Aims. Extensive photometry of RR Lyr was obtained over a 421-day interval in 2003-2004, covering more than 10 Blazhko cycles in a multisite campaign. The length and density of this data set allow for a detailed analysis. Methods. We used Fourier techniques to study RR Lyr's behavior over the pulsation and the Blazhko cycle. We propose a twofrequency model for decomposing the frequency spectrum. Results. The light variations were fitted with the main radial frequency, its harmonics up to 11th order, and the detected triplet frequencies. No significant quintuplet components were found in the frequency spectrum. Given the total time span of the measurements, we can now unambiguously conclude that the Blazhko period has become notably shorter than the previously known value of 40.8 days, whereas the main pulsation period remained roughly the same. Changes in the modulation period have been reported for other well-studied Blazhko variables. They challenge the explanations for the Blazhko effect which link the modulation period directly to the rotation period. The new photometry reveals an interval in the pulsation cycle of RR Lyr during which the star's intensity barely changes over the Blazhko cycle. This interval occurs during the infalling motion and between the supposed phases of the early and the main shock. The data also permit a more detailed study of the light curve shape at different phases in the Blazhko period through Fourier parameters.