Fourier decompositions are performed for the V magnitude variations of a sample of 57 Cepheids ranging in period from 2 to 17 days. The coefficients have been tabulated to allow rapid reconstruction of the light curves. It is shown that combinations of the low-order coefficients quantitatively describe the progression of curve shape with period. The pulsation amplitude plays only a minor role. Sharp breaks in the progression, occurring at around 10 days, are attributed to the resonance PdPo =0.5. It is suggested that the Fourier decompositions provide a straightforward method for resolving a number of controversies concerning theoretical interpretations of the Hertzsprung sequence. The paper closes 'With a brief discussion of three short-period stars which seem to occupy a unique position in our sample.