# Vibroacoustic Descriptors of Central Africa Harps

F. Fabre, J.-L. Le Carrou, Baptiste Chomette, Sylvie Le Bomin

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F. Fabre, J.-L. Le Carrou, Baptiste Chomette, Sylvie Le Bomin. Vibroacoustic Descriptors of Central Africa Harps. 10th Convention of the European Acoustics Association Forum Acusticum 2023, Sep 2023, Turin, France. pp.3429-3432, 10.61782/fa.2023.0712 . hal-04895022

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# VIBROACOUSTIC DESCRIPTORS OF CENTRAL AFRICA HARPS

François Fabre<fnref n="1" />*

Jean-Loïc Le Carrou<fnref n="1" />

Baptiste Chomette<fnref n="2" />

Sylvie Le Bomin<fnref n="3" />

## ABSTRACT

Central Africa harps are string instruments, often anthro-
pomorphic, whose soundbox is built from a hollowed out
tree trunk. They contain a set of strings (usually be-
tween 5 and 11) which are bound to wooden tuning pegs
on the neck and attached to a tailpiece placed under the
soundboard. The constitutive material of each instrument-
making element may vary according to ethnic groups and
material availability which induces acoustic differences.
The present study deals with the definition of relevant vi-
broacoustic descriptors in order to assess the specificities
of a Central Africa harp. Experimental data, collected on
specimens from several ethnic groups, allow to test fre-
quency domain descriptors already discussed in the litera-
ture for other musical instruments.

**Keywords:** harp, central Africa, vibroacoustics, descriptors

## 1. INTRODUCTION

Harps from Central Africa play an essential role in social activities such as initiation rites and therapeutic practices [1]. They usually are at the center of musical pieces with an important symbolic representation. The different ethnic groups reveal a great diversity of harps in terms of repertoires, designations, morphological and acoustic

characteristics. In the frame of an interdisciplinary re-
search project (Ngombi) aiming at determining the evolu-
tionary mechanisms of these instruments, vibro-acoustic
descriptors (destined to be collected on-site) are looked
for.

The present study, which follows on a previous pa-
per [2], focuses on 6 gabonese harps at our disposal (com-
ing from 5 different ethnic groups) and is about testing
frequency domain vibro-acoustic descriptors already pro-
posed in the literature on other musical instruments such
as guitars [3] or concert harps [4].

A brief presentation of the harps studied in this paper
is given in section 2. Then section 3 presents the exper-
imental setup used to collect data. Experimental results
regarding the vibratory descriptors investigated are then
analyzed in section 4, giving rise to prospects for future
works.

## 2. CORPUS OF HARPS

The 6 harps included in this paper (see Fig. 1) repre-
sent 5 ethnic groups: Eshira, Fang, Massango, Nkomi and
Tsogho. They all have a soundbox made of a hollowed out
tree trunk on which a soundboard made of animal skin is
stretched and nailed. Their soundboard is made of a single
piece except for the 2nd Fang harp and the Tsogho harp.
A principal opening is present at the bottom of all sound-
board and the two Fang harps also show multiple smaller
holes near the top. They all contain 8 strings in fishing line
of gauge ranging from 0.8 mm to 1.1 mm. These strings
are coupled to the soundboard through a tailpiece placed
under it and are wrapped around the neck and wooden
pegs crossing it, thus allowing for their tuning. Finally,
the neck is fitted on top of the soundbox and bound to it

<footnote n="1">¹ Sorbonne Université CNRS Institut Jean Le Rond d'Alembert
Equipe Lutheries-Acoustique-Musique F-75005 Paris, France</footnote>

<footnote n="2">² Univ Lyon, Ecole Centrale de Lyon, CNRS, ENTPE, LTDS, UMR5513, 69130 Ecully, France</footnote>

<footnote n="3">³ Institut de Recherche en Musicologie, Quai François Mauriac, 75706 Paris, France</footnote>

<footnote>*Corresponding author: francois.fabre@sorbonne-universite.fr</footnote>

<footnote>Copyright: ©2023 François Fabre et al. This is an open-access
article distributed under the terms of the Creative Commons
Attribution 3.0 Unported License, which permits unrestricted
use, distribution, and reproduction in any medium, provided the
original author and source are credited.</footnote>
using a metallic wire or plant-based material going trough
two previously drilled holes.

<figure><img src="image_3.png" /><figcaption>Nkomi Massango Tsogho Eshira Fang Fang2</figcaption></figure>

<caption>**Figure 1:** Corpus of harps investigated</caption>

In the following, the strings are numbered from 1 to
8, 1 being the longest (lowest pitch) and 8 the shortest
(highest pitch). It should be noted that only the relative
tuning between strings is pertinent, harpists may adjust the
absolute tuning to obtain a desired tension or to facilitate
the acoustic radiation. Independently of the ethnic group,
strings 7 and 8 are tuned at the octave of strings 1 and 2.

3. EXPERIMENTAL SETUP

In order to compute the descriptors presented in section 4,
experimental data are collected following the experimen-
tal setup shown in Fig. 2. Hanging the harps using bungee
cords allow to approximate free boundary conditions dur-
ing the measurement. The static string/body coupling is
kept but a strip of felt is intertwined with the strings to
dampen their transverse vibrations and avoid a dynamic
coupling. The strings are tuned as close as possible to
their original tuning. The vibratory behavior of the body
is obtained through frequency response functions (FRF)
measured using a roving automatic impact hammer (force
sensor PCB 086E80) and four reference accelerometers
(PCB M352C65) placed at the coupling point of string
n°3 with the neck (in two transverse polarisations), at the
coupling point of string n°3 with the tailpiece and in the
middle of the back of the soundbox as shown in Fig. 2. A
fifth accelerometer (PCB 352C23) is moved alongside the

impact hammer to measure collocated FRFs at each string
attachment point.

<figure><img src="image_4.png" /><figcaption>**Figure 2:** Experimental setup. Ⓐ: automatic impact hammer, Ⓑ: accelerometers, Ⓒ: strip of felt, Ⓓ: bungee cord</figcaption></figure>

4. DESCRIPTORS

4.1 Conductance map

The representation of collocated conductances (real part
of the mobility) along string attachment points is an ef-
ficient tool to report on the spatial and frequency evo-
lution of the soundboard response in the low frequency
range. The superposition of strings’ partials, in com-
bination with the knowledge of the modal basis of the
soundboard, allows for a quick interpretation of potential
string/soundboard and string/string couplings. A conduc-
tance map for each harp of the corpus is shown in Fig. 3
with white arrows linking some conductance peaks with
the corresponding mode shapes presented in Fig. 4. It
should be noted that the original tuning of the Eshira and
Nkomi harps are not known by the authors, however po-
tential tuning ranges can be estimated from the gauge and
length of the strings following the work of Woodhouse [5].
These are represented in Figs. 3f and 3e by horizontal
lines of different shades of gray linked to the partial or-
ders.

From Fig. 3, it clearly appears that the Massango harp
has an overall higher conductance, followed by the Es-
hira harp, which indicates that energy transfers between
the strings and the soundboard will be more pronounced
<figure><img src="image_5.png" /></figure>

**Figure 3:** Conductance maps. Each plot shows a range of 7 dB. Red squares: fundamental string partials. Red circles: higher order partials. Grey shaded horizontal lines: potential tunings of the Nkomi and Eshira harps. (a) Tsogho, (b) Fang, (c) Fang2, (d) Massango, (e) Nkomi and (f) Eshira

for those harps thus increasing the acoustic radiation at the cost of a shorter decay time. When looking at Figs. 3a, 3b, 3c and 3e, one sees that, for all harps, modes 1,1 and 2,1 exhibit the highest response, followed by the mode 3,1. The spatial spread of string attachment points may thus strongly influence the potential for sympathetic vibrations between strings. Finally, the frequency of the first bending

mode (1,1) doesn't coincide with any fundamental string partial of the Tsogho harp while it coincides with the one of the fourth and fifth strings of the Fang harps and the seventh and eighth strings of the Eshira, Massango and Nkomi harps. This further explains timbre variations between all these harps.

<figure><img src="image_6.png" /><figcaption>**Figure 4:** Modeshapes of the soundboard</figcaption></figure>

## 4.2 Mean Value of Mobility

Analyzing separate modal contributions in the low to medium frequency ranges gives useful insight on the vibratory behavior of the harps. However, once these contributions overlap in such a way that it becomes impossible to discriminate them, a global analysis becomes more relevant. One descriptor proposed in the literature [6] to summarize the response of a structure in the medium to high frequency ranges is called the Mean Value of the Mobility (MVM) and simply consists in averaging the mobility level in dB over a given frequency band. Fig. 5 presents the evolution of the MVM over string attachment points for all harps of the corpus. The frequency range used to compute these MVM starts at 500 Hz, since the modal overlap factor is around 30 %, and is limited to 2000 Hz due to the hammer force.

<figure><img src="image_7.png" /><figcaption>**Figure 5:** Mean Value of collocated Mobilities on the tailpiece of all the harps</figcaption></figure>

It is worth noting that the two Fang harps show similar trends of the MVM with important variations between
adjacent strings which may introduce an inhomogeneity of the instruments. It would be interesting to further investigate this on a wider sampling of Fang harps. The second Fang harp has the highest MVM of all the corpus with -19.5 dB at the fourth string, followed by its second string (which is in agreement with Fig. 3c). Apart from this harp, the higher global mobility of the Massango, followed by the Eshira harp, is recovered with respect to conductance maps. The MVM of the Eshira, Massango and Tsogho harps are the most uniform despite having different spatially spread string attachment points.

When conducting the experimental modal analysis of the harps, a non-negligible influence of the air humidity on the modal frequencies of the harps was observed (leading to wrongly identified poles' multiplicity). In order to investigate the robustness of the MVM with respect to these changes in air humidity, the soundboard mobility of the second Fang harp is measured at different instants. The results are displayed in Fig. 6 for an air humidity ranging from 36 % to 46 %.

Despite important shifts in resonance frequencies (for example a deviation of approximately 7.5 % at 400 Hz for the mode 2,1) the global trend of the mobility remains stable, except for a pronounced drop in modulus around 1.4 kHz for an air humidity of 46 %. This is confirmed by the five MVMs which show a maximum difference of only 1.8 dB. This tends to indicate that the MVM is a robust descriptor in view of on-site measurement. In light of this result, further investigation is to be conducted on a longer period of time, a wider range of air humidity and several harps.

<figure><img src="image_8.png" /><figcaption>**Figure 6:** Soundboard mobility for an air humidity in the range [36-46] % (2^nd^ Fang harp)</figcaption></figure>

## 5. CONCLUSION

This study of 6 Gabonese harps lead to a modal and frequency analysis of their soundboard in order to report on their vibro-acoustic specificities. The Massango and Eshira harps show a similar trend both on conductance

maps and via the MVM descriptor with the Massango being globally more mobile in high frequencies. Secondly, on all harps the first 3 bending modes contributions have the highest response and by varying the absolute tuning, harpists may change which fundamental string partials coincide with these contributions thus adjusting the timbre. Regarding the averaged mobilities, both Fang harps show a high variation along string attachment points with a similar trend with a maximum at the fourth string. This indicates that these harps should have a less consistent acoustic radiation from string to string compared to other harps of the corpus. Finally, results regarding the robustness of the MVM to changes in air humidity are encouraging, despite the strong influence these changes have on the local behavior of the mobility through shifts in modal frequencies. The MVM is thus a promising descriptor with a view to on-site measurement and it will be further investigated on a wider corpus of harps in the future.

## 6. ACKNOWLEDGMENTS

This work, part of the project Ngombi, was funded by the Agence Nationale de la Recherche (French National research agency), grant number ANR-19-CE27-0013-01.

## 7. REFERENCES

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[3] A. Paté, J.-L. Le Carrou, and B. Fabre, "Predicting the decay time of solid body electric guitar tones," *J. Acoust. Soc. Am.*, vol. 135, pp. 3045-3055, May 2014.

[4] J.-L. Le Carrou, S. Le Conte, and J. Dugot, "18th and 19th French harp classification using vibration analysis," *Journal of Cultural Heritage*, vol. 27, pp. S112-S119, Oct. 2017.

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