Circuitry-Based Sound

Group live performance at the ZKM

"Circuitry-Based Sound" is an artistic workshop in the fields of electronic music, sound art, and performance. This project equips artists with practical hands-on skills for building their own musical circuitry or modifying existing audio hardware. It offers practical knowledge of electronics useful for sound creation, noise making and music interaction. Participants are introduced to soldering and assembling audio circuits on breadboards or perfboards in the context of audio, composition, live performance and sound art. A major portion of the project will be devoted to hardware prototyping, including test and fault finding sessions. The emphasis will be upon the designing of electronic instruments as well as interfacing transducers and developing alternative controllers. Artistic and practical use of the circuits will also be explored and discussed.

Below is a documentation of the workshop's study materials and findings.

TABLE OF CONTENTS

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INTRODUCTION

• Unconventional Electronic Sound
• CMOS Chips for Sound Creation
• Basic Example
• Logic Control

ELECTRONIC COMPONENTS

• Numerical Index

BASIC PRINCIPLES AND APPLICATIONS

• Signal Mixing
• Passive Filters
• Pull-up and Pull-down Resistors
• Linear Feedback Shift Register
• Step Sequencer
• Voltage Starve

MATERIALS

• Requirements
• Bill of Materials
• Literature
• License

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Disclaimer

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Introduction

Photo: Yunfei Zhang

Aside from the established way of using electronics to generate and process sound, which can be found in analog synthesizers, there are also unconventional applications of electronics to create sound or experimental music, which will be introduced below. Analog synthesizers apply techniques like subtractive synthesis to produce sound. A common concept of the analog signal flow is filtering the output of an oscillator and shaping the overall volume. Variations of this concept can be found in most synthesizers, both analog and digital. Parameters can be altered through control signals. This offers a wide range of musical expression, like tuning oscillators in a 12-tone musical scale or key triggered envelopes for amplifiers, filters or other effect processors. To obtain these functionalities, circuits of analog synthesizers are relatively complex, involve a high part count and often require precision components.

Unconventional Electronic Sound

Another concept of creating sound with electronics derived from techniques like hardware hacking and circuit bending. In particular the use of digital integrated logic circuits outside of their typical field of application is a remarkable approach to build customized instruments for artistic sound production and interactive music. The required components are easy to source and low cost. What makes these types of chips even more handy is that they don't need much external components and wiring. They can be used for generating and processing sound without large expenditure.

CMOS Chips for Sound Creation

Various CMOS chips

CMOS chips are designed to execute Boolean functions. Complementary metal–oxide–semiconductor (CMOS) is a technique where p-type and n-type MOSFETs are used for manufacturing logic gates. Voltage levels represent the binary states 0 and 1. Produced as integrated circuits, individual components relate to basic logical functions like NOT, AND, OR, NAND, XOR, XNOR or implement multiplexers, counters, dividers, flip-flops and registers. When logical operations and their relation to voltage and sound are understood, CMOS-logic chips are an inexhaustible source for unconventional electronic sound. They produce digital signals - square waves - that can be modified, shaped, gated, sequenced, layered, and many more. Combining different logic functions allows generating a multitude of unique sounds and temporal music structures, while they produce the richness of analog sound. These circuits also yield unpredictable behavior, produce rhythmic glitches or digital noise.

Logical operations can be implemented as switching circuits with single pole single throw switches representing the input and an LED indicating the result. The switch and the LED can have two distinct states: on and off. The open switch corresponds to a logical 0 and the closed position stands for a logical 1. A lit LED means 1 and a non-lit 0.

A truth table is used in Boolean algebra to show all possible values of a logical expression.

Output comparison of 2-input logic gates:

INPUT A	INPUT B	AND	NAND	OR	NOR	XOR	XNOR
0	0	0	1	0	1	0	1
0	1	0	1	1	0	1	0
1	0	0	1	1	0	1	0
1	1	1	0	1	0	0	1

Due to its simplicity, CMOS chips can be used for educational reasons, since most of its technical operations can easily be understood and relate to basic electronic knowledge. This subject is also a matter of various publications, most notably Nicolas Collins' „Handmade Electronic Music, The Art of Hardware Hacking" (2006). American Composer David Tudor (1926 - 1996) is considered a pioneer of self-made electronic circuits and instruments, which he used for his compositions. Stanley Lunetta (1937 - 2016), avant-garde composer and artist, incorporated in the 70s digital electronics into his compositions and sound art sculptures and shared his techniques with other artists. In the experimental music community, CMOS synthesizers are therefore often referred to as "Lunettas".

Basic Example

The „hello world“ of CMOS-Synthesizers as a measure of how simple it is to produce sound is illustrated through the picture above. It shows a square wave sound generator that can be built with only three components, jumper wires and a power supply:

• inverting Schmitt trigger IC, e.g. CD40106
• capacitor C
• resistor R

An inverting Schmitt trigger is an active electronic component whose output state can be triggered complementarily through an input signal, while the positive trigger threshold differs from the negative one, which is called hysteresis. Feeding the output back to its input via a resistor R and connecting a capacitor C between the input and ground, known as RC circuit, creates a relaxation oscillator or astable multivibrator. The resistor limits the current for charging the capacitor and both together determine the charging time.

The frequency can be roughly calculated with this formula $f=\frac{1}{T}=\frac{1}{RC ln [(\frac{V_P}{V_N})(\frac{V_{DD}-V_N}{V_{DD}-V_P})]}$, where V_P is the positive trigger threshold voltage and V_N the negative trigger threshold voltage.

However, manufacturing tolerances of all involved parts make it difficult to achieve exact results based on the formula. Since the field of application is artistic sound production, circuits should be evaluated by ear. But the formula shows that bigger RC values produce lower frequencies and vice versa. The frequency is determined through the capacitor C and the resistor R. Therefore, a potentiometer instead of the latter enables pitch control. Other ways of controlling the frequency may be inserting photoresistors, force-sensitive resistors (FSR) or flex sensors. Adding circuit points to alter the sound through interaction allows building customized and versatile instruments.

Logic Control

A logic gate is a single input - output device, designed to carry out a specific Boolean operation, mapped to two voltage levels. Over time, the two alternating voltage levels may form a periodic rectangular waveform and the speed of switching between the two levels is perceived as pitch. Aperiodic switching will produce other sonic qualities such as noise or all kinds of texturized sounds. The ratio between the on- and off-states is by default close to 1:1, a 50% duty cycle. Further circuitry is needed to change this ratio, which alters the ratio of the amplitudes of the harmonic components to the fundamental.

In digital electronics 2-level logic, binary numbers are represented by two defined voltage levels that are specified by the used technology and circuit. Everything below a certain voltage threshold level is recognized as 0 and everything above a certain threshold level is recognized as 1. A voltage level in between the two thresholds is not defined or forbidden and will produce false output triggers. CMOS digital inputs have a high impedance and pick up thermal noise voltages if left floating. Unused inputs should be tied to a defined voltage. Other input configurations (e.g. taster, toggle switches,) require pull-up or pull-down resistors. The two states "0" and "1" are also often referred to as "(logical) high" and "(logical) low", "true" and "false" or "ON" and "OFF".

V_IH is the minimum input voltage that will be interpreted as a logical high, while V_IL is the maximum input voltage that will be interpreted as a logical low. The region in between is undefined and may trigger unpredictable highs or lows (chattering). This problem is solved by implementing a Schmitt trigger with different thresholds for negative-going and positive-going input voltages, depending on whether the input signal is changing from high to low (V_N) or low to high (V_P). When the input is between the two thresholds the output retains its value.

The square wave contains only overtones with odd numbered harmonics (⅓, ⅕, ⅐, etc). The relative amplitudes of the harmonics are equal to 1/harmonic number n.

Electronic Components

The following is a list of CMOS chips and other integrated circuits for sound creation and processing. This list will be constantly extended during the seminar. It outlines for each chip its main applications and gives a short explanation. Pinout, functional diagram, truth tables and some basic example circuits are also shown. However, the overview is not completed with these examples and the main approach is to find variations, modifications or new creative combinations for experimental sound and music. Please refer to the manufacturer's technical data sheet for more detailed information.

Numerical Index

• CD40106
• CD4093
• CD4070
• CD4015
• CD4022
• CD4040
• CD4046
• CD405x
• CD4066
• CD4060
• CD4013
• CD4018
• 555 Timer
• LM386

CD40106

The inverter is a basic part in digital electronics and performs the logic operation of negation. When the input is connected to ground, the output is pulled to V_DD and vice versa. The CD40106 hex Schmitt trigger inverter offers six separate inverters in one chip. The Schmitt trigger action permits unlimited rise and fall times on the input. The chip can be wired externally to build one or more square wave oscillators (see illustration). When using a potentiometer for frequency control, a resistor should be placed in series in order to prevent too low resistance between output and input.

Applications:

• Square Wave Generator
• Inverting Buffer

Truth table for NOT

Inputs	Outputs
0	1
1	0

"1" = High Level
"0" = Low Level

CD40106 Sheet

CD4093

The CD4093 contains 4 NAND Schmitt triggers, each providing 2 inputs and 1 output.

It acts as a square wave oscillator when the inputs are connected to form an inverter. The last two rows of the truth table indicate that one input has to be set to a logical high in order to attain inversion of the signal being present at the other input. When one of the inputs is wired like the CD40106 in the previous example, while the remaining input is set to high, the CD4093 generates square waves too.

Applications:

• Square Wave Generator
• Gated Oscillator

Oscillators built with 2 input NAND Schmitt triggers can be switched on and off manually by using a push button. If the push button is not pressed (normally open) the logical low at the second input will always cause a logical high at the output, no matter which state is present at the other input (see NAND truth table). The image above shows how to set up a normally open push button as an ON switch to control the sound. A pull down resistor defines the logic state at the input when the push button is open. When the push button is closed, the power supply produces a logical high and the NAND gate oscillates. This way, the second input acts as a control input for gating the oscillator. Instead of a manually controlled push button, a logic signal can be applied to the second input.

Truth table for NAND

A	B	J=A NAND B
0	0	1
0	1	1
1	0	1
1	1	0

CD4093 Data Sheet

CD4070

The CD4070 contains four Exclusive-OR logic gates. Each gate has two inputs and one output. The output is high when only one of the inputs is high and the other is low and vice versa. If both inputs are high or low, the output is low. If two square wave signals are connected to the input, the output extracts the difference which results in a frequency mixer like output signal. Frequency doubling can be achieved if one square wave is applied directly to one input and connected via a resistor to its second input with a capacitor to ground. The rising and falling edge of an incoming square wave force the output to high, hence doubles the incoming frequency. The pulse width of the output signal depends on the chosen values and is shorter than the width of the input signal; approximately the length of the RC time constant. Shifting a tone up by an octave may only sound satisfactorily within a small value range.

CD4077 is the Exclusive-NOR version.

Applications:

• Digital Frequency Mixer
• Frequency Doubler

Truth table for XOR (CD4070)

A	B	Y = A XOR B
0	0	0
0	1	1
1	0	1
1	1	0

CD4070 Data Sheet

CD4015

CD4015 IC consists of two four stage shift registers.

A shift register is built of a series of interconnected flip-flops. A flip-flop or latch is a bistable multivibrator circuit. This means it has two stable states which represent either 0 or 1. The state of a flip-flop can be controlled by a clock. The value to be stored is based on the signal's input state at the transition of the clock signal. A flip-flop is used to store 1 bit. In a shift register the incoming serial input data D is transferred to a parallel output register Qn. More specifically, when a memory content is stored in the first flip-flop, it is shifted to the next one, synchronized to the rising edge of a dedicated clock signal CL. A logical high at the reset pin is setting all outputs to zero. The reset pin should be set to low for a continuous operation.

Applications:

• Sequencer
• Noise Generator
• Linear-feedback Shift Register (LFSR)

Truth table for four stage shift register

CL	D	R	Q1	Qn
/	0	0	0	Qn-1
/	1	0	1	Qn-1
⧹	X	0	Q1	Qn
X	X	1	0	0

X = Don't Care Case
/ = Rising Edge
⧹ = Falling Edge

CD4015 Data Sheet

CD4022

CD4022 and CD4017 ICs implement a binary counter/divider function with 8 outputs in the CD4022 and 10 outputs in the CD4017. The positive edge of an incoming square wave, usually referred to as "clock signal", triggers successively the outputs. "Carry out" is outputting one cycle over 8 (CD4022) respectively 10 (CD4017) clock pulses. A logical high at "clock inhibit" pauses the counting process. A logical high at the "reset" pin sets the counter pulse back to the first output.

Applications:

• Sequencer
• Staircase Wave Form Generator
• Wave Shaper

CD4022 Data Sheet

CD4040

This IC performs frequency division and comes with 12 outputs in the CD4020 and the CD4040 versions and 7 outputs in the CD4024 version, whereby the CD4020 is a 14-stage device. Output stages 2 and 3 (divide by 4 and 8) are not accessible. The CD4024 has 3 pins without internal connection (pin 8, 10, 13). If a square wave is applied to the input, each output creates square waves at half the frequency of its preceding output, at which the first output Q1 applies its division to the input signal and oscillates at a rate at one half, Q2 at one quarter, Q3 at one eighth Q4 at one sixteenth and so on. Several units can be cascaded for higher counting.

Control input "reset" triggers all output stages to "low". For continuous frequency division it should be kept at a logical low.

Applications:

• Frequency Divider
• Sub Octave Generator
• Representation of Binary Numbers

In terms of generating sound, each output producing one octave lower than its previous output, respectively input.

The timing diagram shows the relation of voltage levels between all outputs of the CD4024 IC, a 7-output stage version:

CD4040 Data Sheet

CD4046

Phase locked loop

Applications:

• Tone Distortion
• Pitch Tracking
• Frequency Multiplication
• Voltage Controlled Square Wave Generator

CD4046 Data Sheet

CD405x

CD405x Multiplexer/Demultiplexer series comes in a 16 DIP package and is useful for switching and routing analog or digital signals.

The contact resistance (R_ON) of a CMOS switch in the closed position depends on the input voltage, power supply voltage, and temperature. For the CD405x types this on-resistance is approximately in the range of 120Ω - 200Ω or more ohms and can distort the input signal in some cases. This value is quite low and negligible for the field of applications described in this article.

If any of the control pins of the CD405x are not used, it must be connected to GND or V_DD.

All channels are off when inhibit input is set to "high" (active low).

V_EE (Pin 7) is for dual supply operation. It is tied to ground in single supply mode.

Applications:

• Wave Shaper
• Digitally-controlled Analog Switching
• Signal Routing
• controlling LEDs

CD4051

CD4051 is a switch in a single pole octal throw configuration with three binary control inputs for setting the contacts.

Truth table for the CD4051

INHIBIT	C	B	A	ON CHANNEL(S)
0	0	0	0	0
0	0	0	1	1
0	0	1	0	2
0	0	1	1	3
0	1	0	0	4
0	1	0	1	5
0	1	1	0	6
0	1	1	1	7
1	X	X	X	None

X = Don't Care

CD4052

CD4052 can be used for multiplexing one differential channel in a double-pole quad-throw configuration and has two binary control inputs.

Truth table for the CD4052

INHIBIT	B	A	ON CHANNEL(S)
0	0	0	X0, Y0
0	0	1	X1, Y1
0	1	0	X2, Y2
0	1	1	X3, Y3
1	X	X	None

X = Don't Care

CD4053

CD4053 offers individual control over 3 channels in a single-pole double-throw configuration with an independent binary control input for each channel.

Truth table for the CD4053

INHIBIT	C	B	A	ON CHANNEL(S)
0	X	X	0	ax
0	X	X	1	ay
0	X	0	X	bx
0	X	1	X	by
0	0	X	X	cx
0	1	X	X	cy
1	X	X	X	None

X = Don't Care

CD405x Data Sheet

CD4066

Quad Bilateral Single Pole Single Throw Switch

IC CD4066 includes four identical digitally controlled switches for analog or digital signals. Inputs and outputs are interchangeable as with conventional switches. Each switch can be controlled independently by a control input.

On-state resistance is between few hundred ohms to one thousands ohms, depending on V_DD. Absolute maximum current into any input is 10mA.

control logic 1 = switch on
control logic 0 = switch off

Applications:

• Signal Gating
• Signal Routing
• Transmission Gate Inverter

CD4066 Data Sheet

CD4060

14 stage ripple-carry binary counter/divider and oscillator. Q1, Q2, Q3 and Q11 are not connected to the outside of the package. A high level on input pin 12 resets the counter and disables the oscillator.

Applications:

• Frequency Divider
• Square Wave Generator

CD4060 Data Sheet

CD4013

The CD4013 IC flip-flop is called a D flip-flop type to characterize its behavior, while D stands for "data" or "delay". It contains two identical D flip-flop arrangements. The device stores a digital state 0 or 1, which is accessible at the output Q. The second output /Q presents the inverse of Q. The control input Clock transfers the input state D to the output Q respectively /Q. The CD4013 is positive-edge-triggered, which means that the positive-going transition of a clock impulse triggers the device to hold the state that is present at the input and provides it at the output until the next positive-going clock signal. The additional control inputs Set and Reset have priority over the clock. With a high level on the Set input, the output follows its state and goes low with a high level on the Reset input, ignoring D and Clock.

Applications:

• Frequency Divider
• Counter
• Toggle Switch

D flip-flop truth table

C	D	R	S	Q	/Q
/	0	0	0	0	1
/	1	0	0	1	0
⧹	X	0	0	no change	no change
X	X	1	0	0	1
X	X	0	1	1	0
X	X	1	1	1	1

X = Don't Care
/ = Rising Edge
⧹ = Falling Edge

CD4013 Data Sheet

CD4018 (under construction)

Divide-By-'N' Counter

When the outputs are fed back to the input Data, divide by 10, 8, 6, 4, 2, is calculated. For odd numbers 9, 7, 5, 3, simply use CD4011 or CD4093 to NAND two corresponding output stages and feed the inverted result back into Data. By combining multiple devices, higher divide-by functions can be calculated. Preset enable will transfer Data on the input Jam to its corresponding /Q (inverted). A logical high on the reset input causes all /Q Outputs to high.

Divide by 9: /Q4 & /Q5 via 1/2 CD4011 connected to input Data
Divide by 7: /Q3 & /Q4 via 1/2 CD4011 connected to input Data
Divide by 5: /Q2 & /Q3 via 1/2 CD4011 connected to input Data
Divide by 3: /Q1 & /Q2 via 1/2 CD4011 connected to input Data

Divide by 10: /Q5 connected to input Data
Divide by 8: /Q4 connected to input Data
Divide by 6: /Q3 connected to input Data
Divide by 4: /Q2 connected to input Data
Divide by 2: /Q1 connected to input Data

Applications:

• Divide by 10, 8, 6, 4, 2
• Divide by 9, 7, 5, 3
• Rhythm/Chord Generator

FUNCTIONAL TRUTH TABLE FOR CD4018

Clock	Reset	Preset Enable	Jam Input	/Qn
⧹	0	0	X	/Qn
/	0	0	X	/Dn
X	0	1	0	1
X	0	1	1	0
X	1	X	X	1

/Dn = Data input for that stage
X = Don't Care
/ = Rising Edge
⧹ = Falling Edge

CD4018 Data Sheet

555 Timer

Note: The bipolar version (NE555) and the CMOS version (TLC555, LMC555) have the same pinout and are exchangeable. The CMOS version consumes significantly less power. Its name derives from the three 5kΩ resistors that form a voltage divider network. This IC generates output pulses for precision timing or works as an oscillator with adjustable duty cycle. The timing function can be configured with just a few external components.

Applications:

• Frequency Divider
• Timer
• Pulse Delay
• Square Wave Generator
• Pulse Width Modulator

Pin	Function
1	Ground.
2	Start of timing input. TRIG < ½ CONT sets output high and discharge open.
3	High current timer output signal.
4	Active low reset input forces output and discharge low.
5	Controls comparator thresholds, Outputs 2/3 VCC, allows bypass capacitor connection.
6	End of timing input. THRES > CONT sets output low and discharge low.
7	Open collector output to discharge timing capacitor.
8	Input supply voltage, 4.5 V to 16 V.

In the astable configuration or multivibrator mode, the circuit generates a string of pulses by retriggering itself. Different values for $R_A$ and $R_B$ allow for changing the ratio of the high time and the low time. A low at reset pin 4 stops the oscillation. The time to complete one cycle (high and low) can be calculated with $T= ln(2) \cdot (R_A + 2R_B)C$ and the frequency with $f=\frac{1}{T}$.

For mono stable operation, a negative going pulse at the trigger input causes the output to go high for a defined amount of time (one shot). A second pulse within that time period has no effect on the output pulse and will be ignored. This circuit can be used for debouncing switches. The time the output stays high is set through the RC circuit and can be calculated with $T_H = ln(3) \cdot R_1C_1 \approx 1.1 \cdot R_1 C_1$.

LMC555 Data Sheet
TLC555 Data Sheet

LM386 - Power Operational Amplifier (under construction)

Although not part of the CMOS logic family this ubiquitous power op amp is a very versatile component when it comes to amplification or driving small speakers.

LM386 Data Sheet

Pin	Function
1	Gain setting
2	Inverting input
3	Noninverting input
4	Ground reference
5	Output
6	Power supply voltage
7	Bypass decoupling path
8	Gain setting pin

	min Voltage	max Voltage
Supply Voltage	4V	12V
Analog input voltage	-0.4V	0.4V

Basic Principles and Applications

Mixing

There are various ways of mixing signals together. Using CMOS chips like the XOR CD4070 works for digital signals. If more than two signals should be mixed or merged, several logic gates can be chained together. Even though the resulting signal is not the sum of the source signals but some modulated result, the output signal is still compatible with digital electronics. This is not the case with active and passive mixing, which alters the amplitude of the output. Active mixing involves components, such as operational amplifiers, that need a power supply. Passive mixing works without an additional power supply, but introduces a voltage drop.

Passive Mixing

Passive mixing is a very simple method that can be accomplished by using resistors for each source. The mixing resistors work as a voltage divider network and lower the amplitude of each signal. Therefore, the passive mixer doesn't give the sum of all input signals but the average. Small resistance values will drain more current and create distortion. Good values are between 10kΩ - 50kΩ. The advantage of this method is its low part count. To avoid attenuation and interaction between the signals and to obtain individual gain control, active mixing using an operational amplifier is preferred.

Active Mixing

For most audio applications it is desired to control the portion of each input signal in the sum of the output mix. For this, another class of active electronic components can be used, the operational amplifier (op amp). The basic wiring is shown below.

By adding voltage dividers or potentiometers, it allows for gain control over every individual input. Besides its function as a mixer, it can also be used to achieve the desired output gain by modifying the feedback resistor R_F in relation to the input resistors R_IN of each input. The minus sign in the formula indicates that the output voltage is inverted. To undo inversion, a second stage following the shown circuit can be used.

$V_{OUT} = - [ \frac{R_F} {R_{IN1}} V_{IN1} + \frac{R_F} {R_{IN2}} V_{IN2} + \frac{R_F} {R_{IN3}} V_{IN3} + etc.]$
$- V_{OUT} = \frac{R_F} {R_{IN}} [V_{IN1} + V_{IN2} + V_{IN3} + etc.]$ if all $R_{IN}$ are the same.

It should be underlined that the example shown is a single supply based circuit, which is uncommon for audio mixing where usually symmetrical dual supply voltages are used. It is important therefore to create a reference voltage of 1/2 V_CC at the non-inverting input. When working with logic circuits, the signals are almost at the supply levels. Even with rail-to-rail op amps caution is required to keep the summed signals below the working range of the op amp.

Passive Filters

Tone control, modifying the frequency spectrum of a signal or creative equalization are very important processes when working with audio. A filter is frequency-selective and passes only a desired range of frequencies, which is called the pass band. Outside of this pass band, frequencies are attenuated or ideally completely reduced. The boundary between pass and stop band is called cutoff frequency. The simplest way to shape an electronic signal is the use of a combination of resistor and capacitor, an RC element. This forms a first order filter. The circuit can be considered as a frequency dependent potential divider. A band-pass filter can be built with two RC elements, as a combination of a high-pass and a low-pass configuration. Since no amplifying components are involved, the amplitude of the output is lower than the input amplitude. When a filter is designed with two passive components, the transition from pass to stop band is rather smooth. For instance, a first order low-pass filter will have a 6dB/octave roll-off with increasing frequency. Unfortunately, the properties of passive filters are not sufficient to achieve a higher steepness or musical effects like resonance, which requires active filter designs. However, the simplicity and the low part count make this method very attractive for subtle tone control.

Pull-up and Pull-down Resistors

When external circuits or devices are added to a logic input, care must be taken to keep the inputs in a defined state. When switches or transistors are used to control a logic gate, they can physically disconnect the inputs. For example, when a normally-open push button is in its default position, the high impedance input is open. This causes the pin to act like an antenna that is very susceptible to electromagnetic noise and forces the output to do unwanted operations like generating random highs or lows. This is called "floating" and introduces undesired effects.

To avoid this unpredicted behavior, a resistor should be connected to ground or to the high voltage, so that the input pin will see a defined state even when nothing else is connected, for example when a switch is opened. The pin will be able to accept an input signal when the switch is closed. A connection to V_CC is called "pull-up" and a connection to ground "pull-down". For CMOS-logic, the resistor values can be several thousand ohms.

Even unused logic gates can cause problems since coupled-in interference voltages result in unwanted triggers and excess current draw. If a proper operation is desired, all unused inputs should not be left floating and connected together to GND or V_CC.

Linear Feedback Shift Register

A linear feedback shift register (LFSR) can be used for generating deterministic pseudorandomness. In terms of electronic sound production it can be used to build a noise source. An LFSR consists of n numbers of flip-flops which are connected in series to form a shift register as described for the CD4015. This shift register is controlled by a clock that triggers the shift process. Two junctions at a specific position within that chain of flip-flops are directed into an XOR logic gate. The resulting value is fed back into the first register. The number of stages can be extended by connecting multiple devices. The produced values are determined by the shift register's current states and total length. Since the states are finite it will repeat after a certain number of steps. The goal is to choose those taps that form the longest possible sequence of zeros and ones before they repeat. Other implementations of an LFSR exist and work similarly. To activate an LFSR each stage needs to be loaded with an initial value. This is called the seed. By using an XOR function for the feedback, having the value 0 in all flip-flops is forbidden. By using an XNOR function it is forbidden to set all flip-flops to 1. A maximum-length sequence is therefore 2ⁿ - 1. No matter if XOR or XNOR functions are used, the sequences will have the same length. The duration of one cycle is determined by the clock frequency. When looked at a shift register from the viewpoint of a musician, the long LFSR arrangements will create white and pink noise when controlled with a high frequency (several ten thousands of hertz). Shorter cycles produce grainy tones, stuttering textures or short noise loops.

The Xilinx application note XAPP210 (V1.3) and the Maxim Integrated (now Analog Devices) application note APP4400 (Jun 30, 2010) show tables for maximum length sequences, which are presented here for up to 32 bits:

n	taps from	length		n	taps from	length		n	taps from	length
3	3,2	7		13	13,4,3,1	8,191		23	23,18	8,388,607
4	4,3	15		14	14,5,3,1	16,383		24	24,23,22,17	16,777,215
5	5,3	31		15	15,14	32,767		25	25,22	33,554,431
6	6,5	63		16	16,15,13,4	65,535		26	26,6,2,1	67,108,863
7	7,6	127		17	17,14	131,071		27	27,5,2,1	134,217,727
8	8,6,5,4	255		18	18,11	262,143		28	28,25	268,435,455
9	9,5	511		19	19,6,2,1	524,287		29	29,27	536,870,911
10	10,7	1,023		20	20,17	1,048,575		30	30,6,4,1	1,073,741,823
11	11,9	2,047		21	21,19	2,097,151		31	31,28	2,147,483,647
12	12,6,4,1	4,095		22	22,21	4,194,303		32	32,22,2,1	4,294,967,295

Depending on the desired operation, other applicable devices may be CD4094, CD4014, CD4021 which are all 8-stage shift registers.

This video displays an excerpt of a maximum sequence length of 2147483647 bits, generated with a 31 bit long shift register and the 28th tap. The clock rate is 5 Hz.

Pseudo-random_sequence_V2.mp4

Step Sequencer (under construction)

This circuit for a step sequencer is shown in N. Collins book 'Handmade Electronic Music'. It makes use of the built-in voltage controlled oscillator (VCO) of the CD4046 Phase-Locked Loop. The voltage levels of the output pulses of the CD4022 counter can be scaled down by the potentiometer voltage dividers and are mixed together via the diodes D1-D8 (1N4148). The CD4046’s voltage controlled oscillator is then generating a frequency according to the input voltage level. Therefore, each step Q0-Q7 of the CD4022 can be used to produce a single tone.

Input voltage (blue graph) and VCO frequency (yellow graph) of the CD4046.

A logical high on the 'Clock Inhibit' of the CD4022 stops the counter advancement and hence the sequence. A manual push button switch with a pull down resistor to GND or a control logic circuit can be used to pause the sequence for rhythmic effects. A logical high on the 'Reset' input restarts the counter. Connecting one of the outputs of the counter to the 'Reset' pin shortens the length of the sequence by one in regard to the number of the used output. (Step length = Qx-1, if Qx is connected to 'Reset'). More complex patterns can be created when the reset and the inhibit functionality is dynamically controlled by logic circuits.

A clock source is needed for triggering the CD4022. When the clock is set to an audio frequency, the step sequencer works as a wave shaper. Pin 5 (Inhibit) of the CD4046 must be set to a logical low for operation. The frequency range of the CD4046 VCO can be set via the two resistors connected between pin 12 and ground and pin 11 and ground. According to the schematic below, a rough approximation can be calculated with the following formula:

$f_{min} = \frac{1} {{R_5}(C_1 + 32 pF)}$
$f_{max} = \frac{1} {({R_4}+VR)(C_1 + 32 pF)} + f_{min}$

The output of the VCO can be gated with the clock source through a CMOS switch, e.g. CD4066.

Bill of Material:

Designator	Description	Value
D1, D2, ... (for each step)	Diode	1N4148
VR	Potentiometer $f_{max}$	100K
VR1, VR2, ... (for each step)	Potentiometer	100K
R1*, R2*	Resistor	1K - 10K
R3	Resistor	100K
R4	Resistor $f_{max}$	10K
R5	Resistor $f_{min}$
C1	Capacitor	100nF
SW1, SW2 (optional)	push button or toggle switch	on - off
CD4022	Counter
CD4046	PLL
Clock	Clock Generator (eg. CD40106)

Voltage Starve

"Voltage starve" or "voltage sag" can be used as an unconventional modulation technique for experimental music. It describes the effect that low supply voltage and limited current have on a circuit's behavior. Especially battery powered guitar pedals create unique dynamic distortion when the battery's voltage and current delivering capacity is unstable due to aging factors.

Changing the supply voltage will have different effects on a signal, depending on the actual circuit and the used components. Bypassing capacitors will mitigate these effects. For instance, the hysteresis thresholds in Schmitt trigger elements vary with the supply voltage. Lowering the supply voltage affects the frequency and the signal amplitude of Schmitt trigger oscillators.

When working with an adjustable power supply or an according circuit, the impacts of limited current and voltage levels around or below the minimum requirements of an IC can be examined. A similar performance can be simulated with a simple series resistor in the power rail. 500Ω - 10kΩ potentiometers may be worth experimenting with to create odd modulation effects.

Materials

Instructions, parts, tools, shopping lists, components, assemblies, and other materials required to create electronic projects in this field.

Requirements

Helpful tools and useful materials:

• Small mixing desk.
• Active loudspeakers.
• Worktables.
• Pen and paper for drawing schematics.
• Screw drivers.
• ESD electronic diagonal cutter.
• Precision cutter.
• Stranded wires.
• Crocodile clips.
• Laboratory power supply & connectors (preferable 4mm banana laboratory connectors).
• Jumper cables and jumper wires.
• Digital multimeter (DVM).
• Digital storage oscilloscope (DSO).
• Temperature-controlled soldering station.
• Breadboards.
• 9V Batteries.
• Battery clips.
• Good light conditions.

Bill of Materials (BoM)

This BOM helps to source necessary components for electronic art projects and self-built instruments.

Authors

Marc Bendt
Bent van den Berg
Fangchao Bi
Zhen Bian
Yinxuan Chen
Hangyan Chen
Siting Chen
Haram Choi
Mark Damian
Tobias Ehrhardt
Jung Eun Lee
Damiana Facen
Bi Fangchao
Qianqian Feng
Zufilkar Filandra
Hongyu Guo
Jeongmin Han
Juhee Han
Anna-Lina Helsen
Jihye Jang
Hoin Ji
Minsu Kim
Florian Knöbl
László Kőrösi
Sangyi Lee
Xingchen Liu
Su Lu
Daniel Lythgoe
Victoria Mikhaylova
Jiun-You Ou
Isabella Panigada
Pavel Polenz
Max Pospiech
Ruoyi Qiu
Bob Reinert
Vivian Reuter
Arno Schlipf
Dario Schmid
Florian Schwarz
Yifan Su
Anna Szilágyi
Eveline Vervliet
Christina Vinke
Julian Vollmert
Aaron Wagner
Niklas Wallbaum
Dakang Wang
Yudong Wang
Lutz Ben Wesch
Eunchae Won
Le Yang
Sayuki Yoneda 
Jiahui Yong
Huiyeon Yun
Rui Zhang
Yunfei Zhang
Xinyi Zhao
Yange Zheng
Pei Zhou

Lorenz Schwarz - lecturer

Acknowledgment

Thanks to Holger Förterer and Dr. Paul Modler

Literature

Anderton, Craig. Electronic Projects for Musicians. Amsco, 1980.

Barlow, Klarenz. On Musiquantics. Bereich Musikinformatik, Musikwissenschaftliches Institut, Johannes Gutenberg-Universität Mainz, 2012.

Brindley, Keith. Starting Electronics. Newnes, 2011.

Collins, Nicolas. Handmade Electronic Music: The Art of Hardware Hacking. Taylor & Francis, 2009.

Horowitz, Paul and Winfield Hill. The art of electronics. Cambridge University Press, 2021.

Lancaster, Don. Das CMOS-Kochbuch. IWT-Verlag, 1980.

Maxfield, Clive. Bebop to the Boolean Boogie: An Unconventional Guide to Electronics. Newnes, 2003.

Roads, Curtis. Computer Music Tutorial. The MIT Press, 1996.

Self, Douglas. Small Signal Audio Design. Focal Press, 2020.

Links

Below are a few links to resources from across the internet on topics of relevance to audio electronic and Synth DIY as well as inspiring websites from artists and researchers:

Nicolas Collins - Sound artist, composer and performer of electronic music.
https://www.nicolascollins.com

Handmade Electronic Music - Hands-on guide to DIY electronic instruments by Nicolas Collins.
www.HandmadeElectronicMusic.com

Klarenz Barlow - Pioneer and celebrated composer in the field of computer music and influential teacher.
http://clarlow.org/texts

Eberhard Sengpiel - Sound engineer, musician, lecturer. Sound studio and audio calculations, audio and acoustics conversions.
http://www.sengpielaudio.com

John Richards - British musician and artist. Self-made instruments, installations and sound projects with electronics.
https://www.dirtyelectronics.org/about.html

audiodiwhy - DIY music technology, programming.
https://audiodiwhy.blogspot.com

Electric Druid - About audio electronics and analogue synthesizers.
https://electricdruid.net

Synthesizer DIY website of René Schmitz
https://www.schmitzbits.de

Elliott Sound Products - Professional results for the Do-It-Yourself enthusiast.
https://sound-au.com

The Institute of Sonology - Informational website from the Royal Conservatoire in Den Haag about electronics for art and education.
https://electronics.koncon.nl

Adrian Freed - Former Research Director of UC Berkeley's Center for New Music and Audio Technologies (CNMAT).
Ideas, projects, examples regarding creative and artistic use of electronics in sound and music.
http://www.adrianfreed.com

diyaudio forum - DIY audio community forum for learning and sharing knowledge about music technology and audio electronics.
https://www.diyaudio.com

electro-music forum - Dedicated to experimental electro-acoustic and electronic music.
https://electro-music.com

modwiggler forum - Source of information about modular synthesizers and DIY analog circuits.
https://www.modwiggler.com

License

The content of this documentation is licensed under the Creative Commons Attribution 3.0 Unported license, software is licensed under the MIT License - see the LICENSE.md file for details. Copyright remains with the author(s)