Virtual reality (VR) offers novel possibilities of design choices for Digital Musical Instruments in terms of shapes, sizes, sounds or colours, removing many constraints inherent to physical interfaces. In particular, the size and position of the interface components of Immersive Virtual Musical Instruments (IVMIs) can be freely chosen to elicit large or small hand gestures. In addition, VR allows for the manipulation of what users visually perceive of their actual physical actions, through redirections and changes in Control-Display Ratio (CDR). Visual and gestural amplitudes can therefore be defined separately, potentially affecting the user experience in new ways. In this paper, we investigate the use of CDR to enrich the design with a control over the user perceived fatigue, sense of presence and musical expression. Our findings suggest that the CDR has an impact on the sense of presence, on the perceived difficulty of controlling the sound and on the distance covered by the hand. From these results, we derive a set of insights and guidelines for the design of IVMIs.