Human Voice Polar Patterns Opea Singer and Speakers

7/24/2019 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.

[email protected]

[email protected]

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

Documents

Human Voice Polar Patterns Opea Singer and Speakers