RingBuffer (Posts about spatial_audio:ambisonics)

Tools for Live Ambisonics Applications

Henrik von Coler — Sat, 16 Aug 2025 12:00:00 GMT

The following tables inlcude examples for software that can be used to create real time and interactive spatial audio systems, mostly using Ambisonics, but also with other rendering approaches, All examples are able to recieve control data, usually via OSC, to allow object-based spatialisation.

Free & Cross-Platform (all OS)

This is the preferred selection of free/ open source software. All solutions in this catecory run on all major platforms.

Tool	Platforms	License	Why use this solution?	Link
Reaper + IEM Plug‑in Suite	Windows / macOS / Linux (Reaper via WINE on Linux)	Reaper: low‑cost (unlimited evaluation); IEM: Free, Open Source	Complete Ambisonics toolchain (encode/rotate/decode); fast to learn; robust for live; widely used; allows automation in DAW trajectories.	IEM Plugins
SuperCollider + ATK / SC-HOA	Windows / macOS / Linux	Free, Open Source	Live coding; flexible real-time control; strong research/edu community; scalable for large projects.	Ambisonic Toolkit
Pure Data (with HOA library)	Windows / macOS / Linux	Free, Open Source	Patch-based; lightweight; great for teaching signal flow and rapid prototyping; Ambisonics externals available.	pd-ambisonics
SoundScape Renderer (SSR)	Windows / macOS / Linux	Free, Open Source	Supports a wide range of formats (HOA, VBAP, WFS); offers OSC and GUI control; helpful visualization of audio scenes.	SSR
SPARTA Plug‑ins	Windows / macOS / Linux	Free, Open Source	Ambisonics, VBAP, beamforming; complements IEM.	SPARTA

Creative Standards

While not free or open source, the following table contains the standards used in (experimental) music and media art. Solutions based on Max and Ableton Live benefit from the huge popularity of these platforms. Support on Linux systems is not provided. The code is colsed source.

Tool	Platforms	License	Why use this solution?	Link
IRCAM Spat~ (Max)	Windows / macOS (Max required)	Commercial	Classic real‑time spatialisation in Max; widely used in electroacoustic works; OSC/MIDI.	Spat~
SPAT Revolution (FLUX + IRCAM)	Windows / macOS	Commercial (edu available)	De‑facto standard for creative spatial audio; Ambisonics/VBAP/binaural; powerful routing; OSC.	SPAT Revolution
Ableton Live + Envelop for Live (E4L)	Windows / macOS	Free (E4L), Ableton Live + Max for Live required	Spatial audio toolkit inside Ableton Live. Includes Ambisonics encoder/decoder, spatial FX, and binaural render. Ideal for electronic music and live performance workflows. Integrates with VR/immersive setups; can export Ambisonics mixes for YouTube 360 or external renderers.	Envelop for Live
Zirkonium MK3	macOS (Linux experimental)	Free (closed source)	Trajectory‑based spatialisation; friendly for performances; OSC/MIDI.	Zirkonium

Proprietary / Commercial (Industry Standards)

Tools in this category are industry standards in content creation and music production. While not free or open source, they are widely used to create consumer-ready content, inlcuding Apple 3D and cinema formats.

Tool	Platforms	License	Why use this solution?	Link
Dolby Atmos (Renderer, plugins)	Windows / macOS	Commercial (subscription/bundle)	Film/game/streaming standard; binaural + speaker workflows; deep DAW integration; emerging home entertainment standard; Dolby Atmos = Apple Music 3D, Amazon Music & TIDAL	Dolby Atmos
Nuendo (Steinberg)	Windows / macOS	Commercial DAW	Built‑in Ambisonics/immersive tools; post/game pipelines; integrates Atmos.	Nuendo
Pro Tools Ultimate	Windows / macOS	Commercial DAW	Post‑production standard; Atmos/immersive tooling; widely adopted in studios.	Pro Tools

HOA Encoding

Henrik von Coler — Sat, 16 Aug 2025 14:00:00 GMT

This page shows how a monophonic audio signal is rendered to Ambisonics by providing angular direction. This procedure is the standard approach for creating virtual sound sources in object-based spatialisation. This example assumes a plane-wave (far-field) source model. -----

Some Conventions

Cartesian coordinates:
- $x=\text{front->back}$
- $y=\text{left->right}$
- $z=\text{up->down}$
Angles:
- azimuth $\varphi \in (-\pi, \pi]$ (CCW from +x toward +y),
- elevation $\theta \in [-\pi/2, \pi/2]$ (up from horizontal plane).
Normalisation/order:
- AmbiX (ACN channel order, SN3D normalisation), unless noted.
- ACN index $n=\ell(\ell+1)+m$.
- For FOA (order $\ell=1$), the mapping is $[n]=[0,1,2,3] \leftrightarrow [W,Y,Z,X]$.

First-Order Ambisonics for a Single Point Source

A monophonic source $s(t)$ at direction $(\varphi,\theta)$ encodes to the FOA vector $\mathbf a(t)=\begin{bmatrix}W&Y&Z&X\end{bmatrix}^{\mathsf T}$ (AmbiX ordering) as:

\begin{equation*} \begin{aligned} W(t) &= s(t)\,Y_0^0(\theta,\varphi),\\ Y(t) &= s(t)\,Y_1^{-1}(\theta,\varphi),\\ Z(t) &= s(t)\,Y_1^{0}(\theta,\varphi),\\ X(t) &= s(t)\,Y_1^{1}(\theta,\varphi), \end{aligned} \end{equation*}

with the real SN3D first-order spherical harmonics:

\begin{equation*} \begin{aligned} Y_0^0(\theta,\varphi) &= 1,\\ Y_1^{1}(\theta,\varphi) &= \cos\theta\,\cos\varphi,\\ Y_1^{-1}(\theta,\varphi) &= \cos\theta\,\sin\varphi,\\ Y_1^{0}(\theta,\varphi) &= \sin\theta. \end{aligned} \end{equation*}

Thus, explicitly:

\begin{equation*} \begin{aligned} W(t) &= s(t),\\ X(t) &= s(t)\,\cos\theta\,\cos\varphi,\\ Y(t) &= s(t)\,\cos\theta\,\sin\varphi,\\ Z(t) &= s(t)\,\sin\theta. \end{aligned} \end{equation*}

FOA — Multiple Point Sources (Object-Based)

For $N$ sources $s_i(t)$ at $(\varphi_i,\theta_i)$, FOA channels are a linear sum:

\begin{equation*} \mathbf a(t) = \sum_{i=1}^{N} s_i(t)\, \begin{bmatrix} 1\\[2pt] \cos\theta_i\,\sin\varphi_i\\[2pt] \sin\theta_i\\[2pt] \cos\theta_i\,\cos\varphi_i \end{bmatrix} \quad \text{(AmbiX/ACN order } [W,Y,Z,X]\text{).} \end{equation*}

Higher-Order Ambisonics (General Order $L$)

Let $Y_{\ell}^{m}(\theta,\varphi)$ be the real SN3D spherical harmonics with $\ell=0..L$ and $m=-\ell..\ell$. For a single source:

\begin{equation*} a_{\ell m}(t) = s(t)\,Y_{\ell}^{m}(\theta,\varphi),\qquad \ell=0..L,\; m=-\ell..\ell. \end{equation*}

For $N$ sources:

\begin{equation*} a_{\ell m}(t) = \sum_{i=1}^{N} s_i(t)\,Y_{\ell}^{m}\!\bigl(\theta_i,\varphi_i\bigr). \end{equation*}

References

2019

Franz Zotter and Matthias Frank. Ambisonics: A Practical 3D Audio Theory for Recording, Studio Production, Sound Reinforcement, and Virtual Reality. Springer, 2019.
[details] [BibTeX▼]

@book{zotter2019ambisonics,
    author = "Zotter, Franz and Frank, Matthias",
    publisher = "Springer",
    title = "{Ambisonics: A Practical 3D Audio Theory for Recording, Studio Production, Sound Reinforcement, and Virtual Reality}",
    year = "2019"
}

2015

Matthias Frank, Franz Zotter, and Alois Sontacchi. Producing 3d audio in ambisonics. In Audio Engineering Society Conference: 57th International Conference: The Future of Audio Entertainment Technology–Cinema, Television and the Internet. Audio Engineering Society, 2015.
[details] [BibTeX▼]

@inproceedings{frank2015producing,
    author = "Frank, Matthias and Zotter, Franz and Sontacchi, Alois",
    title = "Producing 3D audio in ambisonics",
    booktitle = "Audio Engineering Society Conference: 57th International Conference: The Future of Audio Entertainment Technology--Cinema, Television and the Internet",
    year = "2015",
    organization = "Audio Engineering Society"
}

2009

Frank Melchior, Andreas Gräfe, and Andreas Partzsch. Spatial audio authoring for ambisonics reproduction. In Proc. of the Ambisonics Symposium. 2009.
[details] [BibTeX▼]

@inproceedings{melchior2009spatial,
    author = {Melchior, Frank and Gr{\"a}fe, Andreas and Partzsch, Andreas},
    title = "Spatial audio authoring for Ambisonics reproduction",
    booktitle = "Proc. of the Ambisonics Symposium",
    year = "2009"
}

1973

Michael A. Gerzon. Periphony: With-Height Sound Reproduction. Journal of the Audio Engineering Society, 21(1):2–10, 1973.
[details] [BibTeX▼]

@article{gerzon1973periphony,
    author = "Gerzon, Michael A.",
    journal = "Journal of the Audio Engineering Society",
    number = "1",
    pages = "2--10",
    title = "{Periphony: With-Height Sound Reproduction}",
    volume = "21",
    year = "1973"
}

Understanding Ambisonics

Henrik von Coler — Thu, 28 Apr 2022 14:00:00 GMT

Mid–Side Stereo: 1D Ambisonics

Mid–Side (MS) stereo can be understood as a one-dimensional decomposition of a sound field along a single horizontal axis and works with the same principle as Ambisonics. MS represents the sound field using:

M (Mid) — an cardioid (or omnidirectional) component
S (Side) — a bidirectional (figure-of-eight) component along the left–right axis

MS configuration with omni (blue) and figure of 8 (greed/red).

This structure already mirrors the first-order Ambisonic idea of decomposing the sound field into orthogonal basis functions.

MS Encoding

Given conventional stereo signals $L$ and $R$:

\begin{equation*} M = \frac{L + R}{2} \end{equation*}

\begin{equation*} S = \frac{L - R}{2} \end{equation*}

The inverse decoding is:

\begin{equation*} L = M + S \end{equation*}

\begin{equation*} R = M - S \end{equation*}

Interpretation

$M$ corresponds to an omnidirectional pressure term
$S$ corresponds to a dipole aligned left–right

The phases of the dipole encode the spatial information.

Mathematically, this is equivalent to a 1D first-order harmonic expansion:

$M \leftrightarrow Y_0^0$ (monopole)
$S \leftrightarrow Y_1^{\pm1}$ (horizontal dipole)

In first-order Ambisonics (ACN/SN3D), the related components are:

$W$ — omnidirectional
$Y$ — left/right dipole

Matrix Form

MS encoding can also be written as a matrix transform:

\begin{equation*} \begin{bmatrix} M \\ S \end{bmatrix} = \frac{1}{2} \begin{bmatrix} 1 & 1 \\ 1 & -1 \end{bmatrix} \begin{bmatrix} L \\ R \end{bmatrix} \end{equation*}

and decoding:

\begin{equation*} \begin{bmatrix} L \\ R \end{bmatrix} = \begin{bmatrix} 1 & 1 \\ 1 & -1 \end{bmatrix} \begin{bmatrix} M \\ S \end{bmatrix} \end{equation*}

A vs B Format

A-format refers to the raw microphone capsule signals (e.g., tetrahedral mic outputs) when capturing 3D sound fields. This format is mic-specific and not interchangeable. To further process it, it usually needs to be converted to B-format. A→B conversion matrices are microphone-model-specific, considering capsule geometry and calibration. Microphone vendors need to supply the decoder.

B-format is made up of the spherical-harmonic components of the sound field. This is the standard Ambisonics format with defined channel order and normalization. B-format is portable and can be reproduced on any rendering system (loudspeaker setups, binaural), following standardized decoding algorithms.

Spherical Harmonics

Basic Ambisonics does not define a sound filed through positions, but through angles of incedence. Ambisonics is based on a decomposition of a sound field into spherical harmonics and dates back to Gerzon's theory of Peryphony (Gerzon, 1973). These spherical harmonics encode a sound field into to different axes, The number of Ambisonics channels $N$ is equal to the number of spherical harmonics. It can be calculated for a given order $M$ with the following formula:

\begin{equation*} N = (M+1)^2 \end{equation*}

Figure 1 shows the first 16 spherical harmonics. The first row ($N=1$) is the omnidirectional sound pressure for the order $M=0$.

Rows 1-2 together represent the $N=4$ spherical harmonics of the first order Ambisonics signal.
Rows 1-3 correspond to $M=2$, respectively $N=9$.
Rows 1-4 to the third order Ambisonics signal with $N=16$ spherical harmonics.

First order ambisonics is sufficient to encode a threedimensional sound field. The higher the Ambisonics order, the more precise the directional encoding and the better the localization of virtual sound sources.

Fig. 1: Spherical harmonics up to order 3 [1].

Common B-format Conventions

B-format conventions define the relation between Ambisonic channel order and spherical harmonics. There are different conventions for the sequence of the individual signals, as well as for the normalization.

Ambisonics conventions (Common B-format variants)
Convention	Type	Channel order (1st order)	Normalization	Notes / Where used
FuMa (Furse–Malham)	B-format (FOA)	`W, X, Y, Z`	FuMa (“maxN” style; `W` is scaled by `1/√2`)	Legacy 1st-order B-format used in older DAWs and toolchains; awkward for higher orders (≥2).
AmbiX	B-format (FOA/HOA)	`ACN` order → `[0:W, 1:Y, 2:Z, 3:X]`	SN3D	De-facto modern production standard (Reaper+AmbiX, many VR/AR SDKs, YouTube VR). Portable and HOA-friendly.
ACN/N3D	B-format (FOA/HOA)	`ACN` order → `[0:W, 1:Y, 2:Z, 3:X]`	N3D (orthonormal)	Common in research and HOA libraries; convenient for math/analysis and per-order processing.

Ambisonic Formats

An Ambisonics B Format file or signal carries all $N$ spherical harmonics. Figure 2 shows a first order B Format signal.

Fig. 2: Four channels of a first order Ambisonics signal.

Fig. 2: Spherical harmonics of a first order Ambisonics signal.

ACN, Normalizations, and 1st-Order Mappings

ACN (Ambisonic Channel Numbering)

The channel index $n$ is

\begin{equation*} n = \ell(\ell+1) + m, \qquad \ell = 0..L,\ \ m = -\ell..\ell. \end{equation*}

For 1st order ($\ell = 0,1$), the ACN indices map to channels as

\begin{equation*} [\,0:\ Y_0^0 = W,\quad 1:\ Y_1^{-1} = Y,\quad 2:\ Y_1^{0} = Z,\quad 3:\ Y_1^{1} = X\,]. \end{equation*}

Normalizations

SN3D (“semi-normalized”): $Y_0^0 = 1$. Widely used in production (AmbiX).
N3D (fully normalized): spherical harmonics are orthonormal over the unit sphere, i.e.,

\begin{equation*} \int_{S^2} Y_n^m(\Omega)\, Y_{n'}^{m'}(\Omega)\, d\Omega = \delta_{nn'}\,\delta_{mm'} \end{equation*}

This normalization yields consistent energy per order and simplifies theoretical work, analysis, and algorithm design in higher-order Ambisonics; however, the order-dependent scaling can increase peak amplitudes in higher orders, requiring additional headroom or gain compensation to avoid clipping in practical implementations.
FuMa (legacy): distinct scaling; notably $W_{\text{FuMa}} = \tfrac{1}{\sqrt{2}}\,W_{\text{SN3D}}$.

1st-Order Mappings (FuMa ↔ AmbiX/ACN–SN3D)

Channel order

FuMa order: [W, X, Y, Z]
AmbiX (ACN/SN3D) order: [W, Y, Z, X] (i.e., ACN indices [0,1,2,3] -> [W,Y,Z,X])

References

2019

Franz Zotter and Matthias Frank. Ambisonics: A Practical 3D Audio Theory for Recording, Studio Production, Sound Reinforcement, and Virtual Reality. Springer, 2019.
[details] [BibTeX▼]

@book{zotter2019ambisonics,
    author = "Zotter, Franz and Frank, Matthias",
    publisher = "Springer",
    title = "{Ambisonics: A Practical 3D Audio Theory for Recording, Studio Production, Sound Reinforcement, and Virtual Reality}",
    year = "2019"
}

2015

@inproceedings{frank2015producing,
    author = "Frank, Matthias and Zotter, Franz and Sontacchi, Alois",
    title = "Producing 3D audio in ambisonics",
    booktitle = "Audio Engineering Society Conference: 57th International Conference: The Future of Audio Entertainment Technology--Cinema, Television and the Internet",
    year = "2015",
    organization = "Audio Engineering Society"
}

2009

Frank Melchior, Andreas Gräfe, and Andreas Partzsch. Spatial audio authoring for ambisonics reproduction. In Proc. of the Ambisonics Symposium. 2009.
[details] [BibTeX▼]

@inproceedings{melchior2009spatial,
    author = {Melchior, Frank and Gr{\"a}fe, Andreas and Partzsch, Andreas},
    title = "Spatial audio authoring for Ambisonics reproduction",
    booktitle = "Proc. of the Ambisonics Symposium",
    year = "2009"
}

1973

Michael A. Gerzon. Periphony: With-Height Sound Reproduction. Journal of the Audio Engineering Society, 21(1):2–10, 1973.
[details] [BibTeX▼]

@article{gerzon1973periphony,
    author = "Gerzon, Michael A.",
    journal = "Journal of the Audio Engineering Society",
    number = "1",
    pages = "2--10",
    title = "{Periphony: With-Height Sound Reproduction}",
    volume = "21",
    year = "1973"
}

The Ambisonics Workflow

Henrik von Coler — Sat, 30 Apr 2022 14:00:00 GMT

Basic Workflow

A basic Ambisonics production workflow can be split into three stages, as shown in Figure 1. The advantage of this procedure ist that the production is independent of the output format, since the intermediate format is in the Ambisonics domain. A sound field produced in this way can subsequently be rendered or decoded to any desired loudspeaker setup or headphones.

Figure 1: Basic Ambisonics production workflow.

Stages

1: Encoding Stage

In the encoding stage, Ambisonics signals are generated. This can happen via recording with an Ambisonics microphone or through encoding of mono sources with individual angles (azimuth, elevation). A plain Ambisonics encoding does not include distance information - altough it can be added through attenuation. All encoded signals have the same amount of $N$ ambisonics channels.

2: Summation Stage

All individual Ambisonics signals can be summed up to create one scene, respectively one sound field.

3: Decoding Stage

In the decoding stage, individual output signals can be calculated. This requires either head-related transfer functions or loudspeaker coordinates.

More advanced workflows may feaure additional stages for manipulating encoded Ambisonics signals, inlcuding directional filtering or rotation of the audio scene.

References

2019

Franz Zotter and Matthias Frank. Ambisonics: A Practical 3D Audio Theory for Recording, Studio Production, Sound Reinforcement, and Virtual Reality. Springer, 2019.
[details] [BibTeX▼]

@book{zotter2019ambisonics,
    author = "Zotter, Franz and Frank, Matthias",
    publisher = "Springer",
    title = "{Ambisonics: A Practical 3D Audio Theory for Recording, Studio Production, Sound Reinforcement, and Virtual Reality}",
    year = "2019"
}

2015

@inproceedings{frank2015producing,
    author = "Frank, Matthias and Zotter, Franz and Sontacchi, Alois",
    title = "Producing 3D audio in ambisonics",
    booktitle = "Audio Engineering Society Conference: 57th International Conference: The Future of Audio Entertainment Technology--Cinema, Television and the Internet",
    year = "2015",
    organization = "Audio Engineering Society"
}

2009

Frank Melchior, Andreas Gräfe, and Andreas Partzsch. Spatial audio authoring for ambisonics reproduction. In Proc. of the Ambisonics Symposium. 2009.
[details] [BibTeX▼]

@inproceedings{melchior2009spatial,
    author = {Melchior, Frank and Gr{\"a}fe, Andreas and Partzsch, Andreas},
    title = "Spatial audio authoring for Ambisonics reproduction",
    booktitle = "Proc. of the Ambisonics Symposium",
    year = "2009"
}

1973

Michael A. Gerzon. Periphony: With-Height Sound Reproduction. Journal of the Audio Engineering Society, 21(1):2–10, 1973.
[details] [BibTeX▼]

@article{gerzon1973periphony,
    author = "Gerzon, Michael A.",
    journal = "Journal of the Audio Engineering Society",
    number = "1",
    pages = "2--10",
    title = "{Periphony: With-Height Sound Reproduction}",
    volume = "21",
    year = "1973"
}

RingBuffer (Posts about spatial_audio:ambisonics)

Tools for Live Ambisonics Applications

Free & Cross-Platform (all OS)

Creative Standards

Proprietary / Commercial (Industry Standards)

HOA Encoding

Some Conventions

First-Order Ambisonics for a Single Point Source

FOA — Multiple Point Sources (Object-Based)

Higher-Order Ambisonics (General Order \(L\))

References

2019

2015

2009

1973

Understanding Ambisonics

Mid–Side Stereo: 1D Ambisonics

MS Encoding

Interpretation

Matrix Form

A vs B Format

Spherical Harmonics

Common B-format Conventions

Ambisonic Formats

ACN, Normalizations, and 1st-Order Mappings

Normalizations

1st-Order Mappings (FuMa ↔ AmbiX/ACN–SN3D)

References

2019

2015

2009

1973

The Ambisonics Workflow

Basic Workflow

Stages

1: Encoding Stage

2: Summation Stage

3: Decoding Stage

References

2019

2015

2009

1973