Families of Subtractive Synthesis

During the past decades, the subtractive principle has been implemented in many different ways, evolving along with the technology. Although based on the same principle, different families of subtractive synthesizers can be identified, all based on the same basic components. Representatives of these families have different characteristics and are used for different musical applications. Without claim to completeness these families are:

  • Analog modular

  • Analog monophonic

  • Analog polyphonic

  • Virtual analog / analog modeling

Analog Modular

The first subtractive synthesizers were large, cupboard-like devices and rather expensive. Although multiple voices are possible, they were designed as monophonic instruments. Two well known and opposite examples are the first models released by Bob Moog on the US east coast and Don Buchla on the west coast. The latter makes use of distortion techniques, whereas the Moog systems used the standard subtractive paradigm.

Moog Synthesizer (1965)

  • Switched on Bach, Wendy Carlos, 1968

    Bob Moog brought the typical VCO-VCA-VCF approach in a rack with a keyboard. It could hence be performed like a typical piano-like instrument. In productions like Switched on Bach it was made polyphonic through dubbing with tape recording techniques. This video shows the artist, Wendy Carlos, in an interview (since the LP is not available there):

Analog Monophonic

Analog monophonic synthesizers used the same techniques, yet in a more compact design and not fully modular. This made them more affordable and hence more disseminated and used.

Minimoog Model D (1970)

The idea of monophonic analog subtractive synthesis - and maybe of the synthesizer in general - is usually associated with the Minimoog.


Designed as a fully integrated musical instrument, the Minimoog could be used in virtuous expressive musical performances, was portable and affordable. Chick Corea's Minimoog solo, starting at 4:20, is an example of a virtuous performance, making use of modwheel and pitchbend:

EMS VCS 3 (1969)

The semi-modular EMS allows access to the signal flow with a patching matrix. It is thus especially suited for experimental sounds, as used by Pink Floyd in Welcome to the Machine for the wobbling machine sounds in the beginning:

Roland TB 303 (1982)

Although released several years later - and for a different application - the TB303 fits best into this family. The TB 303 was intended to be used as an accompanying instrument for musicians. It has a different interface, a programmable step sequencer.


Due to the quirky filters it failed as a bass accompaniment but gave birth to techno and related genres. It creates the typical acid basses and leads:

Analog Polyphonic

After the monophonic analog synths of the 70s, which were intended as solo instruments, came the polyphonic ones. Polyphonic analog synthesizers shaped the sound of 80s pop (and especially synth-pop) music with their recognizable sound, often used as pads and harmonic foundation or for bass lines.

Yamaha CS-80 (1977)

Oberheim OBx (1979)

Virtual Analog

When digital technology was ready, it took over and various synthesizers were released which emulated the principles of subtractive synthesis. These devices were much cheaper and the digital means could provide more voices with better memory options. Virtual analog synthesizers were the backbone of trance development. They lack some of the analog warmth but are tighter in sound. Some examples:

Clavia Nord Lead

  • 1995

Roland JP-8000

  • 1996

    The Supersaw

Access Virus

  • 1997

Yamaha AN1x

  • 1997

AM & Ringmodulation: Example

The following example shows both AM and ring modulation:

Carrier Frequency

Modulator Frequeny

Modulator Offset

Output Gain:

Time Domain:

Frequency Domain:

Fourier Series: Square Wave


The square wave has a faster decay towards higher partials than the sawtooth. It can be found in spectra of wind instruments.

  • only odd harmonics

  • constant sign

\begin{equation*} X(t) = \frac{4}{\pi} \sum\limits_{i=0}^{N} \frac{\sin(2 \pi (2i+1)ft)}{(2i + 1)} \end{equation*}

Interactive Example

Pitch (Hz):

Number of Harmonics:

Output Gain:

Time Domain:

Frequency Domain:

Like the sawtooth, the square wave shows the occurrence of ripples at the steep edges of the waveform. The higher the number of partials, the denser the ripples. This is referred to as the Gibbs phenomenon.

Faust: Compile for Puredata

Faust can compile Puredata objects:

$ faust2puredata sine.dsp

On linux systems this will create a file sine~.pd_linux, on MacOS a file sine~.pd_darwin. Place the file in your PD search paths and use it, as in the help file sine~-help.pd. Parameters are set with messages.


Faust: Parallel Composition

Parallel processes in Faust are separated with the , operator. The following example uses two square wave oscillators, each passing through a lowpass filter. These chains are running in parallel, creating an output signal with two channels for the left and right audio output:


This example is a parallel combination of two sequential compositions. In Faust syntax, these need to be put in parenthesis.

Load this example in the Faust online IDE for a quick start:


freq  = hslider("Cutoff Frequency",100, 10, 1000, 0.001);

sig1  = os.square(50);
sig2  = os.square(70);

filt = fi.lowpass(5,freq);

process = (sig1:filt),(sig2:filt);

Online Tools and Materials

Faust Code

The Faust project features a rich set of properly documented examples. Nevertheless, this class has an accompanying Git Repository for code snippets and small tutorials.

IEM Plugins

The IEM Plug-in Suite was created by staff and students student of the Institute of Electronic Music and Acoustics in Graz. It is free and open source. Downloads and documentation can be found here https://plugins.iem.at/.

An in depth documentation of the IEM plugins features detailed information on installing and using the tools inside Reaper: https://plugins.iem.at/docs/.

The following pages include additional information on how to use the plugins with external software for control and processing, such as PD, SuperCollider and others.

A First Arduino-Sensor-Circuit

The Arduino

For all examples in this section, the Arduino UNO is used. The documentation on the official Arduino website covers all details on the connection possibilities and many examples to get started. The most important bit of information for most tutorials and basic applications is the pinout map:


Arduino pinout (https://docs.arduino.cc/).

Besides power and ground pins, the following connections are of interest for these examples:

  • 6 analog inputs (0-5V)

  • 14 digital pins (in and output mode can be set for each pin)

  • 5 PWM output pins

  • serial receive

  • serial transmit

The Sensor

This very first step shows how to use basic sensors with the Arduino. These sensors are variable resistors, which change their conductivity based on physical quantities. Examples are temperature, distance or force. The following examples us a light dependent resistor (LDR). The brighter the light it is exposed to, the lower its resistance.


Figure: Approximated curve of the LDR in this example.

The Voltage Divider

In order to use the light dependent sensor in a measurement setup, a so called voltage divider is needed. It compares the variable resistor R1 (in this case the LDR) with a fixed resistor R2:


Figure: Voltage divider circuit.

For a full use of the voltage range, R3 needs to be chosen properly. The voltage measured at the output depends on the reference voltage of 5V and the ratio between the two resistors:

$$ V_{out} = 5V \frac{R_2}{R_1 + R_2} $$

Some components, like potentiometers and faders, have the voltage divider integrated and thus have three pins for connection. They do not require an additional resistor.

Breadboard Wiring

The above-shown circuit can be realized using all components, a mini breadboard and three jumper cables. The documentation on the original Arduino website (Getting Started with Arduino introduces the board with all its connection capabilities in detail. For this example, we need a small breadboard, the LDR, one resistor and three jumper cables. A $100 \Omega$ resistor is chosen. For first steps, the Arduino can be powered via USB, which will also be used to read the sensor data into the Arduino serial monitor.


Figure: Arduino breadboard wiring.

Arduino Code

The easiest way to program an Arduino is the dedicated Arduino IDE, which is available for all major operating systems. Install and use instructions are thoroughly documented on the official Arduino website.

The Arduino code for testing this sensor circuit is minimalistic. Like most Arduino sketches, basic setup is carried out in the setup() function on boot. In this case, the serial interface is started with a baud rate (speed in symbols per second) of 9600 bauds. Afterwards, the loop() function is carried out infinitely. It reads the given voltage at the selected pin A0 and prints it to the serial output.

Follow the instructions on the Arduino website to upload the below code to your board. In general, the serial port of the board needs to be selected in the IDE's dropdown manual, alongside the Arduino model - in this case the Arduino UNO.

void setup() {


void loop() {

int sensorValue = analogRead(A0);



Without any manipulation, the values from the analogRead() function range from 0 to 1024, since the Arduino analog-digital converters have 10 bit resolution:

$$ N = 2^{10} = 1024 $$



Chose a different sensor (varying resistor) and use it with this Arduino example. The reference resistor might need to be changed, too.

Max for Live: A Short Introduction

Max for Live makes max patches run as part of an Ableton Live session. Depending on the nature of the patch, it can be inserted as a device in Audio or MIDI tracks by drag and drop. MIDI and audio outlets of the patch will be visible and usable inside Live like the connection of any other component. Over the years, many devices have been created by the community, some for free, some for sale: https://maxforlive.com/

The concept and its details are best described on Ableton's Live page. This short introduction should only cover the very basics for a quick start.

Max Audio Effects

Dragging the default Max Audio Effect into a track gives a basic patch connecting audio inlets (plugin~) with audio outlets (plugout~). Any processing can be inserted in between.

The default Max Audio Effect.

The default Max Audio Effect.

The following example uses the degrade~ object inside a Max Audio Effect.

A degrader effect.

A degrader effect inside Max for Live.

Max Instruments

The default Max Instrument can be dragged into a MIDI channel. It gives a patch with a midiin object to receive any incoming MIDI data and the plugout~ object to send audio into Live. Unlike the default Audio Effect, this patch is not functional.

The default Max Instrument.

The default Max Instrument.

Like the midiin object, other MIDI objects in Max can also be used inside Max For Live devices. The following mini saw example shows how to control a patch with MIDI from Live, using the notein and the ctlin objects.

A mini saw synthesizer.

A mini saw synthesizer.

Automation to Max for Live

The Inspector View

Although controlling Max for Live with MIDI is a good solution for many applications, Device Parameter Automation offers more flexibility and can also be used in audio channels. Most parameters in a Max for Live patch can be activated for automation, by editing inside the number inspector:

The number inspector in Max for Live.

The number inspector in Max for Live.

The following adjustments need to be made:

  • Parameter Mode Enable: check

  • Name (long/short): foo

  • Type: match parameter

  • Range: match parameter

  • Modulation Mode: match parameter

  • Parameter Visibility: Automated and Stored

Track Automation

After making the Max for Live parameters ready for automation, the general automation mode needs to be enabled in the Arranger view (the tiny blue button above the audio track). Afterwards, each tack shows the available automation parameters and they can be edited.

Automation in the arranger window.

Automation in the arranger window.

Clip Automation

The automation panel in the clip view gives access to all activated Max for Live parameters. This kind of modulation is tightly linked to the audio material, which can be both helpful and complicated.

Clip automation.

Clip automation.

Find more information on live parameters: https://docs.cycling74.com/max5/vignettes/core/live_parameters.html


Exercise I

Create a MIDI instrument and generate a sequence with parameter changes.

Exercise I

Realize a short acousmatic composition with Max for Live audio effects and automated parameters.

Binaural Introduction

Binaural Listening

Two-ear (binaural) listening encodes information on the direction and distance of a sound source by several cues. Figure 1 shows a listener with a sound source and its properties azimuth elevation and distance.

Interaural cues are based on the signal of both ears, more precisely their differences. They are in particular relevant for the horizontal Localization, respectively the azimuth:

  • interaural time differences (medium frequencies)

  • interaural level differences (high frequencies)

  • interaural phase differences (low frequencies)

In addition to the interaural cues, the coloration gives information on the elevation of a sound source, as well as on opposing azimuth angles which have identical interaural cues.


Figure 1: Sound source with angles and distances to left and right ear.

Binaural Recording Technology

Dummy Head

Dummy Head recordings use the principles of binaural listening with two microphones and a model head, carrying these microphones at the position of the ear drum.

When the dummy head is placed in any environment, it listens and records the signals of both ears to two channels.

Many binaural records were released during the 1970s, yet without larger success.


In Ear Microphones

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With the increased use of in ear headphones and streaming, binaural techniques became more and more popular in the 2010s. ASMR artists, for example, use close-up binaural recordings to create intimate


HRTF Generation



Binaural Room Impulse Responses

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  • Elizabeth M Wenzel, Marianne Arruda, Doris J Kistler, and Frederic L Wightman. Localization using nonindividualized head-related transfer functions. The Journal of the Acoustical Society of America, 94(1):111–123, 1993.
    [details] [BibTeX▼]


  • Henrik Møller. Fundamentals of binaural technology. Applied acoustics, 36(3-4):171–218, 1992.
    [details] [BibTeX▼]