Introducing the Ambisonic Toolkit: table of contents
Guides (extension) | Libraries > Ambisonic Toolkit

Introducing the Ambisonic Toolkit

Introduction to the Ambisonic Toolkit

The paradigm

The Ambisonic Toolkit (ATK) brings together a number of classic and novel tools and transforms for the artist working with Ambisonic surround sound and makes these available to the SuperCollider3 user. The toolset in intended to be both ergonomic and comprehensive, and is framed so that the user is encouraged to ‘think Ambisonically’. By this, it is meant the ATK addresses the holistic problem of creatively controlling a complete soundfield, allowing and encouraging the artist to think beyond the placement of sounds in a sound-space (sound-scene paradigm). Instead the artist is encouraged to attend to the impression and imaging of a soundfield, therefore taking advantage of the native soundfield-kernel paradigm the Ambisonic technique presents.

The ATK's production model is illustrated below:

ATK paradigm

Here you'll see that the ATK breaks down the task of working with Ambisonics into three separate elements:

Capture or synthesise an Ambisonic soundfield.
Spatially filter an Ambisonic soundfield.
Playback or render an Ambisonic soundfield.

The below sections go into more detail as to the specifics of each task. For examples that show more concise examples for usage in SynthDef and NRT, see SynthDef and NRT examples for ATK


Most users approaching Ambisonics are usually presented with two avenues to author an Ambisonic soundfield: capture a natural soundfield directly with a Soundfield microphone, 1 or author a planewave from a monophonic signal.2 SuperCollider's inbuilt PanB provides the latter solution.

The ATK provides a much wider palate of authoring tools via FoaEncode. These include:

The pseudoinverse encoding technique provides the greatest flexibility, and can be used with both microphone arrays and synthetic signals. In the absence of a Soundfield microphone, this feature gives the opportunity to deploy real-world microphone arrays (omni, cardioid, etc.) to capture natural soundfields. With synthetic signals, pseudoinverse encoding is usually regarded as the method of choice to generate spatially complex synthetic Ambisonic images. In combination with the ATK's imaging tools these can then be compositionally controlled as required.

See FoaEncode, FoaEncoderMatrix and FoaEncoderKernel for more details about encoding.


For the artist, the real power of the ATK is found in the imaging transforms. These are spatial domain filters which reorient, reshape or otherwise spatially filter an input soundfield. Many users will be familiar with the soundfield rotation transform, as SuperCollider provides the inbuilt Rotate2.

The ATK provides a much wider and comprehensive toolset, including:

The imaging tools are provided in two forms: static and dynamic implementations. While most transforms are provided in both categories, a number are found in only one guise.3

See FoaTransform, FoaXform and FoaXformerMatrix for more details about imaging.

Reading imaging illustrations

As artists working with sound, we should expect most users to be very capable expert listeners, and able to audition the results of spatial filtering of an input soundfield. However, it is often very convenient to view a visual representation of the effect of a soundfield transform. The ATK illustrates a number of its included transforms in the form shown below.

The X-Y axis is shown, as viewed from above with the top of the plot corresponding to the front of the soundfield, +X. On the left hand side of the figures, an unchanged soundfield composed of eight planewave is shown. These are indicated as coloured circles, and arrive from cardinal directions:

Three useful features are displayed in these plots, providing inportant insight as to how an input soundfield will be modified by a transform:

Individual planewaves are coloured with respect to the gain scale at the far left of the figures. Additionally, Front, Left, Back-Left and Back are annotated with a numerical figure for gain, in dB.

Soundfield quality

The meaning of transformation to soundfield incidence and gain should be clear. Understading the meaning of soundfield quality takes a little more effort. This feature describes how apparently localised an element in some direction will appear.

A planewave has a quality measure of 1.0, and is heard as localised. At the opposite end of the scale, with a quality measure of 0.0, is an omnidirectional soundfield. This is heard to be without direction or "in the head". As you'd expect, intermediate measures are heard as scaled between these two extremes.

Reading ZoomX


ZoomX imaging

With changing ZoomX's angle, we see the eight cardinal planewaves both move towards the front of the image and change gain. When angle is 90 degrees, the gain of the planewave at Front has been increased by 6dB, while Back has disappeared.7 We also see the soundfield appears to have collapsed to a single planewave, incident at 0 degrees.8

Reading PushX


PushX imaging

PushX also distorts the incident angles of the cardinal planewaves. However, here we see two differences with ZoomX. The gains of the individual elements don't vary as considerably. More intriguingly, a number of the encoded planewaves are illustrated as moving off the perimeter of the plot, indicating a change in soundfield quality.

Moving from the edge of the plot towards the centre does not imply the sound moves from the edge of the loudspeakers towards the centre, as one might expect. Instead, what we are seeing is the loss of directivity. Moving towards the centre means a planewave moves toward becoming omnidirectional, or without direction. (This becomes clearer when we look at DirectO.) A reducing radius indicates a reducing soundfield quality.

When PushX's angle is 90 degrees, all encoded planewaves have been pushed to the front of the image. Unlike ZoomX, gain is retained at 0 dB for all elements.9

Reading DirectO


DirectO imaging

DirectO adjusts the directivity of the soundfield across the origin. Here we see the cardinal planewaves collapsing towards the centre of the plot. At this point the soundfield is omnidirectional, or directionless. See further discussion of soundfield quality above.

See FoaZoomX, FoaPushX and FoaDirectO for more details regarding use of these associated UGens.

Illustrated transforms

Additionally, the following UGens include figures illustration imaging transformation:

Explore these to get a sense of the wide variety of image transformation tools available in the ATK.


Perhaps one of the most celebrated aspects of the Ambisonic sound technique has been its design as a hierarchal reproduction system, able to target a number of varying loudspeaker arrays. Users may be familiar with SuperCollider's inbuilt regular polygon decoder, DecodeB2.

The ATK provides a much wider palate of optimised monitoring tools via FoaDecode. These include:

While the regular decoders will be suitable for many users, diametric decoding enables the greatest flexibility, and allows the user to design substantially varying semi-regular arrays suitable for a wide variety of playback situations.

NOTE: All decoders presume loudspeakers are placed at equal radii from the origin of the array, and gain is normalised. Loudspeaker arrays with unequal radii may be realised if the resulting wavefront arrival times are compensated through the use of delay lines.

See FoaDecode, FoaDecoderMatrix and FoaDecoderKernel for more details about decoding.


If you're reading this document, the atk-sc3 Quark has most likely been corectly installed.


ATK for SuperCollider3 requires version 3.9 or later. Download the latest version here, or fork the source code at GitHub.

atk-sc3 Quark

The ATK for SuperCollider3's classes, extension methods and documentation are distributed via the atk-sc3 Quark. Start by reviewing the Quark installation instructions found here. See also Using Quarks.

With git installed, you can easily install the atk-sc3 Quark directly by running the following line of code in SuperCollider:



The ATK's compiled UGen component releases are available from the sc3-pluginsreleases page.

Place the downloaded SC3plugins folder in your Extensions folder. On Mac OS X, this resolves to:

~/Library/Application Support/SuperCollider/Extensions

You may need to create the Extensions folder if it does not already exist.

On other platforms, you can find where this is by running the following line of code in SuperCollider:

// post the directory in which to move the SC3Plugins folder
// alternatively, SC can open it for you
// (assuming it already exists! - you may need to create /Extensions)

Kernels, Matrices & Recordings

Additionally, the SuperCollider3 version of the ATK has further dependencies:

If you are using Ambisonic Toolkit with Reaper as well, the convolution kernels and matrices are installed in the same place and have the exact same content. We do not expect this to cause any conflicts.

If you want to take a look at the installed files and do not see the Library folder in Finder, please press the ALT button while clicking the Go menu in Finder. The Library folder will show up as an additional option.


The examples below are intended to briefly illustrate playback and imaging of soundfields with the ATK. The user is encouraged to explore the ATK's documentation to gain a deeper understanding of the flexibility of these tools.

As the Ambisonic technique is a hierarchal system, numerous options for playback are possible. These include two channel stereo, two channel binaural, pantophonic and full 3D periphonic. With the examples below, we'll take advantage of this by first choosing a suitable decoder with with to audition.

Choose a decoder

A number of decoders are defined below. Please choose one suitable for your system. Also, don't forget to define ~renderDecode !

NOTE: If you choose a kernel decoder, FoaDecoderKernel, be sure to free the kernel after use.
// ------------------------------------------------------------
// boot server
        s = Server.default;

// ------------------------------------------------------------
// define convenience function to verify number of server outputs
~checkMyServerOutputs = { arg server, decoder;
        (decoder.numOutputs > server.options.numOutputBusChannels).if({
            "Number of Server output bus channels is less than number required by Decoder!".warn;
            "Server Outputs: %\n".postf(server.options.numOutputBusChannels);
            "Decoder Outputs: %\n\n".postf(decoder.numOutputs);
            "Update number of Server outputs as illustrated here: ".post;
        }, {
            "Server has an adequate number of output bus channels for use with this Decoder!".postln;

// ------------------------------------------------------------
// choose a decoder

// stereophonic / binaural
~decoder = FoaDecoderMatrix.newStereo((131/2).degrad, 0.5) // Cardioids at 131 deg
~decoder = FoaDecoderKernel.newUHJ                         // UHJ (kernel)
~decoder = FoaDecoderKernel.newSpherical                   // synthetic binaural (kernel)
~decoder = FoaDecoderKernel.newCIPIC                       // KEMAR binaural (kernel)

// pantophonic (2D)
~decoder = FoaDecoderMatrix.newQuad(k: 'dual')             // psycho optimised quad
~decoder = FoaDecoderMatrix.newQuad(pi/6, 'dual')          // psycho optimised narrow quad
~decoder = FoaDecoderMatrix.new5_0                         // 5.0
~decoder = FoaDecoderMatrix.newPanto(6, k: 'dual')         // psycho optimised hex

// periphonic (3D)
~decoder = FoaDecoderMatrix.newPeri(k: 'dual')             // psycho optimised cube
~decoder = FoaDecoderMatrix.newDiametric(                  // psycho optimised bi-rectangle
    [[30, 0], [-30, 0], [90, 35.3], [-90, 35.3]].degrad,

// inspect
~checkMyServerOutputs.value(s, ~decoder)

// ------------------------------------------------------------
// define ~renderDecode
~renderDecode = { arg in, decoder;
    var kind;
    var fl, bl, br, fr;
    var fc, lo;
    var sl, sr;
    var flu, blu, bru, fru;
    var fld, bld, brd, frd;
    var slu, sru, sld, srd;

    kind = decoder.kind;

        { decoder.numChannels == 2 }
                // decode to stereo (or binaural)
      , decoder)
        { kind == 'quad' }
                // decode (to quad)
                #fl, bl, br, fr =, decoder);

                // reorder output to match speaker arrangement
                [fl, fr, bl, br]
        { kind == '5.0' }
                // decode (to 5.0)
                #fc, fl, bl, br, fr =, decoder);
                lo =;

                // reorder output to match speaker arrangement
                [fl, fr, fc, lo, bl, br]
        { kind == 'panto' }
                // decode (to hex)
                #fl, sl, bl, br, sr, fr =, decoder);

                // reorder output to match speaker arrangement
                [fl, fr, sl, sr, bl, br]
        { kind == 'peri' }
                // decode (to cube)
                #flu, blu, bru, fru, fld, bld, brd, frd =, decoder);

                // reorder output to match speaker arrangement
                [flu, fru, blu, bru, fld, frd, bld, brd]
        { kind == 'diametric' }
                // decode (to bi-rectangle)
                #fl, fr, slu, sru, br, bl, srd, sld =, decoder);

                // reorder output to match speaker arrangement
                [fl, fr, bl, br, slu, sru, sld, srd]

// ------------------------------------------------------------
// now we're ready to try the examples below!
// ------------------------------------------------------------

Produced via the Ambisonic Toolkit

The following three sound examples are excerpts from recordings produced via the ATK.

If you haven't already choosen a ~decoder and defined ~renderDecode, do so now.

// ------------------------------------------------------------
// B-format examples, produced via the ATK
// B-format soundfile read from disk

// read a whole sound into memory
// remember to free the buffer later!
// (boot the server, if you haven't!)
~sndbuf =, Atk.userSoundsDir ++ "/b-format/Anderson-Pacific_Slope.wav")
~sndbuf =, Atk.userSoundsDir ++ "/b-format/Howle-Calling_Tunes.wav")
~sndbuf =, Atk.userSoundsDir ++ "/b-format/Pampin-On_Space.wav")

    var sig;                            // audio signal

    // display encoder and decoder
    "Ambisonic decoding via % decoder".format(~decoder.kind).postln;

    // ------------------------------------------------------------
    // test sig
    sig =, ~sndbuf,, doneAction:2);   // soundfile

    // ------------------------------------------------------------
    // decode (via ~renderDecode)
    ~renderDecode.value(sig, ~decoder)


// free buffer
// ------------------------------------------------------------
NOTE: Soundfile Credits

Natural soundfields, with imaging transforms

This example illustrates the application of various spatial filtering transforms to natural soundfields, recorded via the Soundfield microphone.

The soundfield is controlled by MouseY, which specifies the transform angle argument (90 deg to 0 deg; top to bottom of display). With the mouse at the bottom of the display, the recorded soundfield is unchanged. At the top, the transform is at its most extreme.

If you haven't already choosen a ~decoder and defined ~renderDecode, do so now.

NOTE: See FoaTransform for further details.
// ------------------------------------------------------------
// B-format examples, natural soundfield with imaging transform
// B-format soundfile read from disk

// choose transformer
~transformer = 'zoomX'
~transformer = 'pushX'
~transformer = 'directO'

// read a whole sound into memory
// remember to free the buffer later!
// (boot the server, if you haven't!)
~sndbuf =, Atk.userSoundsDir ++ "/b-format/Hodges-Purcell.wav")
~sndbuf =, Atk.userSoundsDir ++ "/b-format/Leonard-Orfeo_Trio.wav")
~sndbuf =, Atk.userSoundsDir ++ "/b-format/Courville-Dialogue.wav")
~sndbuf =, Atk.userSoundsDir ++ "/b-format/Leonard-Chinook.wav")
~sndbuf =, Atk.userSoundsDir ++ "/b-format/Leonard-Fireworks.wav")
~sndbuf =, Atk.userSoundsDir ++ "/b-format/Anderson-Nearfield.wav")

    var sig;                            // audio signal
    var angle;                          // angle control

    // display transformer & decoder
    "Ambisonic transforming via % transformer".format(~transformer).postln;
    "Ambisonic decoding via % decoder".format(~decoder.kind).postln;

    // gain ---> top            = 90 deg
    //           bottom         = 0 deg
    angle =, 0);

    // ------------------------------------------------------------
    // test sig
    sig =, ~sndbuf,, doneAction:2);   // soundfile

    // ------------------------------------------------------------
    // transform
    sig =, ~transformer, angle);

    // ------------------------------------------------------------
    // decode (via ~renderDecode)
    ~renderDecode.value(sig, ~decoder)


// free buffer
// ------------------------------------------------------------
NOTE: Soundfile Credits

[1] - J.-M. Batke, "The B-Format Microphone Revised," presented at the Ambisonics Symposium 2009, Graz, 2009.
[2] - D. G. Malham and A. Myatt, "3-D Sound Spatialization using Ambisonic Techniques," Computer Music Journal, vol. 19, no. 4, pp. 58-70, 1995.
[3] - It is also useful to note that the dynamic transforms are also available as individual UGens. However, users are advised to use FoaTransform for convenience.
[4] - Incidence is measured in terms of the (Active) Intensity vector.
[5] - Quality is measured as the magnitude of the Energy Normalised (Active) Intensity vector, aka rE.
[6] - Gain reported is the Potential-Kinetic Energy Mean, aka Soundfield Energy.
[7] - Decreased to -inf dB
[8] - Or, we might describe this as applying directionally dependent gains across the whole soundfield, mixing, and then re-incoding to a single planewave.
[9] - Equivalent to mixing all elements (scaled by 0dB), and then re-incoding to a single planewave.