The magnetic excitation spectrum and Hamiltonian of the quantum magnet BaCuTe 2 O 6 is studied by inelastic neutron scattering (INS) and density functional theory (DFT). INS on powder and single crystal samples reveals overlapping spinon continua-the spectrum of an antiferromagnetic spin-1/2 spin chain-due to equivalent chains running along the a, b, and c directions. Long-range magnetic order onsets below T N = 6.3 K due to interchain interactions, and is accompanied by the emergence of sharp spin-wave excitations, which replace the continua at low energies. The spin-wave spectrum is highly complex and was successfully modelled achieving excellent agreement with the data. The extracted interactions reveal an intrachain interaction, J 3 = 2.9 meV, while the antiferromagnetic hyperkagome interaction J 2 is the subleading interaction responsible for coupling the chains together in a frustrated way. DFT calculations reveal a similar picture for BaCuTe 2 O 6 of dominant J 3 and subleading J 2 antiferromagnetic interactions and also indicate a high sensitivity of the interactions to small changes of structure, which could explain the very different Hamiltonians observed in the sister compounds SrCuTe 2 O 6 and PbCuTe 2 O 6 .