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Ambisonic Toolkit Matrices

A set of (real) matrix files for use by matrix mixing encoders and decoders.


  • Channel Order: Gerzon / Furse-Malham, aka, Classic first-order (FOA)
  • Normalization: MaxN, aka, Classic first-order (FOA)

The ATK's fixed matrices are designed to support a variety of useful encoding and decoding strategies. Encoding means, converting from some other signal format, e.g., monophonic or stereophonic, to Ambisonic B-format. Decoding means converting from Ambisonic B-format.


  • Omni - Omnidirectional encoding (monophonic). E.g., pressure only. In a well aligned, dampend studio environment, this usually sounds "in the head", while in concert hall listening usually appears as omnipresent.

  • Quad - Quadraphonic encoding. The quadraphonic signal is encoded as four planewaves arriving at [ 45, 135, -135, -45 ] degrees.

  • 5.0 - 5.0 encoding. The 5.0 signal is encoded as five planewaves arriving at [ 0, 30, 110, -110, -30 ] degrees.

  • 7.0 - 7.0 encoding. The 7.0 signal is encoded as seven planewaves arriving at [ 0, 30, 90, 135, -135, -90, -30 ] degrees.

  • A to B - A-format to B-format encoding. Encodes to a variety of tetrahedral orientations and W channel weights. The A-format encoder is often used in conjunction with the B-format to A-format decoder to form signal processing networks which preserve the spatial encoding. On its own, is often used to author immersive, periphonic (3D) decorrelated soundfields.

  • HOA1 - First order Ambisonic format exchange encoding. Encodes a variety of formats to traditional B-format. Encoding means encoding from one Ambisonic channel componenent orderding and normalisation to that of traditional B-format. In other words, from some standard scheme to Gerzon (aka Furse-Malham) ordering with MaxN normalisation.


  • Mirror - Mirroring across the origin and each of the coordinate axes.


  • 5.0 - Bruce Wiggins' optimised ITU 5.0 decoders. Three kinds are available:

    • Focused returns a focused, but front weighted image.
    • Equal equalises the angles across the image.
    • Four is similar to Equal, but doesn't use the centre speaker.
  • B to A - B-format to A-format decoding. Decodes to a variety of tetrahedral orientations and W channel weights. The B-format to A-format decoder is primarily intended to be used in conjuction with the A-format to B-format encoder. Though the use of BtoA/AtoB decoder/encoder pairs, signal processing networks can be constructed which preserve the spatial encoding found in the original input B-format signal.

  • HOA1 - First order Ambisonic format exchange decoding. Decodes traditional B-format to a variety of formats. Decoding means decoding from traditional B-format to another Ambisonic channel componenent orderding and normalisation. In other words, from Gerzon (aka Furse-Malham) ordering with MaxN normalisation to some other standard scheme.

    Note: You should have received a license notice with these matrices. Please see the included Third Party Notices for further details on the Wiggins contribution.

Matrix formats

Each matrix is provided in several formats:


A YAML file containing the matrix along with verbose metadata. Refer to flu-dec.yml for an example.


A text file containing the matrix, with one row per line, and cell values separated by spaces. Refer to flu-dec.txt for an example.


A text file containing one cell value per line. The first two values gives the dimension of the matrix as number of rows and number of columns. Empty lines can be used for improved readability. Comment lines can be added, starting with # or ;. Inline comments are also supported. Refer to flu-dec.mosl.txt for an example.

Using Matrices with Reaper

The matrices are included as part of the ATK for Reaper install, and there is no need to download and install the matrices separately.

Using Matrices with SuperCollider

Install ATK for SuperCollider. Launch SuperCollider3, and run the following code:

ATK Matrix Installation
// Create ATK support directory
// Place unzipped matrices in the directory opened  


If ATK for SuperCollider has been correctly installed, the above code will open the ATK's user support directory. Place the downloaded matrices here.

If you use ATK for Reaper as well as ATK for SuperCollider on Mac OSX, the matrices are shared between the two programs, and they will reside in the same location. We do not expect this to cause any problems.

Feedback and Bug Reports

Known issues are logged at GitHub.

If you experience problems or have questions pertaining to the ATK Matrices, please create an issue in the ATK-Matrices issue tracker.

If you use the matrices for an artistic project, please let us know. We plan on adding a gallery of example artistic and creative projects that make use of the Ambisonic Toolkit.

If you wish to use the matrices as part of a technical or software project, we'd like to know about that too. We're planning to link to other projects making use of Ambisonic Toolkit assets.

List of Changes

Version 1.0.3

  • Issue fixes:
    • github action for release archive: include matrices super folder

Version 1.0.2

  • Organizational:
    • add github action for release archive

Version 1.0.1

  • Issue fixes:
    • fix: refactor mosl.txt to use JSFX comment char #

Version 1.0.0

  • Initial release


The matrix files distributed with the Ambisonic Toolkit are licensed under a Creative Commons Attribution-Share Alike 3.0 Unported (CC BY-SA 3.0) License and are copyright the Ambisonic Toolkit Community and Joseph Anderson, 2017-22.



Third Party Notices


Irregular array decoding

Irregular array decoding coefficients (5.0) are kindly provided by Bruce Wiggins:

B. Wiggins, "An Investigation into the Real-time Manipulation and Control of Three-dimensional Sound Fields," PhD Thesis, University of Derby, Derby, 2004.