By expressing the fluxes associated with a range of experimental period measurements as linear combinations of several trial functions, a generalization of the inhour formula relating measured periods to linear functionals of the perturbation is obtained. The formula is applied to finding the fast periods and values of keff associated with the early stages of super-prompt critical-burst experiments or pulsed die-away experiments. By appropriate choice of trial functions, the formula may be rearranged so that it relates period to a single reactivity-like quantity and other small corrections. Since this quantity is a linear functional, values of it corresponding to different perturbations are additive, even when the over-all flux shapes associated with these perturbations differ. When two trial functions alone are sufficient for a range of experiments, further rearrangement results in a relationship that has the form of the so-called seven-group inhour equation.