  In this paper we revisit observational data concerning RR Lyrae stars in
Galactic globular clusters, presenting frequency histograms of fundamentalized
periods for the 32 clusters having more than 12 pulsators with well recognized
period and pulsation mode. One finds that the range of fundamentalized periods
covered by the variables in a given cluster remains fairly constant in varying
the cluster metallicity all over the metallicity range spanned by the cluster
sample, with the only two exceptions given by M15 and NGC6441. We conclude that
the width in temperature of the RR Lyrae instability strip appears largely
independent of the cluster metallicity. At the same time, it appears that the
fundamentalized periods are not affected by the predicted variation of
pulsators luminosity with metal abundance, indicating the occurrence of a
correlated variation in the pulsator mass. We discuss mean periods in a
selected sample of statistically significant "RR rich" clusters with no less
than 10 RRab and 5 RRc variables. One finds a clear evidence for the well known
Oosterhoff dichotomy in the mean period <Pab> of ab-type variables, together
with a similarly clear evidence for a constancy of the mean fundamentalized
period <Pf> in passing from Oosterhoff type II to type I clusters. On this
basis, the origin of the Oosterhoff dichotomy is discussed, presenting evidence
against a strong dependence of the RR Lyrae luminosity on the metal content.
