The Karplus-Strong algorithm is a proto-physical model. The underlying theory is covered in the Karplus-Strong Section of the Sound Synthesis Introduction. Although the resulting sounds are very interesting, the Karplus-Strong algorithm is easy to implement, especially in C/C++. It is based on a single buffer, filled with noise, and a moving average smoothing.

The Noise Buffer

Besides the general framework of all examples in this teaching unit, the karplus_strong_example needs just a few additional elements, defined in the class`s header:

// the buffer length
int l_buff = 600;

// the 'playback position' in the buffer
int buffer_pos=0;

/// noise buffer
double  *noise_buffer;

/// length of moving average filter
int l_smooth = 10;

// feedback gain
double gain =1.0;

Note that the pitch of the resulting sound is hard-coded in this example, since it is based only on the sampling rate of the system and the buffer length. In contrast to the original Karplus-Strong algorithm, this version uses an arbitrary length for the moving average filter, instead of only two samples. This results in a faster decay of high frequency components.

Initializing the Buffer

Since the noise buffer is implemented as a pointer to an array of doubles, it first needs to be allocated and initialized. This happens in the constructor of the karplus_strong_example class:

// allocate noise buffer
noise_buffer = new double [l_buff];
for (int i=0; i<l_buff; i++)
  noise_buffer[i]=0.0;

Plucking the Algorithm

Each time the Karplus-Strong algorithm is excited, or plucked, the buffer needs to be filled with a sequence of random noise. At each call of the JACK callback function (process), it is checked, whether a new event has been triggered via MIDI or OSC. If that is true, the playback position of the buffer is set to 0 and each sample of the noise_buffer is filled with a random double between -1 and 1:

cout << "Filling buffer!";
buffer_pos = 0;
for(int i=0; i<=l_buff; i++)
  noise_buffer[i]=  rand() % 2 - 1;

Running Through the Buffer

The sound is generated by directly writing the samples of the noise_buffer to the JACK output buffer. This is managed in a circular fashion with the buffer_pos counter. Wrapping the counter to the buffer size makes the process circular. This example uses a stereo output with the mono signal.

for(int sampCNT=0; sampCNT<nframes; sampCNT++)
{

    // write all input samples to output
    for(int chanCNT=0; chanCNT<nChannels; chanCNT++)
    {
      out[chanCNT][sampCNT]=noise_buffer[buffer_pos];
    }


    // increment buffer position
     buffer_pos++;
     if (buffer_pos>=l_buff)
      buffer_pos=0;
}

Smoothing the Buffer

The above version results in a never-ending oscillation, a white tone. The timbre of this tone changes with every triggering, since a unique random sequence is used each time. With the additional smoothing, the tone will decay and lose the high spectral components, gradually. This is done as follows:

// smoothing the buffer
double sum = 0;
for(int smoothCNT=0; smoothCNT<l_smooth; smoothCNT++)
  {
    if(buffer_pos+smoothCNT<l_buff)
      sum+=noise_buffer[buffer_pos+smoothCNT];
    else
      sum+=noise_buffer[smoothCNT];
  }
  noise_buffer[buffer_pos] = gain*(sum/l_smooth);

Compiling

To compile the KarplusStrongExample, run the following command line:

g++ -Wall -L/usr/lib src/yamlman.cpp src/main.cpp src/karplus_strong_example.cpp src/oscman.cpp src/midiman.cpp -ljack -llo -lyaml-cpp -lsndfile -lrtmidi -o karplus_strong

This call of the g++ compiler includes all necessary libraries and creates the binary karplus_strong.

Running the Example

The binary can be started with the following command line:

./karplus_strong -c config.yml -m "OSC"

This will use the configurations from the YAML file and wait for OSC input. The easiest way of triggering the synth via OSC is to use the Puredata patch from the example's directory.

Exercises

Using MIDI with RtMidi

Henrik von Coler

2021-12-10 00:00

Although the MIDI protocol is quite old and has several drawbacks, it is still widely used and is appropriate for many applications. Read the MIDI section in the Computer Music Basics for a deeper introduction.

The development system used in this class relies on the RtMidi framework. This allows the inclusion of any ALSA MIDI device on Linux systems and hence any USB MIDI device. The RtMidi Tutorial gives a thorough introduction to the use of the library.

ALSA MIDI

The Advanced Linux Sound Architecture (ALSA) makes audio- and MIDI interfaces accessible for software. As an API it is part of the Linux kernel. Other frameworks, like JACK or Pulseaudio work on a higher level and rely on ALSA.

Finding your ALSA MIDI Devices

After connecting a MIDI device to an USB port, it should be available via ALSA. All ALSA MIDI devices can be listed with the following shell command:

$ amidi -l

The output of this request can look as follows:

Dir     Device        Name
IO      hw:1 ,0 ,0   nanoKONTROL MIDI 1
IO      hw:2 ,0 ,0   PCR-1 MIDI 1
I       hw:2 ,0 ,1   PCR-1 MIDI 2

In this case, two USB MIDI devices are connected. They can be addressed by their MIDI device ID (hw:0/1).

The MIDI Tester Example

The MIDI tester example can be used to print all incoming MIDI messages to the console. This can be helpful for reverse-engineering MIDI devices to figure out their controller numbers.

The MIDI Manager Class

The MIDI Manager class introduced in this test example is used as a template for following examples which use MIDI. For receiving messages, RtMidi offers a queued MIDI input and a user callback mode. In the latter case, each incoming message triggers a callback function. For the queued mode, as used here, incoming messages are collected until retrieved by an additional process.

The midiMessage struct is used to store incoming messages. It holds the three standard MIDI message bytes plus a Boolean for the processing state.

/// struct for holding a MIDI message
typedef struct  {
    int byte1             = -1;
    int byte2             = -1;
    double byte3          = -1;
    bool hasBeenProcessed = false;

}midiMessage;

SuperCollider Granular Example

Henrik von Coler

2021-05-02 10:40

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

The Fourier Transform

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 $k=2$:

No description has been provided for this image

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

The Fourier Transform

Henrik von Coler

2021-04-14 16:00

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

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

NT

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

Nils Tonnaett

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 SSH for Remote Access

Henrik von Coler

2021-04-07 14:00

SSH (Secure Shell Protocol) gives remote access to remote computer. In its basic form it allows the execution of command lines in a terminal, if the remote machine is running an SSH server. It can also be used for remote graphical user interfaces.

Connecting to an SSH Server

For connecting to a remote machine, it needs to run an SSH server. On the client side, an SSH connection can be established without additional installations from the terminal on Linux and MAC machines and - since version 10 - from Windows. SSH receives the following command, with the remote user's credentials (username and ip-address). This user needs to be installed on the remote machine. The remote SSH server will ask for the user's password, if no SSH key has been installed.

$ ssh username@address

X11 Forwarding

X11, or the X Window System is a framework for a graphical user interface (GUI) environment, used on Unix systems. With X11 Forwarding, SSH can also be used to run applications with a GUI, remotely. When connecting to an SSH server from a Linux machine, simply add the -X argument to do so:

$ ssh -X username@address

X11 On Mac

On Mac you need to install xqwartz <https://www.xquartz.org/> to enable X11 Forwarding. Afterwards, the -X argument will enable X11 Forwarding:

$ ssh -X username@address

X11 on Windows

Although SSH will be possible from Windows' builtin Power Shell or Windows Terminal, X11 Forwarding requires Putty and additional tools:

install putty
install vcxsrv
enable X11 in Putty

Remote Commands

SSH can also be used to send single commands, without starting a remote session. This example launches the jack_simple_client, which plays a continuing sine tone on the remote machine.

$ ssh -t username@address 'jack_simple_server'