Context. Complex organic molecules (COMs) are commonly detected in and near star-forming regions. However, the dominant process in the release of these COMs from the icy grains – where they predominately form – to the gas phase is still an open question. Aims. We investigate the origin of COM emission in a high-mass protostellar source, CygX-N30 MM1, through high-angular-resolution interferometric observations over a continuous broad frequency range. Methods. We used 32 GHz Submillimeter Array observations with continuous frequency coverage from 329 to 361 GHz at an angular resolution of ~1″ to do a line survey and obtain a chemical inventory of the source. The line emission in the frequency range was used to determine column densities and excitation temperatures for the COMs. We also mapped out the intensity distribution of the different species. Results. We identified approximately 400 lines that can be attributed to 29 different molecular species and their isotopologues. We find that the molecular peak emission is along a linear gradient, and coincides with the axis of red- and blueshifted H₂CO and CS emission. Chemical differentiation is detected along this gradient, with the O-bearing molecular species peaking towards one component of the system and the N- and S-bearing species peaking towards the other. The chemical gradient is offset from but parallel to the axis through the two continuum sources. The inferred column densities and excitation temperatures are compared to other sources where COMs are abundant. Only one deuterated molecule is detected, HDO, while an upper limit for CH₂DOH is derived, leading to a D/H ratio of <0.1%. Conclusions. We conclude that the origin of the observed COM emission is probably a combination of the young stellar sources along with accretion of infalling material onto a disc-like structure surrounding a young protostar and located close to one of the continuum sources. This disc and protostar are associated with the O-bearing molecular species, while the S- and N-bearing species on the other hand are associated with the other continuum core, which is probably a protostar that is slightly more evolved than the other component of the system. The low D/H ratio likely reflects a pre-stellar phase where the COMs formed on the ices at warm temperatures (~30 K), where the deuterium fractionation would have been inefficient. The observations and results presented here demonstrate the importance of good frequency coverage and high angular resolution when disentangling the origin of COM emission.