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Fig. 5

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Left: case of a “magic” spin, where the strongest resonances could occur at the same radius. For completeness we present the relevant simple combinational frequencies νθ − νr, νθ + νr, νK − νθ, νK − νr (grey dashed lines). The “magic” spin am = 0.983 represents the only case where the combinational and direct orbital frequencies coincide at the shared resonance radius. Right: another example of the characteristic frequency ratio set 3:2:1 that appears at different radii.

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