Dissonance is measured by the complexity of the frequency ratios between notes. For a "dissonance-free" start, use simple ratios, then introduce complexity to build tension:
Move one of the clashing notes up or down an octave. This maintains the tension but reduces the physical "crunch".
Unison (1:1), Octave (2:1), and Perfect Fifth (3:2).
Soften the volume of the dissonant note so it doesn't overwhelm the listener.
Dissonance is most effective when it moves toward a resolution.