Both two-dimensional (pantophonic) and three-dimensional (periphonic) representations of soundfields are common place in ambisonics. Reproducing either on rigs essentially designed for the other is common place. What though if one synthesises a four (or more) dimensional soundfield and reproduces this on a standard rig? As there appears to be no source on hyperspherical harmonics applicable to ambisonics, the mathematical basis is first set out. The manipulation of hyperambisonic soundfields (rotation, mirroring, dominance) is then discussed. During that discussion various `proofs` are advanced as to the finite range of transformations that can be applied to ambisonic soundfields, of whatever dimension.
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