The TGrains UGen is an easy to use granular synth. It uses a Hanning window for each grain and offers control over position, pitch and length of the grains. The help files offer multiple examples for using this unit generator. The following example uses a simple pulse train for triggering grains.

Reading Channels

A single channel is loaded to a buffer from a sample for this granular example. The duration in seconds can be queried from the buffer object, once loaded.

~buffer = Buffer.readChannel(s,"/some/wavefile.wav",channels:0);

~buffer.duration;

The Granular Node

The granular node uses an Impulse UGen to create a trigger signal for the TGrains UGen. This node has several arguments to control the granular process:

The density defines how often a grain is triggered per second.
Every grain can be pitch shifted by a value (1 = default rate).
The grain duration is specified in seconds.
The grain center is defined in seconds.
A gain parameter can be used for amplification.
buffer specifies the index of the buffer to be used.

Once the node has been created with a nil buffer, the buffer index of the previously loaded sample can be passed. Depending on the nature of the sample, this can already result in something audible:

~grains =
{
    |
    density = 1,
    pitch   = 1,
    dur     = 0.1,
    center  = 0,
    gain    = 1,
    buffer  = nil
    |

    var trigger = Impulse.kr(density);

    Out.ar(0,   gain * TGrains.ar(1, trigger, buffer, pitch, center, dur));

}.play();


~grains.set(\buffer,~buffer.bufnum);

Manual Parameter Setting

As with any node, the arguments of the granular process can be set, manually. Since the center is specified in seconds, the buffer duration is useful at this point.

~grains.set(\center,0.2);
~grains.set(\density,100);
~grains.set(\dur,0.2);
~grains.set(\pitch,0.8);

Exercise

Exercise I

Use the mouse with buses for a fluid control of granular parameters.

Exercise II

Use envelopes for an automatic control of the granular parameters.

Frequency Domain

Henrik von Coler

2021-04-14 16:00

The Discrete Fourier Transform¶

The frequency-domain representation gives insight into the composition of time series and hence of musical signals. In the digital domain we are formemost interested in discrete signals and will thus introduce the Discrete Fourier Transform (DFT). This section does not aim at a full introduction of the DFT, but illustrates a few aspects which help to better understand the basics of computer music and sound synthesis.

The DFT $X[k]$ of a discrete signal $x$ with the length $N$ and the sampling frequency $f_s$ is calculated as follows. For every frequency bin $k=1 ... N, N \in \mathbb{N}$ of the output, the correlation of the signal with a complex oscillation with the frequency $2 \pi \frac{k}{N}$ is calculated:

$$ \begin{eqnarray} X[k] & = & \sum\limits_{n=0}^{N-1} x[n] \left( \cos \left(2 \pi k \frac{n}{N}) -j \sin(2 \pi k \frac{n}{N} \right) \right) \\ X[k] & = & \sum\limits_{n=0}^{N-1} x[n] e^{-j 2 \pi k \frac{n}{N}} \end{eqnarray} $$

Since real and imaginary part of the complex oscillation have a relative phase of $\frac{\pi}{2}$, the correlation does not only deliver information on the magnitude of spectral components, but also on their phase. The real part is a cosine, whereas the imaginary part is a sine function. The following plot shows the real and imaginary component of the complex oscillations for the indices $k=1$ and $k=2$:

DFT of a Sine Wave¶

In the field of musical signal processing, the sine wave (respectively the cosine wave) are the basic elements of complex sounds. They can be used to model and synthesize any periodic signal. Hence, the frequency domain representation of these harmonic functions is fundamental to the understanding of many algorithms for analysis and synthesis. In most visualizations in the spectral domain, a sinusoidal component is shown as a single peak at the oscillation's frequency. However, when viewed closely, this peak is smeared accompanied by several side lobes. The following example derives these characteristics, based on a $1024$ sample sine wave with a frequency of $f_0 = 100\ \mathrm{Hz}$ at a sampling rate of $f_s = 16\ \mathrm{kHz}$:

For calculating the DFT of sinusoidal signals, it makes sense to express them in the complex notation through Euler's formula:

$$ \sin(2 \pi f_0 \frac{n}{fs}) = \frac{1}{2j} \left( e^{j 2 \pi f_0 \frac{n}{fs} } -e^{-j2 \pi f_0 \frac{n}{fs}} \right) \\ $$

The DFT of the sine wave thus extends to:

$$ X[k] = \sum\limits_{n=0}^{N-1} \frac{1}{2j} \left(e^{j 2 \pi \frac{f_0}{fs} n} -e^{-j2 \pi \frac{f_0}{fs} n} \right) e^{-j 2 \pi k \frac{n}{N}} \\ $$

Solving:

$$ \begin{eqnarray} X[k] & = & \frac{1}{2j} \sum\limits_{i=0}^{N-1} e^{- j 2 \pi k \frac{n}{N} + j 2 \pi \frac{f_0}{fs} n } - e^{- j 2 \pi k \frac{n}{N} - j 2 \pi\frac{f_0}{fs} n} \\ % % & = & \frac{1}{2j} \sum\limits_{i=0}^{N-1} e^{- j 2 \pi ( \frac{k}{N} - \frac{f_0}{fs} ) n } - e^{- j 2 \pi ( \frac{k}{N} + \frac{f_0}{fs}) n} \\ % % & = & \frac{1}{2j} \sum\limits_{i=0}^{N-1} e^{- j 2 \pi ( \frac{k}{N} - \frac{f_0}{fs} ) n } - \frac{1}{2j} \sum\limits_{i=0}^{N-1} e^{- j 2 \pi ( \frac{k}{N} + \frac{f_0}{fs}) n} \\ % % \end{eqnarray} $$

Geometric Series

Using the geometric series formula (with acknowledgements to 1)

$$ \sum\limits_{n=0}^{N-1} a^n = \frac{1-a^{N}}{1-a} $$

the above equation results in:

$$ X[k] = \frac{1}{2j} \frac{1-e^{-j 2 \pi \left( \frac{k}{N} - \frac{f_0}{fs} \right) N}}{1-e^{-j 2 \pi \left( \frac{k}{N} - \frac{f_0}{fs} \right)}} % + \frac{1}{2j} \frac{1-e^{-j 2 \pi (\left( \frac{k}{N} + \frac{f_0}{fs} \right)) N}}{1-e^{-j 2 \pi \left( \frac{k}{N} + \frac{f_0}{fs} \right)}} $$

¹ http://www.eecs.umich.edu/courses/eecs452/overview.html

Factoring out

The above equation features the following term:

$$ E = \frac{1-e^{-j \Lambda N}}{1-e^{-j \Lambda}} $$

After factoring out the term $\frac{e^{-j \Lambda \frac{N}{2}}}{e^{-j \frac{\Lambda}{2}}}$ we can solve further, using Euler's formula:

$$ \begin{eqnarray} E & = & \frac{e^{-j \Lambda \frac{N}{2}}} {e^{-j \frac{\Lambda}{2}}} \cdot \frac{e^{j \Lambda \frac{N}{2}} - e^{-j \Lambda \frac{N}{2}}}{e^{j \frac{\Lambda}{2}} - e^{-j \frac{\Lambda}{2}}} \\ % % & = & e^{-j \Lambda \frac{N+1}{2} } \underbrace{\frac{\sin(\Lambda \frac{N}{2} )}{\sin(\frac{\Lambda}{2})}}_{\text{Dirichlet function}} \end{eqnarray} $$

As the plot below shows, the term is characterized by a Dirichlet function, which is related to the sinc function. Inserting

$$ \begin{eqnarray} \Lambda(-f_0) & = & 2 \pi \left( \frac{k}{N} - \frac{f_0}{fs} \right) \\ \Lambda(+f_0) & = & 2 \pi \left( \frac{k}{N} + \frac{f_0}{fs} \right) \\ \end{eqnarray} $$

we get the following result for the spectrum of the sinusoid:

$$ \begin{eqnarray} X [k] & = & \frac{1}{2j} \left( e^{-j \Lambda(-f_0) \frac{N+1}{2} } \frac{\sin(\Lambda(-f_0) \frac{N}{2} )}{\sin(\frac{\Lambda(-f_0) }{2})} % + e^{-j \Lambda(+f_0) \frac{N+1}{2} } \frac{\sin(\Lambda(+f_0) \frac{N}{2} )}{\sin(\frac{\Lambda(+f_0)}{2})} \right) \end{eqnarray} $$

According to the shift theorem, the above equation holds two components - one cenered at $f_0$, another centered at $-f_0$, each with a main lobe and an infinite number of sidelobes:

Magnitude Plot

The plot below visualizes the result, with a two main lobes and the decaying side lobes:

Exercise: Calculate the DFT spectrum of a cosine and compare it to the sine example above. What do the different outcomes show?

Absolute Representation¶

In many cases, the absolute values of DFT spectra will be shown only for the positive frequencies. This representation is used in most examples in the following sections. The sine wave becomes a single peak at its frequency:

DFT Support Points¶

For a DFT with $N$ points and a sampling rate $f_s$, the DFT bins $b[k]$ - or support points - are located at the following frequencies:

$$ b[k] = k \frac{f_s}{N} $$

Only for harmonic signals located at these exact frequencies, the DFT results can be expressed by the Dirac-Delta function.

Links¶

This website visualizes the DFT very nicely for a better understanding: https://jackschaedler.github.io/circles-sines-signals/dft_walkthrough.html

Writing UGens for SuperCollider

Henrik von Coler

2021-04-10 10:40

Background

Henrik von Coler

2021-04-07 14:00

The EOC

The Electronic Orchestra Charlottenburg (EOC) was founded at the TU Studio in 2017 as a place for developing and performing with custom musical instruments on large loudspeaker setups.

EOC Website: https://eo-charlottenburg.de/

Initially, the EOC worked in a traditional live setup with sound director. Several requests arose during the first years:

enable control of the mixing and rendering system through musicians
- control spatialization
flexible spatial arrangement of musicians
- break up rigid stage setup
distribution of data
- scores
- playing instructions
- visualization of system states

The SPRAWL System

During Winter Semester 2019-20 Chris Chafe was invited as guest professor at Audio Communication Group. In combined classes, the SPRAWL network system was designed and implemented to solve the above introduced problems in local networks:

https://hvc.berlin/projects/sprawl_system/

Quarantine Sessions

The quarantine sessions are an ongoing concert series between CCRMA at Stanford, the TU Studio in Berlin, the Orpheus Institute in Gent, Belgium and various guests:

These sessions use the same software components as the SPRAWL System. Audio is transmitted via JackTrip and SuperCollider is used for signal processing.

Back to NSMI Contents

SuperCollider for the Remote Server

2021-04-07 14:00

SuperCollider is per default built with Qt and X for GUI elements and the ScIde. This can be a problem when running it on a remote server without a persistent SSH connection and starting it as a system service. However, for service reasons a version with full GUI support is a useful tool. One solution is to compile and install both versions and make them selectable via symbolic links:

build and standard-install a full version of SuperCollider
build a headless version of SuperCollider (without system install)
replace the following binaries in /usr/bin with symbolic links to the headless version
- scsynth
- sclang
- supernova
create scripts for changing the symlink targets

This allows you to redirect the symlinks to the GUI version for development and testing whereas they point to the headless version otherwise.

Compiling a Headless SC

The SC Linux build instructions are very detailed: https://github.com/supercollider/supercollider/blob/develop/README_LINUX.md Compiling it without all graphical components is straightforward. Simply add the flags NO_X11=ON and -DSC_QT=OFF for building a headless version of SuperCollider.

Using JackTrip in the HUB Mode

John Doe

2021-04-07 14:00

About JackTrip

In this class we will use JackTrip for audio over network connections but there were some successful tests with the Zita-njbridge. JackTrip can be used for peer-to-peer connections and for server-client setups. For the latter, JackTrip was extended with the so called HUB Mode for the SPRAWL System and the EOC in 2019-20.

---

Basics

For connecting to a server or hosting your own instance, the machine needs to be connected to a router directly via Ethernet. WiFi will not result in a robust connection and leads to significant dropouts. JackTrip needs the following ports for communication. If a machine is behind a firewall, these need to be added as an exception:

JackTrip Ports
Port	Protocol	Purpose
4464	TCP/UDP	audio packages
61002-62000	UDP	establish connection (server only)

The Nils Branch

Due to the increasing interest, caused by the pandemic, and the endless list of feature requests, the Jacktrip project has been growing rapidly in since early 2020 and the repository has many branches. In this class we are using the nils branch, which implements some unique features we need for the flexible routing system. Please check the instructions for compiling and installing a specific branch: Compiling JackTrip

Starting JackTrip

JACK Parameters

Before starting JackTrip on the server or the clients, a JACK server needs to be booted on the system. Read the chapter Using JACK Audio from the Computer Music Basics class for getting started with JACK. A purely remote server, as used in this class, does not have or need an audio interface and can thus be booted with the dummy client:

$ jackd -d dummy [additional parameters]

To this point, the version of JackTrip used with the SPRAWL system requires all participants to run their JACK server at the same sample rate and buffer size. Recent changes to JackTrip dev branch allow the mixing of different buffer sizes but have not been tested with this setup. The overall system's buffer size is defined by the weakest link, respectively the client with the worst connection. Although tests between two sites have shown to work with down to $16$ samples, a buffer size of $128$ or $256$ samples usually works for a group. Experience has shown that about a tenth of all participants has an insufficient internet connection for participating without significant dropouts.

JackTrip Parameters

As with most command line programs, JackTrip gives you a list of all available parameters with the help flag: $ jacktrip -h A single instance is launched on the SPRAWL Server with the following arguments:

$ jacktrip -S -p 5 -D --udprt

The following arguments are needed for starting a JackTrip client instance and connecting to the SPRAWL server (the server.address can be found in the private data area):

$ jacktrip -C server.address -n 2 -K AP_

Using Shell Scripts

Henrik von Coler

2021-04-07 14:00

Shell scripts can be helpful for organizing sequences of terminal commands to execute them in a specific order with a single call. Shell scripts usually have the extension .sh and should start with a so called shebang (#!...), telling the interpreter what binary to use. After that, single commands can be added as separate lines, just as using them in the terminal. The following script test.sh starts the JACK server in the background, waits for 3 seconds and afterwards launches the simple client, playing a sine tone.

#! /bin/bash

jackd &
sleep 3
jack_simple_client

The script can be executed from its source location as follows:

$ bash test.sh

Shell scripts can be made executable with the following command:

$ chmod +x test.sh

Afterwards, they can be started like binaries, when including the correct shebang:

$ ./test.sh

Exercise

Create an executable shell script in your personal directory on the server. Use the echo command in that script to print a simple message and run the file via SSH.

Waveshaping

Henrik von Coler

2020-12-01 13:29

Waveshaping is one of the basic ways of distortion synthesis. In its simplest form it works like any overdrive effect by limiting a signal with a non-linear shaping function. Depending on the implementation, these shaping functions can have any form.

Shaping Function¶

The following example shows a simple tangential shaping function $y=\mathrm{tanh}(g x)$. For high pre-gain values, the function converges towards a step function and the output of a sinusoidal imput signal becomes a square wave.

Faust

Henrik von Coler

2020-11-05 14:01

Faust is a functional audio programming language, developed at GRAME, Lyon. It is a community-driven, free open source project. Faust is specifically suited for quickly designing musical synthesis and processing software and compiling it for a large variety of targets. The fastest way for getting started with Faust in the Faust online IDE which allows programming and testing code in the browser, without any installation. The online materials for the class Sound Synthesis- Building Instruments with Faust introduce the basics of the Faust language and give examples for different synthesis techniques.

Faust and Web Audio

Besides many targets, Faust can also be used to create ScriptProcessor nodes (Letz, 2015).

References

Stephane Letz, Sarah Denoux, Yann Orlarey, and Dominique Fober. Faust audio dsp language in the web. In Proceedings of the Linux Audio Conference. 2015.
[BibTeX▼]

@inproceedings{letz2015faust,
    author = "Letz, Stephane and Denoux, Sarah and Orlarey, Yann and Fober, Dominique",
    title = "Faust audio DSP language in the Web",
    booktitle = "Proceedings of the Linux Audio Conference",
    year = "2015",
    location = "Mainz, Germany"
}

Realtime Weather Sonification

Henrik von Coler

2020-11-05 13:47

OpenWeatherMap

This first, simple Web Audio sonification application makes use of the Weather API for real-time, browser-based sonification of weather data. For fetching data, a free subscription is necessary: https://home.openweathermap.org

Once subscribed, the API key can be used to get current weather information in the browser:

https://api.openweathermap.org/data/2.5/weather?q=Potsdam&appid=eab7c410674e15bfdd841f66941a92c2

JSON Data Structure

The resulting output in JSON looks like this:

{
  "coord": {
    "lon": 13.41,
    "lat": 52.52
  },
  "weather": [
    {
      "id": 804,
      "main": "Clouds",
      "description": "overcast clouds",
      "icon": "04d"
    }
  ],
  "base": "stations",
  "main": {
    "temp": 9.74,
    "feels_like": 6.57,
    "temp_min": 9,
    "temp_max": 10.56,
    "pressure": 1034,
    "humidity": 93
  },
  "visibility": 8000,
  "wind": {
    "speed": 4.1,
    "deg": 270
  },
  "clouds": {
    "all": 90
  },
  "dt": 1604655648,
  "sys": {
    "type": 1,
    "id": 1275,
    "country": "DE",
    "sunrise": 1604643143,
    "sunset": 1604676458
  },
  "timezone": 3600,
  "id": 2950159,
  "name": "Berlin",
  "cod": 200
}

All entries of this data structure can be used as synthesis parameters in a sonification system with Web Audio.

Temperatures to Frequencies

Mapping

In this example we are using a simple frequency modulation formula for turning temperature and humidity into more or less pleasing (annoying) sounds. The frequency of a first oscillator is derived from the temperature:

$\displaystyle f_1 = 10 \frac{1}{{T^2 / C^{\circ} }}$

The modulator frequency is controlled by the humidity $H$:

$y = sin(2 \pi (f_1 + 100 \cdot \sin(2 \pi H t))t)$

The Result

The resulting app fetches the weather data of a chosen city, extracts temperature and humidity and sets the parameters of the audio processes:

Where would you rather be?

What does the weather sound like in ...?

Links and More Examples

Using the API in JavaScript is thoroughly explained here: https://bithacker.dev/fetch-weather-openweathermap-api-javascript