First and Second Order Ambisonic Decoding Equations

This document contains Ambisonic decoding matrices for a number of speaker rigs for both first and second order signals and some discussion of the mathematics behind them. The second order format used is Furse-Malham Higher Order Format which provides a full 3D second order Ambisonic implementation.

This data is used by the MN Audio Library (MNLib) Ambisonic Player, Ambisonic Command-Line Decoder and MN Ambisonic Decoder Unit.

MNLib is a set of C++ libraries and programs for audio processing and music. MNLib is designed with portable C++ code for use on Linux, Microsoft platforms and others. MNLib, its documentation and this data are Copyright 1999-2000 Richard W.E. Furse (all rights reserved).

The Encoding

Conventions

Directions are expressed using unit vectors. Such vectors can be expressed using an Angle/Elevation representation or a Cartesian representation. These are related by x=cos(A)cos(E), y=sin(A)cos(E), z=sin(E).

Note that in both encoding formats described below, the individual channels are orthogonal but not orthonormal.

The first order Ambisonic encoding format (B-Format) uses the following channels:

Label Angle/Elevation Representation Cartesian Representation
W 0.707107 0.707107
X cos(A)cos(E) x
Y sin(A)cos(E) y
Z sin(E) z

The second order Ambisonic encoding (Furse-Malham Higher Order Format) uses the following channels:

Label Angle/Elevation Representation Cartesian Representation
W 0.707107 0.707107
X cos(A)cos(E) x
Y sin(A)cos(E) y
Z sin(E) z
R 1.5sin(E)sin(E)-0.5 1.5zz-0.5
S cos(A)sin(2E) 2zx
T sin(A)sin(2E) 2yz
U cos(2A)cos(E)cos(E) xx-yy
V sin(2A)cos(E)cos(E) 2xy

Justification of the Furse-Malham Higher Order Format

The second order components are related to the formal complex set (defined in terms of associated Legrendre polynomials). Working for the standard formulation for this and taking x=cos(PHI)sin(THETA), y=sin(PHI)sin(THETA) and z=cos(THETA), the relationship between the formal set and the Cartesian set above is given by:

Relationship between real and complex spherical harmonic sets

Interpreting the Tables

For each rig an initial table provides an overview of the rig's behaviour, including its level of support for each second order spherical harmonic. The information is presented in the following ways:

Recreated Harmonics:These are the harmonics of the encoded soundfield that the rig reproduces. The more of these the better.
Absent Harmonics:These are harmonics that the speaker rig cannot reproduce however the matrices are configured. For instance a flat rig cannot reproduce height information so the Z channel (amongst others) will be absent.
Discarded Ambiguous Harmonics:These are harmonics that have been discarded because inclusion would confuse a lower-order harmonic. For instance a single-speaker rig would produce an ambiguous signal if directional information was played over it, so all harmonics present except W (omnidirectional) should be discarded. This issue can be thought of as similar to filtering before A/D conversion. Without filtering, frequencies above the Nyquist frequency fold back and confuse frequencies below.
Discarded Coarse Harmonics:Decode matrices for unusual shapes of rig sometimes produce very large decoding scalars. Although these may be mathematically correct according to the idealised matching equation, they are likely to result in highly distorted soundfields and possible clipping. An example of this is a square rig that has been changed so that one of the speakers is very slightly higher than is usual. In this case the Z channel would cease to be absent but would be discarded as coarse.
Symmetry Distortion Rating:This is a measure of how stable a speaker rig's response is. For symmetric rigs this value should be zero.

Three further tables are provided containing the gains that should be appled to an encoded soundfield to produce each channel of a speaker feed.

The first of these tables provides the scalars that should be used to reproduce the soundfield in the idealised `matching' mathematical form of the problem. This is calculated by consideration of an idealised Ambisonic Microphone at the centre of a rig with an infinite number of speakers. These values are valid for both first and second order encodings.

The second and third tables contain `controlled opposite' formulations separately for first and second order. These forms guarantee that speakers will never generate an `anti-phase' signal (this is also known as `in-phase' decoding). Also, for second order cases the speaker response has only a single maximum. Below are coloured plots of the response of a speaker from a cubic rig. The plots indicates the strength of response for one speaker for different locations of a single sound source in the encoded soundfield. Source angle is horizontal and elevation vertical, green is used to indicate a positive response and cyan is used to indicate a negative `anti-phase' response. Note the faint cyan `anti-phase' band and second maximum in the `matching' plot.

MatchingControlled Opposites
Example `Matching' Response Plot Example `Controlled Opposites' Response Plot

In general I find the `controlled opposite' equations produce a larger listening area at the expense of some directional information. Compromises can be struck by choosing intermediate scalars. In some of the MNLib programs this can be done using a `fudge factor.'

Decoding for Custom Rigs

The code that generates this web page is part of the MN Ambisonic Decoder Unit. This is also used by the MNLib Ambisonic Command-Line Decoder. This will attempt to find sensible decode matrices for many shapes of speaker rig.

Mono

Rig Overview

First OrderSecond Order
Recreated Harmonics: W W
Absent Harmonics: Y, Z Y, Z, S, T, V
Discarded Ambiguous Harmonics: X X, R, U
Discarded Coarse Harmonics: - -
Symmetry Distortion Rating: 0.0000 0.0000

Rig Decode Matrix to Reproduce Spherical Harmonics (First Order)

This rig configuration produces a strict idealised response that satisfies the Ambisonic matching equations. Generally this type of configuration produces a relatively small stable listening area. (See controlled opposites below.)

Speaker W X Y Z
<1.0000,0.0000,0.0000> 1.4142 0.0000 0.0000 0.0000

Rig Decode Matrix to Reproduce Spherical Harmonics (Second Order)

This rig configuration produces a strict idealised response that satisfies the Ambisonic matching equations. Generally this type of configuration produces a relatively small stable listening area. (See controlled opposites below.)

Speaker W X Y Z R S T U V
<1.0000,0.0000,0.0000> 1.4142 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Rig `Controlled Opposites' Decode Matrix (First Order)

This rig configuration produces an `in-phase' response.

Speaker W X Y Z
<1.0000,0.0000,0.0000> 1.4142 0.0000 0.0000 0.0000

Rig `Controlled Opposites' Decode Matrix (Second Order)

This rig configuration produces an `in-phase' response and each speaker will have only a single maximum given a moving virtual sound source.

Speaker W X Y Z R S T U V
<1.0000,0.0000,0.0000> 1.4142 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Stereo

Rig Overview

First OrderSecond Order
Recreated Harmonics: W, Y W, Y
Absent Harmonics: X, Z X, Z, S, T, V
Discarded Ambiguous Harmonics: - R, U
Discarded Coarse Harmonics: - -
Symmetry Distortion Rating: 0.0000 0.0000

Rig Decode Matrix to Reproduce Spherical Harmonics (First Order)

This rig configuration produces a strict idealised response that satisfies the Ambisonic matching equations. Generally this type of configuration produces a relatively small stable listening area. (See controlled opposites below.)

Speaker W X Y Z
<0.0000,1.0000,0.0000> 0.7071 0.0000 0.5000 0.0000
<0.0000,-1.0000,0.0000> 0.7071 0.0000 -0.5000 0.0000

Rig Decode Matrix to Reproduce Spherical Harmonics (Second Order)

This rig configuration produces a strict idealised response that satisfies the Ambisonic matching equations. Generally this type of configuration produces a relatively small stable listening area. (See controlled opposites below.)

Speaker W X Y Z R S T U V
<0.0000,1.0000,0.0000> 0.7071 0.0000 0.5000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
<0.0000,-1.0000,0.0000> 0.7071 0.0000 -0.5000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Rig `Controlled Opposites' Decode Matrix (First Order)

This rig configuration produces an `in-phase' response.

Speaker W X Y Z
<0.0000,1.0000,0.0000> 0.7071 0.0000 0.5000 0.0000
<0.0000,-1.0000,0.0000> 0.7071 0.0000 -0.5000 0.0000

Rig `Controlled Opposites' Decode Matrix (Second Order)

This rig configuration produces an `in-phase' response and each speaker will have only a single maximum given a moving virtual sound source.

Speaker W X Y Z R S T U V
<0.0000,1.0000,0.0000> 0.7071 0.0000 0.5000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
<0.0000,-1.0000,0.0000> 0.7071 0.0000 -0.5000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Square

Rig Overview

First OrderSecond Order
Recreated Harmonics: W, X, Y W, X, Y, V
Absent Harmonics: Z Z, S, T, U
Discarded Ambiguous Harmonics: - R
Discarded Coarse Harmonics: - -
Symmetry Distortion Rating: 0.0000 0.0000

Rig Decode Matrix to Reproduce Spherical Harmonics (First Order)

This rig configuration produces a strict idealised response that satisfies the Ambisonic matching equations. Generally this type of configuration produces a relatively small stable listening area. (See controlled opposites below.)

Speaker W X Y Z
<0.7071,0.7071,0.0000> 0.3536 0.3536 0.3536 0.0000
<0.7071,-0.7071,0.0000> 0.3536 0.3536 -0.3536 0.0000
<-0.7071,-0.7071,0.0000> 0.3536 -0.3536 -0.3536 0.0000
<-0.7071,0.7071,0.0000> 0.3536 -0.3536 0.3536 0.0000

Rig Decode Matrix to Reproduce Spherical Harmonics (Second Order)

This rig configuration produces a strict idealised response that satisfies the Ambisonic matching equations. Generally this type of configuration produces a relatively small stable listening area. (See controlled opposites below.)

Speaker W X Y Z R S T U V
<0.7071,0.7071,0.0000> 0.3536 0.3536 0.3536 0.0000 0.0000 0.0000 0.0000 0.0000 0.2500
<0.7071,-0.7071,0.0000> 0.3536 0.3536 -0.3536 0.0000 0.0000 0.0000 0.0000 0.0000 -0.2500
<-0.7071,-0.7071,0.0000> 0.3536 -0.3536 -0.3536 0.0000 0.0000 0.0000 0.0000 0.0000 0.2500
<-0.7071,0.7071,0.0000> 0.3536 -0.3536 0.3536 0.0000 0.0000 0.0000 0.0000 0.0000 -0.2500

Rig `Controlled Opposites' Decode Matrix (First Order)

This rig configuration produces an `in-phase' response.

Speaker W X Y Z
<0.7071,0.7071,0.0000> 0.3536 0.1768 0.1768 0.0000
<0.7071,-0.7071,0.0000> 0.3536 0.1768 -0.1768 0.0000
<-0.7071,-0.7071,0.0000> 0.3536 -0.1768 -0.1768 0.0000
<-0.7071,0.7071,0.0000> 0.3536 -0.1768 0.1768 0.0000

Rig `Controlled Opposites' Decode Matrix (Second Order)

This rig configuration produces an `in-phase' response and each speaker will have only a single maximum given a moving virtual sound source.

Speaker W X Y Z R S T U V
<0.7071,0.7071,0.0000> 0.3536 0.2434 0.2434 0.0000 0.0000 0.0000 0.0000 0.0000 0.0964
<0.7071,-0.7071,0.0000> 0.3536 0.2434 -0.2434 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0964
<-0.7071,-0.7071,0.0000> 0.3536 -0.2434 -0.2434 0.0000 0.0000 0.0000 0.0000 0.0000 0.0964
<-0.7071,0.7071,0.0000> 0.3536 -0.2434 0.2434 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0964

Pentagon

Rig Overview

First OrderSecond Order
Recreated Harmonics: W, X, Y W, X, Y, U, V
Absent Harmonics: Z Z, S, T
Discarded Ambiguous Harmonics: - R
Discarded Coarse Harmonics: - -
Symmetry Distortion Rating: 0.0000 0.0000

Rig Decode Matrix to Reproduce Spherical Harmonics (First Order)

This rig configuration produces a strict idealised response that satisfies the Ambisonic matching equations. Generally this type of configuration produces a relatively small stable listening area. (See controlled opposites below.)

Speaker W X Y Z
<0.8090,0.5878,0.0000> 0.2828 0.3236 0.2351 0.0000
<-0.3090,0.9511,0.0000> 0.2828 -0.1236 0.3804 0.0000
<-1.0000,0.0000,0.0000> 0.2828 -0.4000 0.0000 0.0000
<-0.3090,-0.9511,0.0000> 0.2828 -0.1236 -0.3804 0.0000
<0.8090,-0.5878,0.0000> 0.2828 0.3236 -0.2351 0.0000

Rig Decode Matrix to Reproduce Spherical Harmonics (Second Order)

This rig configuration produces a strict idealised response that satisfies the Ambisonic matching equations. Generally this type of configuration produces a relatively small stable listening area. (See controlled opposites below.)

Speaker W X Y Z R S T U V
<0.8090,0.5878,0.0000> 0.2828 0.3236 0.2351 0.0000 0.0000 0.0000 0.0000 0.1236 0.3804
<-0.3090,0.9511,0.0000> 0.2828 -0.1236 0.3804 0.0000 0.0000 0.0000 0.0000 -0.3236 -0.2351
<-1.0000,0.0000,0.0000> 0.2828 -0.4000 0.0000 0.0000 0.0000 0.0000 0.0000 0.4000 0.0000
<-0.3090,-0.9511,0.0000> 0.2828 -0.1236 -0.3804 0.0000 0.0000 0.0000 0.0000 -0.3236 0.2351
<0.8090,-0.5878,0.0000> 0.2828 0.3236 -0.2351 0.0000 0.0000 0.0000 0.0000 0.1236 -0.3804

Rig `Controlled Opposites' Decode Matrix (First Order)

This rig configuration produces an `in-phase' response.

Speaker W X Y Z
<0.8090,0.5878,0.0000> 0.2828 0.1618 0.1176 0.0000
<-0.3090,0.9511,0.0000> 0.2828 -0.0618 0.1902 0.0000
<-1.0000,0.0000,0.0000> 0.2828 -0.2000 0.0000 0.0000
<-0.3090,-0.9511,0.0000> 0.2828 -0.0618 -0.1902 0.0000
<0.8090,-0.5878,0.0000> 0.2828 0.1618 -0.1176 0.0000

Rig `Controlled Opposites' Decode Matrix (Second Order)

This rig configuration produces an `in-phase' response and each speaker will have only a single maximum given a moving virtual sound source.

Speaker W X Y Z R S T U V
<0.8090,0.5878,0.0000> 0.2828 0.2227 0.1618 0.0000 0.0000 0.0000 0.0000 0.0238 0.0733
<-0.3090,0.9511,0.0000> 0.2828 -0.0851 0.2619 0.0000 0.0000 0.0000 0.0000 -0.0624 -0.0453
<-1.0000,0.0000,0.0000> 0.2828 -0.2753 0.0000 0.0000 0.0000 0.0000 0.0000 0.0771 0.0000
<-0.3090,-0.9511,0.0000> 0.2828 -0.0851 -0.2619 0.0000 0.0000 0.0000 0.0000 -0.0624 0.0453
<0.8090,-0.5878,0.0000> 0.2828 0.2227 -0.1618 0.0000 0.0000 0.0000 0.0000 0.0238 -0.0733

Hexagon

Rig Overview

First OrderSecond Order
Recreated Harmonics: W, X, Y W, X, Y, U, V
Absent Harmonics: Z Z, S, T
Discarded Ambiguous Harmonics: - R
Discarded Coarse Harmonics: - -
Symmetry Distortion Rating: 0.0000 0.0000

Rig Decode Matrix to Reproduce Spherical Harmonics (First Order)

This rig configuration produces a strict idealised response that satisfies the Ambisonic matching equations. Generally this type of configuration produces a relatively small stable listening area. (See controlled opposites below.)

Speaker W X Y Z
<0.8660,0.5000,0.0000> 0.2357 0.2887 0.1667 0.0000
<0.0000,1.0000,0.0000> 0.2357 0.0000 0.3333 0.0000
<-0.8660,0.5000,0.0000> 0.2357 -0.2887 0.1667 0.0000
<-0.8660,-0.5000,0.0000> 0.2357 -0.2887 -0.1667 0.0000
<0.0000,-1.0000,0.0000> 0.2357 0.0000 -0.3333 0.0000
<0.8660,-0.5000,0.0000> 0.2357 0.2887 -0.1667 0.0000

Rig Decode Matrix to Reproduce Spherical Harmonics (Second Order)

This rig configuration produces a strict idealised response that satisfies the Ambisonic matching equations. Generally this type of configuration produces a relatively small stable listening area. (See controlled opposites below.)

Speaker W X Y Z R S T U V
<0.8660,0.5000,0.0000> 0.2357 0.2887 0.1667 0.0000 0.0000 0.0000 0.0000 0.1667 0.2887
<0.0000,1.0000,0.0000> 0.2357 0.0000 0.3333 0.0000 0.0000 0.0000 0.0000 -0.3333 0.0000
<-0.8660,0.5000,0.0000> 0.2357 -0.2887 0.1667 0.0000 0.0000 0.0000 0.0000 0.1667 -0.2887
<-0.8660,-0.5000,0.0000> 0.2357 -0.2887 -0.1667 0.0000 0.0000 0.0000 0.0000 0.1667 0.2887
<0.0000,-1.0000,0.0000> 0.2357 0.0000 -0.3333 0.0000 0.0000 0.0000 0.0000 -0.3333 0.0000
<0.8660,-0.5000,0.0000> 0.2357 0.2887 -0.1667 0.0000 0.0000 0.0000 0.0000 0.1667 -0.2887

Rig `Controlled Opposites' Decode Matrix (First Order)

This rig configuration produces an `in-phase' response.

Speaker W X Y Z
<0.8660,0.5000,0.0000> 0.2357 0.1443 0.0833 0.0000
<0.0000,1.0000,0.0000> 0.2357 0.0000 0.1667 0.0000
<-0.8660,0.5000,0.0000> 0.2357 -0.1443 0.0833 0.0000
<-0.8660,-0.5000,0.0000> 0.2357 -0.1443 -0.0833 0.0000
<0.0000,-1.0000,0.0000> 0.2357 0.0000 -0.1667 0.0000
<0.8660,-0.5000,0.0000> 0.2357 0.1443 -0.0833 0.0000

Rig `Controlled Opposites' Decode Matrix (Second Order)

This rig configuration produces an `in-phase' response and each speaker will have only a single maximum given a moving virtual sound source.

Speaker W X Y Z R S T U V
<0.8660,0.5000,0.0000> 0.2357 0.1987 0.1147 0.0000 0.0000 0.0000 0.0000 0.0321 0.0556
<0.0000,1.0000,0.0000> 0.2357 0.0000 0.2294 0.0000 0.0000 0.0000 0.0000 -0.0643 0.0000
<-0.8660,0.5000,0.0000> 0.2357 -0.1987 0.1147 0.0000 0.0000 0.0000 0.0000 0.0321 -0.0556
<-0.8660,-0.5000,0.0000> 0.2357 -0.1987 -0.1147 0.0000 0.0000 0.0000 0.0000 0.0321 0.0556
<0.0000,-1.0000,0.0000> 0.2357 0.0000 -0.2294 0.0000 0.0000 0.0000 0.0000 -0.0643 0.0000
<0.8660,-0.5000,0.0000> 0.2357 0.1987 -0.1147 0.0000 0.0000 0.0000 0.0000 0.0321 -0.0556

Octagon1

Rig Overview

First OrderSecond Order
Recreated Harmonics: W, X, Y W, X, Y, U, V
Absent Harmonics: Z Z, S, T
Discarded Ambiguous Harmonics: - R
Discarded Coarse Harmonics: - -
Symmetry Distortion Rating: 0.0000 0.0000

Rig Decode Matrix to Reproduce Spherical Harmonics (First Order)

This rig configuration produces a strict idealised response that satisfies the Ambisonic matching equations. Generally this type of configuration produces a relatively small stable listening area. (See controlled opposites below.)

Speaker W X Y Z
<0.9239,0.3827,0.0000> 0.1768 0.2310 0.0957 0.0000
<0.3827,0.9239,0.0000> 0.1768 0.0957 0.2310 0.0000
<-0.3827,0.9239,0.0000> 0.1768 -0.0957 0.2310 0.0000
<-0.9239,0.3827,0.0000> 0.1768 -0.2310 0.0957 0.0000
<-0.9239,-0.3827,0.0000> 0.1768 -0.2310 -0.0957 0.0000
<-0.3827,-0.9239,0.0000> 0.1768 -0.0957 -0.2310 0.0000
<0.3827,-0.9239,0.0000> 0.1768 0.0957 -0.2310 0.0000
<0.9239,-0.3827,0.0000> 0.1768 0.2310 -0.0957 0.0000

Rig Decode Matrix to Reproduce Spherical Harmonics (Second Order)

This rig configuration produces a strict idealised response that satisfies the Ambisonic matching equations. Generally this type of configuration produces a relatively small stable listening area. (See controlled opposites below.)

Speaker W X Y Z R S T U V
<0.9239,0.3827,0.0000> 0.1768 0.2310 0.0957 0.0000 0.0000 0.0000 0.0000 0.1768 0.1768
<0.3827,0.9239,0.0000> 0.1768 0.0957 0.2310 0.0000 0.0000 0.0000 0.0000 -0.1768 0.1768
<-0.3827,0.9239,0.0000> 0.1768 -0.0957 0.2310 0.0000 0.0000 0.0000 0.0000 -0.1768 -0.1768
<-0.9239,0.3827,0.0000> 0.1768 -0.2310 0.0957 0.0000 0.0000 0.0000 0.0000 0.1768 -0.1768
<-0.9239,-0.3827,0.0000> 0.1768 -0.2310 -0.0957 0.0000 0.0000 0.0000 0.0000 0.1768 0.1768
<-0.3827,-0.9239,0.0000> 0.1768 -0.0957 -0.2310 0.0000 0.0000 0.0000 0.0000 -0.1768 0.1768
<0.3827,-0.9239,0.0000> 0.1768 0.0957 -0.2310 0.0000 0.0000 0.0000 0.0000 -0.1768 -0.1768
<0.9239,-0.3827,0.0000> 0.1768 0.2310 -0.0957 0.0000 0.0000 0.0000 0.0000 0.1768 -0.1768

Rig `Controlled Opposites' Decode Matrix (First Order)

This rig configuration produces an `in-phase' response.

Speaker W X Y Z
<0.9239,0.3827,0.0000> 0.1768 0.1155 0.0478 0.0000
<0.3827,0.9239,0.0000> 0.1768 0.0478 0.1155 0.0000
<-0.3827,0.9239,0.0000> 0.1768 -0.0478 0.1155 0.0000
<-0.9239,0.3827,0.0000> 0.1768 -0.1155 0.0478 0.0000
<-0.9239,-0.3827,0.0000> 0.1768 -0.1155 -0.0478 0.0000
<-0.3827,-0.9239,0.0000> 0.1768 -0.0478 -0.1155 0.0000
<0.3827,-0.9239,0.0000> 0.1768 0.0478 -0.1155 0.0000
<0.9239,-0.3827,0.0000> 0.1768 0.1155 -0.0478 0.0000

Rig `Controlled Opposites' Decode Matrix (Second Order)

This rig configuration produces an `in-phase' response and each speaker will have only a single maximum given a moving virtual sound source.

Speaker W X Y Z R S T U V
<0.9239,0.3827,0.0000> 0.1768 0.1591 0.0659 0.0000 0.0000 0.0000 0.0000 0.0342 0.0342
<0.3827,0.9239,0.0000> 0.1768 0.0659 0.1591 0.0000 0.0000 0.0000 0.0000 -0.0342 0.0342
<-0.3827,0.9239,0.0000> 0.1768 -0.0659 0.1591 0.0000 0.0000 0.0000 0.0000 -0.0342 -0.0342
<-0.9239,0.3827,0.0000> 0.1768 -0.1591 0.0659 0.0000 0.0000 0.0000 0.0000 0.0342 -0.0342
<-0.9239,-0.3827,0.0000> 0.1768 -0.1591 -0.0659 0.0000 0.0000 0.0000 0.0000 0.0342 0.0342
<-0.3827,-0.9239,0.0000> 0.1768 -0.0659 -0.1591 0.0000 0.0000 0.0000 0.0000 -0.0342 0.0342
<0.3827,-0.9239,0.0000> 0.1768 0.0659 -0.1591 0.0000 0.0000 0.0000 0.0000 -0.0342 -0.0342
<0.9239,-0.3827,0.0000> 0.1768 0.1591 -0.0659 0.0000 0.0000 0.0000 0.0000 0.0342 -0.0342

Octagon2

Rig Overview

First OrderSecond Order
Recreated Harmonics: W, X, Y W, X, Y, U, V
Absent Harmonics: Z Z, S, T
Discarded Ambiguous Harmonics: - R
Discarded Coarse Harmonics: - -
Symmetry Distortion Rating: 0.0000 0.0000

Rig Decode Matrix to Reproduce Spherical Harmonics (First Order)

This rig configuration produces a strict idealised response that satisfies the Ambisonic matching equations. Generally this type of configuration produces a relatively small stable listening area. (See controlled opposites below.)

Speaker W X Y Z
<1.0000,0.0000,0.0000> 0.1768 0.2500 0.0000 0.0000
<0.7071,0.7071,0.0000> 0.1768 0.1768 0.1768 0.0000
<0.0000,1.0000,0.0000> 0.1768 0.0000 0.2500 0.0000
<-0.7071,0.7071,0.0000> 0.1768 -0.1768 0.1768 0.0000
<-1.0000,0.0000,0.0000> 0.1768 -0.2500 0.0000 0.0000
<-0.7071,-0.7071,0.0000> 0.1768 -0.1768 -0.1768 0.0000
<0.0000,-1.0000,0.0000> 0.1768 0.0000 -0.2500 0.0000
<0.7071,-0.7071,0.0000> 0.1768 0.1768 -0.1768 0.0000

Rig Decode Matrix to Reproduce Spherical Harmonics (Second Order)

This rig configuration produces a strict idealised response that satisfies the Ambisonic matching equations. Generally this type of configuration produces a relatively small stable listening area. (See controlled opposites below.)

Speaker W X Y Z R S T U V
<1.0000,0.0000,0.0000> 0.1768 0.2500 0.0000 0.0000 0.0000 0.0000 0.0000 0.2500 0.0000
<0.7071,0.7071,0.0000> 0.1768 0.1768 0.1768 0.0000 0.0000 0.0000 0.0000 0.0000 0.2500
<0.0000,1.0000,0.0000> 0.1768 0.0000 0.2500 0.0000 0.0000 0.0000 0.0000 -0.2500 0.0000
<-0.7071,0.7071,0.0000> 0.1768 -0.1768 0.1768 0.0000 0.0000 0.0000 0.0000 0.0000 -0.2500
<-1.0000,0.0000,0.0000> 0.1768 -0.2500 0.0000 0.0000 0.0000 0.0000 0.0000 0.2500 0.0000
<-0.7071,-0.7071,0.0000> 0.1768 -0.1768 -0.1768 0.0000 0.0000 0.0000 0.0000 0.0000 0.2500
<0.0000,-1.0000,0.0000> 0.1768 0.0000 -0.2500 0.0000 0.0000 0.0000 0.0000 -0.2500 0.0000
<0.7071,-0.7071,0.0000> 0.1768 0.1768 -0.1768 0.0000 0.0000 0.0000 0.0000 0.0000 -0.2500

Rig `Controlled Opposites' Decode Matrix (First Order)

This rig configuration produces an `in-phase' response.

Speaker W X Y Z
<1.0000,0.0000,0.0000> 0.1768 0.1250 0.0000 0.0000
<0.7071,0.7071,0.0000> 0.1768 0.0884 0.0884 0.0000
<0.0000,1.0000,0.0000> 0.1768 0.0000 0.1250 0.0000
<-0.7071,0.7071,0.0000> 0.1768 -0.0884 0.0884 0.0000
<-1.0000,0.0000,0.0000> 0.1768 -0.1250 0.0000 0.0000
<-0.7071,-0.7071,0.0000> 0.1768 -0.0884 -0.0884 0.0000
<0.0000,-1.0000,0.0000> 0.1768 0.0000 -0.1250 0.0000
<0.7071,-0.7071,0.0000> 0.1768 0.0884 -0.0884 0.0000

Rig `Controlled Opposites' Decode Matrix (Second Order)

This rig configuration produces an `in-phase' response and each speaker will have only a single maximum given a moving virtual sound source.

Speaker W X Y Z R S T U V
<1.0000,0.0000,0.0000> 0.1768 0.1721 0.0000 0.0000 0.0000 0.0000 0.0000 0.0482 0.0000
<0.7071,0.7071,0.0000> 0.1768 0.1217 0.1217 0.0000 0.0000 0.0000 0.0000 0.0000 0.0482
<0.0000,1.0000,0.0000> 0.1768 0.0000 0.1721 0.0000 0.0000 0.0000 0.0000 -0.0482 0.0000
<-0.7071,0.7071,0.0000> 0.1768 -0.1217 0.1217 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0482
<-1.0000,0.0000,0.0000> 0.1768 -0.1721 0.0000 0.0000 0.0000 0.0000 0.0000 0.0482 0.0000
<-0.7071,-0.7071,0.0000> 0.1768 -0.1217 -0.1217 0.0000 0.0000 0.0000 0.0000 0.0000 0.0482
<0.0000,-1.0000,0.0000> 0.1768 0.0000 -0.1721 0.0000 0.0000 0.0000 0.0000 -0.0482 0.0000
<0.7071,-0.7071,0.0000> 0.1768 0.1217 -0.1217 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0482

Surround1

Rig Overview

First OrderSecond Order
Recreated Harmonics: W, X, Y W, X, Y, U, V
Absent Harmonics: Z Z, S, T
Discarded Ambiguous Harmonics: - R
Discarded Coarse Harmonics: - -
Symmetry Distortion Rating: 0.1295 116.0904

Note that the second order rig has a high symmetry distortion rating. Such a rig is likely to provide an unstable image.

Rig Decode Matrix to Reproduce Spherical Harmonics (First Order)

This rig configuration produces a strict idealised response that satisfies the Ambisonic matching equations. Generally this type of configuration produces a relatively small stable listening area. (See controlled opposites below.)

Speaker W X Y Z
<0.8660,0.5000,0.0000> 0.1690 0.2238 0.2500 0.0000
<1.0000,0.0000,0.0000> 0.1635 0.2591 0.0000 0.0000
<0.8660,-0.5000,0.0000> 0.1690 0.2238 -0.2500 0.0000
<-0.5000,0.8660,0.0000> 0.4563 -0.3533 0.4330 0.0000
<-0.5000,-0.8660,0.0000> 0.4563 -0.3533 -0.4330 0.0000

Rig Decode Matrix to Reproduce Spherical Harmonics (Second Order)

This rig configuration produces a strict idealised response that satisfies the Ambisonic matching equations. Generally this type of configuration produces a relatively small stable listening area. (See controlled opposites below.)

Speaker W X Y Z R S T U V
<0.8660,0.5000,0.0000> 0.0000 1.3660 0.3660 0.0000 0.0000 0.0000 0.0000 -1.3660 0.3660
<1.0000,0.0000,0.0000> 0.4714 -1.8214 0.0000 0.0000 0.0000 0.0000 0.0000 2.4880 0.0000
<0.8660,-0.5000,0.0000> 0.0000 1.3660 -0.3660 0.0000 0.0000 0.0000 0.0000 -1.3660 -0.3660
<-0.5000,0.8660,0.0000> 0.4714 -0.4553 0.3660 0.0000 0.0000 0.0000 0.0000 0.1220 -0.2113
<-0.5000,-0.8660,0.0000> 0.4714 -0.4553 -0.3660 0.0000 0.0000 0.0000 0.0000 0.1220 0.2113

Rig `Controlled Opposites' Decode Matrix (First Order)

This rig configuration produces an `in-phase' response.

Speaker W X Y Z
<0.8660,0.5000,0.0000> 0.1690 0.0797 0.0891 0.0000
<1.0000,0.0000,0.0000> 0.1635 0.0923 0.0000 0.0000
<0.8660,-0.5000,0.0000> 0.1690 0.0797 -0.0891 0.0000
<-0.5000,0.8660,0.0000> 0.4563 -0.1259 0.1543 0.0000
<-0.5000,-0.8660,0.0000> 0.4563 -0.1259 -0.1543 0.0000

Rig `Controlled Opposites' Decode Matrix (Second Order)

Not provided for this rig configuration because of unusual characteristics.

Cube

Rig Overview

First OrderSecond Order
Recreated Harmonics: W, X, Y, Z W, X, Y, Z, S, T, V
Absent Harmonics: - U
Discarded Ambiguous Harmonics: - R
Discarded Coarse Harmonics: - -
Symmetry Distortion Rating: 0.0000 0.0000

Rig Decode Matrix to Reproduce Spherical Harmonics (First Order)

This rig configuration produces a strict idealised response that satisfies the Ambisonic matching equations. Generally this type of configuration produces a relatively small stable listening area. (See controlled opposites below.)

Speaker W X Y Z
<0.5774,0.5774,-0.5774> 0.1768 0.2165 0.2165 -0.2165
<0.5774,-0.5774,-0.5774> 0.1768 0.2165 -0.2165 -0.2165
<-0.5774,-0.5774,-0.5774> 0.1768 -0.2165 -0.2165 -0.2165
<-0.5774,0.5774,-0.5774> 0.1768 -0.2165 0.2165 -0.2165
<0.5774,0.5774,0.5774> 0.1768 0.2165 0.2165 0.2165
<0.5774,-0.5774,0.5774> 0.1768 0.2165 -0.2165 0.2165
<-0.5774,-0.5774,0.5774> 0.1768 -0.2165 -0.2165 0.2165
<-0.5774,0.5774,0.5774> 0.1768 -0.2165 0.2165 0.2165

Rig Decode Matrix to Reproduce Spherical Harmonics (Second Order)

This rig configuration produces a strict idealised response that satisfies the Ambisonic matching equations. Generally this type of configuration produces a relatively small stable listening area. (See controlled opposites below.)

Speaker W X Y Z R S T U V
<0.5774,0.5774,-0.5774> 0.1768 0.2165 0.2165 -0.2165 0.0000 -0.1875 -0.1875 0.0000 0.1875
<0.5774,-0.5774,-0.5774> 0.1768 0.2165 -0.2165 -0.2165 0.0000 -0.1875 0.1875 0.0000 -0.1875
<-0.5774,-0.5774,-0.5774> 0.1768 -0.2165 -0.2165 -0.2165 0.0000 0.1875 0.1875 0.0000 0.1875
<-0.5774,0.5774,-0.5774> 0.1768 -0.2165 0.2165 -0.2165 0.0000 0.1875 -0.1875 0.0000 -0.1875
<0.5774,0.5774,0.5774> 0.1768 0.2165 0.2165 0.2165 0.0000 0.1875 0.1875 0.0000 0.1875
<0.5774,-0.5774,0.5774> 0.1768 0.2165 -0.2165 0.2165 0.0000 0.1875 -0.1875 0.0000 -0.1875
<-0.5774,-0.5774,0.5774> 0.1768 -0.2165 -0.2165 0.2165 0.0000 -0.1875 -0.1875 0.0000 0.1875
<-0.5774,0.5774,0.5774> 0.1768 -0.2165 0.2165 0.2165 0.0000 -0.1875 0.1875 0.0000 -0.1875

Rig `Controlled Opposites' Decode Matrix (First Order)

This rig configuration produces an `in-phase' response.

Speaker W X Y Z
<0.5774,0.5774,-0.5774> 0.1768 0.0722 0.0722 -0.0722
<0.5774,-0.5774,-0.5774> 0.1768 0.0722 -0.0722 -0.0722
<-0.5774,-0.5774,-0.5774> 0.1768 -0.0722 -0.0722 -0.0722
<-0.5774,0.5774,-0.5774> 0.1768 -0.0722 0.0722 -0.0722
<0.5774,0.5774,0.5774> 0.1768 0.0722 0.0722 0.0722
<0.5774,-0.5774,0.5774> 0.1768 0.0722 -0.0722 0.0722
<-0.5774,-0.5774,0.5774> 0.1768 -0.0722 -0.0722 0.0722
<-0.5774,0.5774,0.5774> 0.1768 -0.0722 0.0722 0.0722

Rig `Controlled Opposites' Decode Matrix (Second Order)

This rig configuration produces an `in-phase' response and each speaker will have only a single maximum given a moving virtual sound source.

Speaker W X Y Z R S T U V
<0.5774,0.5774,-0.5774> 0.1768 0.1140 0.1140 -0.1140 0.0000 -0.0369 -0.0369 0.0000 0.0369
<0.5774,-0.5774,-0.5774> 0.1768 0.1140 -0.1140 -0.1140 0.0000 -0.0369 0.0369 0.0000 -0.0369
<-0.5774,-0.5774,-0.5774> 0.1768 -0.1140 -0.1140 -0.1140 0.0000 0.0369 0.0369 0.0000 0.0369
<-0.5774,0.5774,-0.5774> 0.1768 -0.1140 0.1140 -0.1140 0.0000 0.0369 -0.0369 0.0000 -0.0369
<0.5774,0.5774,0.5774> 0.1768 0.1140 0.1140 0.1140 0.0000 0.0369 0.0369 0.0000 0.0369
<0.5774,-0.5774,0.5774> 0.1768 0.1140 -0.1140 0.1140 0.0000 0.0369 -0.0369 0.0000 -0.0369
<-0.5774,-0.5774,0.5774> 0.1768 -0.1140 -0.1140 0.1140 0.0000 -0.0369 -0.0369 0.0000 0.0369
<-0.5774,0.5774,0.5774> 0.1768 -0.1140 0.1140 0.1140 0.0000 -0.0369 0.0369 0.0000 -0.0369

Dodecahedron1

Rig Overview

First OrderSecond Order
Recreated Harmonics: W, X, Y, Z W, X, Y, Z, R, S, T, U, V
Absent Harmonics: - -
Discarded Ambiguous Harmonics: - -
Discarded Coarse Harmonics: - -
Symmetry Distortion Rating: 0.0000 0.0000

Rig Decode Matrix to Reproduce Spherical Harmonics (First Order)

This rig configuration produces a strict idealised response that satisfies the Ambisonic matching equations. Generally this type of configuration produces a relatively small stable listening area. (See controlled opposites below.)

Speaker W X Y Z
<0.0000,0.0000,1.0000> 0.1179 0.0000 0.0000 0.2500
<0.0000,0.0000,-1.0000> 0.1179 0.0000 0.0000 -0.2500
<0.7236,0.5257,0.4472> 0.1179 0.1809 0.1314 0.1118
<-0.7236,-0.5257,-0.4472> 0.1179 -0.1809 -0.1314 -0.1118
<0.7236,-0.5257,0.4472> 0.1179 0.1809 -0.1314 0.1118
<-0.7236,0.5257,-0.4472> 0.1179 -0.1809 0.1314 -0.1118
<-0.2764,0.8507,0.4472> 0.1179 -0.0691 0.2127 0.1118
<0.2764,-0.8507,-0.4472> 0.1179 0.0691 -0.2127 -0.1118
<-0.2764,-0.8507,0.4472> 0.1179 -0.0691 -0.2127 0.1118
<0.2764,0.8507,-0.4472> 0.1179 0.0691 0.2127 -0.1118
<-0.8944,0.0000,0.4472> 0.1179 -0.2236 0.0000 0.1118
<0.8944,0.0000,-0.4472> 0.1179 0.2236 0.0000 -0.1118

Rig Decode Matrix to Reproduce Spherical Harmonics (Second Order)

This rig configuration produces a strict idealised response that satisfies the Ambisonic matching equations. Generally this type of configuration produces a relatively small stable listening area. (See controlled opposites below.)

Speaker W X Y Z R S T U V
<0.0000,0.0000,1.0000> 0.1179 0.0000 0.0000 0.2500 0.4167 0.0000 0.0000 0.0000 0.0000
<0.0000,0.0000,-1.0000> 0.1179 0.0000 0.0000 -0.2500 0.4167 0.0000 0.0000 0.0000 0.0000
<0.7236,0.5257,0.4472> 0.1179 0.1809 0.1314 0.1118 -0.0833 0.2023 0.1469 0.0773 0.2378
<-0.7236,-0.5257,-0.4472> 0.1179 -0.1809 -0.1314 -0.1118 -0.0833 0.2023 0.1469 0.0773 0.2378
<0.7236,-0.5257,0.4472> 0.1179 0.1809 -0.1314 0.1118 -0.0833 0.2023 -0.1469 0.0773 -0.2378
<-0.7236,0.5257,-0.4472> 0.1179 -0.1809 0.1314 -0.1118 -0.0833 0.2023 -0.1469 0.0773 -0.2378
<-0.2764,0.8507,0.4472> 0.1179 -0.0691 0.2127 0.1118 -0.0833 -0.0773 0.2378 -0.2023 -0.1469
<0.2764,-0.8507,-0.4472> 0.1179 0.0691 -0.2127 -0.1118 -0.0833 -0.0773 0.2378 -0.2023 -0.1469
<-0.2764,-0.8507,0.4472> 0.1179 -0.0691 -0.2127 0.1118 -0.0833 -0.0773 -0.2378 -0.2023 0.1469
<0.2764,0.8507,-0.4472> 0.1179 0.0691 0.2127 -0.1118 -0.0833 -0.0773 -0.2378 -0.2023 0.1469
<-0.8944,0.0000,0.4472> 0.1179 -0.2236 0.0000 0.1118 -0.0833 -0.2500 0.0000 0.2500 0.0000
<0.8944,0.0000,-0.4472> 0.1179 0.2236 0.0000 -0.1118 -0.0833 -0.2500 0.0000 0.2500 0.0000

Rig `Controlled Opposites' Decode Matrix (First Order)

This rig configuration produces an `in-phase' response.

Speaker W X Y Z
<0.0000,0.0000,1.0000> 0.1179 0.0000 0.0000 0.0833
<0.0000,0.0000,-1.0000> 0.1179 0.0000 0.0000 -0.0833
<0.7236,0.5257,0.4472> 0.1179 0.0603 0.0438 0.0373
<-0.7236,-0.5257,-0.4472> 0.1179 -0.0603 -0.0438 -0.0373
<0.7236,-0.5257,0.4472> 0.1179 0.0603 -0.0438 0.0373
<-0.7236,0.5257,-0.4472> 0.1179 -0.0603 0.0438 -0.0373
<-0.2764,0.8507,0.4472> 0.1179 -0.0230 0.0709 0.0373
<0.2764,-0.8507,-0.4472> 0.1179 0.0230 -0.0709 -0.0373
<-0.2764,-0.8507,0.4472> 0.1179 -0.0230 -0.0709 0.0373
<0.2764,0.8507,-0.4472> 0.1179 0.0230 0.0709 -0.0373
<-0.8944,0.0000,0.4472> 0.1179 -0.0745 0.0000 0.0373
<0.8944,0.0000,-0.4472> 0.1179 0.0745 0.0000 -0.0373

Rig `Controlled Opposites' Decode Matrix (Second Order)

This rig configuration produces an `in-phase' response and each speaker will have only a single maximum given a moving virtual sound source.

Speaker W X Y Z R S T U V
<0.0000,0.0000,1.0000> 0.1179 0.0000 0.0000 0.1316 0.0491 0.0000 0.0000 0.0000 0.0000
<0.0000,0.0000,-1.0000> 0.1179 0.0000 0.0000 -0.1316 0.0491 0.0000 0.0000 0.0000 0.0000
<0.7236,0.5257,0.4472> 0.1179 0.0952 0.0692 0.0589 -0.0098 0.0238 0.0173 0.0091 0.0280
<-0.7236,-0.5257,-0.4472> 0.1179 -0.0952 -0.0692 -0.0589 -0.0098 0.0238 0.0173 0.0091 0.0280
<0.7236,-0.5257,0.4472> 0.1179 0.0952 -0.0692 0.0589 -0.0098 0.0238 -0.0173 0.0091 -0.0280
<-0.7236,0.5257,-0.4472> 0.1179 -0.0952 0.0692 -0.0589 -0.0098 0.0238 -0.0173 0.0091 -0.0280
<-0.2764,0.8507,0.4472> 0.1179 -0.0364 0.1119 0.0589 -0.0098 -0.0091 0.0280 -0.0238 -0.0173
<0.2764,-0.8507,-0.4472> 0.1179 0.0364 -0.1119 -0.0589 -0.0098 -0.0091 0.0280 -0.0238 -0.0173
<-0.2764,-0.8507,0.4472> 0.1179 -0.0364 -0.1119 0.0589 -0.0098 -0.0091 -0.0280 -0.0238 0.0173
<0.2764,0.8507,-0.4472> 0.1179 0.0364 0.1119 -0.0589 -0.0098 -0.0091 -0.0280 -0.0238 0.0173
<-0.8944,0.0000,0.4472> 0.1179 -0.1177 0.0000 0.0589 -0.0098 -0.0295 0.0000 0.0295 0.0000
<0.8944,0.0000,-0.4472> 0.1179 0.1177 0.0000 -0.0589 -0.0098 -0.0295 0.0000 0.0295 0.0000

Dodecahedron2

Rig Overview

First OrderSecond Order
Recreated Harmonics: W, X, Y, Z W, X, Y, Z, R, S, T, U, V
Absent Harmonics: - -
Discarded Ambiguous Harmonics: - -
Discarded Coarse Harmonics: - -
Symmetry Distortion Rating: 0.0000 0.0000

Rig Decode Matrix to Reproduce Spherical Harmonics (First Order)

This rig configuration produces a strict idealised response that satisfies the Ambisonic matching equations. Generally this type of configuration produces a relatively small stable listening area. (See controlled opposites below.)

Speaker W X Y Z
<1.0000,0.0000,0.0000> 0.1179 0.2500 0.0000 0.0000
<-1.0000,0.0000,0.0000> 0.1179 -0.2500 0.0000 0.0000
<0.4472,0.0000,-0.8944> 0.1179 0.1118 0.0000 -0.2236
<-0.4472,0.0000,0.8944> 0.1179 -0.1118 0.0000 0.2236
<0.4472,0.8507,-0.2764> 0.1179 0.1118 0.2127 -0.0691
<-0.4472,-0.8507,0.2764> 0.1179 -0.1118 -0.2127 0.0691
<0.4472,-0.8507,-0.2764> 0.1179 0.1118 -0.2127 -0.0691
<-0.4472,0.8507,0.2764> 0.1179 -0.1118 0.2127 0.0691
<0.4472,0.5257,0.7236> 0.1179 0.1118 0.1314 0.1809
<-0.4472,-0.5257,-0.7236> 0.1179 -0.1118 -0.1314 -0.1809
<0.4472,-0.5257,0.7236> 0.1179 0.1118 -0.1314 0.1809
<-0.4472,0.5257,-0.7236> 0.1179 -0.1118 0.1314 -0.1809

Rig Decode Matrix to Reproduce Spherical Harmonics (Second Order)

This rig configuration produces a strict idealised response that satisfies the Ambisonic matching equations. Generally this type of configuration produces a relatively small stable listening area. (See controlled opposites below.)

Speaker W X Y Z R S T U V
<1.0000,0.0000,0.0000> 0.1179 0.2500 0.0000 0.0000 -0.2083 0.0000 0.0000 0.3125 0.0000
<-1.0000,0.0000,0.0000> 0.1179 -0.2500 0.0000 0.0000 -0.2083 0.0000 0.0000 0.3125 0.0000
<0.4472,0.0000,-0.8944> 0.1179 0.1118 0.0000 -0.2236 0.2917 -0.2500 0.0000 0.0625 0.0000
<-0.4472,0.0000,0.8944> 0.1179 -0.1118 0.0000 0.2236 0.2917 -0.2500 0.0000 0.0625 0.0000
<0.4472,0.8507,-0.2764> 0.1179 0.1118 0.2127 -0.0691 -0.1606 -0.0773 -0.1469 -0.1636 0.2378
<-0.4472,-0.8507,0.2764> 0.1179 -0.1118 -0.2127 0.0691 -0.1606 -0.0773 -0.1469 -0.1636 0.2378
<0.4472,-0.8507,-0.2764> 0.1179 0.1118 -0.2127 -0.0691 -0.1606 -0.0773 0.1469 -0.1636 -0.2378
<-0.4472,0.8507,0.2764> 0.1179 -0.1118 0.2127 0.0691 -0.1606 -0.0773 0.1469 -0.1636 -0.2378
<0.4472,0.5257,0.7236> 0.1179 0.1118 0.1314 0.1809 0.1189 0.2023 0.2378 -0.0239 0.1469
<-0.4472,-0.5257,-0.7236> 0.1179 -0.1118 -0.1314 -0.1809 0.1189 0.2023 0.2378 -0.0239 0.1469
<0.4472,-0.5257,0.7236> 0.1179 0.1118 -0.1314 0.1809 0.1189 0.2023 -0.2378 -0.0239 -0.1469
<-0.4472,0.5257,-0.7236> 0.1179 -0.1118 0.1314 -0.1809 0.1189 0.2023 -0.2378 -0.0239 -0.1469

Rig `Controlled Opposites' Decode Matrix (First Order)

This rig configuration produces an `in-phase' response.

Speaker W X Y Z
<1.0000,0.0000,0.0000> 0.1179 0.0833 0.0000 0.0000
<-1.0000,0.0000,0.0000> 0.1179 -0.0833 0.0000 0.0000
<0.4472,0.0000,-0.8944> 0.1179 0.0373 0.0000 -0.0745
<-0.4472,0.0000,0.8944> 0.1179 -0.0373 0.0000 0.0745
<0.4472,0.8507,-0.2764> 0.1179 0.0373 0.0709 -0.0230
<-0.4472,-0.8507,0.2764> 0.1179 -0.0373 -0.0709 0.0230
<0.4472,-0.8507,-0.2764> 0.1179 0.0373 -0.0709 -0.0230
<-0.4472,0.8507,0.2764> 0.1179 -0.0373 0.0709 0.0230
<0.4472,0.5257,0.7236> 0.1179 0.0373 0.0438 0.0603
<-0.4472,-0.5257,-0.7236> 0.1179 -0.0373 -0.0438 -0.0603
<0.4472,-0.5257,0.7236> 0.1179 0.0373 -0.0438 0.0603
<-0.4472,0.5257,-0.7236> 0.1179 -0.0373 0.0438 -0.0603

Rig `Controlled Opposites' Decode Matrix (Second Order)

This rig configuration produces an `in-phase' response and each speaker will have only a single maximum given a moving virtual sound source.

Speaker W X Y Z R S T U V
<1.0000,0.0000,0.0000> 0.1179 0.1316 0.0000 0.0000 -0.0246 0.0000 0.0000 0.0368 0.0000
<-1.0000,0.0000,0.0000> 0.1179 -0.1316 0.0000 0.0000 -0.0246 0.0000 0.0000 0.0368 0.0000
<0.4472,0.0000,-0.8944> 0.1179 0.0589 0.0000 -0.1177 0.0344 -0.0295 0.0000 0.0074 0.0000
<-0.4472,0.0000,0.8944> 0.1179 -0.0589 0.0000 0.1177 0.0344 -0.0295 0.0000 0.0074 0.0000
<0.4472,0.8507,-0.2764> 0.1179 0.0589 0.1119 -0.0364 -0.0189 -0.0091 -0.0173 -0.0193 0.0280
<-0.4472,-0.8507,0.2764> 0.1179 -0.0589 -0.1119 0.0364 -0.0189 -0.0091 -0.0173 -0.0193 0.0280
<0.4472,-0.8507,-0.2764> 0.1179 0.0589 -0.1119 -0.0364 -0.0189 -0.0091 0.0173 -0.0193 -0.0280
<-0.4472,0.8507,0.2764> 0.1179 -0.0589 0.1119 0.0364 -0.0189 -0.0091 0.0173 -0.0193 -0.0280
<0.4472,0.5257,0.7236> 0.1179 0.0589 0.0692 0.0952 0.0140 0.0238 0.0280 -0.0028 0.0173
<-0.4472,-0.5257,-0.7236> 0.1179 -0.0589 -0.0692 -0.0952 0.0140 0.0238 0.0280 -0.0028 0.0173
<0.4472,-0.5257,0.7236> 0.1179 0.0589 -0.0692 0.0952 0.0140 0.0238 -0.0280 -0.0028 -0.0173
<-0.4472,0.5257,-0.7236> 0.1179 -0.0589 0.0692 -0.0952 0.0140 0.0238 -0.0280 -0.0028 -0.0173

Links

The author Richard Furse can be emailed as richard@muse.demon.co.uk.

Thanks to Philip Cotterell for providing the dodecahedral speaker geometries used and for spotting a number of slips on this page. Any further errors are entirely my fault!

"Ambisonics" is a registered trademark of Nimbus Communications International.