch in the balani, for example, shows that the physical structure of an instrument does not necessarily pre determine its pitch producing capacity. When one observes that a xylophone has four keys fitted in between an octave, it is now clear that it is not safe to assume that that instrument must therefore have a pentatonic tuning structure.

     A third and final aspect of perceived pitch which I found with respect to the balani is that one strike on any given lamel produces two pitches simultaneously. Both pitches are clearly audible and detectible on spectrum analysis, but further investigation should be taken up to find out how these pitches are perceived and organized by the listener, the producer, or by any given community.