BACHELOR THESIS University of Applied Sciences Technikum Wien, Electronic Engineering
Turntable for an Automatic Acquisition System for Measuring the Directional Characteristic of Musical Instruments
Author: Martin Lahmer Student ID: 1210254005
Academic Supervisor: FH-Prof. Dipl.-Ing. Christian Kollmitzer Company 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 fully acknowledged in the appropriate places with adequate footnotes and citations. Quotations have been properly acknowledged and marked with appropriate punctuation. The works consulted are listed in the bibliography. This paper has not been submitted to another examination panel in the same or a similar form, and has not been published.“
Vienna, June 4, 2014
Place, Date Signatur Abstract
Musical instruments are complex physical systems. This paper deals with the class of brass wind instruments especially the Tuba. Brass instruments are excited by the vibrating lips of the musician and radiates the played tone at the end of the tube via the bell into the acoustic room. How the sound is radiated, is determined by individual characteristics of an musical instrument. One of these attributes is the directivity, which will be considered in greater detail in this work. It defines how the sound is radiated as a function of position and frequency. For this purpose an automatic measuring system was developed which allows stimulating 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 which is 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 radiation of the instruments over a number of frequency bands. This success serves as a basis for further 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 instruments for further purpose.
Keywords: Brass Wind Instruments, Directional Characteristic, Automated Acquisition System, Step Motor driven Turntable, Arduino, LabVIEW Kurzfassung
Musikinstrumente sind komplexe physikalische Systeme. Diese Arbeit beschäftigt sich mit der Klasse der Blechblasinstrumente, speziell der Tuba. Diese werden durch die schwingenden Lippen des Spielers angeregt und am Ende der "Röhre" wird der Ton über den Schalltrichter in den akustischen Raum abgegeben. Wie der Schall abgestrahlt wird, wird durch die in- dividuelle Charakteristik des jeweiligen Musikinstruments bestimmt. Eines dieser Attribute ist deren Richtwirkung, die in dieser Arbeit genauer betrachtet wurde. Sie beschreibt, wie ein Musikinstrument den Schall in Abhängigkeit von Ort und Frequenz abstrahlt. Dafür wurde ein automatisches Messsystem entwickelt, das es ermöglicht ein Blechblasinstrument anzuregen und den abgestrahlten Schalldruck für verschiedene Winkel zu messen. Realisiert wurde dies durch ein automatisierten Drehtischsystem, das per Schrittmotoren angetrieben wird. Durch das Messen von zwei verschiedenen Tuben wurde das System erfolgreich getestet. Dabei wurden brauchbare Diagramme gewonnen, die die winkelabhängige Schallabstrahlung der Tuben über mehrere Frequenzbänder abbilden. Dieser Erfolg dient als Grundlage um weitere Musikinstrumente zumindest in einer Ebene ausmessen zu können. Das Systemkonzept 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. Introduction1
2. Brass Wind Instruments2 2.1. Basic Knowledge...... 2 2.2. Characterisation...... 4 2.3. Directional Characteristic...... 5
3. Technical Implementation of the Automated Acquisition System7 3.1. Turntable-System with Step-Motors...... 7 3.1.1. Mechanical Design...... 7 3.1.2. Electrical Parameters...... 11 3.2. Step Motor Control - SMC...... 12 3.2.1. Stepper Motor Driver Carrier...... 13 3.2.2. Communication over Serial Interface...... 14 3.2.3. Step Losses Detection...... 16 3.2.4. Manual Control...... 16 3.2.5. Power Management...... 17 3.3. High Air Pressure Artificial Mouth - HAPAM...... 18 3.4. Final Measurement Set-Up...... 19 3.5. Supervising Computer Program with LabVIEW...... 20 3.5.1. Top Layer Architecture...... 20 3.5.2. Measuring Layer...... 20 3.5.3. Data Processing Layer...... 22
4. Acoustical Measurements and Acquisition of the Directional Sound Pattern 23 4.1. Input Impedance...... 24 4.2. Transfer Response...... 26 4.3. 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
5 B. Schematic of the Turntable’s Step-Motor-Control (SMC) 37
C. LabVIEW-Screenshot of HAPAMv15 38 1. Introduction
The quality of musical instruments is designated by their acoustical characterisation. But what 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 aspects have to be considered both from the side of the listener as well as the player, which are two completely different viewpoints. Features of interest for the listener are timbre, loudness, pitch, etc. in the far field, however, for the player it is important how well a sound appeals besides how well the intonation of an instrument is and how the instrument sounds in the near field. In addition, it should be noted that in addition to objectively recorded measurement data, the player’s subjective impressions but also the individual variation play a large 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 of brass instruments especially the Tuba. First of all, how a sound is excited on a Tuba and how it is spread into room will be explained. The spreading is mainly determined by the acoustical 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 to plot 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 testing object[2]. Therefore a high amount of microphones will be needed to allow recordings in as many directions as preferred besides a high-capacity processing unit will be required. If the amount 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 to several kilograms weight (finally a grand piano should also be turned) and rotates the load automatically. It is controlled by a supervising system, which also executes the acoustical measurements, over a serial interface. The acoustic radiation is captured either with one microphone for one plane or with a arched microphone array, which completes the recording to 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 of brass wind instruments especially the Tuba and its selected characteristics like the directional sound pattern or the input impedance. The impedance is important for the intonation of an instrument [1]. The next topic will deal with the technical preparation of the turntable and the measuring set-up. In the last section the resulting measurements of an elected number of Tubas will be documented.
1 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 air column in the instrument. These air column is limited by the brass tube which encases it. As a result of this standing waves occur. The oscillated standing waves determine the oscillator which vibrates at a frequency forced by instrument and player. Finally, the resonator has the task to transform wave energy into sound energy. Since the swinging air column of brass instruments has not to be transformed to sound vibrations any more the brass’s oscillator is simultaneous 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 Instruments
The oscillating media of brass wind instruments is a standing wave formed by the air column inside the brass tube. The resulting resonant frequency and its harmonic multiples are defined by the circular tour time of one standing sound wave which moves from the mouthpiece to the bell and back again in sound velocity. This is because at resonance the most energy of the standing wave is reflected from the bell mouth back into the tube and only a short term is spread as audible sound. The reflected energy comes back to the mouthpiece where it will be amplified by the synchronously oscillating lips of the musician, and the standing wave will develop again. This leads to maintaining the acoustic system and helps the musician holding a note on the preferred resonance frequency. As a result of this the wavelength of the standing sound wave is defined by the double length of the brass tube (λ = 2 ∗ lBRASS). −1 In Formula 2.1 the relation between sound wave velocity (cs) (normally it is 343 ms in a 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 have influence 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 slide which 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 natural tones have the same distance in Hertz to their harmonic neighbours, they do not fit the common musical (chromatic) scale. This is due to the fact that human sense of hearing and as a consequent of that the musical scale is not linear but logarithmic. Therefore a chromatic scale seems to be consistent in advance. Actually, the interval between the first and the second resonant frequency is a musical octave, for example, instead it is only a quint between second and third resonance and so on. The higher the compared frequencies lies the closer will be the musical distance (e.g. see the measured resonant frequencies of a Tuba in Figure 4.1). So additional tones have to be produced for lower octaves to fulfil the
2 CHAPTER 2. BRASS WIND INSTRUMENTS complete scale. In this case valves with additional tubes are applied on Trumpets or Tubas for instance. This extends the length of the whole tube and lowers the resonant frequency adaptively. 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 usually consists 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) and a mouthpiece with a semi-spherical cup. Additionally, there are 4 valves which are able to alter the natural tones variably. The natural tones are determined by the first harmonic frequency of the instrument. It is also known as fundamental or pedal tone (f1). Usually, the pedal tone is seldom played by the musician because the gap to the next resonance demands too many intermediate tones and consequently more additional valves. Instead, the second resonant tone (f2) is decisive as standard tuning frequency. It is a B[1 (German: Contra B[) for the contrabass Tuba. Nominally this note should be at a frequency of 58.26 Hz in normal conditions and with a reference frequency for standard pitch A4 (German: a1) at 440 Hz [5]. Higher natural tones (F2, B[2, D3, F3, etc. . . ) are harmonic integer multiples of the fundamental tone. Comparing the resultant standard musical pitch (≡ f2) of Equation 2.2 with the theoretically calculated frequency of 58.26 Hz by [5] shows that the tuning pitch cannot be defined generally, since the standard tuning frequency varies from instrument to instrument or rather the surrounding condition have influence on the pitch.
Bell
Mouthpiece Brass Tube Valves
Figure 2.1.: Image of a contrabass Tuba in B[ with its elements.
3 CHAPTER 2. BRASS WIND INSTRUMENTS
c c = λ ∗ f ⇒ f = s , where λ = 2 ∗ l , s λ BRASS 343 ms−1 f = = 29.57 s−1, 1 2 ∗ 5.8 m −1 ⇒ f2 = 2 ∗ f1 = 59.14 s . (2.2)
2.2. Characterisation of Brass Wind Instruments
Every single tone which reaches our ear in the course of a musical work, contains a fullness of information. It is not only described by its fundamental frequency instead the heard tone comprehends several overtones which all of them are integer multiples of the fundamental frequency too. This overtones which are also called partial tones or simply partials, are responsible for the tone colour. The number of overtones and the magnitude of the harmonics ultimately determine how we perceive a sound. The more harmonics are included, the more brilliant and brighter a tone sounds. Contrariwise, the less harmonics a sound spectrum exhibits, the darker and softer it is perceived. This fact deals with every single kind of musical instrument. However, there are special regions with a couple of overtones where the magnitudes change very little besides they usually are more intensive as the actual fundamental tone. This amount of harmonics are called formants and they define the sound colour of individual instruments [6]. In Table 2.1 the region of formants of different brass instruments are listed. Instrument Formants in Hz Horn 350 Trumpet 1200 - 1500 Trombone 500 - 600 Tuba 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 the sound 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 to distinguish 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 developed from complete rest to its final state. During this initial process the overtones develops steadily. 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 practically not subjected to change. At this particular time the partial tones keep constant for instruments which can stabilize the oscillating system like brass wind instruments. That instruments are supported by the constant feeding of energy by the musicians air excitation.
3. The decay, i.e., that portion of time during which the tone, after completion of the excitation, dies out to complete silence. The decay depends on the reverberation and
4 CHAPTER 2. BRASS WIND INSTRUMENTS
plays a special role for plucked- and percussion instruments, since in the absence of continuing 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 can be caught by measuring either the acoustical input impedance or the acoustical transfer response. Several scientific papers deals with these topics [1][7][8]. For simplicity, both methods are contrasted in Chapter4 of this paper by execution on two Tubas. Finally, the Directional Characteristic which is the main topic as known, will complete this introduction of brass wind instruments.
2.3. Directional Characteristic
Since the main topic of the paper is the directional characteristic of musical instruments the following part will give basics about this thematic. For the sound of an instrument or even of orchestras sound radiation and the effect of the room is a significant criterion and like other sound sources musical instruments have a more or less pronounced directional dependence of sound radiation. It varies significantly depending on the frequency spectrum. The simplest case 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 comparison to the radiated wavelength. This occurs at low frequencies besides the constant radiation remains virtually unaffected. In the case of higher frequencies the directional characteristic is non-linear and is affected by numerous influences like the position of the player, the direction of 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 acoustician Jürgen Meyer [6]. The spheric radiation depends much on the form of structure and the dimension of the individual bells so long as the bell is the transducer. For instance, the bell of a Tuba is relatively wide in comparison to that of a Trumpet. So a Tuba spreads sound omnidirectional at lower frequencies (about 30 Hz up to 90 Hz) instead of a Trumpet (about 180 Hz up to 500 Hz).
French horn Trumpet Trombone Tuba 20 50 100 200 500 2000 Hz 10000 Frequency
Figure 2.2.: Spheric sound radiation of brass instruments by Meyer [6].
In 1970, Meyer and Wogram measured and documented the directional characteristic of Trumpets, Trombones, and Tubas and publicised the results [10]. It turned out that it is necessary to define those angular regions for which the sound level does not sink by more than 3 dB or more than 10 dB respectively below the directed maxima. The 3 dB limit describes the half width. This is the difference where the sound intensity is just half the
5 CHAPTER 2. BRASS WIND INSTRUMENTS value related to the maximum. For simplification sound pressure above the 3 dB limit was supposed as quasi equal. Otherwise a level difference of 10 dB is perceived as approximately one-half the loudness. Figure 2.3 illustrates the directional characteristic of a Tuba within the 3 dB limit. As it can be seen, the effective radiation angle will narrow if the frequency raises.
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, to those which would be caused by a sound source of equal total power with omnidirectional characteristics 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, stronger radiation; 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 the boundary of the 10 dB region, to 0.3 of the maximum value. For sound level considerations it is advantageous to convert the statistical directivity factor to a dB value. The quantity is designated as “directivity index.” It specifies how much the sound level is higher in the direction considered than it would be for an omni-directionally radiating sound source of equal power [6].
6 3. Technical Implementation of the Automated 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 be a device which is able to rotate the device-under-test without human supervision. This is enforced by the fact that measurements are made in a quasi anechoic chamber where no one can enter during the process. As carrier a motor-driven turntable is a possibility. In this case a massive turntable was equipped with step-motors. Lastly, the storage and the processing of measured data and the control of the turntable and its step-motors have to be 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 any measurement or control system. With it, the PC is capable of communicating with the Step- Motor-Control (SMC), executing the acoustical measurements and processing the acquired information with this feature.
3.1. Turntable-System with Step-Motors
For this project a existing turntable was chosen for modification. It consists of a huge bearing ring of a semi-trailer coupling with a diameter of about 65 cm which was attached on a heavy metal-frame. The actual table board can be placed on the bearing ring by four screws, however, other installations can be mounted on the bearing ring too. For instance, a stable construction with a Tuba to be measured is shown in Figure 3.1. This build-up was made of a flexible assembly kit with mounting rails. It was the final mechanical set-up for the acoustical acquirement of Tubas.
3.1.1. Mechanical Design For 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 tensile force was measured at the outer edge of the bearing ring with a spring balance. It turned out that the mean force was at about 200 Newton, however, the top force was measured at about 400 Newton at some points of the wheel. This can be explained that the semi-trailer’s coupling ring is not ideal and possesses higher friction losses at several points. Multiplied with 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 platform can rotate smoothly. A few stepper motors with a nominal holding torque of 44 Ncm (equal to 0.44 Nm) were available at the institute. It should be mentioned that the holding torque nearly corresponds to the driving torque at lower stepper frequencies. Since comparing these
7 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. For this use a nearly 1:300 gear reduction was calculated by dividing load torque by the motor torque. 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 bearing ring 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. This leads to a radius of 9.549 mm. It was possible to attach a timing band with 411 teeth and a length of 2055 mm onto the edge of the semi-trailer’s bearing ring. So a provisional "belt pulley" was created with a radius of about 327.063 mm since the complete diameter of the turning ring is 654 mm.
toothed belt 9.5 mm
bearing
327 mm ring
motor belt disc
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, can be calculated where the input belt wheel has radius ri and the output belt wheel has radius ro, or rather the number of output teeth (No) is divided by number of input cogs (Ni):
8 CHAPTER 3. TECHNICAL IMPLEMENTATION OF THE AUTOMATED ACQUISITION SYSTEM
ω r N GR = i = o = o , ωo ri Ni 327.063 mm ⇒ GR = = 34.251, 9.549 mm 411 ⇒ GR = = 34.25. (3.1) 12 As it can be seen in Equation 3.1 the resulting mechanical advantage (GR = 1 : 34.25) is too less to drive the turntable’s bearing. Furthermore, the gear will not be able to stabilize the system if the motor is turned off. For that reason, another gearing mechanism had to be combined with the pre-designed system. In this case, a worm gear for further reduction was selected. The self-locking feature and the property of achieving a high gear transmission ratio are few advantages of worm gears. For this use, a worm with a module of 1.0 was purchased. A module of 1.0 signifies dimension of a cog. The more force is applied on the cogs the higher should be their module. Since the worm is a special form of a helical gear the angle of the helical toothing is defined by the winds around the wheel axle. The cog/tooth is referred to in this case as a gear or a start. One start indicates that one rotation of the worm screw will rotate the worm wheel by one cog. A higher gear/start stands for a faster turn and 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 of teeth of the worm wheel (Nwheel) with the starts of the worm (Nworm) will lead to the gear transmission ratio:
N GR = wheel , (3.2) Nworm 20 ⇒ GR = = 10. 2 Equation 3.2 depicts that the mechanical advantage of the planned worm gear accomplishes a ratio of 1:10. So the worm gear and the belt drive were united and finally, the collective gear ratio reached a reduction of 1:350. Of course, this was only a ideal result because friction losses of the advanced gearing mechanism derogated the transmission.
9 CHAPTER 3. TECHNICAL IMPLEMENTATION OF THE AUTOMATED ACQUISITION SYSTEM
worm driving- step- wheel motor
fixture bearing ring bearing ring step- motor worm wheel
Figure 3.3.: Principle of the designed gearing mechanism. Left: ground plan, right: sheer plan.
The principal composition of the gear unit is charted in Figure 3.3. This graph shows how the torque is transmitted from the step motor to the terminal turntable ring in ground plan on 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 finally transferred to the turntable’s gearing ring by the driving wheel. This last transmission had a ratio of 1:35. Thereby the direct transmission ratio of 1:350 can be calculated by simply multiplying. In order to complete, the sheer plan of the gear mechanism is on the right side of Figure 3.3. It also shows the transmission of power from the step motor with its worm gear, via worm wheel and the connected axis, to the closing driving wheel connected with the 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.
10 CHAPTER 3. TECHNICAL IMPLEMENTATION OF THE AUTOMATED ACQUISITION SYSTEM
As aforementioned, the bearing ring of the semi-trailer’s coupling ring is not ideal and so the outer edge of it is not circular because of the simple reason that such rings do not have to be ideal for their actually defined use. That was a reason to deal with. To compensate these unevenness of the ring the motor was not fixed stable onto the mounted driving belt instead, it was pulled against the edge by a spring. However, this fixture raised a problem so that 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 total torque was doubled and the stepping losses were compensated by the mutual engagement of both 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 of energy (about 132 Nm) more than enough. It has to be taken into account that the angular velocity of the turntable system is slowed by the reduction of a factor of 350 (cf. Formula of gear ratio with ωi as motor velocity and ωo as output velocity in Equation 3.1). That leads to increasing the rotational speed of both motors simultaneously to balance the velocity decrease. As mentioned above, increasing the stepper frequency leads to lowering the step motor torque. In addition, unbalanced load could destabilise the system and induce disparate force actions on the bearing. That would require a higher torque of the gear and accordingly of the step motors. After all, it is of use to have a overpowered system which can deal with possible force problems.
3.1.2. Electrical Parameters This 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 calculated and so the required motor torque is known, two convenient step motors can be selected. For this set-up two step motors from RS-Components [12] were taken. Table 3.1 shows several attributes of the motors.
Specification Value Model 535-0401 Step Angle 0.9 ◦ Rated Voltage 2.8 V Current / Phase 1.68 A Resistance / Phase 1.65 Ω Holding Torque 0.44 Nm Number Of Leads 4 (corresponds to a bipolar stepper motor with 2 coils)
Table 3.1.: Specifications of the selected step motors [12].
11 CHAPTER 3. TECHNICAL IMPLEMENTATION OF THE AUTOMATED ACQUISITION SYSTEM
Since the step angle is 0.9 degrees, the engine needs 400 steps for a full turn. With that specification and the known gear reduction, the number of steps for one full rotation of the turntable can be calculated. The following breakdown will analyse how often the engine has to 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 the engines is handled by the step motor controller which will be described in the next section.
3.2. Step Motor Control - SMC
The Step Motor Control (SMC) - Unit is responsible for the automatic process of regulating the 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 tasks the 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 the most adequate solution for this cause. Subsequently, further important properties of the micro-controller board which are of value for the project’s purpose, should be mentioned in Table 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’s functions will be explained subsequently. Since there are five tasks to describe, they will be separated in equivalent sections. A picture of the assembled SMC board is shown in Ap- pendixA and the schematic is in AppendixB.
12 CHAPTER 3. TECHNICAL IMPLEMENTATION OF THE AUTOMATED ACQUISITION SYSTEM
Feature Micro-controller ATmega328 Crystal Oscillator 16 MHz Operating Voltage 5 V Digital I/O Pins 14 (of which 6 provide Pulse Width Modulation(PWM) output) Analogue Input Pins 8 DC Current per I/O Pin 40 mA Flash Memory 32 KB (of which 2 KB used by bootloader) Programming Per Serial Programming over USB-to-Serial adapter or RS232 Program Memory/ 2 KB Static Random Access Memory(SRAM) Additional Features Two available Timers, one Serial Interface, several Bus-Systems like Serial Programming Interface(SPI), etc. . .
Table 3.2.: Characteristics of the Arduino Mini Board [13].
3.2.1. Stepper Motor Driver Carrier Stimulating the two step motors was realised by choosing applicable driver elements. For the 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). Since a high gear reduction is applied, there is no use of micro-stepping and only the full-step mode should be executed. It operates from 8 – 35 V and can deliver up to approximately 1 Ampere per phase without a heat sink or forced air flow, or 2 Ampere per coil with sufficient additional cooling. Compared to the required current per phase of one step motor in Section 3.1.2 it is distinct that the motor driver should be able to supply the engine decently but only with a heat 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 with logic voltages. Since the driver should work in full-step mode the three MSx inputs have to be held at Ground(GND) level. Instead of that the inputs RESET and SLEEP (which has a similar function as ENABLE) have to be driven at the HIGH level voltage (VDD) because they 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 equal to the incoming logic HIGH level (VDD is nominal 3 - 5.5 V). Second, the power converter needs more power so the input voltage can reach from 8 V up to 35 V. The reason for this is that the converter operates as a fixed current regulator where the current limit is adapted
13 CHAPTER 3. TECHNICAL IMPLEMENTATION OF THE AUTOMATED ACQUISITION SYSTEM
motor power supply (8-35 V)
A4988 ENABLE VMOT MS1 GND MS2 2B VDD MS3 2A RESET 1A microcontroller SLEEP 1B STEP VDD GND DIR GND
logic power supply (3-5.5 V)
Figure 3.5.: Wiring diagram for connecting a micro-controller to an A4988 stepper motor driver carrier [15]. by a reference potentiometer. So the motor voltage only determines how fast the current will raise in a coil until the current limit is reached. Therefore the rated voltage of the stepper motor (see Section 3.1.2) takes no effect on this application because the given voltage rating is 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 Interface The 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 direction is needed. Additionally, the RS-232 cable is equipped with a screen against electromagnetic interference. Although it is replaced more and more by Universal Serial Bus (USB), it has proved that RS-232 is more practical and cheaper for this cause. Also the total length of the USB cable is limited by maximal 5 m. As the turntable system and the control computer can be located in distances of up to 12 m, simple RS-232 comunication can be done with less effort. Another reason is that the ATmega328 has no USB terminal but still includes a Universal Asynchronous Receiver Transmitter (UART) interface [14] which is compatible to the 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 have a complex peripheral circuit additionally. RS-232 needs only a simple MAX232 chip which transforms the 0 to 5 V logic level to a ±7 V output voltage and vice versa. Another reason is that the Arduino Mini Board including a convenient boot-loader can be programmed over the serial interface [13]. Because USB-to-Serial adapters are cheaply purchasable, the problem of 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 CHAPTER 3. TECHNICAL IMPLEMENTATION OF THE AUTOMATED ACQUISITION SYSTEM where the door is completely locked during the measuring process, the monitoring PC is located outside this room. This allows laboratory personnel checking and controlling the progress. 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.
Transmitting Command Description Rxxx 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.
Receiving Message Description ACKxxx 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.
Failures Message Description ECOM 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 CHAPTER 3. TECHNICAL IMPLEMENTATION OF THE AUTOMATED ACQUISITION SYSTEM
3.2.3. Step Losses Detection Although engine and gear were developed so that the turntable should also carry heavier loads, nevertheless step losses could occur. This could happen when the table is blocked by something. For instance, the load could be placed to unbalanced, or a solid obstacle like a fixed microphone stand would block continued rotation. In this case, the step motors will stop turning immediately because they need a momentum after acceleration otherwise the magnetic field will circuit around the rotor. Under load, the slipping field will not be able for setting the rotor back into motion. This happens because the frequency of the stepper motor relative to the rotor inertia is too high and would require an acceleration again. Since this is a fatal failure, it must be avoided by a automatic watchdog unit. Such a monitoring system is simply realised by checking whether one motor revolution is equal to its needed steps. Every completed turn, a magnet mounted on one rotor raises an electric impulse in a Hall sensor. This impulse triggers a binary signal in a Schmitt trigger and consequently, it raises an external interrupt in the micro-controller. The interrupt routine handles the flag by 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 sequence will be suspended and an error will be raised (see Table 3.3), or else, the program will be continued 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 has 400 steps, the tolerance could take a value of a full turn for example, which would detect step losses approximately greater than one degree. This helps to identify where the failure has occurred at a accuracy of nearly one degree.
3.2.4. Manual Control Furthermore the SMC should provide a manual control due to the fact that calibrating the system 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 the buttons 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 eventual restarts. Finally, a stop button (BSTOP) for emergency cases was implemented. The push buttons 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 simultaneous with 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 display have been realised by the MAX7221CNG from Maxim [16] which is an Integrated Circuit
16 CHAPTER 3. TECHNICAL IMPLEMENTATION OF THE AUTOMATED ACQUISITION SYSTEM
(IC) for driving seven-segment displays up to 8 digits. Its registers can be manipulated by a serial bus like SPI which the operating micro-controller provides.
3.2.5. Power Management The load supply voltage which is used for generating the motor output current, has a range from at least 8 V up to 35 V. The second voltage level is at 5 V because all used ICs are Complementary Metal-Oxide-Semiconductor (CMOS). Only the micro-controller has an integrated voltage regulator which is able converting an input voltage range of 7 to 9 V down to a level of 5 V. However, the power does not suffice for all 5V-Logic-ICs which summarised are the seven-segment driver, the logic part of the stepper motor driver, MAX232, and the Schmitt 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 35 V), and delivers enough power for all devices. For this reason, a LM7805 was chosen. It is a 3-Terminal Positive Voltage Regulator with a stable output of 5 V, and provides 1 A output current [17]. With an absolute maximum rated input voltage of 35 V, it should not pose a problem if the device was driven at recommended 25 V. This would also conveniently fit the input range of the stepper motor driver’s power part. Figure 3.6 shows the power management constellation with all involved devices.
25 V / max. 35 V
2x LM7805 Stepper Motor Driver 5 V Others like 7 seg. driver Pullup Resistor Load Supply Voltage Logic Supply Voltage MAX232 Schmitt Trigger
Figure 3.6.: Power Management Principle.
Conducting the 25 V supply input of SMC to a laboratory power supply was implemented over a Cannon X Lockable and Rubber insulated connection (commonly known as XLR connector). Conventionally, it is most commonly associated with balanced audio intercon- nection. Since the anechoic chamber has several ports connecting in- and outside, a couple of XLR connectors for audio application like connecting microphones or loudspeaker, have been implemented too. One of these was used for supplying the SMC. A crafted XLR cable was connected with a laboratory power supply with high voltage on Plus lead and ground level on GND lead. The inverted Minus lead and the screen shield was not connected. The power input connector on the SMC is already a compatible XLR linkage.
17 CHAPTER 3. TECHNICAL IMPLEMENTATION OF THE AUTOMATED ACQUISITION SYSTEM
3.3. High Air Pressure Artificial Mouth - HAPAM
For oscillating the air column in the tube of brass wind instruments a convenient stimulation system is required. Therefore, a loudspeaker had to be adapted for this use. Since Tubas with an immense volume of air should be measured, a low frequency speaker with a rated output power of 50 Watt from RS-Components was chosen. It has an impedance of 8 Ohm and a diameter of 5.25 Inch. This large-dimensioned speaker was covered in a box made of plywood. A circle of the size of the membrane was cut out of the front plate besides a holed plastic cone was placed over the hole in order to focus the sound energy. The mouthpiece of the brass instrument could be mounted with clips, and between both parts a rubber ring 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 1/8 Inch 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 filled behind the membrane with foam plastics. Figure 3.7 shows the completed HAPAM box in blue.
Figure 3.7.: High Air Pressure Artificial Mouth mounted on a Tuba.
18 CHAPTER 3. TECHNICAL IMPLEMENTATION OF THE AUTOMATED ACQUISITION SYSTEM
3.4. Final Measurement Set-Up
Finally, all listed devices above were composed to the final acquisition and measurement set-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, an additional probe microphone for measuring the directed sound pressure, several laboratory devices like power supply and mic pre-amplifier, and lastly the musical instrument under test. Figure 3.8 pictures the final measurement set-up with all involved components. Port Terminal SMC Door HAPAM
Probe Mic Step Motor
Anechoic Chamber
Figure 3.8.: Finale Test Set-up.
R A ROGA RG-50 ICP 1/4 Inch probe microphone [19] is placed in front of the musical instrument to be rotated and measured. It has a linear frequency response (±1 dB) from 30 Hz up to 4 kHz. Since lower frequencies should be measured too, it should be refereed to the fact that the microphone has an accuracy of ±1.5 dB down to 4 Hz. It is connected with 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, is connected with a BSWA Tech Co. MC702 pre-amplifier. Both pre-amplifiers were connected with a port which is linked with a 19 Inch rack terminal tower outside the chamber. This port provides several terminal points like Bayonet Neill Concelman (BNC)-, cinch-, phone jacks, RS-232-, and XLR-connectors. Consequently, the input signal for HAPAM’s loudspeaker is provided over the port too. That signal is amplified by Orion Profi Mosfet Amplifier from Zoffmusic. Next, a converted XLR connector supplies the SMC with power besides the communication is realised over a RS-232 link. Finally, all described functions routed by the rack tower are connected with the Data Acquisition Input/Output (DAQ I/O) interface card from vendor National Instruments which is compatible to LabVIEW.
19 CHAPTER 3. TECHNICAL IMPLEMENTATION OF THE AUTOMATED ACQUISITION SYSTEM
3.5. Supervising Computer Program with LabVIEW
Controlling the rotation of the step motor controller and conducting the measurements were applied by a program based on designing software LabVIEW [11]. The cycle of the acquisition can be divided in several parts. First of all, a top layer sequence can be defined. This level describes 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’s micro-controller program by the reason that both program cycles work synchronously. The second layer describes one acoustical measurement at a given position of degrees. It is encapsulated 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 is the data processing layer which computes all acquired information. It is also part of the top layer but it only will be executed as the final procedure.
3.5.1. Top Layer Architecture The main program starts with a initialization process where the turntable is driven to the origin 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 can be calibrated precisely. This could happen either by operating the push buttons on SMC or by sending drive commands over the serial interface. Then the actual acquisition of the sound pattern begins. At zero degree the first measuring starts. It is a acoustical transfer response measurement where the output sound pressure of the instrument is set in relation to the input sound pressure caught inside the mouthpiece’s cup. After then the turntable will rotate to its next position and a further measuring will begin. This will be repeated as long as the preselected end position will be reached. At that end the analysis of data will start and the result will be plotted. The flow-chart of this sequence is plotted in Figure 3.9.
Start Initialisation Calibration First Origin reached, Send Calib OK Measurement Settings completed
Drive turntable Postprocess with command Wait until RDY Measuring Is end positionYes the gathered Rxxx degrees is received reached? data
No
End
Figure 3.9.: Top layer flow-chart of the turntable program.
3.5.2. Measuring Layer The 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 CHAPTER 3. TECHNICAL IMPLEMENTATION OF THE AUTOMATED ACQUISITION SYSTEM 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 musical instrument to be measured is oscillated by a logarithmic sine sweep which was outputted over the Data Acquisition Output (DAQout) interface prepared by LabVIEW. That sweep is defined by the pre-settings which consist of frequency range, measuring duration, sampling rate and sampling buffer size (which defines how long a signal at a given frequency will be analysed). Usually, the sampling rate in this LabVIEW program was at 50000 samples per second and the buffer had a size of 5000 samples. This means that ten analysis per second could be managed. One analysis considers one frequency step. In connection with the duration which was 180 seconds by default, there were examined 1800 frequency steps per one complete measurement. These steps were logarithmically interpolated over the selected frequency range. Consequently, the output sine sweep was generated thereby, because the magnitude 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 relative sound radiation at different angles. Another one was put into the HAPAM’s cavity as near as possible to the mouth piece plain as reference. Since the measuring is a transfer response analysis, both input signals were compared in LabVIEW. First, the signals were put into an input buffer where a Discrete Fourier Transformation (DFT) analysed them. After that sin- gle tone information per channel with maximum magnitude were extracted. This simplified further calculation because only one magnitude per channel was considered. Calculating the transfer response was realised by dividing output by input where the corresponding frequency was 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 response was also plotted on a display window of the LabVIEW panel which is shown in Appendix C. For post-processing both input signals were put in storage as WAVE file. The current direction in degrees was integrated in the names of both files. For simplicity the schematic Figure 3.10 should explain this topic pictorially.
Settings WAVE VIAS file file
Extracting Generating Output Calculating Catching DFT Single Tone T (f) = frequency steps output input Information Input
Audio Input LabVIEW HAPAM Probe Graph Panel Mic Reference Output
Figure 3.10.: Block diagram of the measurement cycle.
21 CHAPTER 3. TECHNICAL IMPLEMENTATION OF THE AUTOMATED ACQUISITION SYSTEM
3.5.3. Data Processing Layer After all directions of radiation have been acquired, this information should be transformed into 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 transfer response of convenient WAVE files including input and output channel. When all amplitude responses 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 the direction with the maximum sound pressure level because it is located directly in front of the instrument’s bell. The normalisation was achieved by multiplying the individual curves with the inverse of the zero-degree curve. The result for the zero-degree curve itself was a straight line 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. So all amplitude/frequency characteristics were separated in several frequency divisions which could be defined manually. The arithmetic mean was formed over the individual sub-divisions to give a pointed value for it. Composing the same frequency divisions over all directions in a circle completes one curve. For that reason, there are so many circles as frequency classification in the composed polar diagram. The scale of that polar diagram began at the outer boundary and went toward the centre by attenuation steps of 3 dB. An amplification in relation to the frontal directed sound radiation for Trumpets, Trombones, and Tubas will not occur commonly [10]. The advantage of that form of diagram is that a sound attenuation graph in all directions can be drawn where Meyer’s differentiated -3 dB and -10 dB areas could be red out too. For documentation a directional characteristic graph can be exported as a Scripted Vector Graphic (SVG). Examples of directional sound patterns are shown after measuring of two Tubas in Chapter4.
22 4. Acoustical Measurements and Acquisition of the Directional Sound Pattern
This chapter documents the different measurements which were applied in the course of the bachelor project. As test subjects two Tubas of different fundamental tone were considered for comparison. The attributes of these instruments shall be listed in Table 4.1:
Contrabass Tuba in B[ Model Cerveny, Czechoslovakia, BB[-Tuba CBB 681 Pedal tone B0 (29.13 Hz) Tuning pitch B1 (58.26 Hz) Bell mouth diameter 400 mm Bore diameter 20.2 mm Weight 9000 g Unwound length of the brass tube about 5.8 m Valves 4
Bass Tuba in F Model Gebr. Alexander Mainz, Germany, F-Tuba Modell 157 Pedal tone F1 (43.65 Hz) Tuning pitch F2 (87.31 Hz) Bell mouth diameter 380 mm Bore diameter 18.5 mm Unwound length of the brass tube about 4 m Valves 6
Table 4.1.: Characteristics of two analysed Tubas.
Comparing both instruments shows that their pedal frequencies are different. This should not affect the directional characteristic since Meyer said that the frequency dependence of the sound pattern is independent of the pitch played [9]. Only the input impedance of the Tubas is different. In the matter of omnidirectional sound radiation there should not be disparity because the source of sound (the bell) is quasi equal for both objects (narrow difference of 2 cm). 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 directional sound pattern will be shown finally.
23 CHAPTER 4. ACOUSTICAL MEASUREMENTS AND ACQUISITION OF THE DIRECTIONAL SOUND PATTERN
4.1. Input Impedance
MOhm 35
Bb0 30
25
Bb2
20 D3F3 F2 Bb3 Ab3
15 Bb1 D4 C4 F4 10 E4 G4 Ab4 5 A4Bb4
0 Hz 0 100 200 300 400 500 600 700 800 900 1000
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 were taken 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 magnitude of the impedance in Mega Ohms (MOhm). The dark-blue curve’s peaks are the resonances of the air column in the Tuba and equals the natural tones (without a valve is pressed). For comparison the advanced orange curve represents the resultant resonances when the scale is decreased by a tempered whole tone. This is implemented by pushing the first valve. The name of notes of the natural tones are printed into the graph. In order to simplify, the names for 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 between two peaks is always the same, because all harmonics are integer multiples of the fundamental tone. Only the musical interval between two tones will be smaller from one octave to the next. The scale in the third octave (indicated by the number 3) is almost completed with the natural tones and the additional first valve. Furthermore, no valves are required for the fourth octave because the intervals are only a whole-tone step, or only a half-tone at higher frequencies. It also can be seen, that the tones which would be played with or without the first valve pressed, overlap at some points. However, Tuba players perform in the 4th octave and upwards very rarely because it would need a professional musician passing such difficult
24 CHAPTER 4. ACOUSTICAL MEASUREMENTS AND ACQUISITION OF THE DIRECTIONAL SOUND PATTERN passages. How well a sound appeals is evident by the size of the magnitude peaks. The higher 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 tone of the F-Tuba is about 20 Hz higher than that one of the B[-Tuba. However, there are some natural tones which harmonise on both instruments. That special notes are at several kinds of F most. Only at the F1 the instruments are out of sync. There a peak from the F-Tuba is opposed to a tale of the other one. This means that a F1 could never be forced on the B[-Tuba without additional help instead it will sounds well and easily on the Tuba in F.
MOhm 40 F1
35
30
F2
25 F3
20 C4
15
F4
10
5
0 Hz 0 100 200 300 400 500 600 700 800 900 1000
Figure 4.2.: Comparison of the input impedance of a B[- and F-Tuba.
25 CHAPTER 4. ACOUSTICAL MEASUREMENTS AND ACQUISITION OF THE DIRECTIONAL SOUND PATTERN
4.2. Transfer Response
The Transfer Response relates output sound pressure to input sound pressure. Since the transfer response is similar to the acoustical admittance of a musical system, it also can be associated with the input impedance [8]. Further measurements of the directional sound radiation were based on the acquisition of single transfer responses, therefore, it should be explained succinctly.
Bb1 -48 [Cent]
22,809
20
0
-20 -21,747
10 20 30 5056,672 70 100 200 300 500 700 1000 2000 3000 5000
Figure 4.3.: Relation between input impedance and transfer response.
Figure 4.3 shows the input impedance (orange) and the transfer response curve (green) of the contrabass Tuba in B[ (its tuning pitch B[1 is highlighted with a cursor). In this case the graph’s vertical axis is dimensionless and represents only proportions in decibel, however, it does not matter because the graph should only depict the affinity of both curves. Besides the frequency axis is logarithmic that time so higher frequency ranges can be seen. After analysing this figure it should be possible to recognise that one curve could be the reciprocal of the other ones. That does not fit entirely due to that fact that both characteristics were measured with different methods. Finally, it can be seen that the transfer response rises at higher frequencies otherwise the impedance falls there. This indicates that the most inserted energy will be radiated at the output and nothing will be kept inside the tube for establishing an oscillating system. For that reason it is difficult for a Tuba player to perform a tone above 400 Hz moreover it is impossible to play above 600 Hz.
26 CHAPTER 4. ACOUSTICAL MEASUREMENTS AND ACQUISITION OF THE DIRECTIONAL SOUND PATTERN
4.3. The Directional Characteristic of Brass Wind Instruments
At last, the paper has come to its final measurement. After the implementation of the aforementioned turntable acquisition system, it was possible to acquire the directional sound pattern ultimately. For that analysis both Tubas were considered. Figure 4.4 illustrates the directional radiation of the contrabass Tuba in B[ and that one of the F-Tuba is shown in Figure 4.5. 2000-3900 Hz 1000-2000 Hz 500-1000 Hz 240-500 Hz 120-240 Hz 20-120 Hz
-18dB -15dB -12dB -9dB -6dB -3dB 0dB
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 the region where the pedal tone and its first harmonics are located. In the chromatic scale that area 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 CHAPTER 4. ACOUSTICAL MEASUREMENTS AND ACQUISITION OF THE DIRECTIONAL SOUND PATTERN
2000-3900 Hz 1000-2000 Hz 500-1000 Hz 240-500 Hz 120-240 Hz 20-120 Hz
-18dB -15dB -12dB -9dB -6dB -3dB 0dB
Figure 4.5.: Directional Characteristic of the Bass Tuba in F.
28 CHAPTER 4. ACOUSTICAL MEASUREMENTS AND ACQUISITION OF THE DIRECTIONAL SOUND PATTERN below the -3 dB level. According to Meyer [10] such curve of the circle can be accepted as a complete simple sound source at this frequency range. The second range between 120 and 250 Hz complies with the third octave which is also called small octave. This range differs to the previous less but it suffices that the curves lies underneath the -3 dB level more and more. So the instruments cannot be designated as spheric radiator any more. It should be mentioned that the difference between the two curves is greater for the B[-Tuba instead of that one in F. This can be deduced by the fact that the bell in connection with the diapason of 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 colour of the Tubas. As it can be seen, this region from 250 up to 500 Hz keeps only above the -3 dB limit at a range of about 130 degrees for the Tuba in B[ and about 140 degrees for the F-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 reflection will not influence the sound. Instead of that ceiling reflection should be considered because the most radiated sound is directed against the ceiling vertically. This also applies to higher frequency components whose radiation is increasingly narrowed to the axis of the bell. For example, the 500 − 1000 Hz band is emitted only for a width of main radiation lower than 90 degrees for both Tubas. Besides the main radiation field for the 1000 − 2000 Hz range is about 45 degrees for both Tubas too, but between 2000 and 3900 Hz it is only 30 degrees for the 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 components sound 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 colour of the spread tone brighter and more brilliant. If this components are cut off, the instrument sounds dark and it is not possible achieving differently effective dynamic levels. This happens when the narrowed directivity at higher frequencies is neglected. For instance, such problem appears especially with Tubas at open air events since there is no ceiling which could reflect that overtones in the direction of the audience. But even poorly structured ceilings in concert halls 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. The developed set-up fulfilled all requirements. Only during the implementation of the automated turntable, more attention had to be paid for the mechanical development because the input torque of the step motors was too less. This was resolved by designing a convenient gear system. 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 version also 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, the resulting diagrams were two-dimensional. But even these diagrams showed impressively how the sound radiates. Besides the directional characteristic could be imagined three- dimensionally by the reason that the radiation were accepted as symmetric around the bell axis. However, to achieve a truly spatial pattern it would be necessary to design a arch equipped with several microphone. Due to the fact that the automated acquisition system was extensible, it would be possible creating 3D-plottings in the near future. It was also designed to be universal since the measuring signals were independent of the test object. On that account other musical instruments could be proven of their directional characteristic by simply adapting a different excitation mechanism and a different mounting construct respectively.
30 Bibliography
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[10] J. Meyer and K. Wogram, “Die Richtcharakteristiken von Trompete, Posaune und Tuba,” 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 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,” PCB Piezotronics Inc., Depew, USA, 2006. [Online]. Available: http://www.pcb.com/ contentstore/docs/PCB_Corporate/Electronics/products/Manuals/442C04.pdf
32 List of Figures
2.1. Image of a contrabass Tuba in B[ with its elements...... 3 2.2. Spheric sound radiation of brass instruments by Meyer...... 5 2.3. Main radiation area of a Tuba...... 6
3.1. Turntable system with a stable construction for fixing a Tuba...... 8 3.2. Example of a gear belt drive with a reduction of about 1:35...... 8 3.3. Principle of the designed gearing mechanism...... 10 3.4. Picture of the final used gearing mechanism...... 10 3.5. Wiring diagram for connecting a micro-controller to an A4988 stepper motor driver carrier...... 14 3.6. Power Management Principle...... 17 3.7. High Air Pressure Artificial Mouth mounted on a Tuba...... 18 3.8. Finale Test Set-up...... 19 3.9. Top layer flow-chart of the turntable program...... 20 3.10. Block diagram of the measurement cycle...... 21
4.1. Input Impedance of the Contrabass Tuba in B[...... 24 4.2. Comparison of the input impedance of a B[- and F-Tuba...... 25 4.3. Relation between input impedance and transfer response...... 26 4.4. Directional Characteristic of the Contrabass Tuba in B[...... 27 4.5. 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...... 11 3.2. Characteristics of the Arduino Mini Board...... 13 3.3. Communication protocol between SMC and the supervising computer..... 15
4.1. Characteristics of two analysed Tubas...... 23
34 List of Abbreviations
BIAS Brass Instrument Analysing System BNC Bayonet Neill Concelman CMOS Complementary Metal-Oxide-Semiconductor DAQ I/O Data Acquisition Input/Output DFT Discrete Fourier Transformation EIA Electronic Industries Alliance FTDI Future-Technology-Devices-International GR Gear Ratio HAPAM High Air Pressure Artificial Mouth IC Integrated Circuit IWK Institut für Wiener Klangstil LabVIEW Laboratory Virtual Instrumentation Engineering Workbench PC Personal Computer PWM Pulse Width Modulation SMC Step-Motor-Control SPI Serial Programming Interface SVG Scripted Vector Graphic UART Universal Asynchronous Receiver Transmitter USB Universal Serial Bus VIAS Versatile Instrument Analysis System
35 A. Assembled Step-Motor-Control (SMC)
RS-232 Power Supply 7 Segment Driver
tpe oo Driver Motor Stepper
ihHeatsinkwith
MAX232
Arduino Mini rev5
alSnosInput Sensors Hall
Push Buttons
Schmitt Trigger
36 B. Schematic of the Turntable’s Step-Motor-Control (SMC)
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37 C. LabVIEW-Screenshot of HAPAMv15
38