2014 Turntable for an Automatic Acquisition System for Measuring the Directional Characteristic of...

BACHELOR THESISUniversity of Applied Sciences Technikum Wien, Electronic Engineering

Turntable for an Automatic AcquisitionSystem for Measuring the DirectionalCharacteristic of Musical Instruments

Author: Martin LahmerStudent ID: 1210254005

Academic Supervisor: FH-Prof. Dipl.-Ing. Christian KollmitzerCompany Supervisor: Ing. DI (FH) Alexander Mayer

Vienna, June 4, 2014

Declaration„I confirm that this paper is entirely my own work. All sources and quotations have been fullyacknowledged in the appropriate places with adequate footnotes and citations. Quotationshave been properly acknowledged and marked with appropriate punctuation. The worksconsulted are listed in the bibliography. This paper has not been submitted to anotherexamination panel in the same or a similar form, and has not been published.“

Vienna, June 4, 2014

Place, Date Signatur

AbstractMusical instruments are complex physical systems. This paper deals with the class of brasswind instruments especially the Tuba. Brass instruments are excited by the vibrating lipsof the musician and radiates the played tone at the end of the tube via the bell into theacoustic room. How the sound is radiated, is determined by individual characteristics of anmusical instrument. One of these attributes is the directivity, which will be considered ingreater detail in this work. It defines how the sound is radiated as a function of positionand frequency. For this purpose an automatic measuring system was developed which allowsstimulating a brass instrument and measuring the radiated sound pressure in different angles.So a complete sound pattern can be created. This was realized by a turntable system whichis driven by automatic controlled stepper motors.By the measurement of two different Tubas the system has been successfully tested.

Thereby, useful diagrams were obtained that represent the angle-dependent sound radiationof the instruments over a number of frequency bands. This success serves as a basis forfurther acquisitions which could be done in one plane at least. The developed system con-sisting of hard- and software is simply adaptable for almost all kinds of musical instrumentsfor further purpose.

Keywords: Brass Wind Instruments, Directional Characteristic, Automated AcquisitionSystem, Step Motor driven Turntable, Arduino, LabVIEW

KurzfassungMusikinstrumente sind komplexe physikalische Systeme. Diese Arbeit beschäftigt sich mitder Klasse der Blechblasinstrumente, speziell der Tuba. Diese werden durch die schwingendenLippen des Spielers angeregt und am Ende der "Röhre" wird der Ton über den Schalltrichterin den akustischen Raum abgegeben. Wie der Schall abgestrahlt wird, wird durch die in-dividuelle Charakteristik des jeweiligen Musikinstruments bestimmt. Eines dieser Attributeist deren Richtwirkung, die in dieser Arbeit genauer betrachtet wurde. Sie beschreibt, wieein Musikinstrument den Schall in Abhängigkeit von Ort und Frequenz abstrahlt. Dafürwurde ein automatisches Messsystem entwickelt, das es ermöglicht ein Blechblasinstrumentanzuregen und den abgestrahlten Schalldruck für verschiedene Winkel zu messen. Realisiertwurde dies durch ein automatisierten Drehtischsystem, das per Schrittmotoren angetriebenwird.Durch das Messen von zwei verschiedenen Tuben wurde das System erfolgreich getestet.

Dabei wurden brauchbare Diagramme gewonnen, die die winkelabhängige Schallabstrahlungder Tuben über mehrere Frequenzbänder abbilden. Dieser Erfolg dient als Grundlageum weitere Musikinstrumente zumindest in einer Ebene ausmessen zu können. DasSystemkonzept von Hard- und Software wurde für weiterführende Messzwecke so ausgelegt,dass es für nahezu sämtliche Musikinstrumente angepasst werden kann.

Schlagwörter: Blechblasinstrumente, Richtcharakteristik, Automatisches Messsystem,Drehtisch mit Schrittmotor, Arduino, LabVIEW

Contents

1. Introduction 1

2. Brass Wind Instruments 22.1. Basic Knowledge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.2. Characterisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.3. Directional Characteristic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3. Technical Implementation of the Automated Acquisition System 73.1. Turntable-System with Step-Motors . . . . . . . . . . . . . . . . . . . . . . . 7

3.1.1. Mechanical Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73.1.2. Electrical Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.2. Step Motor Control - SMC . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.2.1. Stepper Motor Driver Carrier . . . . . . . . . . . . . . . . . . . . . . . 133.2.2. Communication over Serial Interface . . . . . . . . . . . . . . . . . . . 143.2.3. Step Losses Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.2.4. Manual Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.2.5. Power Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.3. High Air Pressure Artificial Mouth - HAPAM . . . . . . . . . . . . . . . . . . 183.4. Final Measurement Set-Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.5. Supervising Computer Program with LabVIEW . . . . . . . . . . . . . . . . . 20

3.5.1. Top Layer Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . 203.5.2. Measuring Layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.5.3. Data Processing Layer . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4. Acoustical Measurements and Acquisition of the Directional Sound Pattern 234.1. Input Impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.2. Transfer Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264.3. The Directional Characteristic of Brass Wind Instruments . . . . . . . . . . . 27

5. Conclusion 30

Bibliography 31

List of Figures 33

List of Tables 34

List of Abbreviations 35

A. Assembled Step-Motor-Control (SMC) 36

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B. Schematic of the Turntable’s Step-Motor-Control (SMC) 37

C. LabVIEW-Screenshot of HAPAMv15 38

1. IntroductionThe quality of musical instruments is designated by their acoustical characterisation. Butwhat are these characteristics? And what is meant by quality of an instrument?

"In the definition of the quality features you have to be clear that several aspectshave to be considered both from the side of the listener as well as the player, whichare two completely different viewpoints. Features of interest for the listener aretimbre, loudness, pitch, etc. in the far field, however, for the player it is importanthow well a sound appeals besides how well the intonation of an instrument is andhow the instrument sounds in the near field.In addition, it should be noted that in addition to objectively recorded measurementdata, the player’s subjective impressions but also the individual variation play alarge role in the evaluation of quality."

Winkler, W. and Widholm, G. 1996: 95 [1].

So this paper deals with the determination of such quality criteria of brass wind instru-ments. Since the author was playing the Tuba, the precise focus is on the low register ofbrass instruments especially the Tuba. First of all, how a sound is excited on a Tuba andhow it is spread into room will be explained. The spreading is mainly determined by theacoustical conditions of the ambient room and by the directional characteristic of the instru-ment itself. To measure the directional characteristic at least one microphone is necessary toplot radiation in plane. If a stereoscopic acquisition of the directional pattern is preferred,a microphone array will be required. This array can be arranged equally around the testingobject[2]. Therefore a high amount of microphones will be needed to allow recordings in asmany directions as preferred besides a high-capacity processing unit will be required. If theamount should kept low, the object to be tested should be moved around and recorded sep-arately. For this procedure a rotating platform, which turns automatically, is advantageous.In the course of a project announced and supported by the Institute of Music Acoustics (In-stitut für Wiener Klangstil - IWK ) at the University of Music and Performing Arts Vienna,a turntable system had to be implemented which is able to carry musical instruments up toseveral kilograms weight (finally a grand piano should also be turned) and rotates the loadautomatically. It is controlled by a supervising system, which also executes the acousticalmeasurements, over a serial interface. The acoustic radiation is captured either with onemicrophone for one plane or with a arched microphone array, which completes the recordingto a half globe by a 360 degrees turn.Knowledge of this characteristics will be explained, discussed and experimentally proven in

the following chapters step by step. First, the paper will explain the theoretical background ofbrass wind instruments especially the Tuba and its selected characteristics like the directionalsound pattern or the input impedance. The impedance is important for the intonation of aninstrument [1]. The next topic will deal with the technical preparation of the turntable andthe measuring set-up. In the last section the resulting measurements of an elected numberof Tubas will be documented.

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2. Brass Wind Instruments

Musical instruments basically exist of three parts: a stimulator, an oscillator and a resonator.The stimulator of brass instruments are the lips on the brass mouthpiece. They excite an aircolumn in the instrument. These air column is limited by the brass tube which encases it. Asa result of this standing waves occur. The oscillated standing waves determine the oscillatorwhich vibrates at a frequency forced by instrument and player. Finally, the resonator hasthe task to transform wave energy into sound energy. Since the swinging air column of brassinstruments has not to be transformed to sound vibrations any more the brass’s oscillator issimultaneous the resonator. Contrariwise, for stringed instruments the bow is the stimulator,the strings are the oscillator besides the resonator consists of whose corpuses [3].

2.1. The Basic Knowledge of Brass Wind InstrumentsThe oscillating media of brass wind instruments is a standing wave formed by the air columninside the brass tube. The resulting resonant frequency and its harmonic multiples are definedby the circular tour time of one standing sound wave which moves from the mouthpiece tothe bell and back again in sound velocity. This is because at resonance the most energy ofthe standing wave is reflected from the bell mouth back into the tube and only a short termis spread as audible sound. The reflected energy comes back to the mouthpiece where it willbe amplified by the synchronously oscillating lips of the musician, and the standing wavewill develop again. This leads to maintaining the acoustic system and helps the musicianholding a note on the preferred resonance frequency. As a result of this the wavelength ofthe standing sound wave is defined by the double length of the brass tube (λ = 2 ∗ lBRASS).In Formula 2.1 the relation between sound wave velocity (cs) (normally it is 343 ms−1 ina dry air at 20 C [4]), the sound wavelength (λ) and the resonant frequency (f) is given.However, the surrounding conditions like temperature and stationary air-pressure also haveinfluence on the speed of sound and simultaneously on the resonant frequency. For instance,a higher temperature affects a higher resonance and vice versa. An additional tuning slidewhich all brass instruments have implemented, should compensate such tuning fluctuations.

cs = λ ∗ f. (2.1)

Resonant frequencies are also called natural tones by musicians. Although the naturaltones have the same distance in Hertz to their harmonic neighbours, they do not fit thecommon musical (chromatic) scale. This is due to the fact that human sense of hearingand as a consequent of that the musical scale is not linear but logarithmic. Therefore achromatic scale seems to be consistent in advance. Actually, the interval between the firstand the second resonant frequency is a musical octave, for example, instead it is only aquint between second and third resonance and so on. The higher the compared frequencieslies the closer will be the musical distance (e.g. see the measured resonant frequencies of aTuba in Figure 4.1). So additional tones have to be produced for lower octaves to fulfil the

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CHAPTER 2. BRASS WIND INSTRUMENTS

complete scale. In this case valves with additional tubes are applied on Trumpets or Tubasfor instance. This extends the length of the whole tube and lowers the resonant frequencyadaptively. On Trombones the variation of notes is realized by pulling the Trombone’s slide[3].Figure 2.1 is an image of one tested contrabass Tuba in B[. It highlights the basic elements

and the run of the 5.8 m long conical brass tube. The basic elements of Tubas usuallyconsists of the bell mouth (or simply called bell) with a diameter of about 40 cm, a cone-shaped tube with a total length of about 5.8 m (see the calculation in Equation 2.2) anda mouthpiece with a semi-spherical cup. Additionally, there are 4 valves which are ableto alter the natural tones variably. The natural tones are determined by the first harmonicfrequency of the instrument. It is also known as fundamental or pedal tone (f1). Usually, thepedal tone is seldom played by the musician because the gap to the next resonance demandstoo many intermediate tones and consequently more additional valves. Instead, the secondresonant tone (f2) is decisive as standard tuning frequency. It is a B[1 (German: ContraB[) for the contrabass Tuba. Nominally this note should be at a frequency of 58.26 Hz innormal conditions and with a reference frequency for standard pitch A4 (German: a1) at 440Hz [5]. Higher natural tones (F2, B[2, D3, F3, etc. . . ) are harmonic integer multiples of thefundamental tone. Comparing the resultant standard musical pitch (≡ f2) of Equation 2.2with the theoretically calculated frequency of 58.26 Hz by [5] shows that the tuning pitchcannot be defined generally, since the standard tuning frequency varies from instrument toinstrument or rather the surrounding condition have influence on the pitch.

Bell

Mouthpiece

Valves

Brass

Tub

e

Figure 2.1.: Image of a contrabass Tuba in B[ with its elements.

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cs = λ ∗ f ⇒ f = cs

λ, where λ = 2 ∗ lBRASS ,

f1 = 343 ms−1

2 ∗ 5.8 m = 29.57 s−1,

⇒ f2 = 2 ∗ f1 = 59.14 s−1. (2.2)

2.2. Characterisation of Brass Wind InstrumentsEvery single tone which reaches our ear in the course of a musical work, contains a fullnessof information. It is not only described by its fundamental frequency instead the heard tonecomprehends several overtones which all of them are integer multiples of the fundamentalfrequency too. This overtones which are also called partial tones or simply partials, areresponsible for the tone colour. The number of overtones and the magnitude of the harmonicsultimately determine how we perceive a sound. The more harmonics are included, the morebrilliant and brighter a tone sounds. Contrariwise, the less harmonics a sound spectrumexhibits, the darker and softer it is perceived. This fact deals with every single kind ofmusical instrument. However, there are special regions with a couple of overtones wherethe magnitudes change very little besides they usually are more intensive as the actualfundamental tone. This amount of harmonics are called formants and they define the soundcolour of individual instruments [6]. In Table 2.1 the region of formants of different brassinstruments are listed.

Instrument Formants in HzHorn 350Trumpet 1200 - 1500Trombone 500 - 600Tuba 230 - 290

Table 2.1.: Region of formants of several brass wind instruments [6].

Not only the spectral events with the aforementioned overtones and formants describe thesound of an instrument but also transient events contribute to the instrument’s characteri-zation. Composing spectral information with the three transient sections of a tone helps todistinguish between musical instruments. The three sections of a tone are [6]:

1. The starting transient, i.e., that portion of time during which the tone is developedfrom complete rest to its final state. During this initial process the overtones developssteadily. This is primarily responsible for recognising the kind of instrument.

2. The stationary condition, i.e., that portion of time during which the tone is practicallynot subjected to change. At this particular time the partial tones keep constant forinstruments which can stabilize the oscillating system like brass wind instruments.That instruments are supported by the constant feeding of energy by the musicians airexcitation.

3. The decay, i.e., that portion of time during which the tone, after completion of theexcitation, dies out to complete silence. The decay depends on the reverberation and

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plays a special role for plucked- and percussion instruments, since in the absence ofcontinuing excitation there is no stationary state.

After all the most significant attributes of brass instruments are their resonant frequencies.They define the intonation the musician has to deal with. For determination, they canbe caught by measuring either the acoustical input impedance or the acoustical transferresponse. Several scientific papers deals with these topics [1][7][8]. For simplicity, bothmethods are contrasted in Chapter 4 of this paper by execution on two Tubas. Finally, theDirectional Characteristic which is the main topic as known, will complete this introductionof brass wind instruments.

2.3. Directional CharacteristicSince the main topic of the paper is the directional characteristic of musical instruments thefollowing part will give basics about this thematic. For the sound of an instrument or even oforchestras sound radiation and the effect of the room is a significant criterion and like othersound sources musical instruments have a more or less pronounced directional dependence ofsound radiation. It varies significantly depending on the frequency spectrum. The simplestcase is a spheric source radiation when sound is expanded in all directions equally. Usually,this case will occur if the sound source is a "breathing sphere" or it is small in comparisonto the radiated wavelength. This occurs at low frequencies besides the constant radiationremains virtually unaffected. In the case of higher frequencies the directional characteristic isnon-linear and is affected by numerous influences like the position of the player, the directionof the bell, the acoustical consistence of the instrument, etcetera. [6][9].In Figure 2.2 the omnidirectional sound radiation for individual frequency regions of some

brass wind instruments is given. This measurements were taken by the German acousticianJürgen Meyer [6]. The spheric radiation depends much on the form of structure and thedimension of the individual bells so long as the bell is the transducer. For instance, the bellof a Tuba is relatively wide in comparison to that of a Trumpet. So a Tuba spreads soundomnidirectional at lower frequencies (about 30 Hz up to 90 Hz) instead of a Trumpet (about180 Hz up to 500 Hz).

French hornTrumpetTromboneTuba

Frequency20 50 100 200 500 2000 Hz 10000

Figure 2.2.: Spheric sound radiation of brass instruments by Meyer [6].

In 1970, Meyer and Wogram measured and documented the directional characteristic ofTrumpets, Trombones, and Tubas and publicised the results [10]. It turned out that it isnecessary to define those angular regions for which the sound level does not sink by morethan 3 dB or more than 10 dB respectively below the directed maxima. The 3 dB limitdescribes the half width. This is the difference where the sound intensity is just half the

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value related to the maximum. For simplification sound pressure above the 3 dB limit wassupposed as quasi equal. Otherwise a level difference of 10 dB is perceived as approximatelyone-half the loudness. Figure 2.3 illustrates the directional characteristic of a Tuba withinthe 3 dB limit. As it can be seen, the effective radiation angle will narrow if the frequencyraises.

Figure 2.3.: Main radiation area (0 to -3 dB) of a Tuba by Meyer [10].

Finally, a quantity called the statistical directivity factor is important for room acousti-cal considerations. It represents a relationship between sound pressures actually present, tothose which would be caused by a sound source of equal total power with omnidirectionalcharacteristics at the same distance. The statistical directivity factor can be given in depen-dence on direction: Values larger than 1 indicate directions with, on the average, strongerradiation; values less than 1 indicate directions of below average radiation. For example,an ideal dipole reaches a value of approximately 1.7 in the direction of strongest radiation.On the boundary of the 3 dB region, the statistical directivity factor drops to 0.7; on theboundary of the 10 dB region, to 0.3 of the maximum value. For sound level considerationsit is advantageous to convert the statistical directivity factor to a dB value. The quantityis designated as “directivity index.” It specifies how much the sound level is higher in thedirection considered than it would be for an omni-directionally radiating sound source ofequal power [6].

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3. Technical Implementation of theAutomated Acquisition System

To implement the automated measuring system some technical devices have to be realized.On the one hand there must be the acoustical measuring system in terms of probe micro-phones and a special exciter for the brass instrument. On the other hand there should bea device which is able to rotate the device-under-test without human supervision. This isenforced by the fact that measurements are made in a quasi anechoic chamber where noone can enter during the process. As carrier a motor-driven turntable is a possibility. Inthis case a massive turntable was equipped with step-motors. Lastly, the storage and theprocessing of measured data and the control of the turntable and its step-motors have tobe combined externally outside the chamber by a computing system. Here a Personal Com-puter (PC ) with LabVIEW from National Instruments was used [11]. LabVIEW stands for"Laboratory Virtual Instrumentation Engineering Workbench" and is a software ideal for anymeasurement or control system. With it, the PC is capable of communicating with the Step-Motor-Control (SMC ), executing the acoustical measurements and processing the acquiredinformation with this feature.

3.1. Turntable-System with Step-MotorsFor this project a existing turntable was chosen for modification. It consists of a hugebearing ring of a semi-trailer coupling with a diameter of about 65 cm which was attachedon a heavy metal-frame. The actual table board can be placed on the bearing ring by fourscrews, however, other installations can be mounted on the bearing ring too. For instance, astable construction with a Tuba to be measured is shown in Figure 3.1. This build-up wasmade of a flexible assembly kit with mounting rails. It was the final mechanical set-up forthe acoustical acquirement of Tubas.

3.1.1. Mechanical DesignFor automatic motion it is necessary to install at least one motor onto the turntable con-struction. To ensure conformity between required effort and engine performance the tensileforce was measured at the outer edge of the bearing ring with a spring balance. It turnedout that the mean force was at about 200 Newton, however, the top force was measured atabout 400 Newton at some points of the wheel. This can be explained that the semi-trailer’scoupling ring is not ideal and possesses higher friction losses at several points. Multipliedwith the radius of the ring (33 cm) the resulting maximum load torque amounts 132 Newton-meter (Nm). Therefore, the selected motor must meet this criterion, so that the platformcan rotate smoothly. A few stepper motors with a nominal holding torque of 44 Ncm (equalto 0.44 Nm) were available at the institute. It should be mentioned that the holding torquenearly corresponds to the driving torque at lower stepper frequencies. Since comparing these

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CHAPTER 3. TECHNICAL IMPLEMENTATION OF THE AUTOMATED ACQUISITION SYSTEM

Figure 3.1.: Turntable system with a stable construction for fixing a Tuba.

torques results in a high discrepancy, a convenient power transmission had to be found. Forthis use a nearly 1:300 gear reduction was calculated by dividing load torque by the motortorque. A geared belt drive was chosen to achieve the required power transmission.Figure 3.2 hypothetically shows an example of a gear belt drive which connects the bearingring on the turntable-construction with a toothed belt wheel placed on the axis of the step-per. With 12 teeth and a belt pitch of 5 mm the belt wheel has a perimeter of 60 mm. Thisleads to a radius of 9.549 mm. It was possible to attach a timing band with 411 teeth anda length of 2055 mm onto the edge of the semi-trailer’s bearing ring. So a provisional "beltpulley" was created with a radius of about 327.063 mm since the complete diameter of theturning ring is 654 mm.

motor belt disc

bearing

toothed belt

ring327mm

9.5 mm

Figure 3.2.: Example of a gear belt drive with a reduction of about 1:35.

As a result of this, the Gear Ratio (GR) which is also known as mechanical advantage, canbe calculated where the input belt wheel has radius ri and the output belt wheel has radiusro, or rather the number of output teeth (No) is divided by number of input cogs (Ni):

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GR = ωi

ωo= ro

ri= No

Ni,

⇒ GR = 327.063 mm9.549 mm = 34.251,

⇒ GR = 41112 = 34.25. (3.1)

As it can be seen in Equation 3.1 the resulting mechanical advantage (GR = 1 : 34.25) istoo less to drive the turntable’s bearing. Furthermore, the gear will not be able to stabilizethe system if the motor is turned off. For that reason, another gearing mechanism had tobe combined with the pre-designed system. In this case, a worm gear for further reductionwas selected. The self-locking feature and the property of achieving a high gear transmissionratio are few advantages of worm gears. For this use, a worm with a module of 1.0 waspurchased. A module of 1.0 signifies dimension of a cog. The more force is applied on thecogs the higher should be their module. Since the worm is a special form of a helical gear theangle of the helical toothing is defined by the winds around the wheel axle. The cog/tooth isreferred to in this case as a gear or a start. One start indicates that one rotation of the wormscrew will rotate the worm wheel by one cog. A higher gear/start stands for a faster turnand vice versa. To complete the worm gear an adapted worm wheel had to be combined.Here, one with 20 teeth and a hub diameter of 23 mm was used. Comparing the amount ofteeth of the worm wheel (Nwheel) with the starts of the worm (Nworm) will lead to the geartransmission ratio:

GR = Nwheel

Nworm, (3.2)

⇒ GR = 202 = 10.

Equation 3.2 depicts that the mechanical advantage of the planned worm gear accomplishesa ratio of 1:10. So the worm gear and the belt drive were united and finally, the collectivegear ratio reached a reduction of 1:350. Of course, this was only a ideal result because frictionlosses of the advanced gearing mechanism derogated the transmission.

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step-motor

worm

bearingrin

g

step-motor

worm wheel

fixture

driving-wheel

bearingrin

g

Figure 3.3.: Principle of the designed gearing mechanism. Left: ground plan, right: sheerplan.

The principal composition of the gear unit is charted in Figure 3.3. This graph shows howthe torque is transmitted from the step motor to the terminal turntable ring in ground planon the left side. First, the force is transported over the motor shaft to the worm. After this,it is converted 1:10 to the connected worm wheel thereafter, over an axis the power is finallytransferred to the turntable’s gearing ring by the driving wheel. This last transmission hada ratio of 1:35. Thereby the direct transmission ratio of 1:350 can be calculated by simplymultiplying. In order to complete, the sheer plan of the gear mechanism is on the right sideof Figure 3.3. It also shows the transmission of power from the step motor with its wormgear, via worm wheel and the connected axis, to the closing driving wheel connected withthe bearing ring. Lastly, there is an image of the worm and belt combined gear in Figure 3.4.

Figure 3.4.: Picture of the final used gearing mechanism.

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As aforementioned, the bearing ring of the semi-trailer’s coupling ring is not ideal and sothe outer edge of it is not circular because of the simple reason that such rings do not haveto be ideal for their actually defined use. That was a reason to deal with. To compensatethese unevenness of the ring the motor was not fixed stable onto the mounted driving beltinstead, it was pulled against the edge by a spring. However, this fixture raised a problem sothat the engine would block if the spring was too tight. But when the spring was too loose,the drive wheel would lift off the guide belt and loss of degrees would be a negative effect.So it was decided that an additional motor should reinforce the existing engine. The totaltorque was doubled and the stepping losses were compensated by the mutual engagement ofboth engines.The translated torque of both engines (2 ∗ 0.44 Nm = 0.88 Nm) on the driving belt

of the ring is now 308 Nm (0.88 Nm ∗ 350) which conforms the required expenditure ofenergy (about 132 Nm) more than enough. It has to be taken into account that the angularvelocity of the turntable system is slowed by the reduction of a factor of 350 (cf. Formulaof gear ratio with ωi as motor velocity and ωo as output velocity in Equation 3.1). Thatleads to increasing the rotational speed of both motors simultaneously to balance the velocitydecrease. As mentioned above, increasing the stepper frequency leads to lowering the stepmotor torque. In addition, unbalanced load could destabilise the system and induce disparateforce actions on the bearing. That would require a higher torque of the gear and accordinglyof the step motors. After all, it is of use to have a overpowered system which can deal withpossible force problems.

3.1.2. Electrical ParametersThis part concerns with the electrical parameters of the step motors, mounted on the me-chanical part as described before. Since the gear mechanism has been already calculatedand so the required motor torque is known, two convenient step motors can be selected. Forthis set-up two step motors from RS-Components [12] were taken. Table 3.1 shows severalattributes of the motors.

Specification ValueModel 535-0401Step Angle 0.9

Rated Voltage 2.8 VCurrent / Phase 1.68 AResistance / Phase 1.65 ΩHolding Torque 0.44 NmNumber Of Leads 4 (corresponds to a bipolar

stepper motor with 2 coils)

Table 3.1.: Specifications of the selected step motors [12].

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Since the step angle is 0.9 degrees, the engine needs 400 steps for a full turn. With thatspecification and the known gear reduction, the number of steps for one full rotation of theturntable can be calculated. The following breakdown will analyse how often the engine hasto turn for one revolution:

1 worm rotation = 400 motor steps (3.3)⇒1 worm wheel rotation = 1 belt pulley turn = 10 worm rotations = 4000 motor steps⇒1 turntable rotation = 34.25 belt pulley turns = 137000 motor steps

Moreover, other specifications of Table 3.1 are needed for mechanical, like holding torque,or electronic design like phase current, rated voltage, etc. The electronic regulation of theengines is handled by the step motor controller which will be described in the next section.

3.2. Step Motor Control - SMCThe Step Motor Control (SMC ) - Unit is responsible for the automatic process of regulatingthe step motor drive. The unit has following tasks to do:

• Controlling the two stepper motors by stimulating convenient signals.

• Communicating with the supervising processor unit over a serial interface.

• Monitoring, whether step losses and accordingly degree losses would occur.

• Providing a manual control of the turntable with buttons and a seven-segment display.

• Managing the power for all integrated components.

As micro-controller a Arduino Mini - Board(rev5) [13] was applied for controlling all tasksthe SMC have to do. It is a small micro-controller board assembled with an ATmega328 [14],intended for use on breadboards. Since the whole acquisition concept is a research project,in addition, that such board is relatively cost-efficient, the Arduino Mini seems to be themost adequate solution for this cause. Subsequently, further important properties of themicro-controller board which are of value for the project’s purpose, should be mentioned inTable 3.2.The features in Table 3.2 conform to the requirements of the five predetermined tasks.

Another advantage of the Arduino concept is that there are several predefined function li-braries which simplifies implementing the SMC-software. The individual use of the Arduino’sfunctions will be explained subsequently. Since there are five tasks to describe, they will beseparated in equivalent sections. A picture of the assembled SMC board is shown in Ap-pendix A and the schematic is in Appendix B.

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FeatureMicro-controller ATmega328Crystal Oscillator 16 MHzOperating Voltage 5 VDigital I/O Pins 14 (of which 6 provide

Pulse Width Modulation(PWM) output)Analogue Input Pins 8DC Current per I/O Pin 40 mAFlash Memory 32 KB (of which 2 KB used by bootloader)Programming Per Serial Programming over

USB-to-Serial adapter or RS232Program Memory/ 2 KBStatic Random Access Memory(SRAM)Additional Features Two available Timers,

one Serial Interface,several Bus-Systems likeSerial Programming Interface(SPI),etc. . .

Table 3.2.: Characteristics of the Arduino Mini Board [13].

3.2.1. Stepper Motor Driver CarrierStimulating the two step motors was realised by choosing applicable driver elements. Forthe SMC two A4988 Stepper Motor Driver Carrier from Pololu Robotics and Electronics [15]were selected. The driver board features adjustable current limiting, over-current and over-temperature protection, and five different micro-step resolutions (down to 1/16-step). Sincea high gear reduction is applied, there is no use of micro-stepping and only the full-step modeshould be executed. It operates from 8 – 35 V and can deliver up to approximately 1 Ampereper phase without a heat sink or forced air flow, or 2 Ampere per coil with sufficient additionalcooling. Compared to the required current per phase of one step motor in Section 3.1.2 it isdistinct that the motor driver should be able to supply the engine decently but only with aheat sink. For controlling both drivers three signals are needed at least.Figure 3.5 illustrates the connection of these signals which lead to the stepper driver.

They are responsible for activating the driver (ENABLE), determining the rotating direction(DIR), and specifying the stepper clock (STEP). Additionally, the inputs MS1, MS2, MS3,RESET, and SLEEP are not actively driven, nevertheless, they should be connected withlogic voltages. Since the driver should work in full-step mode the three MSx inputs have tobe held at Ground(GND) level. Instead of that the inputs RESET and SLEEP (which hasa similar function as ENABLE) have to be driven at the HIGH level voltage (VDD) becausethey are LOW-level-sensitive.Finally, the power supply is shown in Figure 3.5 too. There are two ways of supplying

the driver. First, the logic unit has to be connected to GND and a logic level which is equalto the incoming logic HIGH level (VDD is nominal 3 - 5.5 V). Second, the power converterneeds more power so the input voltage can reach from 8 V up to 35 V. The reason for thisis that the converter operates as a fixed current regulator where the current limit is adapted

13


VMOTGND2B2A1A1BVDDGND

A4988

motor power supply(8-35 V)

ENABLEMS1MS2MS3

RESETSLEEPSTEP

DIR

VDD

microcontroller

GND

logic power supply(3-5.5 V)

Figure 3.5.: Wiring diagram for connecting a micro-controller to an A4988 stepper motordriver carrier [15].

by a reference potentiometer. So the motor voltage only determines how fast the current willraise in a coil until the current limit is reached. Therefore the rated voltage of the steppermotor (see Section 3.1.2) takes no effect on this application because the given voltage ratingis just that voltage at which each coil draws the rated current.How the stepper motor driver was supplied will be described in the Power Management

Section 3.2.5.

3.2.2. Communication over Serial InterfaceThe SMC applies the Electronic Industries Alliance (EIA) standard RS-232 as serial interface.It is a simple and often used standard because only one signal line per transmitting directionis needed. Additionally, the RS-232 cable is equipped with a screen against electromagneticinterference. Although it is replaced more and more by Universal Serial Bus (USB), it hasproved that RS-232 is more practical and cheaper for this cause. Also the total length of theUSB cable is limited by maximal 5 m. As the turntable system and the control computercan be located in distances of up to 12 m, simple RS-232 comunication can be done withless effort. Another reason is that the ATmega328 has no USB terminal but still includes aUniversal Asynchronous Receiver Transmitter (UART ) interface [14] which is compatible tothe RS-232 standard. Converting USB to UART would require a Future-Technology-Devices-International (FTDI ) - chip which is relative pricey due to its complexity, and must havea complex peripheral circuit additionally. RS-232 needs only a simple MAX232 chip whichtransforms the 0 to 5 V logic level to a ±7 V output voltage and vice versa. Another reason isthat the Arduino Mini Board including a convenient boot-loader can be programmed over theserial interface [13]. Because USB-to-Serial adapters are cheaply purchasable, the problemof the absence of serial ports on contemporary PCs can be easily solved.As main function the serial communication has to exchange several instructions from and

to the supervising computer. Since the turntable with its control stands in an anechoic room

14


where the door is completely locked during the measuring process, the monitoring PC islocated outside this room. This allows laboratory personnel checking and controlling theprogress. For this communication serial lines with adapted ports already exists between in-and outside of the anechoic room because a digital radio link could produce unwanted signals.To universalise, the communication was defined in a protocol. Table 3.3 shows the com-

munication protocol with all instructions, messages, and errors the SMC has to deal with.

TransmittingCommand DescriptionRxxx moves the turntable about xxx degrees to the right

(higher than 360 will return a value-error).Lxxx moves the turntable about xxx degrees to the left

(higher than 360 will return a value-error).ON turns both step motors on (default: on).OFF turns both step motors off.INIT initialise the SMC again.CALI allows to re-calibrate the turntable manually.OK confirms executed settings (used for continuing after calibration).RST resets the degree count.CNT returns the current degree count.CONT continues the SMC program after an occurred failure with error message.

ReceivingMessage DescriptionACKxxx is Acknowledge of last sent command.Cxxx passes the current degree count.END signals that the end position have been reached.RDY signals that the SMC is ready for new commands.OFF signals that the motors are still turned off.WAIT signals that the SMC is busy.

FailuresMessage DescriptionECOM ERROR! Unusual command.EVAL ERROR! Value of degrees is <0 or >360.ESTEP ERROR! Steps have been lost.EEMER ERROR! Case of emergency has occured.

Table 3.3.: Communication protocol between SMC and the supervising computer.

15


3.2.3. Step Losses DetectionAlthough engine and gear were developed so that the turntable should also carry heavierloads, nevertheless step losses could occur. This could happen when the table is blocked bysomething. For instance, the load could be placed to unbalanced, or a solid obstacle like afixed microphone stand would block continued rotation. In this case, the step motors willstop turning immediately because they need a momentum after acceleration otherwise themagnetic field will circuit around the rotor. Under load, the slipping field will not be ablefor setting the rotor back into motion. This happens because the frequency of the steppermotor relative to the rotor inertia is too high and would require an acceleration again. Sincethis is a fatal failure, it must be avoided by a automatic watchdog unit. Such a monitoringsystem is simply realised by checking whether one motor revolution is equal to its neededsteps. Every completed turn, a magnet mounted on one rotor raises an electric impulse in aHall sensor. This impulse triggers a binary signal in a Schmitt trigger and consequently, itraises an external interrupt in the micro-controller. The interrupt routine handles the flagby checking count of steps. If the count (c0) is lower than the previous count (c−1) −steps for one rotation (∆st) (the steps are decremented!), the running program sequencewill be suspended and an error will be raised (see Table 3.3), or else, the program will becontinued immediately.Since the gear mechanism (especially the worm gear) has a backlash, it should be tolerated

in the step losses detection. So a tolerance factor (tol) should be added to the condition above.Thereby an equation of condition can be set up:

c0 < c−1 −∆st+ tol −→ suspending running program. (3.4)

One rotation of the turntable has 137,000 motor steps as known from Equation 3.3. Con-sequently, one degree is natural a 360th of it, namely 380.5 steps. Since one revolution has400 steps, the tolerance could take a value of a full turn for example, which would detectstep losses approximately greater than one degree. This helps to identify where the failurehas occurred at a accuracy of nearly one degree.

3.2.4. Manual ControlFurthermore the SMC should provide a manual control due to the fact that calibrating thesystem from outside the anechoic room is counterproductive. Therefore several push but-tons and a seven-segment display with four segments were added. In calibration mode thebuttons help moving the turntable. There are two buttons for the direction of rotation(BLEFT/BRIGHT ) and one for confirming the conclusion of the setting (BOK ). Addition-ally, the reset pin of the micro-controller was connected to an external button for eventualrestarts. Finally, a stop button (BSTOP) for emergency cases was implemented. The pushbuttons are realised as active LOW buttons.The display shows the actual direction of motion (L/R at first segment) and the position

related to the origin in degrees. When an error occurs, it will display continuous lettering with("ERROR AT xxx"). During initialisation where the turntable rotates towards its origin,the seven-segments will write ("INIT"). In the end, the display will shut down simultaneouswith the stepper motors if it is desired, before it will show ("OFF") for a second. Vice versa,the display will show ("ON") and turn on instead. Controlling the seven-segment displayhave been realised by the MAX7221CNG from Maxim [16] which is an Integrated Circuit

16


(IC ) for driving seven-segment displays up to 8 digits. Its registers can be manipulated bya serial bus like SPI which the operating micro-controller provides.

3.2.5. Power ManagementThe load supply voltage which is used for generating the motor output current, has a rangefrom at least 8 V up to 35 V. The second voltage level is at 5 V because all used ICsare Complementary Metal-Oxide-Semiconductor (CMOS). Only the micro-controller has anintegrated voltage regulator which is able converting an input voltage range of 7 to 9 V downto a level of 5 V. However, the power does not suffice for all 5V-Logic-ICs which summarisedare the seven-segment driver, the logic part of the stepper motor driver, MAX232, and theSchmitt triggers for the Hall sensors.So the idea was to implement an extra fixed voltage regulator which is able to sustain

an input voltage of up to 35 V (since the stepper motor driver can be supplied with 35V), and delivers enough power for all devices. For this reason, a LM7805 was chosen. Itis a 3-Terminal Positive Voltage Regulator with a stable output of 5 V, and provides 1 Aoutput current [17]. With an absolute maximum rated input voltage of 35 V, it should notpose a problem if the device was driven at recommended 25 V. This would also convenientlyfit the input range of the stepper motor driver’s power part. Figure 3.6 shows the powermanagement constellation with all involved devices.

25 V / max. 35 V

Stepper Motor Driver2x

Load Supply Voltage

Logic Supply Voltage

LM7805

5 V7 seg. driver

MAX232 Schmitt Trigger

Others likePullup Resistor

Figure 3.6.: Power Management Principle.

Conducting the 25 V supply input of SMC to a laboratory power supply was implementedover a Cannon X Lockable and Rubber insulated connection (commonly known as XLRconnector). Conventionally, it is most commonly associated with balanced audio intercon-nection. Since the anechoic chamber has several ports connecting in- and outside, a coupleof XLR connectors for audio application like connecting microphones or loudspeaker, havebeen implemented too. One of these was used for supplying the SMC. A crafted XLR cablewas connected with a laboratory power supply with high voltage on Plus lead and groundlevel on GND lead. The inverted Minus lead and the screen shield was not connected. Thepower input connector on the SMC is already a compatible XLR linkage.

17


3.3. High Air Pressure Artificial Mouth - HAPAMFor oscillating the air column in the tube of brass wind instruments a convenient stimulationsystem is required. Therefore, a loudspeaker had to be adapted for this use. Since Tubaswith an immense volume of air should be measured, a low frequency speaker with a ratedoutput power of 50 Watt from RS-Components was chosen. It has an impedance of 8 Ohmand a diameter of 5.25 Inch. This large-dimensioned speaker was covered in a box made ofplywood. A circle of the size of the membrane was cut out of the front plate besides a holedplastic cone was placed over the hole in order to focus the sound energy. The mouthpieceof the brass instrument could be mounted with clips, and between both parts a rubberring was placed for tightening. Additionally, a probe microphone which serves as reference,was integrated in the plastic cone as near as possible to the mouthpiece plane. It is a 1/8Inch pressure microphone (type: 40DP) from G.R.A.S. which has a linear frequency range(±1 dB) from 10 Hz up to 30 kHz [18]. Finally, to make this box sound-proof it was filledbehind the membrane with foam plastics. Figure 3.7 shows the completed HAPAM box inblue.

Figure 3.7.: High Air Pressure Artificial Mouth mounted on a Tuba.

18


3.4. Final Measurement Set-UpFinally, all listed devices above were composed to the final acquisition and measurementset-up. This included the turntable construction with two stepper motors and gear, the Step-Motor-Control device, the HAPAM excitation tool with an included reference microphone, anadditional probe microphone for measuring the directed sound pressure, several laboratorydevices like power supply and mic pre-amplifier, and lastly the musical instrument undertest. Figure 3.8 pictures the final measurement set-up with all involved components.

Doo

r

Anechoic Chamber

Probe M

ic HAPA

M

Term

inal

Step Motor

SMCPo

rt

Figure 3.8.: Finale Test Set-up.

A ROGA RG-50 ICP R© 1/4 Inch probe microphone [19] is placed in front of the musicalinstrument to be rotated and measured. It has a linear frequency response (±1 dB) from30 Hz up to 4 kHz. Since lower frequencies should be measured too, it should be refereedto the fact that the microphone has an accuracy of ±1.5 dB down to 4 Hz. It is connectedwith the suitable PCB Series 440 sensor signal conditioner [20] with gain of 1x, 10x, 100x.The G.R.A.S. microphone which interacts as reference in the excitation device HAPAM, isconnected with a BSWA Tech Co. MC702 pre-amplifier. Both pre-amplifiers were connectedwith a port which is linked with a 19 Inch rack terminal tower outside the chamber. This portprovides several terminal points like Bayonet Neill Concelman (BNC )-, cinch-, phone jacks,RS-232-, and XLR-connectors. Consequently, the input signal for HAPAM’s loudspeakeris provided over the port too. That signal is amplified by Orion Profi Mosfet Amplifierfrom Zoffmusic. Next, a converted XLR connector supplies the SMC with power besides thecommunication is realised over a RS-232 link. Finally, all described functions routed by therack tower are connected with the Data Acquisition Input/Output (DAQ I/O) interface cardfrom vendor National Instruments which is compatible to LabVIEW.

19


3.5. Supervising Computer Program with LabVIEWControlling the rotation of the step motor controller and conducting the measurements wereapplied by a program based on designing software LabVIEW [11]. The cycle of the acquisitioncan be divided in several parts. First of all, a top layer sequence can be defined. This leveldescribes functions from the initialisation to the conclusion of the measured data abstractly.It can be said that the top layer also provides information about the process of the SMC’smicro-controller program by the reason that both program cycles work synchronously. Thesecond layer describes one acoustical measurement at a given position of degrees. It isencapsulated in the top layer between approaching of the desired positions of the turntable.It will be applied while the end position has not been achieved. The third and last one isthe data processing layer which computes all acquired information. It is also part of the toplayer but it only will be executed as the final procedure.

3.5.1. Top Layer ArchitectureThe main program starts with a initialization process where the turntable is driven to theorigin point. It will rotate counter-clockwise until a Hall sensor triggers an impulse. Ad-ditionally, settings (duration of a measurement, frequency range, number of angles, etc. . . )for LabVIEW can be done. After that process has finished, in addition, the turntable canbe calibrated precisely. This could happen either by operating the push buttons on SMCor by sending drive commands over the serial interface. Then the actual acquisition of thesound pattern begins. At zero degree the first measuring starts. It is a acoustical transferresponse measurement where the output sound pressure of the instrument is set in relationto the input sound pressure caught inside the mouthpiece’s cup. After then the turntablewill rotate to its next position and a further measuring will begin. This will be repeated aslong as the preselected end position will be reached. At that end the analysis of data willstart and the result will be plotted. The flow-chart of this sequence is plotted in Figure 3.9.

Initialisation Calibration FirstMeasurement

Is end positionreached?

Drive turntablewith commandRxxx degrees

Wait until RDYis received Measuring

No

Send Calib OK

Postprocessthe gathered

data

End

Start

Yes

Origin reached,Settings completed

Figure 3.9.: Top layer flow-chart of the turntable program.

3.5.2. Measuring LayerThe heart of the acquisition system is the acoustical measurement of the musical instrument.It will be applied when the turntable is brought into a desired position. For example, if the

20


difference between the individual angles is 10 degrees and a full turn should be executed,the gathering of acoustic information will be applied 36 times. For this use, the musicalinstrument to be measured is oscillated by a logarithmic sine sweep which was outputtedover the Data Acquisition Output (DAQout) interface prepared by LabVIEW. That sweep isdefined by the pre-settings which consist of frequency range, measuring duration, samplingrate and sampling buffer size (which defines how long a signal at a given frequency willbe analysed). Usually, the sampling rate in this LabVIEW program was at 50000 samplesper second and the buffer had a size of 5000 samples. This means that ten analysis persecond could be managed. One analysis considers one frequency step. In connection withthe duration which was 180 seconds by default, there were examined 1800 frequency steps perone complete measurement. These steps were logarithmically interpolated over the selectedfrequency range. Consequently, the output sine sweep was generated thereby, because themagnitude were held on a constant level.Then the actual measuring happened. The DAQ input device gathered two microphone

signals where one was firmly placed in the anechoic room which should acquire the relativesound radiation at different angles. Another one was put into the HAPAM’s cavity as nearas possible to the mouth piece plain as reference. Since the measuring is a transfer responseanalysis, both input signals were compared in LabVIEW. First, the signals were put into aninput buffer where a Discrete Fourier Transformation (DFT ) analysed them. After that sin-gle tone information per channel with maximum magnitude were extracted. This simplifiedfurther calculation because only one magnitude per channel was considered. Calculating thetransfer response was realised by dividing output by input where the corresponding frequencywas determined by the strongest signal. The result was recorded as a special Versatile Instru-ment Analysis System (VIAS) file which is commonly used on the institute. Additionally,the phase, the real and imaginary part were calculated for the file. The frequency responsewas also plotted on a display window of the LabVIEW panel which is shown in AppendixC. For post-processing both input signals were put in storage as WAVE file. The currentdirection in degrees was integrated in the names of both files. For simplicity the schematicFigure 3.10 should explain this topic pictorially.

Calculatingfrequency steps

Settings

Generatingoutput

HAPAM

Audio Input

Reference Output

ProbeMic

Catchinginput DFT

ExtractingSingle ToneInformation

WAVEfile

T (f) = OutputInput

VIASfile

LabVIEWGraph Panel

Figure 3.10.: Block diagram of the measurement cycle.

21


3.5.3. Data Processing LayerAfter all directions of radiation have been acquired, this information should be transformedinto a graphical interpretation. For this an additional LabVIEW subroutine was imple-mented. The latest version was able to either reading out VIAS files or analysing the transferresponse of convenient WAVE files including input and output channel. When all amplituderesponses over the entirely available frequency range for all radiation direction were collected,the obtained curves were normalized by the zero degree directed characteristic. This is thedirection with the maximum sound pressure level because it is located directly in front of theinstrument’s bell. The normalisation was achieved by multiplying the individual curves withthe inverse of the zero-degree curve. The result for the zero-degree curve itself was a straightline at 0 decibel. All other curves were relatives to the zero-degree direction consequently.But the existing information was still too complex to create a clearly arranged diagram. Soall amplitude/frequency characteristics were separated in several frequency divisions whichcould be defined manually. The arithmetic mean was formed over the individual sub-divisionsto give a pointed value for it. Composing the same frequency divisions over all directionsin a circle completes one curve. For that reason, there are so many circles as frequencyclassification in the composed polar diagram. The scale of that polar diagram began at theouter boundary and went toward the centre by attenuation steps of 3 dB. An amplificationin relation to the frontal directed sound radiation for Trumpets, Trombones, and Tubas willnot occur commonly [10]. The advantage of that form of diagram is that a sound attenuationgraph in all directions can be drawn where Meyer’s differentiated -3 dB and -10 dB areascould be red out too. For documentation a directional characteristic graph can be exportedas a Scripted Vector Graphic (SVG).Examples of directional sound patterns are shown after measuring of two Tubas in Chapter 4.

22

4. Acoustical Measurements and Acquisitionof the Directional Sound Pattern

This chapter documents the different measurements which were applied in the course of thebachelor project. As test subjects two Tubas of different fundamental tone were consideredfor comparison. The attributes of these instruments shall be listed in Table 4.1:

Contrabass Tuba in B[Model Cerveny, Czechoslovakia, BB[-Tuba CBB 681Pedal tone B0 (29.13 Hz)Tuning pitch B1 (58.26 Hz)Bell mouth diameter 400 mmBore diameter 20.2 mmWeight 9000 gUnwound length of the brass tube about 5.8 mValves 4

Bass Tuba in FModel Gebr. Alexander Mainz, Germany, F-Tuba Modell 157Pedal tone F1 (43.65 Hz)Tuning pitch F2 (87.31 Hz)Bell mouth diameter 380 mmBore diameter 18.5 mmUnwound length of the brass tube about 4 mValves 6

Table 4.1.: Characteristics of two analysed Tubas.

Comparing both instruments shows that their pedal frequencies are different. This shouldnot affect the directional characteristic since Meyer said that the frequency dependence of thesound pattern is independent of the pitch played [9]. Only the input impedance of the Tubasis different. In the matter of omnidirectional sound radiation there should not be disparitybecause the source of sound (the bell) is quasi equal for both objects (narrow difference of 2cm).In course of this chapter three types of measurements will be described. There will be the

input impedance and transfer response analysis of both instruments. The acquired directionalsound pattern will be shown finally.

23

CHAPTER 4. ACOUSTICAL MEASUREMENTS AND ACQUISITION OF THE DIRECTIONALSOUND PATTERN

4.1. Input Impedance

0

5

10

15

20

25

30

35MOhm

0 100 200 300 400 500 600 700 800 900 1000

Hz

Bb0

Bb1

F2

Bb2

D3F3

Ab3Bb3

C4

D4

E4 F4G4

Ab4A4Bb4

Figure 4.1.: Input Impedance of the Contrabass Tuba in B[.

Figure 4.1 shows the input impedance of the Cerveny B[-Tuba. The measurement weretaken by IWK’s tool named Brass Instrument Analysing System (BIAS) [1]. The non-logarithmic frequency axis ranges from 0 Hz up to 1 kHz. The vertical axis is the magnitudeof the impedance in Mega Ohms (MOhm). The dark-blue curve’s peaks are the resonancesof the air column in the Tuba and equals the natural tones (without a valve is pressed). Forcomparison the advanced orange curve represents the resultant resonances when the scale isdecreased by a tempered whole tone. This is implemented by pushing the first valve. Thename of notes of the natural tones are printed into the graph. In order to simplify, the namesfor the orange curve are not displayed. For the sake of completeness their names are Ab0 -Ab1 - Eb2 - Ab2 - C3 - Eb3 - F]3 - Ab3 - B[3 - C4 - D4 - Eb4 - E4 - F]4 - G4 - Ab4 - A4 - B[4.According to the impedance measurement it should be mentioned that the distance betweentwo peaks is always the same, because all harmonics are integer multiples of the fundamentaltone. Only the musical interval between two tones will be smaller from one octave to thenext. The scale in the third octave (indicated by the number 3) is almost completed withthe natural tones and the additional first valve. Furthermore, no valves are required for thefourth octave because the intervals are only a whole-tone step, or only a half-tone at higherfrequencies. It also can be seen, that the tones which would be played with or without thefirst valve pressed, overlap at some points. However, Tuba players perform in the 4th octaveand upwards very rarely because it would need a professional musician passing such difficult

24


passages. How well a sound appeals is evident by the size of the magnitude peaks. Thehigher a peak of a resonance is the better a tone will approach [3].Since there were two Tubas to be measured, their input impedances were compared and

are plotted in Figure 4.2. The contrabass Tuba in B[ is represented by the dark-blue curve,the bass Tuba in F is displayed as orange function. It can be seen that the fundamental toneof the F-Tuba is about 20 Hz higher than that one of the B[-Tuba. However, there are somenatural tones which harmonise on both instruments. That special notes are at several kindsof F most. Only at the F1 the instruments are out of sync. There a peak from the F-Tubais opposed to a tale of the other one. This means that a F1 could never be forced on theB[-Tuba without additional help instead it will sounds well and easily on the Tuba in F.

0

5

10

15

20

25

30

35

40MOhm

0 100 200 300 400 500 600 700 800 900 1000

Hz

F2F3

C4

F4

F1

Figure 4.2.: Comparison of the input impedance of a B[- and F-Tuba.

25


4.2. Transfer ResponseThe Transfer Response relates output sound pressure to input sound pressure. Since thetransfer response is similar to the acoustical admittance of a musical system, it also can beassociated with the input impedance [8]. Further measurements of the directional soundradiation were based on the acquisition of single transfer responses, therefore, it should beexplained succinctly.

10 20 30 50 70 100 200 300 500 700 1000 2000 3000 5000

-20

0

20

56,672

Bb1 -48 [Cent]

-21,747

22,809

Figure 4.3.: Relation between input impedance and transfer response.

Figure 4.3 shows the input impedance (orange) and the transfer response curve (green) ofthe contrabass Tuba in B[ (its tuning pitch B[1 is highlighted with a cursor). In this case thegraph’s vertical axis is dimensionless and represents only proportions in decibel, however, itdoes not matter because the graph should only depict the affinity of both curves. Besidesthe frequency axis is logarithmic that time so higher frequency ranges can be seen. Afteranalysing this figure it should be possible to recognise that one curve could be the reciprocalof the other ones. That does not fit entirely due to that fact that both characteristics weremeasured with different methods. Finally, it can be seen that the transfer response rises athigher frequencies otherwise the impedance falls there. This indicates that the most insertedenergy will be radiated at the output and nothing will be kept inside the tube for establishingan oscillating system. For that reason it is difficult for a Tuba player to perform a tone above400 Hz moreover it is impossible to play above 600 Hz.

26


4.3. The Directional Characteristic of Brass Wind InstrumentsAt last, the paper has come to its final measurement. After the implementation of theaforementioned turntable acquisition system, it was possible to acquire the directional soundpattern ultimately. For that analysis both Tubas were considered. Figure 4.4 illustrates thedirectional radiation of the contrabass Tuba in B[ and that one of the F-Tuba is shown inFigure 4.5.

0dB

-3dB

-6dB

-9dB

-12dB

-15dB

-18dB

2000-3900 Hz1000-2000 Hz500-1000 Hz240-500 Hz120-240 Hz20-120 Hz

Figure 4.4.: Directional Characteristic of the Contrabass Tuba in B[.

As it can be seen, both Tubas radiate omnidirectional between 20 and 120 Hz. This is theregion where the pedal tone and its first harmonics are located. In the chromatic scale thatarea corresponds the first and the second octave (or also known as contra and great octave).The both spheres are little truncated opposite the bell mouth but their magnitudes lie barely

27


0dB

-3dB

-6dB

-9dB

-12dB

-15dB

-18dB

2000-3900 Hz1000-2000 Hz500-1000 Hz240-500 Hz120-240 Hz20-120 Hz

Figure 4.5.: Directional Characteristic of the Bass Tuba in F.

28


below the -3 dB level. According to Meyer [10] such curve of the circle can be accepted asa complete simple sound source at this frequency range. The second range between 120 and250 Hz complies with the third octave which is also called small octave. This range differsto the previous less but it suffices that the curves lies underneath the -3 dB level more andmore. So the instruments cannot be designated as spheric radiator any more. It should bementioned that the difference between the two curves is greater for the B[-Tuba instead ofthat one in F. This can be deduced by the fact that the bell in connection with the diapasonof the F-Tuba are smaller compared to the B[-Tuba.The next circle describes the last playable region (the fourth octave or one-line octave) of

Tubas. It includes the formant frequencies additionally which characterise the sound colourof the Tubas. As it can be seen, this region from 250 up to 500 Hz keeps only above the -3dB limit at a range of about 130 degrees for the Tuba in B[ and about 140 degrees for theF-Tuba. Additionally radiating maxima and minima occurs at several points in both curves.The magnitude decreases underneath the Tubas by about 9 dB. This is why floor reflectionwill not influence the sound. Instead of that ceiling reflection should be considered becausethe most radiated sound is directed against the ceiling vertically. This also applies to higherfrequency components whose radiation is increasingly narrowed to the axis of the bell. Forexample, the 500 − 1000 Hz band is emitted only for a width of main radiation lower than90 degrees for both Tubas. Besides the main radiation field for the 1000 − 2000 Hz range isabout 45 degrees for both Tubas too, but between 2000 and 3900 Hz it is only 30 degrees forthe Tuba in F where the B[-Tuba still achieves 40 degrees.Appointing to Meyer, the -10 dB limit should be also analysed. So it should be mentioned

that this limit is exceeded at frequencies above 500 Hz. Hence, these spectral componentssound laterally and below the instrument at least half as loud as before the bell [10].The reason why higher frequency components should be also considered is that they arise

as overtones when a Tuba is played very loud (ital. fortissimo). This makes the sound colourof the spread tone brighter and more brilliant. If this components are cut off, the instrumentsounds dark and it is not possible achieving differently effective dynamic levels. This happenswhen the narrowed directivity at higher frequencies is neglected. For instance, such problemappears especially with Tubas at open air events since there is no ceiling which could reflectthat overtones in the direction of the audience. But even poorly structured ceilings in concerthalls can absorb these high-frequency components and thereby the Tuba sounds dull [3][10].

29

5. Conclusion

The acquisition of the directional characteristic of the measured Tubas was successful. Thedeveloped set-up fulfilled all requirements. Only during the implementation of the automatedturntable, more attention had to be paid for the mechanical development because the inputtorque of the step motors was too less. This was resolved by designing a convenient gearsystem. The electronic device SMC worked without fatal errors by reason that the micro-controller’s program code was always debugged while the testing phase. The ultimate versionalso handled with predictable errors like step losses, wrong actuation by human error, etc. . . ,and communicated warnings over the serial interface immediately.The acquired results were meaningful and were confirmed by former publications of J.

Meyer [10]. Since the directivity measurements were taken by only one microphone, theresulting diagrams were two-dimensional. But even these diagrams showed impressivelyhow the sound radiates. Besides the directional characteristic could be imagined three-dimensionally by the reason that the radiation were accepted as symmetric around the bellaxis. However, to achieve a truly spatial pattern it would be necessary to design a archequipped with several microphone. Due to the fact that the automated acquisition systemwas extensible, it would be possible creating 3D-plottings in the near future. It was alsodesigned to be universal since the measuring signals were independent of the test object. Onthat account other musical instruments could be proven of their directional characteristicby simply adapting a different excitation mechanism and a different mounting constructrespectively.

30

Bibliography

[1] W. Winkler and G. Widholm, “BIAS - Blas Instrumenten Analyse System,” in 15 JahreInstitut für Wiener Klangstil (1980-1995), E. Melkus, Ed. Wien: Institut für WienerKlangstil, 1996, pp. 95–106.

[2] G. K. Behler and M. Pollow, “Variable Richtcharakteristik mit Dodekaeder-Lautsprechern,” Fortschritte der Akustik, pp. 67–68, 2008.

[3] G. Widholm, Musikalische Akustik 1. Wien: Institut für Wiener Klangstil - Universitätfür Musik und Darstellenede Kunst, 2013.

[4] D. C. Giancoli, Physik. Pearson Deutschland GmbH, 2010.

[5] C. Reuter, “Tonhöhen in Frequenzen umrechnen,” [Visited on 07.05.2014]. [Online].Available: http://homepage.univie.ac.at/christoph.reuter/reuter/pitch1.php

[6] J. Meyer and U. Hansen, Acoustics and the Performance of Music: Manual for Acousti-cians, Audio Engineers, Musicians, Architects and Musical Instrument Makers, 5th ed.Springer Science+Business Media, LLC, 2009.

[7] P. Anglmayer, “Messung der akustischen Eingangsimpedanz von Blechblasinstru-menten,” Master’s thesis, Insitut für Allgemeine Physik, TU Wien & IWK - Universitätfür Musik und Darstellende Kunst Wien, Wien, 2001, betreuer: Univ. Ass. Dr. WilfriedKausel PDF öff JA.

[8] S. Elliott, J. Bowsher, and P. Watkinson, “Input and transfer response of brass windinstruments,” Journal of the Acoustical Society of America (JASA), vol. 72, no. 6, pp.1747–1760, 1982.

[9] J. Meyer, “Musikalische Akustik,” in Handbuch der Audiotechnik. Springer-VerlagBerlin Heidelberg, 2008, pp. 123–180.

[10] J. Meyer and K. Wogram, “Die Richtcharakteristiken von Trompete, Posaune undTuba,” Das Musikinstrument, vol. 19, pp. 171–80, 1970.

[11] “LabVIEW System Design Software,” National Instruments Corporation, 2014.[Online]. Available: http://www.ni.com/labview/

[12] “RS Schrittmotor 0.9deg 2,8V 44Ncm 42mm,” RS Components Handelsges.m.b.H.,Gmünd, AUT, 2014, [Visited on 7.3.2014]. [Online]. Available: http://at.rs-online.com/web/p/products/5350401/

[13] Arduino Mini, Arduino.cc, Italy, 2014, [Visited on 4.3.2014]. [Online]. Available:http://arduino.cc/en/Main/ArduinoBoardMini

31

http://homepage.univie.ac.at/christoph.reuter/reuter/pitch1.php

http://www.ni.com/labview/

http://at.rs-online.com/web/p/products/5350401/

http://at.rs-online.com/web/p/products/5350401/

http://arduino.cc/en/Main/ArduinoBoardMini

Bibliography

[14] “Atmel 8-bit AVR Microcontroller with 32KBytes In-System Programmable Flash- ATmega328P,” Atmel Corporation, San Jose, USA, 2012. [Online]. Available:http://www.atmel.com/Images/doc7810.pdf

[15] A4988 Stepper Motor Driver Carrier, Pololu Corporation, Las Vegas, USA, 2014,[Visited on 4.3.2014]. [Online]. Available: http://www.pololu.com/product/1182

[16] “MAXIM Serially Interfaced, 8-Digit LED Display Drivers - MAX7219/MAX7221,”Maxim Integrated Products Corporation, San Jose, USA, 2003.

[17] “3-Terminal 1 A Positive Voltage Regulator - LM78XX/LM78XXA,” Fairchild Semi-conductor Corporation, 2006.

[18] “G.R.A.S. 40DP 1/8" Ext. Polarized Pressure Microphone,” G.R.A.S. Sound & Vibra-tion, Holte, Denmark, 2014.

[19] “ROGA RG-50,” ROGA-Instruments, Waldalgesheim, Germany, 2014. [Online].Available: http://www.roga-instruments.com/sensors/measure-mic-rg-50/specification.html

[20] “Model 442B104, 4 CHANNEL ICP R© SENSOR SIGNAL CONDITIONER,” PCBPiezotronics Inc., Depew, USA, 2006. [Online]. Available: http://www.pcb.com/contentstore/docs/PCB_Corporate/Electronics/products/Manuals/442C04.pdf

32

http://www.atmel.com/Images/doc7810.pdf

http://www.pololu.com/product/1182

http://www.roga-instruments.com/sensors/measure-mic-rg-50/specification.html

http://www.roga-instruments.com/sensors/measure-mic-rg-50/specification.html

http://www.pcb.com/contentstore/docs/PCB_Corporate/Electronics/products/Manuals/442C04.pdf

http://www.pcb.com/contentstore/docs/PCB_Corporate/Electronics/products/Manuals/442C04.pdf

List of Figures

2.1. Image of a contrabass Tuba in B[ with its elements. . . . . . . . . . . . . . . 32.2. Spheric sound radiation of brass instruments by Meyer. . . . . . . . . . . . . 52.3. Main radiation area of a Tuba . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3.1. Turntable system with a stable construction for fixing a Tuba. . . . . . . . . . 83.2. Example of a gear belt drive with a reduction of about 1:35. . . . . . . . . . . 83.3. Principle of the designed gearing mechanism. . . . . . . . . . . . . . . . . . . 103.4. Picture of the final used gearing mechanism. . . . . . . . . . . . . . . . . . . . 103.5. Wiring diagram for connecting a micro-controller to an A4988 stepper motor

driver carrier. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.6. Power Management Principle. . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.7. High Air Pressure Artificial Mouth mounted on a Tuba. . . . . . . . . . . . . 183.8. Finale Test Set-up. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.9. Top layer flow-chart of the turntable program. . . . . . . . . . . . . . . . . . . 203.10. Block diagram of the measurement cycle. . . . . . . . . . . . . . . . . . . . . 21

4.1. Input Impedance of the Contrabass Tuba in B[. . . . . . . . . . . . . . . . . . 244.2. Comparison of the input impedance of a B[- and F-Tuba. . . . . . . . . . . . 254.3. Relation between input impedance and transfer response. . . . . . . . . . . . 264.4. Directional Characteristic of the Contrabass Tuba in B[. . . . . . . . . . . . . 274.5. Directional Characteristic of the Bass Tuba in F. . . . . . . . . . . . . . . . . 28

33

List of Tables

2.1. Region of formants of several brass wind instruments [6]. . . . . . . . . . . . . 4

3.1. Specifications of the selected step motors. . . . . . . . . . . . . . . . . . . . . 113.2. Characteristics of the Arduino Mini Board. . . . . . . . . . . . . . . . . . . . 133.3. Communication protocol between SMC and the supervising computer. . . . . 15

4.1. Characteristics of two analysed Tubas. . . . . . . . . . . . . . . . . . . . . . . 23

34

List of AbbreviationsBIAS Brass Instrument Analysing SystemBNC Bayonet Neill Concelman

CMOS Complementary Metal-Oxide-SemiconductorDAQ I/O Data Acquisition Input/Output

DFT Discrete Fourier TransformationEIA Electronic Industries Alliance

FTDI Future-Technology-Devices-InternationalGR Gear Ratio

HAPAM High Air Pressure Artificial MouthIC Integrated Circuit

IWK Institut für Wiener KlangstilLabVIEW Laboratory Virtual Instrumentation Engineering Workbench

PC Personal ComputerPWM Pulse Width ModulationSMC Step-Motor-ControlSPI Serial Programming InterfaceSVG Scripted Vector Graphic

UART Universal Asynchronous Receiver TransmitterUSB Universal Serial BusVIAS Versatile Instrument Analysis System

35

A. Assembled Step-Motor-Control (SMC)Stepper

Motor

Driver

with

Heatsink

Push

Buttons

7 Segment Driver

Arduino Mini rev5

MAX232

SchmittTrigger

RS-232Power Supply

Hall Sensors

Input

36

MAXvcb9CNG

ARDUINO_MINI_RJMINI

Af988_STEPPER_MOTOR_DRIVER_CARRIER

CCJYLbbCGKWA

CCJYLbbCGKWA

CCJYLbbCGKWA

CCJYLbbCGKWA

cJk9VD

D

VD

D

GND

GND

Af988_STEPPER_MOTOR_DRIVER_CARRIER

GND

bk

bk

bk

bk

bk

bk

VD

D

VD

D

b$k

VD

D

b$k

b$k

VD

D

VD

D

b$$n

b$$µ

b$k

b$k

GND

SerialµProgrammingGND

VD

D

RE

SE

T

BU

Tb

BU

Tc

GND GND

b$k

b$k

VD

D

VD

DB

UTd

BU

Tf

GND GND

CDvfACbfEEf CDvfACbfEEfCDvfACbfEEf

HA

Lb

HA

Lc

HA

LdGND

VD

D

VD

D

b$$n

b$$µ b$k

VD

D

BU

TJ

GND

b$$n

fkv

fkv

fkv

b$kGND

v8$J

dd$n

GND

3cfV

3cfV

3cfV

b$$n

b$$n

GND

GND

b$$µ

PWR3cfV

MOTc

MOTd

RScdc

GND

bNfb

f8D

OdJ

LvbN

fbf8

DO

dJLv

GND

VD

D

bNfb

f8D

OdJ

LvbN

fbf8

DO

dJLv

GND

VD

D

MAXcdc

bµ

bµ

bµ

bµ

bµ

GND

VD

D

b$$n

VD

D

GND

GN

D ICb

DIGc Y

DIGd v

DIGf d

DIGJ b$

DIGY J

DIGv 8

SEGA bf

SEGB bY

SEGC c$

SEGD cd

SEGE cb

SEGF bJ

SEGG bv

SEGDP cc

DIGb bbDIG$ c

DINb

DOUTcf

LOADbc

CLKbd

ISETb8

GND9GNDfVCCb9

DIOc c

DIOd d

DIOf f

DIOJ J

DIOY Y

DIOv v

DIO8 8

DIO9 9

DIOb$ b$

DIObb bb

DIObc bc

DIObd bd

DIOv_c IOv

A$ bf

Ab bJ

Ac bY

Ad bv

Af b8

AJ b9

AY c$

Av cb

JV_b

JV

9V9V

JV_c

JVc

GN

D_b

GN

D

GN

D_c

GN

Dc

GN

D_d

GN

Dd

GN

D_f

GN

Df

TX_bTX

RX_bRX

TX_cTXc

RX_cRXc

RESET_bRb

RESET_cRc

µCb

JV_d

JVd

VD

DV

DD

VM

OT

VM

OT

ENEN

RSTRST

SLEEPSLP

STEPSTEP

DIRDIR

MSbMSb

MScMSc

MSdMSd

Ab bA

Ac cA

Bb bB

Bc cB

GN

DG

ND

GN

DM

OT

GN

DM

OT

ICc

LEDbGababcdefg DP f

dY

c

dddf COM dc

d

b

dJ

LEDbGacabcdefg DP 9

d$

Y

c8c9 COM db

8

J

v

LEDbGadabcdefg DP bd

cv

bb

cfcJ COM cd

bc

b$

cY

LEDbGafabcdefg DP b8

cb

bJ

b9c$ COM cc

bv

bf

bY

Rb

VD

DV

DD

VM

OT

VM

OT

ENEN

RSTRST

SLEEPSLP

STEPSTEP

DIRDIR

MSbMSb

MScMSc

MSdMSd

Ab bA

Ac cA

Bb bB

Bc cB

GN

DG

ND

GN

DM

OT

GN

DM

OT

ICd

Rc

Rd

Rf

RJ

RY

Rv

R8

R9

Rb$

Cb

Cc

Rbb

Rbc

JPcb cd fJ Y

JPd

bc

JPf

bc

JPJ

bc

Rbd

Rbf

JPY

bc

JPv

bc

Ad Y f

ICfc

AJ Y Y

ICfd

Ab Y c

ICfb

JP8

bcd

JP9

bcd

JPb$

bcd

Cd

Cf

RbJ

JPbb

bc

CJ

RbY

Rbv

Rb8

Rc$

db

c

ICJGND

IN OUT

CY

Cv

C8

C9

JPbbc

JPbcbcdf

JPbdbcdf

Xb

bY cv d8 f9 J

Gb

Gc

Dc

Dd D

fD

J

ICY

Cb3 b

CbL d

Cc3 f

CcL J

TbIN bbTcIN b$

RbOUT bcRcOUT 9

V3c

VLY

TbOUTbfTcOUTvRbINbdRcIN8

Cb$

Cbb

Cbc

Cbd

Cbf

CbJ

GN

DV

CC

ICYP

bYbJ

GND

MOTc_bA

MOTc_bA

MOTc_cA

MOTc_cA

MOTc_bB

MOTc_bB

MOTc_cB

MOTc_cB

RESET

MOTb_bA MOTb_bAMOTb_cA

MOTb_cA

MOTb_bBMOTb_bB

MOTb_cB

MOTb_cB

µC

ARDUINOMINIvJ

3

33

33

3

3

3

B. Schematic of the Turntable’sStep-Motor-Control (SMC)

37

C. LabVIEW-Screenshot of HAPAMv15

38

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