The generalised hyper-Ramsey resonance formula originally published in Phys. Rev. A, 92, 023416 (2015) is derived using a Cayley - Klein spinor parametrisation. The shape of the interferometric resonance and the associated composite phase shift are reformulated including all individual laser pulse parameters. Potential robustness of signal contrast and phase-shift of the wave-function fringe pattern can now be arbitrarily explored tracking any shape distortion due to systematic effects from the probe laser. An exact and simple analytical expression describing Ramsey's method of separated composite oscillating laser fields with quantum state control allows us to accurately simulate all recent clock interrogation protocols under various pulse defects.