  The rather elusive High-Frequency Quasi-Periodic Oscillations(HFQPO) observed
in the X-ray lightcurve of black holes have been seen in a wide range of
frequencies, even within one source. It is also notable to have been detected
in "pairs" of HFQPOs with a close to integer ratio between the frequencies. The
aim of this paper is to investigate some of the possible observable that we
could obtain from having the Rossby Wave Instability (RWI) active in the
accretion disc surrounding the compact object.
  Using the newly developed GR-AMRVAC code able to follow the evolution of the
RWI in a full general relativistic framework, we explore how RWI can reproduce
observed HFQPO frequencies ratios and if it is compatible with the
observations. In order to model the emission coming from the disc we have
linked our general relativistic simulations to the general relativistic
ray-tracing GYOTO code and delivered synthetic observables that can be
confronted to actual data from binary systems hosting HFQPOs.}{We have
demonstrated in our study that some changes in the physical conditions
prevailing in the part of the disc where RWI can be triggered leads to various
dominant RWI modes whose ratio recovers frequency ratios observed in various
X-ray binary systems. In addition, we have also highlighted that when RWI is
triggered near the last stable orbit of a spinning black hole, the amplitude of
the X-ray modulation increases with the spin of the black hole. Revisiting
published data on X-ray binary systems, we show that this type of relationship
actually exists in the five systems where an indirect measure of the spin of
the black hole is available.
