Institute for Computer Music and Sound Technology / (ICST) Zurich University of the Arts

This is not intended to be a full glossary of ambisonic terms —that would run to hundreds of entries.
Rather it aims to explain the terms used in the pages of this section of this website, and where necessary, compare and contrast them with other usages.

ambisonic channel number
An ambisonic file or stream consists of a collection of ambisonic channels. These have traditionally been described by letters: all ambisonic files/streams contain what were described as W, X and Y. Most files/streams contain other channels as well.This letter code system cannot be extended to higher ambisonics, instead a unique integer (from zero upwards) is assigned to designated each channel.That integer (the ambisonic channel number) is related to the degree (l) and order (m) as follows:
ACN = l * ( l + 1) + m
(‘Ambisonic component number’ has been discussed as an alternative term for this.)
See ambisonic channel number.
Just as a stereo file or a stereo audio stream has a left channel and a right channel, so ambisonics uses multi-channel files/streams. The term ‘signal’ is sometimes used with the same meaning.
Each spherical harmonic is defined by an degree and an order. There are (potentially) an infinite number of degrees, numbered by integers, from zero upwards.The symbol l is used for the degree number.Ambisonic channels are each associated with a specific spherical harmonic and can be designated by the same numbers as the associated SH.
deprecated term
See below.
Symbol for degree.
(1) Symbol for order (meaning (1)).
(2) see also the deprecated usage of m.
(1) Each spherical harmonic is defined by a degree and an order. For three-dimensional SHs (periphonic ambisonics) the number of orders in each degree is one more than twice the degree (2l+1) and these are designated by numbers from m = -l to m = lThe symbol m is used for the order number.Ambisonic channels are each associated with a specific spherical harmonic and can be designated by the same numbers as the associated SH.
(2) An ambisonic file (or stream, etc.) is described as being first order if it contains (only) zero and first degree channels; second order if it contains (only) zero, first and second order channels; etc. (A zero order ambisonic file is -it could be argued- possible: it would be an omnidirectional recording (or synthesised piece).)
(3) see also the deprecated usage of order.)

Deprecated terms and meanings

Some texts use m as a symbol for degree.
Some texts use n as a symbol for order (meaning (1)).
This term has been used for some time, with two distinct meanings in ambisonic literature. Firstly to refer to the total collection of channels, a meaning retained in this glossary. Secondly to refer to the components in that total collection of channels that are of that degree.This glossary deprecates the latter, and uses the term degree (which is common across the rest of the literature on SHs). It continues the usage for the totality of channels: for example, "a third order file", "a second order microphone", "a first order recording".See also the discussion below.
The term order (meaning (1)), is now preferred.


In ambisonics a first-order file has channels W, X, Y and (possibly) Z (channel numbers 0, 1, 3 and, possibly, 2). That is it has components which satisfy both l = 0 and l = 1.
Chris Travis has suggested that the word ‘order’ be retained for usages such as ‘a first-order file’, ‘a second-order microphone’, etc.
Personally, I will try not to say "It is a second-order component" when I mean "It is a degree-2 component". But I will continue to talk about e.g. "second-order" microphones and recordings. And I think "Higher Order Ambisonics" is OK too.
but that for the other usage (e.g. ‘X is a first-order component’) the more generally accepted term of degree is used (e.g. ‘X is a first-degree component’).

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Copyright:This page copyright © 2008 The Ambisonics Association.
Acknowledgements:Grateful thanks to Fons Adriaensen and Philip Cotterell for their encouragement … and corrections.
Published: October 2008. Revised: October 2008.