A set of interacting particles are coupled to a phenomenological core described using the generalized coherent state model. Among the particle-core states a finite set which have the property that the angular momenta carried by the proton and neutron quadrupole bosons and the particles, separately, are mutually orthogonal are identified. The magnetic properties of such states are studied. All terms of the model Hamiltonian exhibit chiral symmetry except the spin-spin interaction. There are four bands of the type with two-quasiparticle-core dipole states, exhibiting properties which are specific for magnetic twin bands. An application is presented, for the isotopes $^{188, 190}$Os.
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