1. Department of Physics and Astronomy
Ithaca College
Senior Project Report
The Light Theremin: Transforming Light Into Sound
A Light Based Instrument
Submitted by,
Scott Robbins
May 11, 2016
2. ITHACA COLLEGE DEPARTMENT APPROVAL
of a Senior Project submitted by
Scott Robbins
This senior project report has been reviewed by the senior project instructor and has been
found to be satisfactory.
Dr. Matthew C. Sullivan, Senior Projects Instructor Date
I understand that a digital copy of my senior project report will remain on file in the Depart-
ment, and may be distributed within the Department or College for educational purposes.
My signature below authorizes the addition of my report to this repository.
Scott Robbins Date
3. Abstract
Using a combination of resistors, photo transistors, op amps and one inexpen-
sive Arduino micro-controller, I designed and created a unique and potentially
educational musical and scientific instrument. The sound production and con-
trol of this instrument relies on the manipulation of light hitting photo tran-
sistors. The Arduino takes this analog voltage from the collector of this photo
transistor and converts it into digital square wave pulses, with frequencies that
can be modulated by controlling the amount of light hitting a second photo
transistor. This device would be a good future project for other undergraduate
students with interests in engineering, computer programming and music. This
device also has the potential to be a good demonstration of how to experience
science in a very different and entertaining way, and in an elementary educa-
tion setting (perhaps with special needs students as well) it has the capacity
to entertain, educate and perhaps even inspire.
i
4. Acknowledgments
I’d like to thank Jennifer Mellott for helping me throughout the construction of this project.
I’d also like to thank Matt Sullivan for his guidance, for motivating me throughout the
construction of this instrument, for his help with writing this report and for suggesting I
analyze the speaker output with Raven. I would also like to thank Dan Briotta for teaching
me so much about analog electronics and computer programming, for helping me develop a
range of skills as a scientist and as an inventor, and for encouraging me to embrace an idea
and turn it into a reality. Thank you all so much!
ii
6. 1. Introduction
The worlds of science and art collided with the invention of the Theremin, a bizarre experi-
mental instrument patented in 1928 by Leon Theremin who subsequently signed a contract
with RCA (Radio Corporation of America) in 1929 making them the “first mass producer
of an electronic instrument” [2]. The Theremin is often cited by historians as being the
first invention to “lay the foundations for modern electronic music” [2]. However, this is not
where his story begins.
Theremin was initially a young physicist doing research for the Russian government,
specializing in the development of “proximity sensors” [3] that would react to changes in
magnetic fields. Theremin took this research, on electromagnetic field sensors, and instead
applied it to create a musical instrument. He brought his invention to Lenin (the current
leader of the the Russian Communist Party at the time) who wanted Theremin to show his
device off to the entire world. This freedom to travel allowed Theremin to come to the United
States to patent and sell his device, but also to spy on the major technology companies [2]
in the United States. He enjoyed life in America, but after marrying an African-American
woman he found his US funding depleting (an unfortunate consequence of the racism in
the US during the 1920s) and was no longer considered an asset by the Soviets. He was
subsequently kidnapped by the KGB and brought back to Russia. Nevertheless, his device
was already being mass produced and generating enormous interest.
The Theremin enables performers to draw out pitches from thin air, without the per-
former ever physically touching the instrument, by using the position of the musicians hand
to control pitch and volume through manipulation of the electric field around an antenna [1].
Although the timbre of the Theremin is quite strange and somewhat unpleasant, it was the
pioneering invention that paved the way for musical instruments rooted in physics and specifi-
cally analog electronics. Robert Moog, who many attribute as the inventor of the synthesizer,
began his career by building Theremins and attributes this instrument as his inspiration [2].
Science is a pursuit of the objective, dealing with concrete logical ideas that exist far
beyond the classroom and far from the hands of students. We run experiments and manip-
ulate the world every day, but most of this is done in a sterile environment. A scientist may
run an experiment but the outcomes (almost) always depend on invisible forces extending
throughout the universe. This quality is what I find so compelling about the concept of
the original Theremin and the device I have built. It can be used to engage people from
outside of the scientific community and spark the curiosity that leads them down the path
of discovering the true magic that is science.
In addition, my mother is an elementary school teacher for students with disabilities, and
a device like this allows handicapped individuals to be both expressive and entertained in a
non-verbal way that requires very little dexterity. I have a passion for music because it has a
similar capacity for experimentation, allowing an individual to share a subjective experience
in an (almost entirely) objective world. The motivation and goal of my project was to unite
my passions for science and music, and in the process design a device that can bring the
abstract and unseen nature of physics to your fingertips.
This can be done in a variety of ways using modern technology. The instrument I have
designed and built relies on the manipulation of light instead of the electric field surround-
1
7. Introduction
ing an antenna (the primary scientific phenomenon that the Theremin utilizes). The Light
Theremin relies on the performer to control the amount of light hitting a photo-transistor
to influence the pitch of a tone being continuously amplified by a speaker.
To do this, a photo-transistor is connected to a power source with the output of the
collector being put into an Arduino Uno and the emitter being connected to ground. Ambi-
ent light hitting the photo-transistor yields an output of zero volts because the transistor is
essentially “shorted” when there is maximum light. As an obstacle blocks light from hitting
the photo-transistor, the voltage at the collector increases. A 100 KΩ resistor is placed in
between the power source and the collector to maximize the possible range in voltage that
can be output by the transistor.
The circuitry becomes a musical instrument by mapping the possible range of voltages to
a range of pitches or frequencies. Therefore as the the voltage being taken from the collector
changes, the Arduino Uno will produce a digital square wave with a pitch that is directly pro-
portional to the voltage and by extension the amount of light hitting the photo-transistor.
The Arduino Uno is a cheap, open source micro-controller that has six analog input-
s/outputs and 13 digital inputs/outputs. Programs for the Arduino are written in the
Arduino Integrated Development Environment (IDE), and are compiled and uploaded to
the micro-controller via USB. Compiling the programs, which are written in a programming
environment that is extremely similar in syntax to Java or Python, puts them into a machine
language that tells the Arduino what to do. Once a sketch is uploaded to the Arduino there
is no need for a computer. The photo-transistor circuit and the Arduino itself can run on
the same power source so the whole device can be contained on the same small area.
Although quite different in circuitry, the philosophy and operation of this instrument is
Figure 1: This is an image of the instrument I have built. The Arduino is depicted in the
middle, with the photo-transistor for pitch control on the left and the photo-transistor for
volume control shown on the right. The speaker is also in this image, and is built into the
board.
analogous to the Theremin because the sounds being created are generated by the performer
manipulating light, requiring no physical contact with the instrument. Pitch is continuously
shifted or altered by moving a hand around or above the photo-transistor, this movement
changes the amount of light hitting the photo-transistors. The sound is much more coarse
than the Theremin because the Arduino outputs rough digital square waves. The sensitiv-
2
8. Introduction
ity is quite impressive however, as the photo-transistor output voltage responds extremely
quickly to changes in light.
Science is an amazing tool for understanding the world around us, but sometimes fails to
inspire students because it feels intangible. Instruments like the Theremin, and the one that
I have built, are good tools for showing how these properties of physics are truly physical
things that we interact with continually and unconsciously but are invisible to the naked eye.
These instruments allow us to tinker with these invisible forces and allow someone to create
something out of (seemingly) nothing, providing the potential for the scientifically inclined
to pursue musical endeavors or for the musically inclined to pursue scientific studies.
3
9. 2. Design
The design of this instrument relies on three distinct stages of circuitry. The first stage is
where ambient light from the performance space is used to control a voltage. This analog
voltage is fed into a micro-controller which is the second stage of the device. The third stage
of the device controls the volume of the output of the micro-controller, which is now a digital
square wave of varying frequency. This modulate of frequency changes based on how the
user is occluding the light hitting the photo-transistor in the first stage.
2.1 First Stage: Pitch Control
The first stage of the device is where light intensity is converted into a proportional voltage.
To understand how the photo-transistor does this, one needs to first understand the opera-
tion of a photo-transistor. Essentially, a photo-transistor operates in a fashion very similar
to a light emitting diode or LED. When a voltage is applied to an LED, current will flow
and the LED with begin emitting light. Once light is emitted there will also be a voltage
potential across the LED.
Similarly an LED can be oriented in an opposite fashion such that a voltage potential
can be induced by light hitting the LED, allowing current to flow. The amount of current
an LED will generate upon illumination is quite small. To increase the current produced by
the LED we connect it to the base of a transistor. Now, when the LED is illuminated it will
allow a much larger current to pass through the collector to the emitter. This use of the
LED is referred to as being reverse biased, and this combination of an LED with a transistor
is called a photo-transistor.
The photo transistors used in this device are sensitive to visible light and also to infrared
Figure 2: Circuit diagram illustrating voltage source, 100 KΩ resistor and photo-transistor
in parallel with Vout coming from the collector.
light. During maximum illumination the photo-transistor puts out a minimum voltage and
total darkness creates a maximum voltage. To understand this, we treat the photo-transistor
a bit like a variable resistor. When fully illuminated, the photo-transistor essentially makes
a short to ground and so the voltage measured at the collector is essentially zero because all
4
10. 2.1 First Stage: Pitch Control Design
of the voltage has been used across the resistor R1. When partially illuminated the photo
transistor begins to act like a variable resistor (with a “resistance” dependent on the amount
of incident light) and there will be a voltage coming out of the collector. If one fully covers
the photo-transistor the equivalent “resistance” is extremely high, because almost no cur-
rent will flow from the collector to the emitter. Therefore the voltage at the collector is at a
maximum because this equivalent resistance of the photo transistor is much larger than the
resistance of R1. This equivalent resistance of the photo transistor will be denoted as Rpt in
Equation 1.
Fundamentally this circuit acts like a voltage divider, with a voltage being connected to
a resistor and photo transistor in series. With our applied voltage being Vcc (in this case a
constant +5V), and the output being taken after the resistor R1, our equation for the Vout
is as follows:
Vout =
Rpt
R1 + Rpt
Vcc (1)
Treating our photo transistor as a variable resistor (this variable resistance denoted as
Rpt) we can make our circuit be equivalent to a voltage divider circuit and use Equation
1 to approximate the maximum and minimum output voltages of the first stage circuit.
When fully illuminated we approximate the equivalent resistance of the photo-transistor
is 100 Ω, and when in complete darkness the equivalent resistance is approximately 1 MΩ.
Calculating for our theoretical minimum and maximum output voltages we find that with
a fully illuminated circuit we should get an output of 4.99 mV. Our theoretical maximum
voltage for our circuit in complete darkness is calculated to be 4.55 V. These numbers are
simply approximations (based on the nature of reverse biased diodes) so we can conceptualize
how to control a voltage by manipulating the amount of light hitting a photo-transistor.
Figure 3: This is an oscilloscope snapshot of how blocking light increases the voltage at
the collector. This figure does not depict the full voltage range, but rather illustrates the
capacity of the circuit to allow a person to manipulate the voltage at the collector.
5
11. 2.2 Second Stage: Micro-controller Design
2.2 Second Stage: Micro-controller
The second stage of the instrument is the Arduino Uno micro-controller. The actions that
the Arduino performs are hardcoded in the Arduino Integrated Development environment.
These programs are called “Sketches”, and are uploaded to the micro-controller through a
USB connection to be stored so that the device can run without being connected to a com-
puter.
The sketch for this project first requires declarations of variables, such as the pin to be
specified for the analog input coming in from the first stage (for this project this is analog
input pin A0). The program itself runs through a “loop” method that performs the con-
tinuous actions we desire from the micro-controller. In the case of the Light Theremin the
micro-controller first sets a serial communication rate of 9600 bits per second, and then takes
a reading of the voltage A0.
The Arduino has a function called “Map”, which requires five parameters. It is de-
signed to take a number and re-assign it to a new value based on a second specified range
of values. In our case the first set of ranges are the digital values for our minimum voltage
and the digital value for our maximum voltage (the voltages that come from the first stage
circuit). The second range of values are the pitches that we will want the Arduino to put out.
int sensorPin = A0; // select the input pin for the photo-transistor
int sensorValue = 0; // variable to store the value coming from the sensor
void setup() {}
void loop() {
//initialize serial communication at 9600 bits per second:
Serial.begin(9600);
//read analog input
sensorValue = analogRead(A0);
int pitch = map(sensorValue,0,1023,100,800);
tone(9,pitch,15);//the pitch!
delay(.25);
tone(9,pitch*2,15);//harmonics!
}
The first parameter of the Map function is the sensor value from reading the voltage at
A0. The next two parameters are the lowest and highest possible digital values which are
0 and 1023 because the resolution of the analogRead function is 10 bits (although a higher
resolution could be achieved, this may slow down the program and sacrifice functionality).
The last two parameters for the Map function are the lowest and highest values of pitch
(in Hertz) that we want the Arduino to produce. This range is currently set to a minimum
of 100 Hertz and a maximum of 800 Hertz, although experimentation with this range will
be necessary to determine what sounds most interesting! The value returned by the Map
function is saved as the variable denoted “int pitch”, and will be used in the next line of
code.
The next step in the program is to call the tone function (not to be confused with the
6
12. 2.3 Third Stage: Volume Control Design
“int pitch” variable calculated and stored as a return from the map function), saved in the
code as the variable “int pitch”.) which requires three arguments. The first argument of the
tone function (the Arduino sketch that is included in the report also illustrates calling the
tone function) included is the digital pin that will output digital square waves. The second
argument is the frequency you want these square waves to have, in our case a value saved
as “pitch” from the map function we previously used. The third and final argument of the
tone function is the length of time (in milliseconds) that the tone will be played.
To try and make the timbre of the instrument somewhat less “rough” sounding, I have
also added a second tone (with twice the frequency, an octave above) to make the rough
digital sound slightly “larger” and more interesting. To add a harmonic, the program is
delayed briefly after the first tone is played and then the tone function is called again. On
the second function call for tone however the pitch is doubled.This series of sensor readings,
calculations and function calls will loop continuously as long as the instrument is powered
on. The result is a seamless stream of tones that can be manipulated in the manner described
above.
2.3 Third Stage: Volume Control
The third stage of the device is a circuit to regulate volume and play our tones through a
small speaker. The first component of this stage is to take the output from the digital pin
of the Arduino. To regulate the volume of this tone using light, we utilize a similar circuit
to that of the first stage. Instead of a constant DC voltage, we use the digital output as our
V+ and again feed this voltage into a resistor and photo-transistor in series, with the emitter
connected to ground.
This will allow us to manipulate the voltages being put out by the Arduino pins by
blocking and partially blocking the light hitting the photo-transistor. However, if we used
the same circuit as the first stage, our overall range of volume would be decreased because
of the first resistor and because of the low power output of the photo-transistor (typical
Collector current of 5 × 10−4
A [4]). Although we would be able to vary the volume of
the tones, the maximum volume will be quieter than we would like because of these power
constraints.
Considering we desire to connect this circuit, which allows us to influence voltage and
subsequently volume, to an 8 Ω speaker we need a way to safely make this connection without
drawing too much power from the photo-transistor (connecting the 8 Ω speaker will draw a
large amount of current). So we need a circuit to amplify the output of this second photo-
transistor without drawing too much power from the it.
The way we do this is to connect the output of the collector (from our third stage
photo-transistor circuit) into an op-amp buffer circuit (operational amplifier). The benefit
of using the op-amp buffer circuit is that it’s input impedance is extremely high so as to not
draw too much additional current from the photo-transistor (no increased load). The output
impedance of the buffer circuit is extremely low as well, which is exactly what we need for
amplification. The most important aspect of the buffer circuit is that the output voltage
exactly follows the input voltage and provides additional power.
Although the buffer circuit has solved our issues of power and impedance for the speaker,
7
13. 2.3 Third Stage: Volume Control Design
Figure 4: Full circuit of the Light Theremin, including the first stage circuit, the Arduino,
and the third stage volume control circuit which consists of another photo transistor system,
along with a buffer circuit and an amplifier circuit which then connects to a speaker. The op
amps used for the buffer and amplification circuit are TVL2362 and are designed for lower
power/voltage applications compared to convential op amps.
we still need to increase the voltage in the third stage to get the signal from the digital
output of the Arduino to get back to an audible level (the buffer circuit provides no voltage
gain). However, now that we have isolated the output signal from the Arduino we can safely
amplify this signal with another op-amp circuit. The best op-amp circuit for this stage is the
non-inverting amplifier because it will provide us with the decibel gain we require to make
this instrument audible. The load put on the non-inverting amplifier should not be an issue
because of the low output impedance from the buffer circuit, however the resistor labeled R2
in Figure 4 should be high enough to prevent this.
In addition the choices for the resistor values in the non-inverting amplifier will depend
on how loud we want the instrument to be, and what Op-Amp we choose. Our Op-Amps are
designed for low power applications so when choosing these resistors we need to maximize
this power without damaging the Op-Amps in order to have sound output at an audible
level. The Gain of a non-inverting amplifier is:
G =
Vout
Vin
= 1 +
Rf
R2
(2)
The maximum power output of the photo-transistor is quite small, as well as the Op-
Amps, so to avoid breaking any of these circuit elements we have designed a buffer and an
amplification circuit with resistors Rf and R2 in the non inverting amplifier of 1 KΩ and
100 KΩ respectively. Now we have a third stage for the Light Theremin which will allow for
volume control through the manipulation of light.
8
14. 3. Test Methods
To asses the overall function of the device, I tested segments of the overall device individually.
These sections operate simultaneously, but I needed to test them individually to make sure
each component does what it should. However, because each part of the design operates
simultaneously, another method of testing was to modify the micro-controller program to
achieve optimal timbre. The final test was to assess the overall operation of the device
including all components, and to evaluate and confirm that the Light Theremin is operating
as intended.
3.1 Testing: Pitch Control
The “pitch” or frequency is actually assigned within the program stored in the micro-
controller, so the first stage is only concerned with manipulating light in order to propor-
tionally change a voltage. To test the first stage I connected the output of the collector to
an oscilloscope, and observed the voltage coming out. The first stage worked properly once
it put out the widest possible range between 0 V and 5 V (we have chosen 5 V because this
is the maximum operating voltage of the Arduino). I confirmed that the pitch control photo
transistor operated as intended by connecting the output to an oscilloscope and verified that
this output was reacting to hand motion (resulting in the obstruction of light), by observing
oscilloscope images that resembled Figure 7. Therefore I concluded that the first stage of
the Light Theremin worked properly, by inspecting the voltage as aforementioned, because
as I occluded more light the voltage steadily rose.
The output will never quite get to a maximum of 5 V, but the circuit is considered to
be functioning properly if the voltage essentially reads zero while all ambient light hits the
photo transistor, and with a hand directly covering the photo transistor the oscilloscope
reads a voltage that is at least 4.5 V, but ideally closer to 4.85 V or higher (but always less
than 5V).
3.2 Testing: Micro-controller
When Testing the micro-controller I first pressed the on-board reset button. Before uploading
the code, I compiled the sketch to make sure all the syntax was correct and when there were
no errors. I then uploaded it to the Arduino to be saved. Once the syntax has been verified
and the sketch is uploaded to the Arduino, I tested whether the program assigned pitches
correctly, as specified by the program, by connecting the digital output pin, assigned by
the program, into an oscilloscope and observed the digital square waves. After observing
the pulse-widths of the digital output being modulated as one varies the amount of light
hitting the first stage photo-transistor, I concluded that the pitch control and micro-controller
portion of the Light Theremin device were working together.
Another test method I utilized was to simply connect the digital output to a speaker
(and ground the other terminal), and listened to the sound that came out. This method will
not ensure that the proper frequencies were being generated, but if the Arduino modulates
9
15. 3.3 Testing: Volume Control Test Methods
Figure 5: This oscilloscope image shows the the signal coming from the Arduino when
the program is modulating frequency properly. I began with my hand covering the photo-
transistor and slowly moved my hand away, resulting in the depicted modulation of the
frequency of the digital square wave output.
the digital pulse widths, as depicted in Figure 5, then as I moved my hand over and around
the photo transistor the sound coming out had an audible change in frequency/pitch.
3.3 Testing: Volume Control
The volume is controlled by the same principles used to control pitch, so testing the volume
control circuit began with testing the operation of the photo transistor portion first. The
output from the collector, from the photo transistor used in the third stage volume control
circuit, is where the signal was tested first. By connecting the collector output to an oscil-
loscope and covering and uncovering this photo transistor, the waveform on the oscilloscope
changed in amplitude in direct response to blocking the light hitting this photo transistor.
The signal coming out of the collector travels into into a buffer circuit. This buffer
circuit provides a boost in voltage and power, however the signal coming in should be nearly
identical to the signal coming out. To test this I used a voltmeter and simply put the con-
tacts before the buffer and after, and checked that these voltages were identical (or at least
extremely close to one another). Connecting the buffer to an oscilloscope proved to be an
ineffective method, for reasons that I cannot explain, however I believe it may have to do
with the oscilloscope itself somehow interfering with the circuit and pinning the op amp.
This is why I chose to use the voltmeter instead.
The last part of the volume control circuit I tested was the non-inverting amplifier. This
was done quickly and subjectively by simply connecting the output of the amplifier to the
speaker and listening to the sound for changes in volume as I covered and uncovered the
photo transistor. This is not the most scientific approach or the most effective way to test
the volume control circuit, but it was most certainly the quickest and easiest test method.
The other test method I utilized was to again use an oscilloscope, and observed the ampli-
tude of the wave forms change as I covered and uncovered the photo transistor. However, as
mentioned earlier, introducing the oscilloscope into the circuit at this point did not influence
10
16. 3.3 Testing: Volume Control Test Methods
Figure 6: This oscilloscope image captures the voltage of the signal being manipulated. This
signal is being measured before the buffer or amplification circuit, directly from the collector,
which is why the maximum voltage is so small and necessitates an amplification circuit. It
is also interesting to notice that the high frequencies appear to be more responsive to the
volume control circuit.
the functioning of the circuit the way it did when trying to test the buffer circuit. This is why
I believe using the oscilloscope to test the buffer circuit must cause some sort of impedance
issue that influences the overall function of the circuit. Regardless, I have established that
the amplifier worked and operated properly by observing infinitesimal voltages when I fully
enclosed the photo transistor with my hands, and seeing extremely large voltages when the
photo transistor was left untouched and all the light in the performance space is allowed to
hit it.
I noticed that the operation of the buffer and amplifier (both of which rely upon the
function of op amps) seemed to be less responsive to lower frequencies than higher frequen-
cies. Although the volume of these lower frequencies had the ability to be manipulated,
they seemed to be controlled less effectively than the higher frequencies. Even when entirely
covered, the output signal had very quiet lower frequency signals coming out and was never
completely silent.
believe this could be addressed with the inclusion of a low pass filter somewhere in the
third stage circuit (this was eventually done later, referenced is Section 5.2). Overall the
entire volume control circuit worked as originally designed, such that there was a maximum
volume when light was completely unblocked, and the speaker is essentially silent (except
for some slight noise) when the photo transistor in the volume control circuit was completely
covered.
11
17. 4. Data and Analysis
4.1 Pitch Control Analysis
The first stage of the circuit was tested under the lighting of a uniform plane of fluorescent
bulbs on the ceiling. This may seem like a mundane detail, but the device does require
some sort of light source to be manipulated, and one that is ideally coming down uniformly
from overhead. With all of this ambient light, unimpeded and hitting the surface of the
first NTE3034A photo-transistor, we observe a minimum voltage of 160 mV. Measuring
the resistance of the R1, the resistor connected to this photo transistor we find that it’s
resistance is actually 87 kΩ. Using these numbers we can use Equation 1 to solve for the
equivalent resistance of the photo-transistor when under this lighting. After some algebra
(again, treating the photo-transistor as Rpt) we solve Equation 1 for Rpt and find that the
equivalent resistance of the photo-transistor under maximum illumination is 287 Ω. This
confirms our design goal of and is quite close to our approximation, but moreover this result
confirms while being fully illuminated the photo transistor is essentially a short to ground.
Figure 7: This oscilloscope image depicts how the voltage slowly increased as I moved my
hand closer to the NTE3034A photo transistor in the first stage of the device, starting at
the minimum of 160 mV and moving steadily to a maximum of 4.56 V.
When fully blocking the photo transistor from all light, the observed voltage was 4.56 V.
This is extremely close to our theoretical values from the design section. Once again solving
the voltage divider equation, to evaluate the equivalent resistance of the photo-transistor in
the dark, we find that it’s equivalent resistance is 0.902 MΩ. This is also quite close to what
we expected.The voltage range achieved by moving our hand from far away to extremely
close was about 4.41 V. This is a good range to map our frequencies, and means we are
utilizing almost 90% of our allowed range of 0 V-5 V.
The oscilloscope image depicted in Figure 8 demonstrated the sensitivity of the device. I
waved my hand rapidly over the photo transistor and observed if the quick physical motion
would correspond to rapidly fluctuating voltages on the oscilloscope. From Figure 8 I have
demonstrated the capacity of the device to respond to extremely quick changes in light
intensity (again, by waving my hand over the photo transistor to rapidly change the amount
12
18. 4.2 Micro-Controller Analysis Data and Analysis
Figure 8: This oscilloscope image illustrates the sensitivity of the first stage circuit utiliz-
ing the NTE3034A photo transistor. Rapid hand motion translates into quickly changing
voltages.
of light incident on it) translating into rapidly changing voltages. In addition, Figure 7
illustrates the circuits capability to steadily increase in a smooth fashion as well. This
means that the device can produce smooth changes in pitch or rapid and large changes in
pitch, depending on how the performer chooses to manipulate the light in the performance
space.
4.2 Micro-Controller Analysis
It was difficult to capture data, on an oscilloscope, of the voltage at analog pin A0 influencing
the modulation of pitch coming out of digital pin 9 in a single image. To do this I edited
the overall values and range of frequency in the program to be smaller. This made it easier
to capture both changes in voltage and subsequently pitch on the same figure (without the
digital waves simply looking like noise or a solid square block.) It was difficult to capture
data, on an oscilloscope, of the voltage at analog pin A0 influencing the modulation of pitch
coming out of digital pin 9 in a single image. To do this I edited the overall values and range
of frequency in the program to be smaller. This made it easier to capture both changes in
voltage and subsequently pitch on the same figure (without the digital waves simply looking
like noise or a solid square block.)
The oscilloscope image depicted in Figure 9 shows how slowly changing the voltage leads
to the micro controller modulating the pulse simultaneously. This motion and voltage change
corresponds to smooth sounding changes in pitch. To make the images look better I also
eliminated the second octave harmonic from the program because it made the pulse width
modulation in the images much more confusing to look at. To analyze the response time
of the Arduino, we captured an image of a rapidly changing voltage overlapped with the
resulting pulse width modulation illustrated in Figure 10.
13
19. 4.2 Micro-Controller Analysis Data and Analysis
Figure 9: The first channel on the oscilloscope is the voltage being taken at analog pin A0,
depicted in yellow in this image. The blue channel represents the digital pulses coming out
of the Arduino. When the voltage is high the corresponding frequencies are high, and as the
voltage drops, the pulse width is appropriately modulated. From this figure we can deduce
that the Arduino is working properly.
Figure 10: The first channel on the scope is again, depicted in yellow, the voltage coming
from the collector of the photo transistor in the first stage. In blue are the digital pulses
coming out of the Arduino. It was especially hard to capture this figure, as the range in
frequencies that will be distinguishable on a single oscilloscope image are constrained by the
timescale, and so trying to having a quickly fluctuating voltage and pulse width together
was a difficult balance to find, but this image illustrates the device’s capacity to do so.
14
20. 4.3 Volume Control Analysis Data and Analysis
4.3 Volume Control Analysis
The third stage is a difficult part of the overall circuit to analyze because there are a lot
of pieces connected together serving many different functions, all of which can be interrupt-
ed/adulterated by the presence of the scope. First we analyzed the individual components
in the circuit and found that the resistance of the feedback resistor was 98.7 kΩ, while the
other resistor (connected to ground) in the amplifier was approximately 1 kΩ (actually mea-
sured 0.97 kΩ but this value fluctuated a bit). It is important to note that at this point in
the analysis the second frequency was added back into the code (the second pitch being an
octave higher or twice the frequency).
Then we analyzed the output at the buffer to be sure that the volume was being manipu-
lated, and to see what the signal going into the amplifier looked like. The buffer is a voltage
follower circuit, so these voltages should not be too much larger than the signal coming out
of the collector of the photo transistor used to control volume in the third stage.
Although the signal is a bit noisy the voltage appears so be starting close to zero and
Figure 11: The voltage coming out of the buffer appears to follow the signal from the photo
transistor as expected, and we see that the voltage has been lifted by the op amp without
influencing the frequency of the signal.
rising to and average value around 5V, which affirms what we expect from the voltage fol-
lower circuit. These figures do seem to indicate that the higher frequency signals are more
responsive to the volume control circuit. Next we analyze the signal coming out of the am-
plifier to examine whether it too will respond to changes in voltage, while also amplifying
the overall signal.
The cursors in Figures 11 and 12 are not well placed, but you can see from Figure 11
that most of the signal is being amplified from an initial infinitesimal voltage to about 5V.
In Figure 12 we see that this signal is noisier but the overall voltage amplification is much
greater, resulting in a much louder maximum volume, while also indicating the dynamic
range of this voltage as we move left to right (during which I began to block light).
It is important to note that in the second stage we observe outputs that are only positive
voltages because the digital output is a square wave. When we move to the third stage, and
15
21. 4.3 Volume Control Analysis Data and Analysis
Figure 12: As we move left to right on the scope face the overall amplitude of the signal
is clearly growing. This illustrates our capacity in the third stage to influence volume by
manipulating the incident light on the photo transistor in the third stage. Note the enormous
gain in signal voltage from left to right as I slowly allow more light to hit the photo transistor.
the op-amps are introduced, we see that we get positive and negative voltages. This helps
increase the overall volume as well in addition to the current and voltage boost that the
TVL2362 op-amps provide.
After analyzing the volume control circuit it is clear that various frequencies behave
differently when passing through the op-amps. This leads to a signal that is noisy both
graphically and aurally. The volume control circuit is also much harder to manipulate in
comparison to the pitch circuit. This may be due to the orientation of the photo transistors
in combination with the arrangement of light sources. This may also be indicative of the fact
that changes in volume are harder to control and also perceive due to the frequency response
of the human ear and the low-power/voltage operating ranges of the op-amps. Regardless,
the volume control circuit allows the loudness of the pitches from the speaker to controlled
by the performer and be audible.
16
22. 5. External Sound Analysis
Using an external microphone (in my laptop) and the audio analysis software Raven (de-
signed for analyzing bird sounds), I can analyze the output of the speaker. All of the analysis
done thus far has been on the circuitry itself, which has indicated that everything is func-
tioning properly. By performing this alternative method of analysis, I can inspect the actual
sound that is heard rather than the raw electronic signal. Raven is a powerful piece of soft-
ware that allows the user to simultaneously capture the waveform of a sound, as well as a
frequency spectrogram of this sound in real time.
A frequency spectrogram is simply a diagram of frequency versus time, where the color
intensity represents the power of each frequency. Before I did any analysis in Raven, I elimi-
nated the secondary octave tone from the Arduino sketch to make the process of interpreting
the figures generated in Raven more straightforward.
In the process of doing this external sound analysis I was reminded of the subtle nature
in which the square waves are actually being generated by the Arduino. In addition, the
usage of pulse-width modulation (PWM) in the Arduino to create the changes in pitch be-
comes important as well when studying the frequency spectrogram of sound from an external
source. A square wave is a mathematically impossible function because it has discontinuities.
Therefore, to replicate or produce a square wave requires the mathematical tool called a
Figure 13: This frequency spectrogram created in Raven illustrates how using a Fourier
series will combine multiple frequencies to approximate the shape of a square wave. The
more frequencies added, the more the signal will resemble a square wave. This image was
taken from an outside source [7].
Fourier series [6]. Essentially, square waves are created by combining an infinite sum of sine
and cosine functions. When analyzing the frequencies being captured by Raven, we expect
to not simply see a straight line at the frequency desired, but rather a sum of (theoretically
infinite) frequencies because of the mathematical necessity of using a Fourier series to create
these square waves. Below is an equation for this Fourier analysis specifically for analyzing
digital pulses, where L equals twice the period of the signal. Equation 3 mathematically
represents how a square wave function is generated by using the summation of an infinite
number of sin and cosine functions in addition to the fundamental frequency [6].
17
23. 5.1 External Frequency Analysis External Sound Analysis
f(t) =
a0
2
+
∞
n=1
ancos(
nπt
L
) +
∞
n=1
bnsin(
nπt
L
) (3)
5.1 External Frequency Analysis
The first part of my analysis with Raven was to analyze the lowest pitch generated when
all of the ambient light is unimpeded and hitting the first (pitch control) photo transistor.
The frequencies captured in this figure were not exactly what is expected of a Fourier series,
and the power of these additional frequencies was surprising as well. However, the frequency
still sounds low despite so many high frequencies being captured. The more interesting
information from this data was the sheer number of additional frequencies. This must be
because it takes more terms in a Fourier series to approximate a signal with a smaller
period/lower pitch. This is why the importance of using PWM in the device is important to
consider when studying the sound externally using Raven.
The next test was to observe and analyze the highest frequencies coming out of the Light
kHz
S
0.500
1.000
1.500
0.000
0.5 1 1.5 2 2.5 3 3.5 4.198
Figure 14: This is the frequency spectrogram produced by Raven when trying to capture
the lowest frequency, while all ambient light is unblocked. The y-axis is frequency and
the x-axis is time in seconds. Although there was a recorded frequency of 102 Hz with a
power of 95.5 dB, there were more than 14 other frequencies captured whose power were not
smaller than the fundamental. We do expect to see a large number of frequencies, however
each increasing frequency should be quieter, and the power/darkness of these additional
frequencies illustrated was unexpected.
Theremin with Raven, with the goal of capturing a powerful frequency at 800 Hz. What was
observed was similar to that of the low frequency spectrogram, however there were fewer
additional frequencies present than when analyzing the lower pitch. To reiterate, the darker
the line the more powerful the frequency captured in the figure is. The maximum frequency
with the most power captured was 771 Hz with a power of 105.7 dB. The other frequencies
were still powerful, but had less power than the fundamental frequency which is what is
expected from the Fourier series expansion as these additional frequencies should become
less powerful.
Overall, Raven revealed that the Arduino is in fact putting out our desired fundamental
frequencies, with a minimum of 102 Hz and a maximum of 796 Hz. However the power of
the additional frequencies, required by a Fourier series to make the square waves, were too
strong at low frequencies. When analyzing the highest fundamental frequency the power of
18
24. 5.1 External Frequency Analysis External Sound Analysis
Table 1: Lowest Frequency Raven Data
Frequency (Hz) Power (dB) Frequency Compared Fundamental
102 95.5 1.02f0
238 90 2.3f0
363 99.9 3.63f0
499 105.2 4.99f0
612 102.2 6.12f0
748 100.9 7.48f0
885 96.5 8.85f0
998 98.8 9.98f0
1123 91.2 11.23f0
1259 89.6 12.59f0
1372 97.9 13.72f0
1497 97 14.97f0
1633 97.7 16.33f0
1894 89.9 18.94f0
Table 2: Highest Frequency Raven Data
Frequency (Hz) Power (dB) Frequency Compared Fundamental
771 105.7 0.96f0
1485 103.8 1.86f0
2250 104.9 2.81f0
2298 96.7 3.74f0
3769 95.3 4.71f0
4511 74.5 5.64f0
5253 82.6 6.57f0
Figure 15: This frequency spectrogram generated by Raven was produced when trying to
capture the highest frequency coming out of the speaker from the Light Theremin. The
y-axis is frequency and the x-axis is time in seconds.The darkness indicates the power of
each frequency. There were many frequencies captured, bother higher and lower than the
target of 800 Hz, however at 771 Hz the signal had a power of 105.7 dB. This was stronger
than the other frequencies that appear on the spectrogram.
19
25. 5.2 External Volume Control Analysis External Sound Analysis
these additional frequencies were overall smaller than the fundamental, and also decreased in
a fashion that would be expected of a Fourier series expansion. The frequencies present were
both even and odd multiples of the fundamental frequencies. This is an interesting result
which may be related to how the Arduino actually performs the pulse width modulation, or
may be a result of something within the circuitry itself.
5.2 External Volume Control Analysis
The next step I took for analyzing the sound output of the Light Theremin, with an external
microphone and the Raven software, was to take a look at the volume manipulation. Before
analyzing the volume control with Raven, I chose to cover the pitch control photo transistor
in order to keep the pitch constant. This choice is subtle but important, because the volume
control circuit is more sensitive to higher frequencies than lower frequencies. This may be due
to the fact that higher frequencies carry more energy and power, and therefore manipulating
the volume of a high frequency will have a more noticeable range in decibel change. The
frequency that was recorded in Raven during the volume control analysis was 796 Hz.
kU
S
-20
-10
10
20
30
0.000
5 10 15 20 25 30 36.052
kHz
S
1.000
1.500
2.000
2.500
3.000
3.500
0.000
5 10 15 20 25 30 36.052
Figure 16: The top image is the waveform of the recorded sound. The units of the waveform
figure on the y-axis are measured in kilo-Pascals, which is indicative of the sound pressure
and therefore the perceived volume. The x-axis of both figures is time in seconds. The
bottom image is the frequency spectrogram. Using Raven to analyze the recording depicted
in this figure, we found a maximum volume of 105.7 dB and a minimum volume of 15.2 dB.
This is visually represented by the varying darkness of the frequency spectral lines, and is
corroborated by simultaneous changes in the amplitude of the waveform.
I also chose to use higher frequencies for this stage of analysis because as mentioned
previously, Raven appears to be designed for higher pitches and therefore creates much
cleaner images when recording higher frequencies. I also decided to add a 1 nF capacitor in
parallel with the volume control photo transistor, which not only made the volume control
20
26. 5.3 External Frequency Modulation Analysis External Sound Analysis
must more responsive, but also allowed for complete silence to be achieved when the light
hitting the volume control photo transistor is completely occluded. This was a somewhat
educated guess that turned out to be highly effective.
From the recording in Raven, I was able to measure a change in volume (of the 796 Hz
frequency that we are choosing to analyze) from 105.7 dB to a volume of 10.2 dB. The decibel
is a logarithmic scale because the power intensity of sounds that the human ear can respond
to covers an enormous range. Therefore this change in decibel created by the volume control
circuit is extremely dramatic. To get a sense of how dramatic this decibel change is, we can
compare these decibel values to commonplace sounds. 105 dB is equivalent to the volume of
a lawn mower, while 10.2 dB is barely perceptible and is essentially silence [5].
5.3 External Frequency Modulation Analysis
In addition to analyzing volume modulation in Raven, I also analyzed the frequency modu-
lation of the Light Theremin with the Raven Software. Similar to the previous examples of
analysis using Raven, the recording of frequency modulation also recorded many frequencies
being captured simultaneously. Again, these other frequencies were unanticipated, and when
analyzing the frequency modulation of the Light Theremin in Raven I chose to only look at
the fundamental pitch range that was programmed into the Arduino (100 Hz -800 Hz).
kHz
S
1
2
3
4
5
0.000
2 4 6 8 10 12 14 16 18 20 22 24 26 28 29.6
Figure 17: This image, created by the Raven audio analysis software, depicts the frequency
spectrogram as the frequency coming from the Light Theremin is modulated from a minimum
frequency of approximately 88 Hz to a maximum of 798 Hz. Again the y-axis is in kHz and
the x-axis in seconds. It is reassuring to see in this figure that the frequencies higher than
the fundamental appear to be quieter than the fundamental, which is how the Fourier series
creation of square waves is supposed to behave.
For the recording of frequency modulation I began with the pitch control photo transistor
being completely unblocked, and slowly moved my hand closer and closer (which manipu-
lates the intensity of light hitting the photo transistor) until it was eventually completely
covered. The frequency of this fundamental pitch was modulated from approximately 88 Hz
to a maximum of 798 Hz. This is a good result because the map function in the Arduino
is programmed to have a frequency range of 100 Hz -800 Hz. From these results it can be
concluded that the frequency modulation of the Light Theremin works properly. It is also
interesting to see how the Fourier series overtones respond to changing the fundamental.
21
27. 6. Conclusion
Overall the instrument I designed and built functions as initially proposed. The pitch coming
out of the speaker was extremely sensitive to the movement of a performer’s hand altering
the amount of incident light on the photo-transistor (in the first stage of the design). This
sensitivity was a result of our ability to get such a wide range of voltages from the first
stage. This range was approximately 4.41 V as denoted in Section 4.1 of this report. Having
such a large voltage range, and the ability to manipulate the voltage so precisely (which
was confirmed and illustrated in Section 4.1 as well), allows the Arduino to have a more
continuous sounding change in pitch or dramatic changes in pitch (depending again on how
the light is being manipulated).
The Arduino quickly and easily translates a voltage to a pitch, using very simple code
included in Section 4.1 of this report. As I have previously mentioned the wide range in
analog input voltages allows the map function to assign many more pitches between the
minimum and maximum frequencies. This leads to outputs with changes in frequency that
can be smooth or erratic, depending on how the performer chooses to play the instrument.
The volume control circuit did not initially work as well as anticipated, however by adding
a capacitor in parallel to the volume control photo transistor the circuit was able to control
volume in a very controlled manner that now functions exactly as I envisioned.
The difficulty is that perceived volume is also dependent on frequency, and in addition the
voltage/power constraints of the Arduino forced me to use op-amps designed for low power
and voltage operation. These limitations may be why the volume control is less responsive
and/or sensitive compared to the pitch control. However, the output signal has a voltage
range that can reach up to 17 V and a minimum of essentially zero volts (as described in the
Section 4.3, even while muted and fully blocked some high frequencies seem to occasionally
slip through). This enormous range in amplification was illustrated in Section 4.3, and
quantified in Section 5.2. By using Raven, this change in volume was quantified and shown
to be a change of almost 90 dB, which is a significant change in volume.
The most interesting part of the analysis of the Light Theremin was the usage of the
audio recording/analysis software Raven. Although Raven utilized an external microphone
to confirm the data and analysis done on the actual electronic signal, it revealed that the
speaker is not simply playing a single tone as I imagined. At first I thought that perhaps
Raven was so sensitive it was picking up another source of noise, however after reviewing the
figures that illustrate changes in volume (found in Section 4.3) and changes in pitch (found
in Section 4.2), it is clear that these frequencies react in accordance with the programmed
fundamental frequency.
After consulting with Professor Sullivan I was reminded of how square waves are produced
using a Fourier series of additional frequencies to construct a square wave. That being said,
these additional frequencies at times do not appear to have volumes that act in accordance
with how a digital pulse is constructed should with a Fourier series. The tables, included in
Section 5.1, indicate that the power of these additional frequencies were far too high at the
low end. Furthermore, when analyzing the highest frequencies in Section 5.1 the additional
frequencies are both odd and even which is not what is to be anticipated, and may be a
byproduct of how the Arduino handles pulse width modulation, or perhaps is an unintended
22
28. Conclusion
consequence somewhere in the volume control or amplification process.
In the construction of this instrument I have encountered many engineering problems
which were handled accordingly, but in the end I believe the Light Theremin functions in
alignment with the philosophy and aesthetic I initially desired. It is a fun and interesting
little device that allows a person to interact with science in a unique and subjective way.
I believe it is important to provide people (especially children) with alternative ways to
experience and interact with science, and I think this device does so in a tangible manner
which also allows for subjective expression and may foster an appreciation for Science for
those already exposed to science.
Similarly, if children were exposed to such a device earlier on (elementary or middle school
perhaps) in a music education environment they may gain a new appreciation for science and
a curiosity that would motivate them to want to learn more! In addition if introduced into
the classroom of students with special needs, this device may allow them to communicate
and be expressive in a non-verbal manner, enable them (despite being disabled) to feel more
connected to the world that has taken so much from them and given back so little, and
hopefully and most importantly it could excite them and bring them joy.
23
29. References Cited
[1] K. D. Skeldon, L. M. Reid, V. McInally, B. Dougan, C. Fulton, Physics of the Theremin,
American Journal of Physics 66 (1998).
[2] M. Vennard, Leon Theremin: The man and the music machine, BBC News, (2012),
available at http://www.bbc.com/news/magazine-17340257.
[3] G. Grimes, How a Theremin Works, How Stuff Works, available at http://
electronics.howstuffworks.com/gadgets/audio-music/theremin1.htm.
[4] NTE Electronics, NTE3034A Photo Transistor Detector, available at http://www.
nteinc.com/specs/3000to3099/pdf/nte3034a.pdf.
[5] S. Fox , Noise Level Chart, Noise Help, available at http://www.noisehelp.com/
noise-level-chart.html.
[6] M. Boas,Mathematical Methods in the Physical Sciences,Third Edition, John Wiley and
Sons, 2006.
[7] W.T. Bridgman, Quantized Redshifts.II.The Fourier Series, Crank Astronomy, (2011),
available at http://2.bp.blogspot.com/_okIcsBieX4U/TRKogEZh16I/AAAAAAAAAIY/
spYsURzN3d0/s1600/squarewave32terms.png.
24
