human voice polar patterns opea singer and speakers
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Acoustic Instrumentation and Measurements April 2015, Argentina
HUMAN VOICE POLAR PATTERN MEASUREMENTS:
OPERA SINGER AND SPEAKERS
AUGUSTO BONELLI TORO1
NAHUEL CACAVELOS1
1Universidad Nacional de Tres de Febrero, Buenos Aires, Argentina.
Abstract - In the present work, a biomechanical source (speaking and singing human voice) and different
loudspeakers polar patterns were measured, with two different sound intensities. First, the polar pattern of the
biomechanical source was obtained, then the loudspeakers patterns were measured with the aim to compare
between them and recognize which is the most similar to the biomechanical source. A Matlab algorithm was
implemented to process the data and plot the polar patterns. Harmonic comparison between the two intensities was
carried out. A figure of merit comparing the different loudspeakers and the biomechanical source was implemented..
1. INTRODUCTION
1.1.Uncertainties in measurements
The uncertainties are defined as parameters
associated with the results obtained after performing
a specific measurement. These serve to characterize
the measurement error of each of the variables
directly related to the measurand. The errors are often
known as dispersion.The final result of any measurement cannot ignore
the uncertainty because the value obtained in the
measurement is not absolute and its meaning can only
be complete when affixed the result with the error.
1.2 Directivity
When a listener hears a source of any kind, this
one reproduces sound in more than one direction,
with a strong dependence on frequency. When a
listener moves off-axis of the source, the perceived
sound will vary, causing a greater variation in high
frequency. These variations also depend on the sizeand the number of subdivisions of the respectivesource.
If a person moves into the room, even if the
listener is positioned on-axis it will perceive the
sounds different. This phenomenon occurs because
what is perceived is given by the sum of the direct
sound and reflections, producing cancellations orenhancements by frequency. The materials
composing the room contribute to the sound due to
absorption that happens in the walls, what gives
certain "colour" to the room, as the material starts
working as an absorptive surface at a certain
frequency.
1.3 Polar pattern measurement
To measure how a source radiates the sound,
several measurements are performed around the
source to get the polar pattern. Discrete points are
taken to cover 360 degrees. Typically the directivityis measured every 5 degrees in both the vertical and
the horizontal plane. Using this information the
points are interpolated to have a complete polar
pattern. It is usual to assume symmetry (at least in the
horizontal plane) to reduce the amount of
measurements.From the measured data, many different pictures
can be drawn: dispersion plot, directivity balloon,
isobars, polar plot, directivity index/factor, power
response, etc. Additional post processing is often
applied to the data: frequency smoothing, level
normalization, etc. [1]
Figure 1: Typical polar pattern measurement
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The polar patterns measurements are not
normalized (in an ISO, for example) but are usuallymeasured in an anechoic chamber or in free field
conditions. Thats becausethe signal must be just the
direct sound to get a real polar pattern of the source.
For a loudspeaker it can be assumed symmetry in
the horizontal plane, only if its symmetrical in thevertical axis (Fig 1). Vertical plane symmetry cannot
be assumed because the speakers are rarely
symmetric in this plane. For biomechanical sources,
it can be also assumed symmetry in the horizontal
axis, but not in the vertical.
1.4 The acoustics of singing voice
A singers voice is like an instrument. It consists
of different parts, each of which is suitable for a
different purpose. The lungs are the organs that act
liked a power supply, the vocal folds are like the
strings of a violin and the vocal tract works like aresonant chamber and altogether they are a generator
of vocal sound. The shape of the tract is determined
by the positions of the lips, the jaw, the tongue and
the larynx. Thereby the singers are taught to assume a
particular posture. The air pressure in the lungs andthe vocal folds mechanical properties determine the
frequency of the vibration, the manifestation of which
is the pitch. A pitch range of two octave bands or
more is the range a singer should develop. The
resonance of the vocal tract is called formant and it is
determined by the vocal tract shape. Changing theshape of the tract, by means of opening the jaw,
modifying the tongue body shape or the tip of thetongue, the formant frequency can be shifted. One of
the most important formants of the human voice is
located in the frequency range of 2500-3000 Hz
where the amplitude, or the spectral energy, for
singing is higher than that at other frequencies or for
speech.
Figure 2: Comparison between the frequency responce
of an orchestra and a soprano.
The frequency at which the third formant islocated, 2500-3000 Hz, is the frequency where the
orchestras sound energy is declining and where asinger can still well control his voice. At the
frequency considered, the singer can sing without
forcing his voice because of the resonance effects orthe so-called formant. In the female voice, in
particular that of the soprano, by means of a more
open jaw, the soprano tries to move the formants to a
higher frequency so that she can enhance the
amplitude of the fundamental with the minimalvariation in loudness. In figure the averageddistribution of energy in the sound of an orchestra,
speech and singer are shown. [2]
1.5 Active energy vs. Reactive energy
Intensity is a vector quantity whose magnitudeindicates the amount of energy a sound wave, and
whose direction indicates the direction of the energy
flow. The sound field radiated by a sound source
usually has a near-field region (where the pressure
and particle velocity of the medium are roughly 90
degrees out of phase with each other) and a far-field
region (where the particle velocity and pressure are inphase). Active Intensity is the product of the pressure
and the in-phase component of the particle velocity.
The time-average of the active intensity is non-zero,
the direction is perpendicular to the sound
wavefronts, and it is identified with the flow of sound
energy.
Reactive Intensity is the product of the pressure
and the 90
degrees out-of-phase component of
particle velocity. The direction of the reactive
intensity is opposite to the pressure gradient, and the
time average of the reactive intensity is zero. The
reactive intensity is associated not with the radiation
of sound energy, but with the local motion of the
medium. [3, 4]
This measure is also very important to determine
the distance at which the microphone should belocated to get the active field.
1.6 Critical Distance
When the listener moves away from a sound
source, in non-anechoic conditions, one will
gradually leave the domain of the direct field and
enter that of the reverberant field. The point where
the two sound fields are equal is known as the critical
distance, beyond which the level of the sound willsoon tend not to reduce any farther as one moves
away from the source. The result is that the critical
distance will be frequency dependent and so the
effect of moving away from the source will not be
perceived equally at all frequencies. [5, 6]
The critical distance equation:
(1)Where Q is the Directivity Coefficient and R is equal
to:
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(2)Si = individual surface area in the roomi = absorption coefficient for individual surface in
the room
m = mean absorption coefficient of the room
1.7 Modal Density
In the most of cases, the distribution of the energy
and variation with frequency of a sound field in an
enclosure is difficult to determine with precision.
Average quantities are often sufficient and
procedures have been developed for determining
these quantities. In the low-frequency range, anenclosure sound field is dominated by standing waves
at certain characteristic frequencies. Large spatial
variations in the reverberant field are observed if the
enclosure is excited with pure tone sound, and the
sound field in the enclosure is said to be dominated
by resonant or modal response. [7]
This equation defines where are placed the nodes
and the peaks of pressure at a certain frequency:
() () () (3)Also, it can be estimated the number of modes at
a certain frequency:
() () (4)The modal analysis becomes very complicated
and difficult to model with increasing frequency. At
high frequencies, there is an overlapping between the
peaks and the nodes, and the pressure level almost
equal in all space (field tends to be diffuse).
There is a limit on the use of the model defined by
the frequency of Schroeder:
1.8 Noise Criteria
The Noise Criteria (NC) is the original standard
suggested by Beranek in the 1950s.
The NC curves (extended from 67Hz to 8000Hz)
are defined from sound pressure level over eightoctave band center frequencies. The measured
spectral noise level is then compared to these curves
and the NC value is obtained (the measured noise
curve will fall between some of the NC curves).
2 PROCEDURE
2.1 Equipment
Tascam US1641
Earthworks M-50
Loudspeakers: KRK Rokit 8, DynaudioBM 6A, Tascam VL-A4
Sound Level Meter SVANTEK 959
Laptop
Absorbent
Biomechanical Source - Tenor
2.2 Characterizationof the Room
To accomplish the characterization of the room, the
Reverberation Time of the room was obtained with a
clap at four different points in the room in order to
get different frequency responses. Then, the Critical
Distance was estimated, according to eq. (1). Theresult was:
Frequency RT (s) r (m)
31,5 1,76 0,69
63 0,67 1,20
125 0,43 1,65
250 1,49 0,75
500 0,55 1,37
1000 0,62 1,27
2000 0,79 1,09
4000 0,82 1,06
8000 0,76 1,12
Table 2: Reverberation Time and Critical Distance in
octave bands
Figure 3: Reverberation Time of the room
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Figure 4: Critical Distance of the room
The estimation of the critical distance is an
important factor to take into account when doing ameasure in a room, because its the distance at which
the direct sound and thereverberant sound are equal
when dealing with a directional source. Then, the
estimation of the critical distance is a parameter that
indicates where to place the microphone during themeasure to get a good relation between the direct
sound and the reflections.
2.3 Noise Criteria
The background noise was measured in octave
bands and then compared with the NC chart. The NC
Criteria found was NC50 as shown in the Figure.
Figure 5: Noise Criteria
This measurement aims to set the sound sources
level above the noise level below.
2.4 Measurement
The polar pattern measurement was performed in
an UNTREF classroom. This classroom was used
because it allows to perform the vertical plane
measurements. The room doesnt fit as well for this
kind of acoustic measurements because it wont be
possible to get only the direct sound. But withcriteria, the direct sound can prevail in the record and
its possible to get a good measurement (as
mentioned before, by knowing the critical distance).Directivity was registered with an Earthworks M50
with steps of 10 (with an error of 0.5) degrees. The
distance from the source was chosen at 1 meter,
taking into account the critical distance and the
relation of theactive energy andreactive energy.
Two
orthogonal axis
were measured for
all sources. To
accomplish that,
the floor was
marked with paper
tape. To get the
orthogonal axis to
the floor, the
vertical andhorizontal distance
were measured
applying elemental
trigonometry as it
follows:Figure 6: Measurement of the
biomechanical source
Degrees Horizontal Vertical
0 1 0
10 0,98 0,17
20 0,94 0,3430 0,87 0,50
40 0,77 0,64
50 0,64 0,77
60 0,50 0,87
80 0,17 0,98
90 0 1Table 2: Distance of the vertical plane microphone
The biomechanical source measurement was
performed by an opera singer. The singer was a tenor,
which typically has a vocal range of C3 (130 Hz) toC5 (523 Hz) (F5 (698 Hz) as extreme). He had to
perform a fragment of a song and a sentence each onein two different intensities. The singer was sat during
measurement to ensure that its kept as still as
possible in order to avoid big errors.
For the horizontal plane only a 180 measurement
was required due to human face symmetry. For the
vertical plane, a 360 measurement was implemented.4 microphones were used, one for the reference and
the others to do the measure in every angle. The
reference microphone was necessary because singers
dont have perfect accuracy in their intensity and
frequency response, then a reference microphone is
http://en.wikipedia.org/wiki/Reverberationhttp://en.wikipedia.org/wiki/Reverberationhttp://en.wikipedia.org/wiki/Reverberationhttp://en.wikipedia.org/wiki/Reverberation -
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very important to make the polar pattern with
precision.
Figure 7: Measurement of one of the loudspeakers.
Subsequently, the KRK, DYNAUDIO, TASCAM
loudspeakers were measured. It was attempted to
follow the singers condition, thats the reasonbecause the comb filter generated by the floor wasnt
avoided in the speaker measurements, but to get the
same height between the source and the floor was
necessary to put a table which also generate another
comb filter.
The critical distance gives a restriction of themaximum distance from the loudspeaker to the
microphone to get the direct sound.
Also, the ratio of the reactive part with the active
part of the acoustic impedance (the product of the
wave number and the distance) was taken into
account to determine the minimum distance to place
the microphone from the loudspeaker. The
microphone used to do the measurements was a
pressure microphone (omnidirectional pattern), so it
cant give information of the pressure gradient, just
its magnitude.To get a total acoustic power, the position of the
microphone was in the Fraunhofer zone, where the
pressure and velocity vector are in phase and the
acoustic intensity is radiated in the same direction.
Thus, the minimum frequency analysis for the critical
distance (where the distance is much larger than thewavelength) is 343 Hz.
It is important to note that the analysis of the
measurement its not placed in the Fresnel zone,where the dimension of the source view from the
microphone is much smaller than the distance apart
the source.The estimation of the minimum and maximum
wavelengths, taking into account the frequency range
of the tenor, result in a bandwidth of 250-16kHz.
3 RESULTS AND DISCUSSION
3.1 Measurements uncertainties
Most common errors are because of uncertainty in
different kind of distances. When measuring with a
microphone, its never placed in the exact place,because it must be supported by a microphone stand,
then, it has milimetric (or centimetric) errors. The
same problem with the angles and the microphonestands.
On the other hand, the biomechanical source
moved,so there might be alterations in the frequency
response (mostly in high frequencies).
Also, the biomechanical source cant performwith exact repeatability the amplitude of the signal.Thats the reason why its very important to put a
reference microphone when each measure is
performed, to minimize the differences between the
comparisons for the polar pattern.
3.2 Data Processing and Analysis
The data was recorded using Pro Tools 10 with 24
bits resolution and 44100 Hz of sample rate. All the
audio files recorded were processed with Matlab
software in order to get the data in third octave bands
and get the polar patterns.
Fast Fourier Transform was applied to eachsample, with a resolution according to its sample size
(approximately 262145 samples) in a frequency range
of up to 22050 Hz. The resolution was taken to the
next power of two with the aim to make faster
calculation [8]. Only the positive side of the Fast
Fourier Transform was taking in account analyzing
just the magnitude.
A smoothing process algorithm was used in order
to identify clearly the information in the spectrum.
The program used an algorithm of average using a
100 points moving average.
By an energetic and frequency analysis of the
reference signals it can be seen that below 100 Hz the
signal is very weak, consistent with the frequency
response of the human voice of a tenor singer and the
frequency range where the energy is reactive mainly.For this reason it was decided to match the curves for
this area in order to have a common gain among all
samples. Sound card SNR is assumed that (input
signal relative to noise preamplifier) is better than the
acoustic SNR.
In the Fig. 7 it can be recognized the frequencycomponents of the human voice speaking and singing
even when the intention and level of the singer are
different. On the other hand, there are some points
that the signals get almost the same level than the
background noise; this situation could be assumed
because of the nodes of 0 pressure relationed with the
acoustical environment.
Figure 8: Signal spectrum of the biomechanical source
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The signal (when measuring the human voice)
used in the measurement wasnt the same in each
take, then it was necessary to make a division
between the audios corresponding to each angle andtheir respective references. This way both signals
could be compared. Just because only a magnitudeanalysis was made, and all microphones had the same
distance from source, it wasnt necessary to set delay
time for the measurement signals. Third octave filter
was applied to the spectra in order to obtain third
octave band analysis.
3.3 Processed Data
Results of each experiment are presented in polar
diagrams, with representative frequencies. The
figures measured in the horizontal position were half-
plotted due to its symmetry, and in order to display
more polar patterns. It can be seen a strong
asymmetry especially at high frequencies. Thevertical pattern (Fig. 10) was full plotted because of
its asymmetry.
Figure 9: Biomechanical Source. Horizontal Polar Pattern
Figure 10: Biomechanical Source. Vertical Plane PolarPattern
Figure 11: KRK. Horizontal Plane Polar Pattern
3.4 Difference in the harmonic component for
different levels
A spectrogram analysis was carried out to
determine the different harmonic components
between two different sound levels of the
biomechanical source.
Figure 12: Spectogram of the singing voice
Figure 13: Spectrogram of the speaking voice
In both figures can be distinguished the tonalcomponent and the harmonics of each of the samples.
At the highest level, the harmonics are more marked,
and it can be seen that there are much more harmonic
components.
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3.5 Comparison between the biomechanical
source and the different loudspeakers
The first step to make the comparison was to
compare the different plots of the loudspeakers and
the biomechanical source.
Figure 14: Comparison between the biomechanical sourceand the different loudspeakers. Right: 125 Hz. Left: 400
Hz.
Figure 15: Comparison between the biomechanical source
and the different loudspeakers. Right: 125 Hz. Left: 400Hz.
This task is very long and it isnt very effective,so a figure of merit was implemented, with the
objective to know which one of the loudspeakers hadthe most similar polar pattern with precision.
The algorithm divides for each one of the octaves
bands of one of the loudspeakers with the
biomechanical source for every angle and provides a
single number at each frequency.
The comparison in octave bands can be seen in
Fig. 16:
Figure 16: Comparison between loudspeakers andbiomechanical source in the horizontal position.
Frequency (Hz) KRK Dynaudio Tascam31 1,094 0,699 0,724
63 0,952 0,839 0,506
125 0,601 0,975 0,858
250 0,781 0,731 0,945
500 0,797 0,796 0,520
1000 1,076 1,238 1,258
2000 0,867 0,911 0,671
4000 1,141 1,210 0,796
8000 1,358 1,738 1,017
16000 1,187 1,311 1,429
Total 1,087 1,018 0,847
Table 3: Figure of merit in octave bands and the average toget a single value.
4 CONCLUSION
It was found that the biomechanical source
selected, as is a tenor singer, has different directivity
indices, not only by frequency, but also according to
the intensity at which reproduces and the artist's
intention at a given time. This is so because thesingers use multiple parts of their body to produce
resonances and sound amplification, functionally
varying them according to whether it is used to talk
or sing. So, according to the intensity of phonation,
different body parts are involved, thus changing the
frequency components of signals and causing
constant acoustic characteristics different polarpatterns. Thus it is not possible to define a unique
mechanical source that can be used to represent a
biomechanical source in the process of characterizing
a concert hall. Likewise, when considering a constant
room acoustics it can recognize different results on
the characterization of acoustic parameters for a
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single point in the audience given different playing
intensities of the biomechanical sources.On the other hand, by understanding the change in
real polar pattern source, it could be implemented a
reform in the type of source for the measurement,
since the current sources doesnt represent the real
directivity of the biomechanical sources in placessuch as theaters. This would include different typesof sources with different polar patterns, located in
different parts of the stage and varying its level of
sound intensity.
Omnidirectional microphones seem to be efficient
in performing measurements; a good option would be
to incorporate binaural measurements to make
psychoacoustic analysis, which are becoming
increasingly important in recent years.
5 REFERENCES
[1] http://www.neumann-kh-line.com/neumann-
kh/home_en.nsf/root/prof-
monitoring_knowledge_glossary_measurement
[2] Linda Parati, Acoustical balance between singer
on the stage and orchestra in the pit, Chapter 1.
European Doctorate in Sound and Vibration Studies.
31st December 2003
[3] Domingo R Acstica Medioambiental Vol.1.
ECU. Spain.
[4]http://www.acs.psu.edu/drussell/Demos/Burns_Ph
D_animations/Burns_PhD_anim.html
[5] Long M. Architectural Acoustics. Elservier
Academic Press. USA. 2006
[6]http://education.lenardaudio.com/en/04_acoustics_
3.html
[7] Bies D, Hansen C Engineering Noise Control.
Spon Press. USA. 2009.
[8] Oppenheim Discrete-Time Signal Processing.
Prentice Hall. USA. 1999
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Annex ISome of the polar patterns obtained are shown in this annex:
Biomechanical Source: Singing voice Low level Horizontal Plane
Biomechanical Source: Singing voice High level Horizontal Plane
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Biomechanical Source: Speaking voice. Low level. Horizontal plane
Biomechanical Source: Speaking voice. High level. Horizontal Plane
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KRK: Singing voice. Low level. Horizontal Plane
| KRK: Singing voice. High level. Horizontal Plane
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KRK: Speaking voice. Low level. Horizontal Plane
KRK: Speaking voice. High level. Horizontal Plane
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Biomechanical Source: Singing voice. Low level. Vertical Plane
Biomechanical Source: Singing voice. High level. Vetical Plane
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Biomechanical Source: Speaking voice. Low level. Vertical Plane
Biomechanical Source: Speaking voice. High level. Vetical Plane