Instrumentation & Measurement Magazine 24-7 - 15

Fig. 3. Diagram of the directivity of a violin: for each point in a sphere around the violin one has a set of energy v/s time
values, for each frequency band. These values are transformed to the frequency domain and described in terms of spherical
harmonics on the surface of the sphere, for each frequency band.
the directivity are usually limited to determining the directivity
(or radiance) pattern.
Overview of the Studies on the Musical
Instruments Directivity
Most of the publications on the acoustic radiation of instruments
[2], [27], [9] focus on the measurement of the directivity
pattern, but the insight that they offer on the comparison of
radiation properties across instruments is rather limited and
only qualitative. Several works ([28] and references therein)
analyze the directivities to describe best practices on " micing "
the instruments or seating in concert halls. In particular,
Meyer's work [29] has become a reference for the directivity of
symphony orchestra instruments, as it: includes an extended
analysis of the directivity of the instruments; highlights the
characteristics of the different families; and offers insight on
how to optimize the orchestra seating. More recently, in [28],
the authors revamped the notion of directivity for symphony
orchestra instruments with a more rigorous measurement procedure
and with an eye on their auralization. These results
suggest that relevant differences in terms of directivity exist
among different instrument families. While brass instruments
showed a somewhat predictable and constant directivity,
woodwinds and string instruments, even more, are characterized
by variable and complex directivity patterns.
The directivity of violins attracted broad interest in the literature
due to its peculiar characteristics. The well-known work
by Weinreich [30] first made clear evidence of the so-called
" directional tone color, " namely the rapid and unpredictable
variation of the directivity across frequency. This property,
which is typical of violins, is known to be related to the acoustic
October 2021
radiation qualities of the
instrument and affects the
listener's perception by
creating " the illusion that
each note played by a solo
violin comes from a different
direction, endowing
fast passages with a special
flashing brilliance " [30].
The accurate measurement
of the instrument's
directivity pattern typically
requires expensive
microphone array setups
and controlled environments.
In addition, they
do not often account for
the presence of the body of
the musician. These limitations
were only recently
addressed by techniques
based on a flexible setup
that can cope with reverberation
through plenacoustic
processing [9].
The ever-growing interest in spatial audio technologies
with application in virtual and augmented reality is adding to
the pressure for collecting more directional information from
musical instruments [31]. This, in fact, comes with the promise
of more immersive and pleasurable listening experiences.
New research opportunities are therefore emerging in the area
of acoustic radiation in musical instruments. Challenges in
this direction are not only limited to pure data acquisition but
also to the storage of the directivity. Formats like Common Instrument
format (http://www.clfgroup.org/cif.htm ), SOFA
[32], or openDAFF [33] can be adopted; the latter two are primarily
employed for Head-Related Transfer Function (HRTF)
data, but they can be directly applied to directivity. As a matter
of fact, the HRTF can be roughly considered the reciprocal of a
directivity function since the former describes the directional
" sensitivity " of a human receiver, while the latter provides the
directional radiation intensity of a sound source.
Future Perspectives on Directivity Processing
When it comes to information retrieval on acoustic properties
of musical instruments, the comparison between directivity
patterns and the quantification of differences is still an open
challenge. Directivity, in fact, is a highly complex frequencydependent
function, which means that multiple bands must
be considered and adapted to the specific range of that instrument.
Furthermore, for each frequency, the directivity is
function of the direction of emission (azimuth and elevation
angles), which makes the comparison of complex patterns extremely
difficult to conduct, and the approaches that we can
adopt are, in fact, typical of image processing. Some simple
metrics, of limited informative extent, have been adopted in
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15

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