A study of particle multiplicity in quark and gluon jets is made using events observed by the ALEPH detector at LEP. Events with three separated jets are selected from approximately 4 million hadronic decays, recorded in the data- taking period 1990-95. The energies of the jets are estimated to allow the multiplicity of each event to be located on a two-dimensional Dalitz plane. A given point on this plane corresponds to a distinct jet topology. Multiplicity distributions across the plane are compared to theoretical predictions, which are based on an expression for the multiplicity of a single quark jet. The gluon jet in each event is not directly identified; instead, the leading order matrix element is used to give the probability that each jet originated from the gluon. This method has the benefit that candidate three-jet events are not biased to include only those which satisfy explicit quark tagging techniques, such as those used to tag heavy flavours. Colour coherence, which is expected to affect particle production in the regions between quark and gluon jets, is incorporated into theoretical predictions via topological scales. These scales allow the multiplicity of a given jet to be described in terms of both the jet energy and the angular proximity of neighbouring jets. Theoretical predictions are corrected for detector effects and compared directly with ALEPH data.