Stereo records two things: what a left ear hears and what a right ear hears. Surround sound records five, seven, or twelve things, each aimed at a specific speaker position. Both formats are tied to a playback geometry from the moment of capture.
Ambisonics does something fundamentally different. Instead of recording the sound field from a fixed perspective, it encodes the complete pressure and pressure-gradient information at a single point in space as a series of spherical harmonic coefficients. You then decode that representation into whatever speaker arrangement or headphone HRTF you actually have, after the fact. The representation is speaker-agnostic. This is what makes it useful for VR, 360 video, and game audio, but the mathematics behind it is what makes it genuinely interesting.
What B-Format Actually Means
The four channels of first-order ambisonics, called B-format, have a direct physical interpretation.
W is what an omnidirectional microphone hears: no directional preference, just scalar sound pressure at the point. It captures energy arriving from all directions equally.
X is what a figure-of-eight microphone hears when aimed front-to-back along the listening axis. Positive values mean sound arriving from the front, negative from the rear.
Y is the same thing for the left-right axis. Z is for up-down.
These four channels represent the zeroth and first-order terms of a spherical harmonic expansion of the sound field. W is the zeroth-order term, a constant function with the same value everywhere on a sphere. X, Y, and Z are the three first-order terms, functions that vary linearly with direction, shaped like a figure-of-eight polar pattern along each coordinate axis.
The practical consequence: any directional polar pattern you can describe, cardioid, hypercardioid, mid-side, anything, is a linear combination of W, X, Y, and Z. You can derive any first-order microphone pattern from B-format in post by mixing these channels with the appropriate coefficients for the desired pointing direction. This is why rotating or re-orienting an ambisonic recording in post-production is mathematically exact at first order.
Recording B-Format: The A-Format Problem
You cannot build a perfect point microphone, because capsules have physical size. Michael Gerzon and Peter Craven addressed this in 1975 by arranging four subcardioid capsules in a tetrahedral configuration, each facing a different vertex of the tetrahedron. This design, the SoundField microphone, produces what is called A-format: the raw four-capsule output.
A-format is not B-format. The capsules are not coincident; they are separated by a few millimeters, which introduces phase and frequency errors in the spatial representation. Gerzon and Craven developed a processing matrix plus frequency-dependent filtering to convert A-format to B-format, compensating for the capsule spacing. Calrec commercialized the first SoundField microphone in 1978. The conversion is still non-trivial. Modern implementations, such as the SoundField by RODE plugin, use time-frequency adaptive methods to align the A-format channels before applying the matrix, producing better results at high frequencies where wavelengths are comparable to the capsule spacing.
Higher Orders: Spatial Resolution Scales as (N+1)²
First-order B-format has limited spatial resolution. A single point source encoded in first-order ambisonics sounds somewhat blurry, and the region where decoding is accurate, called the sweet spot, is small. Adding higher-order spherical harmonic terms sharpens directional resolution.
The channel count for Nth-order ambisonics is (N+1)² for full-sphere 3D:
| Order | Channels | Degrees of freedom |
|---|---|---|
| 0 | 1 | Mono |
| 1 | 4 | W, X, Y, Z |
| 2 | 9 | + 5 quadrupole terms |
| 3 | 16 | + 7 octupole terms |
| 7 | 64 | Roughly the resolution of a 2-meter speaker array |
Each order adds a ring of spherical harmonic functions with increasingly complex angular variation. The spatial aliasing limit follows the condition kr < N, where k = 2pif/c is the wavenumber and r is the reproduction radius. Rearranging: the sweet spot radius for frequency f is r < Nc / (2pi*f). A useful rule of thumb: each order of ambisonics gives accurate spatial reproduction up to roughly 650 Hz per order for a head-sized region (about 8.75 cm radius). First-order handles below 650 Hz accurately. Third-order extends this to around 2 kHz. Above those frequencies the representation remains valid, but localization error increases outside a very small region near the center.
This is the fundamental tradeoff. Higher spatial resolution costs quadratically more channels. Order 7 needs 64 channels; order 10 needs 121.
Decoding: Speakers and Headphones
When you have a B-format signal, you decode it for playback. For loudspeakers, the decoder computes a gain matrix that maps each ambisonic channel to each speaker, reconstructing the original pressure and pressure gradient at the listening position.
For headphones, the approach differs. You convolve each ambisonic channel with a matching HRTF, one that captures how a sound from that direction reaches each ear after reflecting off the pinnae, head, and shoulders. A common method is to decode to a virtual speaker array first, binauralize each virtual speaker with its HRTF, then sum the results.
The problem is that a low-order ambisonic signal paired with a high-density HRTF creates a mismatch. The ambisonic representation captures only smooth, low-frequency directional variation, while the HRTF has fine structure at high frequencies that encodes elevation cues. Research groups have tried to address this by reducing the HRTF to the same order as the ambisonic signal before rendering, or by using neural network-based decoders that learn to fill in the missing detail.
Where You Already Hear This
YouTube added first-order ambisonics support in 2016 for 360-degree video. When you watch a 360 video and rotate your phone or move your head in a VR headset, the audio rotates with you because the player re-decodes the four B-format channels in real time based on your head orientation. The four ambisonic channels are delivered as part of the video file alongside an optional head-locked stereo mix for viewers on non-VR displays.
Game audio middleware, Wwise and FMOD, use ambisonics internally to spatialize sounds from arbitrary 3D positions, rendering the final binaural output per frame as the player moves. Encoding a sound source to ambisonics first, then rendering that representation, is computationally cheaper than convolving each source directly with a full HRTF at every position update.
Dolby Atmos uses discrete object-based routing and speaker beds; it does not officially support higher-order ambisonics as a direct input format, though third-party workflows exist to convert ambisonics signals to Atmos objects. The internal rendering engine converts everything to a common representation before decoding to the target speaker configuration.
The Underlying Idea
Ambisonics works because any sound field in free space, no reflections, no obstacles, can be decomposed into spherical harmonics, the same mathematical functions that describe the hydrogen atom orbitals in quantum mechanics. These functions form a complete orthonormal basis on the sphere: any directional function can be written as an infinite sum of spherical harmonics, and you can reconstruct it exactly if you have all the coefficients.
In practice you truncate the series at some order N, which introduces spatial aliasing error for directions that vary faster than your Nth-order basis can represent. More terms mean finer directional detail, at the cost of more channels.
The consequent elegance: because the spherical harmonics are a mathematical basis independent of any physical speaker layout, you can capture a sound field once, store it as coefficients, and decode it years later for a speaker geometry that did not exist when you recorded it. That flexibility is what Gerzon had in mind in 1974, and it is why ambisonics remains the format underneath most serious spatial audio work today.