facoltÀ di ingegneria - unibo.itacustica.ing.unibo.it/researches/instruments/puczok2007.pdf ·...

UNIVERSITÀ DEGLI STUDI DI BOLOGNA

FACOLTÀ DI INGEGNERIA

Final report from ERASMUS residency

DIENCA - Dipartimento di Ingegneria Energetica, Nucleare e del Controllo Ambientale

DIGITAL MODELLING OF MUSICAL

SOUND SOURCES

Author: Daniel Puczok Supervisor: Prof. Massimo Garai, Ph.D.

Bologna 2007

Digital Modeling of Musical Sound Sources Daniel Puczok

Abstract

This report is guide along basics of room acoustic with a view to directivity of sound sources and power spectrum which are most important in the digital modeling of sound sources. Data necessary to simulate musical instrument are represented here. Description of making directivity files from these parameters is described in this work too. Obtained directivity files were used to simulation of orchestra and to consideration of directivity files and theirs influenced on room acoustics parameters.

Keywords: directivity, frequency spectra, musical instrument, room acoustics, ODEON

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Acknowledgments

I would like to thanks Doc. RNDr. Miroslav Doložílek, CSc. from Brno University of Technology for helping with administration procedures connected with ERASMUS residency. Next I would like to thanks professor Jens Holger Rindel from Technical University of Denmark for providing results from DOREMI project (Directionally Optimised Representation of Musical Instruments). Next I would like to thanks my supervisor Prof. Massimo Garai, Ph.D. for valuable advice in the work on this project. Last but not least I would like to thanks my parents and everyone who helps me somehow during residency.

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Contents

1 Introduction .......................................................................................................................... 5 2 Introduction to Room Acoustics .......................................................................................... 5

2.1 Sound as a Wave ........................................................................................................... 5 2.2 Sound Reflection........................................................................................................... 6 2.3 Diffuse Sound Fields..................................................................................................... 7 2.4 Loudness and Loudness Level ...................................................................................... 7 2.5 Decay Sound ................................................................................................................. 8 2.6 Reverberation ................................................................................................................ 8 2.7 Modeling Methods in Room Acoustics ........................................................................ 9 2.8 The Temporal Distribution of Reflection, Impulse Response .................................... 10 2.9 Auralization................................................................................................................. 11 2.10 Other Room Acoustic Parameters............................................................................... 12

3 Sound Sources Modeling ................................................................................................... 13 3.1 Simulating Sound Sources .......................................................................................... 14 3.2 Simulating Musical Instrument ................................................................................... 14

4 Musical Instruments ........................................................................................................... 18 4.1 String Instrument......................................................................................................... 18

4.1.1 Bowed Instrument ............................................................................................ 20 4.1.2 Plucked Instrument........................................................................................... 21 4.1.3 Striking String Instrument ................................................................................ 21

4.2 Wind Instrument ......................................................................................................... 22 4.2.1 Woodwind Instrument...................................................................................... 22

4.2.1.1 Flutes .......................................................................................................... 22 4.2.1.2 Single-Reed Instrument.............................................................................. 22 4.2.1.3 Double-Reed Instrument ............................................................................ 23

4.2.2 Brass Instrument............................................................................................... 23 4.3 Voice ........................................................................................................................... 25

5 Sound Sources Simulation in Room Acoustics Program................................................... 25 5.1 Directivity in ODEON ................................................................................................ 25 5.2 Directivity in CATT-Acoustics................................................................................... 27 5.3 Conversion of SD1 Input txt File to Input ODEON ‘FULL’ txt File ......................... 29 5.4 Sound Source Rotation and Position........................................................................... 30 5.5 Sound Source Power in ODEON ................................................................................ 31

6 Comparison of Directivity, Influence of Directivity on Room Acoustics Parameters....... 34 6.1 Comparison of Directivity Patterns and Directivity Balloons .................................... 34 6.2 Comparison of Point Response ................................................................................... 38 6.3 Comparison of Grid Response .................................................................................... 40

7 Simulation of Orchestra ..................................................................................................... 42 8 Summary and Further Works ............................................................................................. 46 A1 Axes and Position in CATT SD Files ................................................................................ 47 A2 Point Response ................................................................................................................... 49 A3 Grid Response .................................................................................................................... 61 A4 Grid Response of Orchestra ............................................................................................... 69 References ................................................................................................................................ 73 List of Symbol and Abbreviation ............................................................................................. 76

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Chapter 1 -

Chapter 2 -

)

Introduction

Concert halls, opera houses, lecture rooms and many other rooms are constructed to have a ‘good’ acoustics. Many things impact on acoustical behavior. The most important properties are shape of the room, material of walls and ceiling, volume of the room etc., but there are many things not related to the parameters of the room which influence the acoustical behavior too. Presence of audience, position of sound sources and type of sound sources can be included among these parameters. The simplest sound source is the omnidirectional sound source, but it is unusable in the practice. No real sound sources are omnidirectional. Musical instruments are very important and very often used sound sources. Every type of musical instrument has different properties. The most important characteristic to simulate musical instruments is spatial radiation. Many authors (Rindel, Meyer, Syrový) measured directivity patterns of some musical instrument. Every musical instrument is situated in the orchestra at different position and with different orientation.

The influence of directivity patterns of musical instruments on the acoustical quality is considered in this work. A complete physical description of musical instruments, necessary to simulate musical instruments in room acoustics, is presented here with a short description of tone creation. Simulation of the orchestra is described at the end of this report.

Introduction to Room Acoustics

2.1 Sound as a Wave

Sound is longitudinal wave motion within matter (gas, liquid, solid).The air is the medium of interest in room acoustics. In the air the sound wave causes a fluctuation of the atmospheric pressure above and below its mean value, which produces periodic movement of air molecules along the direction of the wave. The velocity of the sound depends on the temperature of the air by equation [12]:

( Θ⋅+= 6.04.331c (2.1) where Θ is temperature in degrees Celsius (°C) and c is sound velocity.

Fermat’s principle (principle of least time) says the path taken between two points by a ray of wave is the path that can be traversed in the least time. In case the medium is homogenous in the space, the speed of sound is uniform in this space and the shortest path is also the fastest. It means that sound propagate along the straight line.

Every wave can be described mathematically by the D’Alembert equation (wave equation) [12]

2

22

tppc

∂∂

=Δ . (2.2)

p is sound pressure (difference between momentary and static pressure). This equation has many solutions. Especially plain and spherical waves are used in physics.

Mathematical form of plane wave is )](exp[),( rktikPtrp rrr

−= ω (2.3) and that of the spherical wave is

[ ]r

krtiPtrp )(exp),( −=

ω (2.4)

Wave vector k is vector whose dimension is k and has direction of wave propagation.

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2.2 Sound Reflection

At the beginning we assume that wave impacts perpendicularly to the perfect rigid wall (so-called normal incident). The incident wave is described by formula [12]

)](exp[ kxtiPpi −= ω . (2.5) Some part of the energy is reflected back and some part is absorbed. The reflected wave has opposite direction and the amplitude is R -times lower and phase shifted by )exp( ϕi . Reflection coefficient is then

( )ϕiRR exp= (2.6) and reflected wave

)](exp[ kxtiRPpr += ω (2.7) Situation is a little bit complicated when there isn’t normal incident. In the equations (2.5) and (2.7) coordinate x should be replaced to x´, which is rotated around the z-axis by the angle θ [12]

θθ sincos´ yxx += . (2.8) Now the impinging and reflected waves are described by formulas:

)]sincos(exp[ θθ yxikPpi += , (2.9) )]sincos(exp[ θθ yxikRPpr +−= . (2.10)

The reflection wave is different from impinging wave by the sign in coordinate x. This results from the law of reflection stating that the angles of impact and reflection are equal. The time dependence factor is omitted in the equations (2.9) and (2.10) for better clearness. Energy of the sound wave is proportional to the square of the acoustic pressure if coefficient of absorption is

21 R−=α (2.11) Absorption coefficient is dependent on the incident angle.

If there are many warps on the wall, whose dimensions are the same or lower than the wavelength, the law of reflection can’t be used. Energy of the sound is diffracted or scattered along given angle. This case is called diffusion or partial diffusion. Only partial diffusion can be achieved in acoustics but in many cases presumption of total diffusion is preferable to describing reflection from the real wall, especially if multiple reflections are assumed. The total diffusion is described by Lambert cosine law [12]

20cos)(

rdSBrI

πϑ

= (2.12)

where B0 is impinging energy per unit area per second and ϑ is reflection angle. This equation doesn’t assume absorption. According to equation (2.12) every surface element can be a new source of secondary radiation.

Figure 2.1: Lamberts cosine law

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2.3 Diffuse Sound Fields

Diffuse sound fields are characterized by the few properties [5]: • Energy density are the same at every places • Flow of acoustic energy in every direction is equally probable • Phase of the wave are distributed randomly (we neglected interference)

Sound waves come at any position in a diffuse sound field from all directions with equal intensities and with random phase relations.

2.4 Loudness and Loudness Level

The human hearing has not a linear but a logarithmic response to the change in sonic perturbation. It is convenient to measure sound pressures on a logarithmic scale. The unit used in the loudness level is called the decibel (dB). The sound pressure level (SPL or in older literature Lp) is logarithm of the relation between acoustic pressure and the reference pressure p0 [5] [12]

0

1log20ppSPL = . (2.13)

There exists more loudness level except SPL. Sound intensity level (SIL or LI) and sound power level (Lw).

0

1log10IILI = (2.14)

0

1log10PPLW = (2.15)

The reference values are , and . It is advisable to notice, that change of 5 dB give the same change in the hearing feeling whatever the reference level, but a change of 0.01 Pa is a big change at low levels, while not perceptible at high ones.

Pa 102 50

−⋅=p 2120 W/m10−=I W10 12

0−=P

Loudness is a subjective perception of the intensity of a sound. Each sound, which we hear ’the same loudness’, has another value of acoustic pressure [12].

Figure 2.2: Equal loudness curves determined experimentally by Robinson & Dadson in 1956

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Equal loudness curves for the human ear are shown in Figure 2.2. Each curve describes a range of frequencies that are perceived to be equally loud. The curves are rated in phons. Phone is defined as SPL at the frequency 1000 Hz. These curves show that the ear is less sensitive to low frequencies and also that the maximum sensitivity region for human hearing is within the range 1000 and 5000 Hz. The dotted curve represents the threshold of hearing.

Sound measuring tools are usually fitted with a filter whose response to frequency is more like that of the human ear. The most common method is application the A-weighting curve. A-weighted decibels are obviously abbreviated to dBA. Relative response (value of A-weighted function) has to be added to SPL to obtain A-weighted SPL (SPLA). A-weighting function is plotted in the Figure 2.3.

Figure 2.3: A-weighting function

2.5 Decay Sound

Reduction of power is described by the exponential factor mcteA −

0 , (2.16) where A0 is initial amplitude (at time t = 0) and m is attenuation coefficient. Attenuation coefficient depends on the ambient atmospheric temperature and pressure, molar concentration of water vapor, and square of frequency. In Figure 2.4 frequency dependence of attenuation coefficient is plotted.

2.6 Reverberation

Reverberation is result of multiple reflections. Every sound ray passes from the sound source to the receiver another path. W. C. Sabine defines reverberation time (RT60) as a time required by a sound in a space to decrease by 60 dB (decreased to one-millionth of its original strength). Different absorption coefficients at different surfaces have to be taken into account to calculate reverberation time of the enclosure. Therefore it should be calculated with mean absorption coefficient, which can be calculated by formula [15]

∑∑

=

ii

iii

S

Sαα . (2.17a)

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Figure 2.4: Attenuation of sound in air (temperature 20 °C, pressure 1024 hPa, humidity 60%)

αi is absorption coefficient of the different surface of the room and Si is respective area of this surface. Sometimes the modified mean free absorption coefficient is used [34]

∑∑

=′

ii

iii

H

H αα . (2.17b)

In this case, Hi is number of reflection from the surface. Sabine formula can be used now to calculate RT60

α⋅⋅

=S

VRT 161.060 (2.18a)

This formula doesn’t take into account the decay caused by attenuation in the air. The corrected Sabine formula has form [12], [15]

mVSVRT

4161.060+⋅⋅

=α

. (2.18b)

The Sabine formula gives accurate results as long as the absorption is less than around 0.3. This isn't a problem in most real rooms. Norris-Eyring reverberation formula must be used to obtain precision result [15]

)1ln(161.060

α−⋅−⋅

=S

VRT (2.19a)

or

)1ln(4161.060

α−⋅−⋅

=SmV

VRT (2.19b)

which take into account attenuation in the air. Sabine and Norris-Eyring formulas are very simple but very common approximation of reality. They neglected many geometrical factors. Nowadays more complex formulas are used to evaluate RT60 [15].

2.7 Modeling Methods in Room Acoustics

There are three ways to description sound field in room acoustics: empirical methods, wave-based method and geometrical method. The first group of empirical and statistical method is based on Sabine and Eyring models. These methods are often used to evaluate SPL

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or RT60 (see equation (2.18 a) – (2.19 b)) but they are only approximation and for example they are useless to computing auralization [5], [15].

Wave-based methods try to numerically approximate wave equation (2.2). These methods divide the space into small elements or nodes, which interact with each other. The size of these elements has to be much smaller than the size of wavelength. Most used methods are finite element method (FEM), boundary element method (BEM) and finite-difference time domain method. Wave-based methods are only suitable for small enclosures and for low frequencies (the computation time is very long). They are mostly applied in studies of the automotive industry and in studying performance of noise barriers [5].

The last method is based on the geometrical behavior of the rays. The propagation of sound rays through the air is along straight line. The simplest models take into account only specular reflection. Diffraction and diffusion can be partly considered with usage computer technology. The most common geometrical methods are ray-tracing method and image source method.

In the ray-tracing method, the sound source emits the sound rays, which move through the space along the straight lines with the speed of sound. Each ray is reflected after every impact on the obstruction. The rays lost their energy due to collisions and atmospheric attenuation. The energy, which falls to the receiver, depends on the number of reflection and on the length of path.

Figure 2.5: Scheme of ray tracing method

In the image source method, reflected paths from the real source are replaced by direct paths from mirror images of the source. Sound source is mirrored to the other sides of obstacle. Multiple reflections are obtained by mirroring image sources. Scheme of image source method is presented in the Figure 2.6. S is sound source, R is receiver, Sć1, Sć2 and S´f are image sources created mirroring through ceil and floor respectively and Sć2-w is image source created mirroring source Sć2 through the back wall. This method is ineffective to find the higher order reflection or when the room has more complicated non-rectangular shape [5], [15].

2.8 The Temporal Distribution of Reflection, Impulse Response

Impulse response is the time domain response of an enclosure to an idealized infinitely short impulse presented mathematically by Dirac distribution.

It takes different time to get the sound from the source to the receiver. The receiver detect at the first sound, which correspond to the direct path and then follow first-order reflections and multiple-order reflections. The delayed time depends on the differences of path length. Energy of incident sound depends on the air absorption and the absorption coefficient of the surfaces. Each frequency has own impulse response. Impulse response can be divided to three sections: direct sound, first reflection and late reverberation. Choice of bound between first

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reflection and late reverberation varies author by author but mostly there are within the range 50 – 100 ms. Impulse response is often used to evaluate acoustic parameters of the room [12], [5]

Figure 2.6: Scheme of image source method

Figure 2.7: Impulse response of enclosure

2.9 Auralization

Definition of auralization was proposed by Kleiner as the process of rendering audible, by physical or mathematical modeling, the sound field of a source in a space, in such a way as to simulate the binaural listening experience at a given position in the modeled space. In other words, auralization is the process of simulating spatial sound of the room that you are not in.

Head Related Transfer Function (HRTF) describes how the sound wave is changed by the head diffraction and reflection from head, pinna and torso before impact to the eardrum. HRTF depends on azimuth and elevation angle [10].

One of the auralization methods is Binaural Room Impulse Response (BRIR). Principle of BRIR is following [24]:

• Each reflection represents a left and right HRTF • HRTF is convolved with finite impulse response filter for few octave bands • All binaural octave band filters are superposed into one binaural representation of the

reflection

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• The process above is repeated for all reflections in the impulse response and all the reflections are superposed into one resulting BRIR, inserting each binaural reflection filter at the appropriate time of arrival

Sounds in the room under consideration can be obtained by making convolution BRIR with ‘dry’ anechoic records. This is often used to hear sound in the designed room before it is already build.

SPL, RT60, speech intelligibility and clarity can be evaluated with high accuracy from the auralization [24]. The auralization output also allows an evaluation of echo phenomena, directivity and frequency response of sources, frequency dependent reverberation time etc.

2.10 Other Room Acoustic Parameters

There are many parameters, which describe acoustical properties of the rooms. Most of these parameters are evaluate from the impulse response and Schroeder plot.

Schroeder plot can be produced by backward integration of the impulse response h(t) over the measurement interval (0, T) and converting it to a logarithmic scale [10]

∫

∫= T

T

t

dh

dhtL

0

2

2

)(

)(log10)(

ττ

ττ. (2.20)

Formula (2.20) is known as the Schroeder integration.

• RT20 is the reverberation time obtained by linearization of a 20 dB decay range (between -5 dB and -25 dB). In other words, it is the time distance between the -5 dB and the -25 dB points in the Schroeder plot multiplied by 3 [15], [34].

Figure 2.8: Calculating reverberation time from Schroeder curve

• RT30 is the reverberation time obtained similar as RT20 by linearization 30 dB decay range (between -5 dB and -25 dB) [15], [34].

• Early decay time (EDT) is the reverberation time, measured over the first 10 dB of the decay. It is expressed in milliseconds [15], [34].

• Clarity (C80) refers to how clear the sound quality is. It is defined as logarithm ratio of early sound energy, arriving in the first 80 ms, to late sound energy, arriving after 80 ms.

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For speech, in comparison to music, Clarity is measured as the ratio of the first 50 milliseconds (C50) instead of 80 miliseconds (C80) [15], [34].

⎟⎟⎠

⎞⎜⎜⎝

⎛=

∞−

−

80

800log1080EEC (2.20)

• Definition or Deutlichkeit (D) is ratio of early and total energy [15], [34].

∞−

−=0

500

EED (2.21)

• Centre time (TS) is time of the centre of gravity of the squared impulse response. A high

value of TS is an indicator of poor clarity [15], [34].

∞−

⋅=

0EEtTS t (2.22)

• Lateral Energy Fraction (LF80) characterized spaciousness of incident sound and it is

defined as the ratio of sound energy arriving laterally over sound energy arriving from all direction [15], [34].

( )

800

80

5

2cos80

−

=∑

=E

ELF t

tt β (2.23)

• Apparent Source Width (ASW) describes how large and wide the sound source appears to

the listener. It is related to the level, at the listener’s ears, of lateral reflections in the first 50 to 80 milliseconds after the arrival of the direct sound [15], [34].

• Speech transmission index (STI) is number which takes into account background noise, transmission system and characterizes speech intelligibility [15], [34].

Subjective scale STI valueBad 0.00 - 0.30Poor 0.30 - 0.45Fair 0.45 - 0.60

Good 0.60 - 0.75Excellent 0.75 - 1.00

Table 1: Subjective scale of STI

Note: Many other acoustic parameters exist but above mentioned are most common. Some parameters have high correlation with another (e.g. CL80, D and TS or LF80 and ASW).

Chapter 3 - Sound Sources Modeling

An object, which emits to his surroundings sound waves, is called a sound source. Nearly every object can be sound source starting with hammer knocking on nail followed by passing car and finishing with object specified to emit sound waves as animal and human voice (vocal cords), loudspeaker and musical instruments. Every mentioned above sound sources have

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different physical properties and different sound. Perhaps nobody exchange sound of passing car and sound of violin.

3.1 Simulating Sound Sources

Some basic physical properties must be known to model sound sources. The power of a sound source is one of these basic properties, which is high correlated with SPL in ambient of the source. Sound power is dependent on frequency. Sound source is most powerful at eigenfrequency. Power of sound sources is often expressed in octave band (usually 63, 125, 250, 500, 1000, 2000, 4000 and 8000 Hz).

Next physical property is directionality of radiation. This is very important in the case of musical instrument and loudspeaker. The simplest model is called omnidirectional sound source. This source emits the sound to all directions with the same power. Unfortunately this model is a heavy approximation of reality and in most cases we can’t use this model. Application of this model is suitable only at low frequency (especially of small sound sources).

The point source approximation is next approach of reality. In most cases this approximation is very good but for example in the case of grand piano or organ pipe this approach is very far from the reality [25], [26].

3.2 Simulating Musical Instrument

Musical instruments are very important sound sources in room acoustic. Opera houses, concert halls etc. are designed to have the ‘best possible’ acoustic for music.

Power of musical instrument depends not only on frequency but as well on the style of playing and kind of musical instrument. Brass instrument playing ff is much louder than woodwind instrument playing ff and this is louder than bow instrument playing ff. Passages played f or ff are much louder than passages played p or pp. The range between pp and ff are bigger in long individual passage than in fast passage. Averaging both kinds of limits (fast and individual notes) characteristic forte in orchestra can be obtained. A diagram of dynamic range and average forte of orchestral instruments is plotted in the Figure 3.1 [13]. By black bars are marked Characteristic forte for each instrument are marked for each instrument.

Figure 3.1: Dynamic range and average forte of orchestral instruments

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Mute (Italian sordina) is sometimes used in classical music or in jazz. Mute change not only timbre of musical instrument but it influences Lw as well. Mutes are used especially on brass instrument and on string instruments of the violin family. Lw of muted cornet is in detail described in [1].

As mentioned above, musical instruments, like every real sound source, radiate with different intensity to different directions. Most of energy is usually radiated to the front hemisphere of the musician. An omnidirectional radiation is found only at the lowest frequencies of each instrument covering about one octave of the fundamentals. No real musical instrument radiate omnidirectional above frequency 500 Hz. Diagram of frequency range for omnidirectional sound radiation is presented in the Figure 3.2 [13].

Figure 3.2: Frequency range for omnidirectional sound radiation

There are few ways how to express directivity of radiation. First not very common method is mathematical modeling. The resonant mode frequencies of the instrument body account for most of the sound radiation. Each mode frequency of the body has a directivity pattern such as monopole, dipole, quadrupole, or a combination thereof.

Directivity factor and directional gain are advisable to very simple representation of directivity. Directivity factor is the ratio of the intensity in the given place of field generated by a real instrument and the intensity in the same place generated by an omnidirectional source with the same sound power [28]

rIIQ = . (3.1)

Directional gain is logarithm of directivity factor QIQ log10= . (3.2)

Table 3.1 presents the maximum directivity factor of the chosen musical instrument for frequency 500, 1000 and 2000 Hz [28].

Main radiating directions are probably the most graphic representation of the directivity. Main radiating directions represent directions in which Lw don’t fall more than 3 or 10 dB below the maximum value for given frequency. These directions are often plotted in polar diagram in horizontal and vertical plane. This representation offer only qualitative expression of directivity. In the Figure 3.3 are marked main radiating directions for violin [13].

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Instrument 500 Hz 1000 Hz 3000 HzViolin 1.2 2.1 1.8Viola 1.1 1.9 2.6

Violoncello 2.1 2.1 3Double bass 2.1 2.1 2.6

Flute 1.4 1.5 1.5Oboe 1.1 1.5 2

Clarinet 1.1 2 2.1Bassoon 1.4 2 2.5

Horn 1.7 2.4 4.8Trumpet 1.1 1.8 3.4

Trombone 1.6 2.1 4.4Tube 2 4.5 6.6

Table 3.1: Maximum directivity factor

Figure 3.3: Main radiating directions of radiation (0 to -3 dB) for violin

Probability distribution is next possibility how to mark directivity of sound source. These diagrams show angular region for which the intensity remains above one-half of its maximum value. This diagram is well graphic too and it gives more information about directivity representation. Probability distribution of violin is plotted in Figure 3.4 [14].

Directivity patterns offer the most information about directivity of musical instruments. Directivity patterns are polar diagram of power level. They represent usually only differences of radiated power to some reference value. Average directivity pattern, averaged by whole range of musical instrument, are especially used in room acoustics.

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Figure 3.4: Probability distributions of violin. On the left hand side is horizontal plane and on

the right hand side is vertical plane (plane of the bridge).

Figure 3.5: Average directivity pattern of violin at 2000 Hz [11]

Timbre is very important to simulating musical instrument too. In psychoacoustics timbre is known as ‘sound quality’ or ‘sound color’. In music, timbre is quality of sound that distinguishes one musical instrument from another. The main physical characteristics describing timbre are spectrum and envelope.

The sound of musical instruments consists not only of one frequency but it is superposition of many distinct frequencies. The lowest frequency is called the fundamental frequency and the pitch it produces is used to name the note. Remaining frequencies are called overtones. Overtones are divided to harmonics which are integer multiple of fundamental frequency and non harmonics which are non-integer multiple of fundamental frequency. Harmonics compose major part of overtones. A sound waveform is very commoned characterized by the spectrum of harmonics necessary to reproduce the observed waveform. This spectrum can be obtained making Fourier analysis of waveform. The amplitudes of the individual harmonics can be displayed as the function of frequency [28].

The timbre of a sound is also greatly affected by the following factors: attack, decay and vibrato. Figure 3.6 shows the attack and decay of a plucked guitar string and striking a cymbal. If the attack is taken away from the sound of guitar or cymbal, it becomes more

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difficult to identify the sound correctly, since the sound of pluck of string or the hitting cymbal-stick on the string are highly characteristic of those instruments.

Figure 3.6: Attack and decay of plucked guitar string (above) and striking a cymbal (below)

The ordinary definition of vibrato is periodic changes in the pitch of the tone, and the term tremolo is used to indicate periodic changes in the amplitude or loudness of the tone. So vibrato is kind of frequency modulation and tremolo is kind of amplitude modulation of the tone. Actually, both effects are often presented in the voice or in the sound of a musical instrument in some extent.

Amplitude plot of a sustained ‘e’ vowel sound produced by a female voice is plotted in Figure 3.7. The periodic amplitude change would be described as tremolo by the ordinary definition of it but vibrato is presented as well. That is commonly the case.

Figure 3.7: Amplitude plot of a sustained ‘e’ vowel

Timbre isn’t so important in light of room acoustics in contrast to psychoacoustics but it should be mentioned in the case of simulation of musical instrument.

Chapter 4 - Musical instruments

A musical instrument is a device constructed or modified with the purpose of making music. Each instrument has finite range, i.e. distance between lower and highest played note. The range of an instrument depends on the kind of musical instrument. Generally bigger musical instruments have ranges situated at lower frequency. Typical ranges of musical instrument are plotted in the Figure 4.1. Instruments are divided by the way in which they generate sound.

4.1 String instrument

String instruments generate sound by bowing, plucking, hitting, strumming etc. Frequency of tone depends on the length, tension, mass per unit length. String instrument are subdivided to plucked, stringed and bowed instrument.

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Figure 4.1: Typical frequency range of musical instrument (www.wikipedia.org)

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http://www.wikipedia.org/


4.1.1 Bowed instrument

Most common bowed instruments belong to violin family, which include violin, viola, violoncello and double bass. The strings of violin family are stretched across the bridge and nut. Excitation of the string is done by ‘stick-slip’ mechanism – during the greater part of each oscillation, the string is ‘stuck’ to the bow and it is carried with it in its motion. Then the string suddenly detaches itself and moves rapidly backward until it is caught again by the moving bow. A sketch of the reflection of traveling kinks caused by bowing a string is in the Figure 4.3. By continues draw a bow on the string it is formed standing wave among bridge and nut. The motion of the string is transformed by the bridge into a driving force on the top plate of the instrument. Vibration of the top plate is coupled by sound post with the back plate. Bass bar transmit the motion of the bridge over a large area. The position of sound post is critical to the sound of instrument. Small changes can have noticeable effect. The directivity of radiation is often determined in the plane of bridge and horizontal plane. [36]

Timbre of the bowed instrument very depends on the position of bow with respect to the bridge. There are few methods of articulation (playing methods). Pizzicato is except ‘normal’ bowing the most common method of articulation. In pizzicato tone is formed by plucking string (similar as in guitar – see chapter 4.1.2).

• Violin

Violin is one of the most studied instruments in acoustics. Most of sound radiation is emitted to the front-right side of the musician (see Figure 3.3 – 3.5). The lowest G string has fundamental frequency 196 Hz and the highest E string has fundamental frequency 659Hz. Violin sounds most powerful at frequency 260 a 400 Hz. Violin radiates like omnidirectional sound source until frequency 500 Hz. First pointed maxima are at frequency 1000 and 1250 Hz. Bifurcation of maxima appears at frequency 1500 and 2000 Hz in the plane of bridge. Violin radiates poorly at two lowest frequency bands. Maximum of radiation within the frequency range 500 – 2000 Hz where the power is nearly the same. Power level decreases above frequency 2000 Hz. [6] [8] [9] [13] [27] [28] [36]

• Viola

Viola is tuning one fifth below the violin (C string is tuned at 131 Hz) and one octave above the cello so viola serves the middle voice of the violin family. Radiation directivity is basically similar as the violin. Directional dependence starts in horizontal and bridge plane at 600 Hz and at the range of 800 – 1000 Hz the directions are perpendicular to the top plate. Power spectrum of viola is very similar to the power spectrum of violin until frequency 2000 Hz where viola radiates little bit less powerful than violin. Viola radiates noticeably lower above frequency 2000 Hz. [6] [13] [27] [28] [36]

• Violoncello

Cello is tuning in perfect fifth as violin and viola. Frequency range is from 65 Hz to the 630 Hz. The main directions of radiation are in the vertical and horizontal plane mainly oriented to the front of the musician. Exception from this is frequency 250 Hz in which the important role is played by the radiation of the back plate. Till the frequency 150 Hz cello radiates omnidirectional and by contrast from the frequency 2000 Hz the main direction direct to the floor so the favorable radiation to the audience depends on the reflection from the floor.

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Frequency spectrum of the cello is the most flat from all string instruments. Maximum of radiation is within the frequency range 250 – 2000 Hz. The power of radiation drop 10 dB per octave below these frequencies and it drop 14 dB per octave above these frequencies. [6] [13] [27] [28] [36]

• Double bass

Double bass is the largest and lowest pitches of violin family. As only instrument from violin family is tuned to the perfect fourth. The lowest E string has frequency pitch approx 41 Hz and the highest string G has frequency pitch approx 98 Hz. On account of size of the instrument we can find the omnidirectional radiation only around frequency 100 Hz. Big influence to the directivity of double bass have design of stage which can by reason of resonance empower sound radiation. Maximum of radiation in the case of double bass is at three lowest frequency bands. Above these frequencies power constantly fall down. Difference between maximum and minimum of radiation is 42 dB. [6] [13] [27] [28] [36]

4.1.2 Plucked instrument

In plucked string instrument the vibration of string is caused purely by plucking. In contrast to bowing the string is excited by impulse not continuously. High frequency harmonics quickly disappeared so the sound of the note becomes some time after plucking more mellow.

Figure 4.3: A sketch of the reflection of traveling kinks caused by bowing (left hand side) and

plucking (right hand side) a string [36]

• Guitar

Motion of the string is like in violin transfer by the bridge to vibration of plate. Vibration of top plate caused change of the pressure in the air column and the sound. The air inside the body is quite important, especially for the low range on the instrument since the body behaves as the Helmholtz resonator. [6] [28] [36]

4.1.3 Striking String Instrument

• Grand piano

Strings in the case of grand piano are vibrated by striking hammer on the string. A vibrating string has a very poor coupling to the air. To move a lot of air, the vibrations of the string must be transmitted to the sound board, via the bridge. The somewhat irregular shape

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and the off center placement of the bridge help to ensure, that the soundboard will vibrate strongly at all frequencies. Grand piano, in contrast to previous mentioned musical instrument, has one or multiple string to every tone so the musician doesn’t tune by his finger. Grand piano has also the greatest frequency range from string instrument. Grand piano’s directivity patterns are very influenced by opening of the lid. Grand piano radiates most powerful within the frequency range 125 – 1000 Hz. Power falls rapidly down (equal to or greater than 10 dB) outside these frequencies. [6] [27] [28] [36]

4.2 Wind Instrument

A wind instrument is a musical instrument that contains some type of resonator (usually a tube), in which a column of air is set into vibration by the player blowing into (or over) a mouthpiece set at the end of the resonator. The pitch of the vibration is determined by the length of the tube and by manual modifications of the effective length of the vibrating column of air.

4.2.1 Woodwind Instrument

Woodwind instruments have a long, thin column of air. The lowest note is played with all the tone holes closed, when the column is longest. The column is shortened by opening up holes successively, starting from the open end. At the other end there is something that controls air flow: an air jet for the flute family and cane reeds for other woodwinds.

4.2.1.1 Flutes

The flutist blows a rapid jet of air across the embouchure hole. The player provides power continuously: in a useful analogy with electricity, it is like DC electrical power. Sound, however, requires an oscillating motion or air flow (like AC electricity). In the flute, the air jet, in cooperation with the resonances in the air in the instrument, produces an oscillating component of the flow. Once the air in the flute is vibrating, some of the energy is radiated as sound out of the end and any open holes. The column of air in the flute vibrates much more easily at some frequencies than at others (i.e. it resonates at certain frequencies). These resonances largely determine the playing frequency and thus the pitch, and the player in effect chooses the desired set of resonances by choosing a suitable combination of keys. Flutes radiate to its surroundings through mouthpiece and through first open hole. Flutes represent classical dipole and it never behaves like an omnidirectional sound source. Flute radiates very low below frequency 250 Hz (at least 50 dB lower than maximum of radiation). Maximum of radiation is at frequencies 500 – 2000 Hz. The power falls down above these frequencies. [6] [27] [28] [36]

4.2.1.2 Single-Reed Instrument

Clarinet and saxophone belong to this group of musical instrument.

• Clarinet

The clarinet player provides a flow of air at a pressure above that of the atmosphere. In the clarinet, the reed acts like an oscillating valve (technically, a control oscillator). The reed, in cooperation with the resonances in the air in the instrument, produces an oscillating

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component of both flow and pressure. Once the air in the clarinet is vibrating, some of the energy is radiated as sound out of the bell and any open holes. The column of air in the clarinet, like in the flute, resonates at certain frequencies. These resonances largely determine the playing frequency and thus the pitch, and the player in effect chooses the desired resonances by suitable combinations of keys. Clarinet behaves as omnidirectional sound sources till frequency 700 Hz but effect of musician limit omnidirectionality till frequency 500 Hz. Reflection from the floor is very important at the higher frequency. Flute radiates most powerful at frequency 8 kHz to its axis of symmetry. The power is very low at the lowest frequency. Maximum of radiation is within the range 500 – 2000 Hz but at frequencies 250 Hz and 4000 Hz radiation doesn’t differ very much from the maximum value. The power falls rapidly down above 4000 Hz. [2] [6] [19] [27] [28] [36]

4.2.1.3 Double-Reed Instrument

The term double reed comes from the fact that there are two pieces of cane vibrating against each other instead using one reed in the case of single reed instrument.

• Bassoon

The bassoon is the bass of the woodwind family. Its bass tone is caused length of the pipe. The bassoon stands 134 cm tall, but the total length is 254 cm. Bassoon radiates like omnidirectional sound source until the frequency 250 Hz. It radiates most intensive to the audience in the sphere of frequency 500 Hz in which there are most powerful tones of bassoon. Most intensive direction direct to the axis of instrument at the high frequency. Bassoon radiates most powerful at frequency 500 Hz. Power falls down 10 dB per octave below this frequency and it falls down 14 dB per octave above this frequency. [6] [27] [28] [36]

• Oboe

The oboe has a clear and penetrating voice and it plays at high frequency. Careful manipulation of embouchure and air pressure allows the player to express a large timbre and dynamic range. Directionality appears from the frequency 1 kHz. Main directions of radiation are directed in all cases to the front of musician. Reflection from the floor is very important from the frequency 1 kHz. Power spectrum of oboe is very similar to the power spectrum of flute. Oboe radiates very low at two lowest octave band (at least 55dB lower than maximum of radiation). Maximum of radiation is at frequencies 1000 – 2000 Hz. Power falls down above these frequencies. [6] [27] [28] [36]

4.2.2 Brass Instrument

The player provides air at a pressure above that of the atmosphere. This is the source of power input to the instrument, but it is a source of continuous power (like DC electricity). In the brass instruments, the lips act as a vibrating valve. Once the air in the instrument is vibrating, some of the energy is radiated as sound out of the bell. The column of air in the instrument vibrates much more easily at some frequencies than at others. These resonances largely determine the playing frequency and thus the pitch, and the player in effect changes the length of the instrument, and thereby the frequencies of the resonances, by suitable

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combinations of inserting extra pieces of pipe via the valves, or by changing the length of the slide in the case of the trombone. [36]

• French horn

The French horn is tapered, steadily increasing in diameter along its length. Most of newest horns use rotary valves instead piston valves. French horn is omnidirectional sound source until frequency 150 Hz. Though the directionality of brass instrument is easier than in the case of woodwind instrument (only one aperture is opened) bifurcated main directions of radiation appear in the directivity of French horn in the vertical and horizontal plane. These bifurcations are attributing to the insertion of musician right hand to the baffle. Sound of the French horn is reversed from the listener. Maximum of radiation is at frequency band 500 Hz. Power falls down at least 10 dB per octave out this frequency band. [6] [27] [28] [36]

• Trumpet

The trumpet is the highest brass instrument in register. Trumpet uses piston valves in contrast to French horn. The player can select the pitch from a range of overtones or harmonics by changing the lip aperture. There are three piston valves, each of which increases the length of tubing when engaged, thereby lowering the pitch. Main directions of radiation are oriented to the axis of the instrument. Directional radiation begins to exert above frequency 500 Hz. Main directions of radiation taper with the growing frequency but at frequency 800 and 1250 Hz these angles are extended. These are caused by complex phase conditions in the mouth of baffle. Trumpet radiates very weakly at the lowest frequency bands. Maximum of radiation is within the frequency range 1000 – 2000 Hz. Power falls down above these frequencies. [6] [27] [28] [36]

• Trombone

The trombone is usually characterized by a telescopic slide with which the player varies the length of the tube and change pitches. Radiation of trombone is similar to the radiation of trumpet but the frequencies are little bit shifted. Omnidirectional radiation is until 450 Hz. Main directions of radiation, like at trumpet, taper with the growing frequency. Expansions of angles are at frequencies 650 Hz and partially at frequency 1000 Hz. Maximum of radiation, in the case of trombone, is at frequency bands 500 Hz and 1000 Hz. Power falls down below these frequencies but not so rapidly as in the case of trumpet. Power spectrum drops rapidly down above 2000 Hz. [6] [27] [28] [36]

• Tuba

The tuba is the largest and lowest pitched of brass instruments. Tubas are conical in shape as the bore of their tubing steadily increases in diameter along its length, from the mouthpiece to the bell. Directivity patterns of tuba are very complicated and nonsymmetrical. Main directions of radiation are within the frequency range 90 – 180 Hz 360° in the ‘profiled’ direction but main directions are half in the ‘in face’ directions. These asymmetries are caused by complex phase conditions in the surface of baffle. Tuba radiates most powerful at the lowest frequencies. Power falls rapidly down above 500 Hz. [6] [27] [28] [36]

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4.3 Voice

The voice makes sounds using vocal cords which can vibrate at a frequency determined largely by the tension in the muscles that control them (high tension makes the frequency and therefore the pitch high) and by the mass of the tissue (post-pubescent males usually have larger folds and therefore deeper voices). The vibration releases pulses of air into the vocal tract. Pitch, volume and timbre can be changed by altering the shape of chest and neck, the position of the tongue, and the tightness of otherwise unrelated muscles. Maximum of radiation is at frequencies 250 – 1000 Hz. Power falls rapidly down outside these frequencies. [6] [23] [27] [28] [36]

Chapter 5 - Sound Sources Simulation in Room Acoustics Programs

5.1 Directivity in ODEON1

ODEON is room acoustics software, which uses ray tracing and image source method to evaluate most of acoustical parameter including auralization. Auditorium and industrial halls can be processed by this program.

Directivity of sound sources is set by SO8 files. SO8 files can be created directly in directivity polar plot editor (Figure 5.1) by entering data in octave bands or can be created importing from ASCII txt files. The second way is more frequented.

Figure 5.1: Directivity polar plot editor in ODEON v8.51 Combined. Opened file is violin.

1 http://www.odeon.dk

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Three different text input format are used when a new directivity pattern is created; full, polar and symmetric. Syntax is little bit different in each case but some rules should be kept. Each of the subsequent lines of the input file should contain sound levels in dB for a complete 180° of elevation (from the forward axis to the backward axis). The resolution must be 10° hence each line contains 19 values (0°, 10°, 20°.....160°, 170°, 180°). First and last values in each octave band must be in the case of symmetric and full input files the same [34].

Only one line of data for each octave band is used in the symmetric case. The first non comment line of the file should start with the word SYMMETRIC. As a minimum there must be 1 + 8 lines in a symmetric input file. Examples of symmetric sources are a trumpet and the omnidirectional source, where the directivity pattern is rotationally symmetric [34]. Example of symmetric input file (omnidirectional sound source):

SYMMETRIC : 63 Hz 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 : 125 Hz 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 : 250 Hz 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 : 500 Hz 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 : 1000 Hz 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 : 2000 Hz 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 : 4000 Hz 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 : 8000 Hz 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Polar text files are used when only horizontal and vertical polar plots are known. The first non comment line of the file should start with the word POLAR. In the polar case, there are four lines of data for each frequency band. The first four are for 63 Hz, the next four for 125 Hz, and so on. First line in each octave band is vertical upper plot (12 o’clock plot when looking at the source e.g. at a loudspeaker membrane or at musician), second line is horizontal left plot (9 o'clock plot), third line is lower vertical plot (6 o'clock plot) and last forth line is right horizontal plot (3 o’clock plot). Each line should contain 19 values. As a minimum there must be 1 + 4 * 8 lines in a polar input file. Missing values between four polar planes are interpolated using elliptical interpolation independently for each frequency [34]. Example of polar frequency band (guitar 125 Hz):

:125 0 0 0 0.2 0 0 0.8 -1.7 -1.7 -3.3 -2.8 -2.8 -2.4 -3 -3 -4.3 -4.6 -4.6 -5 0 1.2 1.2 2.1 0.1 0.1 0.2 0 0 -0.6 -2.3 -2.3 -2.4 -2.2 -2.2 -3 -4 -4 -5 0 0 0 0 -1.1 -1.1 -0.7 -3 -3 -5.1 -6.1 -6.1 -4.3 -3.8 -3.8 -5 -4.6 -4.6 -5 0 0 0 1.2 2.1 2.1 0.1 0.2 0.2 0 -0.6 -0.6 -2.4 -2.2 -2.2 -3 -4 -4 -5

Full text file format is used when the complete directivity characteristics is known. Full plot gives the most precisions data. The first non comment line of the file should start with the word FULL. In the full case, there are 36 lines of data for each octave band. The first 36 are for 63 Hz, the next 36 for 125 Hz, and so on. Each line in octave band represent polar plane gradually by 10° azimuth. As a minimum there must be 1 + 36 * 8 lines in a full input file. First line is vertical upper plot 0° (12 o'clock plot, when looking at the source e.g. at a loudspeaker membrane or at musician), 10th line is horizontal left plot 90° (9 o'clock plot),

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19th line is lower vertical plot 180° (6 o'clock plot) and 28th line is right horizontal plot 270° (3 o'clock plot) [34]. Example of full frequency band (flute 125 Hz):

:125 0 0 0 0 0 0 0 0 0.1 1.6 0 0 0 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 0 0 0 0.2 0 -0.1 -0.1 0 0 0.1 0.1 0 0 0 0.1 0.1 0 -0.1 -0.1 0 0 0 -0.1 -0.1 -0.1 -0.2 -0.1 -0.1 0 0.2 0 0.1 0 -0.1 -0.2 -0.1 0 -0.1 0 0.1 -0.2 0 -0.2 -0.1 -0.1 -0.2 -0.1 0 0.2 0.1 0 -0.2 -0.2 -0.1 -0.2 0 -0.1 0 0 -0.2 -0.2 0.1 -0.1 0.1 -0.1 -0.1 0 0.2 0 -0.2 -0.2 -0.1 -0.2 -0.2 -0.1 -0.1 0 -0.1 0 0 -0.1 -0.1 -0.1 -0.1 0 0 0.1 -0.1 -0.1 0.1 -0.1 -0.1 -0.1 -0.2 -0.1 0 -0.2 0.1 0 0 -0.1 -0.1 0.1 -0.1 0.1 0.1 0 -0.1 -0.1 -0.1 -0.1 -0.1 -0.3 -0.1 0 -0.2 -0.1 0 -0.1 0.1 0.1 0 -0.1 0.1 0.1 -0.1 0 0 -0.1 -0.1 -0.2 -0.3 -0.1 0 -0.1 -0.2 -0.2 -0.1 0 -0.1 0 0 0 0.1 0 -0.1 -0.1 -0.1 -0.2 -0.2 -0.2 -0.1 0 0 0 0 0 0 0 0 0 0 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 0 -0.1 -0.2 -0.2 -0.1 0 -0.1 0 0 0 0.1 0 -0.1 -0.1 -0.1 -0.2 -0.2 -0.2 -0.1 0 -0.2 -0.1 0 -0.1 0.1 0.1 0 -0.1 0.1 0.1 -0.1 0 0 -0.1 -0.1 -0.2 -0.3 -0.1 0 -0.2 0.1 0 0 -0.1 -0.1 0.1 -0.1 0.1 0.1 0 -0.1 -0.1 -0.1 -0.1 -0.1 -0.3 -0.1 0 -0.1 0 0 -0.1 -0.1 -0.1 -0.1 0 0 0.1 -0.1 -0.1 0.1 -0.1 -0.1 -0.1 -0.2 -0.1 0 0 -0.2 -0.2 0.1 -0.1 0.1 -0.1 -0.1 0 0.1 0 -0.2 -0.2 -0.1 -0.2 -0.2 -0.1 -0.1 0 0.1 -0.2 0 -0.2 -0.1 -0.1 -0.2 -0.1 0 0 0.1 0 -0.2 -0.2 -0.1 -0.2 0 -0.1 0 0 0 -0.1 -0.1 -0.1 -0.2 -0.1 -0.1 0 0 0 0.1 0 -0.1 -0.2 -0.1 0 -0.1 0 0 0 0.2 0 -0.1 -0.1 0 0 0.1 0 0 0 0 0.1 0.1 0 -0.1 -0.1 0 0 0 0 0 0 0 0 0.1 0.1 0 0 0 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 0 0 0.1 0.2 0.1 0 0 0 0 0.1 0 -0.1 -0.1 -0.1 -0.1 0.1 0 -0.1 -0.1 0 0.1 0 -0.1 0 0.1 0.1 0 0 0 -0.1 -0.2 -0.2 -0.1 -0.1 -0.2 -0.1 -0.1 -0.1 0 0.1 -0.1 0 -0.1 -0.1 0 0.1 0 0 -0.1 -0.2 -0.2 -0.2 -0.3 -0.1 -0.2 0 -0.1 0 -0.1 -0.1 -0.2 0 -0.1 -0.1 0.1 0.1 0 -0.1 -0.1 0.1 -0.1 0 -0.2 -0.2 -0.1 -0.1 0 -0.1 0 0 0 0.1 -0.1 0 0.1 0 -0.1 -0.1 -0.1 -0.1 -0.2 -0.1 -0.1 -0.2 -0.1 0 -0.2 0 0 0 -0.1 -0.1 0 0.1 0.1 -0.1 0 -0.1 -0.1 -0.1 -0.1 0 -0.2 -0.1 0 -0.2 -0.1 -0.1 -0.1 0 0.1 0 0.1 0.1 -0.1 -0.1 0 0.1 -0.1 -0.1 -0.2 -0.2 -0.1 0 -0.1 -0.2 -0.1 0 -0.1 0 0 0.1 0 0 0 -0.1 -0.1 -0.2 -0.2 -0.2 -0.2 -0.1 0 0 0 0 0 0 0 0 0 0 0 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 0 -0.1 -0.2 -0.1 0 -0.1 0 0 0.1 0 0 0 -0.1 -0.1 -0.2 -0.2 -0.2 -0.2 -0.1 0 -0.2 -0.1 -0.1 -0.1 0 0.1 0 0.1 0.1 -0.1 -0.1 0 0.1 -0.1 -0.1 -0.2 -0.2 -0.1 0 -0.2 0 0 0 -0.1 -0.1 0 0.1 0.1 -0.1 0 -0.1 -0.1 -0.1 -0.1 0 -0.2 -0.1 0 -0.1 0 0 0 0.1 -0.1 0 0.1 0.2 -0.1 -0.1 -0.1 -0.1 -0.2 -0.1 -0.1 -0.2 -0.1 0 -0.1 -0.1 -0.2 0 -0.1 -0.1 0.1 0.1 0.5 -0.1 -0.1 0.1 -0.1 0 -0.2 -0.2 -0.1 -0.1 0 0.1 -0.1 0 -0.1 -0.1 0 0.1 0 0.8 -0.1 -0.2 -0.2 -0.2 -0.3 -0.1 -0.2 0 -0.1 0 0.1 0 -0.1 0 0.1 0.1 0 0 1.1 -0.1 -0.2 -0.2 -0.1 -0.1 -0.2 -0.1 -0.1 -0.1 0 0 0.1 0.2 0.1 0 0 0 0 1.4 0 -0.1 -0.1 -0.1 -0.1 0.1 0 -0.1 -0.1

5.2 Directivity in CATT-Acoustics2

CATT-Acoustic is a room acoustic prediction program based on the image source model for early part echogram qualitative detail, ray-tracing for audience area color mapping and randomized tail-corrected cone-tracing for full detailed calculation enabling auralization.

CATT-Acoustics uses SD0, SD1 and SD2 files to set directivity of sound source. Input data can be set like in ODEON directly by tool ‘directivity’ or by input txt files. Data are commissioned in the octave band from 125 Hz. Tool ‘directivity’ is plotted in the Figure 5.2.

File format SD0 is used when values are known only in horizontal and vertical plane. Twenty four values on the line represent directivity pattern for every 15° in both planes. First values corresponding to front direction, are set as reference value and must be equal 0. The horizontal and vertical value at 180° (correspond to back direction) must be the same. Input text has reversed sign. This format is most suitable for sources that are entered manually from polar data supplied on loudspeaker data-sheets or for creating generic loudspeaker types. The rest of the values are interpolated. Obligatory SD0 syntax be as follows (keywords are written 2 http://www.catt.se

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in bold, values in italic, explanations in plain text and separated by semicolon, [] items are optional):

Figure 5.2: ‘Directivity’ tool in CATT-Acoustics v8.0b (build 1)

CATT-SD0 ;(file-type tag) Version = n ;(a file format version number) Description = loudspeaker name ;(a descriptive name of the source) OctaveBands = <[125] [250] [500] [1k] [2k] [4k] [8k] [16k]> ;(define which octave band are measured) ;If electro-acoustic source: Sensitivity = <[S125Hz] [S250Hz] … [S8kHz] [S16kHz]> ;(SPL at 1 m distance on the axis for 1 W electrical input) ;If natural source: NomSPL_at_1m = <[N125Hz] [N250Hz] … [N8kHz] [N16kHz]> ;(nominal SPL at 1 m distance on the axis) MaxSPL_at_1m = <[M125Hz] [M250Hz] … [M8kHz] [M16kHz]> ;(max. SPL at 1 m distance on the axis) Extents = xmin xmax ymin ymax zmin zmax ; (for Version >= 1 - lists the min-max 3D-extents of a rectangular ; box surrounding the source) [125 polar data for 125 Hz] [250 polar data for 250 Hz] [500 polar data for 500 Hz] [1k polar data for 1kHz] [2k polar data for 2kHz] [4k polar data for 4kHz] [8k polar data for 8kHz] [16k polar data for 16kHz]

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Format SD1 requires arcs rotated in 10° steps around the source axis and with values every 10° along each arc to be entered or imported. Each octave band is represented by 36 lines with 19 values (10° step in horizontal and vertical plane). Direction of rotation is anticlockwise at back view (see Figure 5.3 [33]). First value in each line must be 0 since it is the reference value. All values at 180° (in the back) must be equal. Obligatory syntax in the case of SD1 is similar as in the case of SD0 with two exceptions. First non-comment line must be CATT-SD1 (file-type tag) in lieu of CATT-SD0 and between lines with keywords Description and OcatveBands should be line

RotGroups = from - to [, from - to ...]

Keyword RotGroups defines how the groups of source rotation data are stored in the file. Angle convention according to Fig. 5.3 is used but an imported file may have another convention. Input txt file has reversed sign. More information about making SD0 and SD1 files is in [33].

Figure 5.3: 10° source directivity angle conventions (SD1)

5.3 Conversion of SD1 Input txt File to Input ODEON ‘FULL’ txt File

Each octave band, in the case of SD1 and ‘FULL’ ODEON, is set by 36 lines with 19 values in each octave band but the syntax of input files is different. The first difference is the obligatory syntax. ODEON’s syntax is less complicated but the input files are also less flexible.

Each octave band must be set in ODEON by 36 lines with 19 values but in the case of CATT-ACOUSTICS it isn’t necessary. Only measured data can be set in CATT-ACOUSTIC. Rests of the data are extrapolated. Table 5.1 present measured data of SD1 files [35]. Non-set data must be completed in the conversion process. The data for low octave bands are completed as omnidirectional sound source and data for 8000 Hz are approximated by the 4000 Hz octave band.

The next problem is connected with rotation of coordinate system. ODEON uses anticlockwise rotation in front view but CATT-ACOUSTICS uses anticlockwise rotation in back view. It means that first lines in each octave band are the same but the 2nd line in CATT correspond to 36th line in ODEON, 3rd line correspond to 35th line in CATT and so on. Reference point in CATT acoustic is the front value. ODEON doesn’t use reference point but it calculates with absolute value of power. The shape of directivity patterns is the same but values are shifted by some value. The values in CATT-ACOUSTICS has reversed sign but in ODEON don’t.

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Instrument 125 Hz 250 Hz 500 Hz 1000 Hz 2000 Hz 4000 HzBassoon – – X X X XClarinet – – X X X X

Double bass X X X X X XFlute X X X X X X

Grand piano – – – X X XGuitar X X X X X XHorn – – X X X XOboe – – – X X X

Singing voice X X X X X XTrombone – – X X X XTrumpet – – – X X X

Tuba X X X X X XViola – – X X X XViolin – X X X X X

Violoncello – X X X X X Table 5.1: Measured frequency band.

Conversion of directivity files from CATT to ODEON can be resumed to following points:

• change the syntax for ODEON • invert the order of lines (change orientation) • change signs • fulfill the octave bands • create SO8 file from obtained txt

5.4 Sound Source Rotation and Position

Position of the sound sources is set in ODEON by Cartesians coordinates x, y, z. Each acoustic parameter is dependent on the sound source position and receiver position since the reflections are different. Rotation of sound source influences greatly the acoustic parameters too since it rotates directivity balloons. Rotation isn’t important in the case of omnidirectional sound sources. Sound source rotation can be set in ODEON by azimuth, elevation and rotation angle.

Axes of directivity patterns measured in CATT-ACOUSTIC [35] are situated to the important directions of musical instrument (like axis of musical instrument) but this rotation doesn’t respond to position of musical instrument in real situation. Axes direction and position of musical instrument are shown in Figure 5.4 and in appendix A1 (compare with Figure 5.1 and 5.3). Rotation of sound source therefore must be correlated by properly chosen azimuth, elevation and rotation angles. Table 5.2 presents azimuth, elevation and rotation angles corresponding to musician without rotation (azimuth, elevation and rotation angles of musician are equal 0°). Keeping of musical instrument is very individual and differs from musician to musician that’s way Table 5.2 determines only an average and don’t have to correspond to every musician.

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Figure 5.4: Guitar axes and position in CATT SD files [35]

Instrument Azimuth [°] Elevation [°] Rotation [°]

5

Basson 0 50 10Clarinet 0 -55 0

Double bass sit 0 15 0Flute -10 0 -10

Grand piano 0 0 0Guitar classic 0 0 -5

Horn -100 -30 -30Oboe 0 -40 0

Singing voice 0 0 0Trombone 0 -10 0Trumpet 0 -10 0

Tuba 10 90 0Viola 10 0 30Violin 10 0 30

Violoncello 0 60 0 Table 5.2: Sound source rotation

5.5 Sound Source Power in ODEON

Each sound source radiates with different power at different frequency. Plot of power dependence on frequency is called power spectrum. Power shaping can be made in ODEON by tool ‘equalization’ in the polar plot editor (see Figure 5.1) or in the point source editor (see Figure 5.5). Equalization made in polar plot editor is fixed and it shift power level according to the required value in the SO8 file. This method is useful to changing power spectrum of sound sources with the same directivity (e.g. for one kind of instrument). Equalization made in the point source editor shift power spectrum only in respective sound source. Shifting of power is used only in the case of calculating acoustic parameter in the enclosure. Flat power spectrum should be used in the case of auralization since the shifting of power level has been already included in the anechoic records [34].

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Figure 5.5: Point source editor

Power spectra of musical instruments were obtained making octave band spectrum analysis of particular musical instrument records. Realtime Analyzer Version 5, 0, 2, 0, Yoshimasa Electronic Inc. and semitone anechoic records of musical instrument, made at The University of Iowa, were used in this project. Power spectra were normalized to value 0 dB at frequency 1 kHz. Obtained power spectra are presented in Table 5.3 and Figure 5.6.

Instruments 63 125 250 500 1000 2000 4000 8000Bassoon -12 -7 0 12 0 -16 -29 -41Clarinet -49 -14 -9 -3 0 -4 -7 -31D. Bass 19 22 16 7 0 -4 -14 -20Flute -51 -55 -15 -5 0 -1 -19 -30French Horn -29 -21 -1 10 0 -13 -33 -50G.Piano -7 2 4 6 0 -11 -25 -4Oboe -58 -62 -18 -12 0 -4 -15 -40Trombone -31 -15 -8 -1 0 -8 -24 -47Trumpet -81 -51 -29 -13 0 -2 -12 -29Tuba -10 3 12 14 0 -16 -16 -14Viola -51 -40 -9 -2 0 0 -11 -36Violin -44 -42 -7 2 0 1 -5 -17Violoncello -20 -10 -1 -1 0 1 -14 -28Voice -40 -25 -1 -2 0 -12 -29 -32

4

Table 5.3: Power spectra of musical instrument in octave bands

The total power level is affected by shape and power shifting of directivity patterns. Total sound source power is shown in point source editor (see Figure 5.5). Total power level can be shifted in point source editor by tool ‘+ Overall gain’, which shifted total power level by required value. Each musical instrument has different directivity, different power spectrum and different overall power so overall gain should be chosen properly to each instrument. Average forte from [13] (see Figure 3.1) was chosen as the overall power of particular instrument. Power of grand piano, which wasn’t measured by Meyer, was set to value 105 dB. Average forte and overall gain corresponding to equalized SO8 file made from [35] are represented in Table 5.7.

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Figure 5.6: Power spectrum of string (above), woodwind and voice (middle) and brass

(below) instrument

Instrument Average forte [dB] Overall gain [dB]Bassoon 92.5 61.1Clarinet 92.5 71.9

Double bass 92.5 57.4Drum 105 96Flute 91.5 76.2

Grand piano 105 84.4Horn 102 84.3Oboe 92.5 75.6

Trombone 101 91.1Trumpet 101 92.6

Tuba 102.5 80.3Viola 88 72.3Violin 90 72.7

Violoncello 91.5 75 Table 5.4: Average forte and overall gain of musical instrument

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Chapter 6 - Comparison of Directivity, Influence of Directivity on Room Acoustics Parameters

The directivity of musical instrument influences heavily room acoustics parameters. This section describes the comparison of directivity files. CATT-ACOUSTICS non rotated [35], CATT-ACOUSTICS rotated (see Chapter 5.4) and ODEON v8.51 Combined (if there were available) directivity files were chosen for each instrument for comparison. ELMIA concert hall in Jönköping, Sweden was chosen as a comparative enclosure. Photo and ground plan of ELMIA concert hall are shown in Figure 6.1. Every calculations and simulations have been made in ODEON version 6.5 Combined.

Figure 6.1: Photo (left hand side) and perspective ground plan (right hand side) of ELMIA

concert hall

Comparison of directivity files must be divided into three groups. Low frequency band, which wasn’t measured in the case of CATT-ACOUSTICS, belong to the first group (see Table 5.1) since these octave bands were approximated as omnidirectional sound source. Octave bands, which were measured in both cases, belong to the second group. This category is the most important since human ear is most sensitive to these frequencies (see Figures 2.2 and 2.3) and most of instruments have maximum power radiation at these frequencies. 8 kHz octave bands belong to the last category. Directivity patterns are approximated by 4 kHz octave bands values. Attenuation in the air plays important role at the frequency 8 kHz but human ear are still very sensitive. Nearly every instrument radiates at the frequency 8 kHz less powerful than in the frequency range 1 kHz to 4 kHz.

6.1 Comparison of Directivity Patterns and Directivity Balloons

Comparison of directivity patterns can be used only for non rotated sound sources since 3D rotation of directivity is very hard to accomplishment manually. This comparison gives only qualitative results since only shape of the directivity patterns can be checked and nothing can be said about influence on the change of acoustical parameters. Power of sound source should be shifted to the same value and the scale of the plots must be chosen properly in each octave bands because for a easier comparison and for obtaining more precise results.

Only directivity patterns of singing voice are shown in this report (Figure 6.2a and 6.2b), because the rest of musical instrument should be rotated (see Table 5.2).

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Figure 6.2a: Directivity patterns of singing voice (continuation on the next page)

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Figure 6.2b: Directivity patterns of singing voice (beginning on the previous page)

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The biggest difference is within the angles range from 240° to 300° in the vertical plane at all frequency except 63 Hz. These differences are caused by placement of microphones and method of measurements. These angles can’t be compared. Directivity of voice is omnidirectional in both cases at the lowest frequency of 63 Hz. Directivities are still omnidirectional at frequency 125 Hz and 250 Hz in the case of ODEON but not in CATT. The maximal difference is equal around 7 dB and the shapes of directivities are very similar. Directivity starts to be little bit elliptical in the horizontal plane at frequency 500 Hz in both cases. The differences not exceed 5 dB in every direction. Nearly the same situation is in the case of vertical plane. The shapes of the directivities are nearly the same and the maximum differences are 5 dB within the angle range from -50° (310°) to 210°. Differences above 500 Hz start to be greater. The differences is greater than 5 dB within the ranges from 110° to 150° and from 220° to 260° in the horizontal plane and within the ranges from 110° to 150° and from 220° to 240° in the vertical plane at frequency 1 kHz. Differences greater than 5 dB are nearly in all direction in both planes at 2 kHz. The only exception is angle range from 0° to 40° in both planes. Directivity patterns are identical in the case of ODEON and CATT at frequency 4 kHz and 8 kHz. Shapes are very similar in vertical plane and the differences not exceed 8 dB. Only exception is at back direction (180°) where the difference is nearly 15 dB. The differences in the horizontal plane are less than 5 dB within the range -60° (300°) to 50° but at other frequencies the differences are much greater. Differences in directivity patterns are caused by individuality of human voice. Everyone has uniqueness timbre, frequency range and hence also directivity patterns. Soprano voice was measured in the case of ODEON but this type of voice isn’t known in the case of CATT.

The comparison of directivity balloons rests on comparison of 3D representation of directivity. It gives only qualitative results but this method has few advantages compared to previous method. The whole directivity of sound sources in 3D space is compared instead of only horizontal and vertical plane values. Rotation of sound sources can be taken into account to a certain degree. Little differences in directivity balloons are heavily noticeable so this method isn’t used in practice. Figure 6.3 show CATT’s and ODEON’s directivity balloon of a singer.

Figure 6.3: Directivity balloons of voice at 1 kHz (left hand side ODEON version, right hand

side CATT version)

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6.2 Comparison of Point Response

The basic principle of this method consists in the comparison of calculated acoustical parameters instead of the comparison directivity patterns. Acoustical parameters are calculated at some important places like director’s place, middle of audience, balcony etc. Results are usual plotted in a bar plot. It gives variation of processing results and it gives well arranged representation. Computing time is the main advantage of this method. This is useful especially in simulating many musical instruments (orchestra) when the calculation time rapidly grows up. The main disadvantage is that the only data in few positions are compared in the whole enclosure.

Receivers and sound source were chosen similar as in the case of Round Robin 23. Position of receivers and sound sources are represented in Figure 6.4 and Table 6.1. Non equalized version of CATT and ODEON directivities were chosen since only the influence of shape of directivity patterns was considered without modification in the ODEON directivity. An omnidirectional sound source was also chosen by reason of investigation of influence of directivity patterns on the acoustics parameters. Figure 6.5 show EDT point response of clarinet. Rests of results are shown in appendix A2.

x [m] y [m] z [m]Sound source 8.5 0 125.1

Receiver 1 13.8 0 124.85Receiver 2 12.9 10.5 128.7Receiver 3 19.9 5.1 126.1Receiver 4 25.5 -4.9 127.75Receiver 5 24.8 11.9 129.1Receiver 6 37.8 6.4 131.85

Table 6.1: Disposition of sound source and receivers in plot point response

Figure 6.4: Disposition of receivers in point response simulation

3 http://www.ptb.de/en/org/1/17/173/roundrobin.htm

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Figure 6.5: EDT plot point response of clarinet

Differences, in the case of SPL, are caused by different power at particular frequency bands. Great difference between CATT and ODEON version are often at frequency 8 kHz. This is caused by approximation made at this frequency (data replaced with 4 kHz values). Results are the same at the lowest frequency that means that musical instruments are omnidirectional at this frequency and substitutions were made correctly. Results aren’t similar at the remaining, not measured, octave bands (see Table 5.1). Results in the case of CATT oriented and not oriented versions are very different that means orientation of musical instrument must be taken into account in the simulation. The lowest differences between oriented and not oriented version are in the case of trumpet and the greatest differences are in the case of French horn. It was possible to forecast these results since angular displacements are the lowest in the case of trumpet and the greatest in the case of French horn (see Table 5.2). Great differences between ODEON and CATT can be often find also at the position of receiver one. This is caused by not measured data within the angle range 230° - 310° in the case of ODEON. Receiver one is the closest to the sound source and the acoustic parameters are very influenced by this part of directivity. Some acoustics parameters are very influenced by rotation of sound sources and some it aren’t. LF80 and C80 belong to the first group. This implies that appropriate rotation of musician on the stage is very important. T30 belongs to group which isn’t very influenced by rotation. Similar results are obtained using ODEON, omnidirectional, CATT oriented and not oriented version so omnidirectional sound source can be used to measure these parameters.

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6.3 Comparison of Grid Response

This method consists in the comparison of calculated acoustics parameters calculated on a grid of receivers. Results are illustrated at scale, as in the figures each receiver is represented by a square in which the receiver is in the middle. The advantage of this method is that acoustical parameters are computed in the whole enclosure not only in few positions as it was in the case of point response. Places with ‘poor’ and ‘good’ acoustic can be located. Calculation of acoustic parameter in so many points leads to extensive increasing of calculation time. Another disadvantage is that a small change of parameter is hardly noticeable since human eye is not able to recognize small changes in coloration.

The same directivity patterns were chosen for comparison as in the case of point response (see chapter 6.2) without omnidirectional directivity. Grid was defined by 1.5 m distance between receivers and 1.2 m height above surface. Results are shown only at frequency 1 kHz since human ear is very sensitive at this frequency and most instruments radiate very powerful at this frequency. C80 grid response is represented in Figure 6.6. Next results are shown in Appendix A3.

C80 Trumpet at 1000 Hz

Not Oriented Oriented ODEON

C80 French Horn at 1000 Hz


Figure 6.6a: C80 grid response (continuation on the next page)

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C80 Clarinet at 1000 Hz Not Oriented Oriented ODEON

C80 Violin at 1000 Hz Not Oriented Oriented ODEON

C80 Singer at 1000 Hz CATT ODEON

Figure 6.6b: C80 grid response (beginning on the previous page)

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The result d from point resp

Chapter 7 -

Orchestra is very common in music. Many musical pieces have been written just for the orc

h century. Occupation of the orchestra has cha

s obtained from grid response confirm previous results obtaineonse. Places closer to the sound source are more influenced by directivity than places far

from the sound source where the parameters are more similar. The lowest differences in all cases are in calculation of T30, so T30 isn’t very influenced by directivity. The greatest differences are in the case of C80 and LF80. Angular displacement of trumpet doesn’t have to be taken into account since the differences in the results aren’t noticeable by human ear. Results are considerably different in the case of other instruments, so only in the case of trumpet angular displacement can be neglected.

Simulation of Orchestra

hestra. There exist many kinds of orchestras starting from chamber bow orchestra, wind orchestra following with jazz and dance orchestras and finishing with huge symphonic orchestra. Each of these orchestras has its own disposition and structure. Symphonic orchestra is considered since this is the largest ensemble.

Symphonic orchestra originates in the 17tnged very much through the years. Symphonic orchestra still hasn’t stable occupation

which depends on the music piece which is presented. Nowadays very common occupation is: 3 flutes, 3 oboes, 3 clarinets, 3 bassoons, 4 French horns, English horn, 3 trumpets, 4 trombones, 1 tuba, percussions + 3 timpani, 3 harps, 8 - 14 first violin, 8 - 14 second violin, 6 - 10 violas, 6 - 10 cellos, 4 double basses. Each instrument has its place and role in the orchestra. Disposition scheme of symphonic orchestra is shown in Figure 7.1.

Figure 7.1: Disposition scheme of symphonic orchestra (www.wikipedia.org)

The whole sets of instruments can’t be considered during simulation of symphonic orchestra since the computation time is too long, therefore only the role of the instrument in the orchestra must be taken into account during these simulations. Bowing instrument are most important in most musical pieces for symphonic orchestra therefore more sources must represent these instruments. Two instruments for first and second violins, violas and cellos were used in this work. Other sources represent only one instrument. Equalized and rotated directivity patterns must be used to obtain the best results. Rotation of whole musician must

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be taken into account too, since the settings of angular displacement (azimuth) of sound sources will be different. Overall settings of sound sources are shown in Table 7.1. Figure 7.2 shows disposition of sound sources on the stage.

Receiver number

Musical instrument x y z Azimuth Elevation Rotation Overall

gain1 First violin 9 -3.5 125.5 100 0 30 72.72 First violin 7 -5 125.5 80 0 30 72.73 Second violin 5.5 -3.5 125.5 60 0 30 72.74 Second violin 6 -1 125.5 30 0 30 72.75 Viola 6 1.5 125.5 -15 0 30 72.36 Double bass 5.5 4.5 125.5 -50 15 0 57.47 Violoncello 9 3.5 125.5 -90 60 0 758 Violoncello 7.5 5 125.5 -70 60 0 759 French horn 4 3.5 125.5 -135 -30 -30 84.310 Oboe 4 1 125.5 -10 -40 0 75.611 Flute 4 -1 125.5 0 0 -10 76.212 Bassoon 2.5 2 125.5 -20 50 10 61.113 Clarinet 2.5 -2.5 125.5 20 -35 0 71.914 Trombone 2 1 125.5 -10 -10 0 91.115 Trumpet 2 -1 125.5 10 -10 0 92.616 Tuba 2 3.5 125.5 -15 90 0 80.317 GrandPiano 3 -4.5 125.5 -15 0 0 82.9

Disposition of orchestra

Table 7.1: Sound source settings

Figure 7.2: Disposition of sound sources on the stage

Some changes were made in ELMIA concert hall model in this simulation. Material of aud

bands 500 Hz, 1 kHz and 2 kHz in the Figure 7.3 and in Appendix A4.

ience surfaces (surfaces number 4, 6, 7, 208 – 210, 1208 – 1210) was changed to material number 907 (audience, heavily upholstered seats) because the field was too reverberant. Simulation in the same enclosure was made with omnidirectional sound sources placed in the middle on the stage since this is the most common way of measuring acoustical properties of the rooms. The total power of omnidirectional sound sources was set to 100 dB. Scale step was adjusted to subjective limen [34]. Only exception is LF80 (when using this scale it was too unnoticed) so the maximum resolution was used. Results are shown at three frequencies

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EDT 500 Hz

Omni Orchestra

1000 Hz

Omni Orchestra

2000 Hz

Omni Orchestra

Figure 7.3: EDT grid response of orchestra and omnidirectional sound source

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Blac etrical representation of ELMIA hall since these places are outside of the enclosure. It can be demonstrated using tool ‘3D investigate rays’ (see Figure 7.4). White places at the rear of the hall, which aren’t hit by any rays, correspond to the black parts of grid response. Two black squares on the stage (see Figure 7.3) are nearly whole situated outside of enclosure and the middle of the squares (points in which the acoustical parameters are calculated) lie outside the enclosure.

k parts, at the same place in every simulation, are caused by geom

Figure 7.4: Ray tracing of ELMIA hall a) ground plan b) perspective

The biggest differences between orchestra and one omnidirectional source are on the stage inside orchestra. These results are caused by number of surrounding sound sources since there is a great difference whether the receiver is surrounded by one or many sound sources.

Great differences between orchestra and one omnidirectional are on the stage inside orchestra. These results are caused by number of surrounding sound sources since there is great difference whether the receiver is surrounded by one or many sound sources.

It could seem that the biggest differences are in the case of SPL but this isn’t true since the value of SPL is very influenced by the total power of sound sources. The total power of omnidirectional sound source is 100 dB but the total power of orchestra is 109.9 dB. Power of orchestra depends on frequency (octave band) too. If 3 dB changes are only considered (changes of the color) the results start to be more similar. Differences between one source and orchestra sources in this case are only close to the changes of colors but in the majority of enclosure the results are the same.

EDT differs in the most part of the enclosure but it can be found some regularity. EDT increases more quickly with increasing distance in the case of omnidirectional sound source than in the case of orchestra. It means that measured EDT with omnidirectional sound source is the same or greater than it is in the case of orchestra.

The most varying parameter is without doubt LF80. This parameter differs nearly at every point in the enclosure. This result was predictable since LF80 characterizes spaciousness of sound sources.

The remaining two parameters (T30 and C80) differ very much but the differences are hardly described. This is noticeable especially in the case of T30 when the differences are distributed randomly all over the enclosure.

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Chapter 8 - Summary and Further Works

The program ODEON reveals as a good environment for digital modeling of musical sound sources. All physical characteristics can be simply set primary by tool ‘Directivity polar plot editor’. Easy usage can be reached by saving directivity in the proper way. Good representation of result can be achieved by combination of ODEON output files and MATLAB programming environment.

The directivity of radiation and the power spectrum of each sound source are the most important physical properties for digital modeling of sound sources. ODEON SO8 directivity files of most common musical instruments were made using these two properties. Turning of musician and angular displacement of musical instrument don’t have to be forgotten since the results are very influenced by these parameters.

Musical instruments can’t be replaced by omnidirectional sound sources. The only one room acoustics parameter which aren’t influenced very much by directivity are T30 and SPL, so these two parameters can be measured with great accuracy using omnidirectional sound sources.

Each acoustics parameter differs if evaluated using an orchestra or one omnidirectional sound source situated in the middle of the stage. SPL is comparable in the case that the differences between the power of orchestra and the omnidirectional sound sources are compensated by proper values in each octave bands. Also, from the simulation it results that values of EDT calculated using one omnidirectional sound source in the middle of the stage are greater or the same that in the case of an orchestra.

Simulation of other kinds of orchestra (bowed chamber orchestra, wind orchestra) should be made in id re ponse picture and output files in order to get a better representation of results. Comparison of aur

the future. Some MATLAB function can be written to elaborate gr s

alization sound files can be substantially significant in subjective perception of hearing.

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Appendix A1 - Axes and Position in CATT SD Files

a

b

c d

e

f

Figure A1.1a: Axes and positron in CATT fines a) violin, viola b) double bass, violoncello c) bassoon d) clarinet e) flute f) oboe [35] (continuation on the next page)

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g

h

i

j

k

l

Figure A1.2: Axes and positron in CATT fines g) French horn h) trombone i) trumpet j) tuba k) grand piano l) voice [35]

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Appendix A2 - Point Response

Figure A2.1: C80 plot point response of clarinet

Figure A2.2: LF80 plot point response of clarinet

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Figure A2.3: SPL plot point response of clarinet

Figure A2.4: T30 plot point response of clarinet

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Figure A2.5: C80 plot point response of French horn

Figure A2.6: EDT plot point response of French horn

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Figure A2.7: LF80 plot point response of French horn

Figure A2.8: SPL plot point response of French horn

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Figure A2.9: T30 plot point response of French horn

Figure A2.10: C80 plot point response of trumpet

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Figure A2.11: EDT plot point response of trumpet

Figure A2.12: LF80 plot point response of trumpet

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Figure A2.13: SPL plot point response of trumpet

Figure A2.14: T30 plot point response of trumpet

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Figure A2.15: C80 plot point response of violin

Figure A2.16: EDT plot point response of violin

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Figure A2.17: LF80 plot point response of violin

Figure A2.18: SPL plot point response of violin

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Figure A2.19: T30 plot point response of violin

Figure A2.20: C80 plot point response of voice

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Figure A2.21: EDT plot point response of voice

Figure A2.22: LF80 plot point response of voice

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Figure A2.23: SPL plot point response of voice

Figure A2.24: T30 plot point response of voice

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Appendix A3 - Grid Response

EDT Trumpet at 1000 Hz Not Oriented Oriented ODEON

EDT French Horn at 1000 Hz Not Oriented Oriented ODEON


EDT Clarinet at 1000 Hz


EDT Violin at 1000 Hz Not Oriented Oriented ODEON

EDT Singer at 1000 Hz CATT ODEON

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LF80 Trumpet at 1000 Hz Not Oriented Oriented ODEON

LF80 French Horn at 1000 Hz


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LF80 Clarinet at 1000 Hz


LF80 Violin at 1000 Hz


LF80 Singer at 1000 Hz

CATT ODEON

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SPL Trumpet at 1000 Hz Not Oriented Oriented ODEON

SPL French Horn at 1000 Hz Not Oriented Oriented ODEON

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SPL Clarinet at 1000 Hz


SPL Violin at 1000 Hz


SPL Singer at 1000 Hz

CATT ODEON

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T30 Trumpet at 1000 Hz Not Oriented Oriented ODEON

T30 French Horn at 1000 Hz Not Oriented Oriented ODEON

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T30 Clarinet at 1000 Hz


T30 Violin at 1000 Hz Not Oriented Oriented ODEON

T30 Singer at 1000 Hz CATT ODEON

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Appendix A4 - Grid Response of Orchestra

C80 500 Hz

Omni Orchestra

1000 Hz

Omni Orchestra

2000 Hz

Omni Orchestra

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LF80

500 HzOmni Orchestra

1000 Hz

Omni Orchestra

2000 Hz

Omni Orchestra

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SPL


1000 Hz

Omni Orchestra

2000 Hz

Omni Orchestra

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T30


1000 Hz

Omni Orchestra

2000 Hz

Omni Orchestra

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List of Symbols and Abbreviations

c velocity of the sound dB decibel dBA A-weighted decibel dS infinitesimally small surface element Ex-y energy arriving within time interval (x, y) h(t) impulse response H number of reflection I sound intensity k wave number k wave vector m attenuation coefficient p atmospheric pressure P pressure magnitude r distance from the source r vector direction R reflection coefficient S surface area V volume t time α absorption coefficient α mean free absorption coefficient Δ Laplace operator ϑ reflection angle ω angular frequency ASW apparent source width BRIR binaural room impulse response C80 clarity CATT-ACOUSTICS room acoustics program D Definition (Deutlichkeit) EDT early decay time f, ff forte, fortissimo HRTF head related transfer function LI intensity level Lw power level LF80 lateral energy fraction ODEON room acoustics program p, pp piano, pianissimo RT20, RT30, RT60 reverberation time SD0, SD1, SD2 CATT-ACOUSTICS directivity file SO8 ODEON directivity file SPL sound pressure level SPLA sound pressure level A-weighted STI speech transmission index TS definition or Deutlichkeit txt text file

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