Coriolis flowmeters are essentially fluid conveying pipe segments excited to transversal oscillation. Thereby the precise form of the oscillation modes depends on the mass flow rate Q(M) of the fluid. For usual flow rates the modes deviate only slightly from those without flow (Q(M) = 0); they can be viewed as small perturbations of those modes. In the paper it is shown that the perturbation of a given oscillation mode of the pipe segment by the fluid flow, which manifests itself as a slight tumbling of the pipe segment, can be interpreted as a mixing of this (working) mode with its (spectral) neighbours. The tumbling in the perturbed mode comes out thereby roughly as an interplay of neighbouring unperturbed modes, with a phase difference of 90-degrees. The mode interference depends strongly on the distance of the involved modes. This suggests a way to increase the sensitivity of the instrument by appropriately influencing the vibration spectrum of the pipe segment, e.g. through change of its geometry.