The Oosterhoff division of globular clusters into two dichotomous mean period groups for the RR Lyrae cluster variables is caused by (1) an increase in the pulsation period due to increased luminosity with decreased metallicity, and (2) the change in the globular cluster HB morphology through the instability strip as the metallicity is decreased. The HB generally moves out of the instability strip far to the blue for the metallicity interval between [Fe/H] of -1.7 and - 1.9, and then back into the strip for even lower metallicities. This causes the apparent separation into two period groups and a decreased number density, appearing usually as a gap in the period distributions in particular samples near a metallicity of [Fe/H] = - 1. 8. Data on periods and metallicities for RR Lyrae stars in clusters and in the field give the relation between the star-by-star period and the metallicity at the blue fundamental edge of the instability strip as log P(ab) = 0.0122/+/-0.02 [Fe/H]-0.500/+/-0.01, on the metallicity scale of Butler. The steep slope of -0.122, long thought to be in conflict with predictions of HB models, is obtained here from (1) the ensemble average of periods over the instability strip in individual clusters, (2) the star-by-star period-metallicity data at the blue fundamental edge for clusters of different metallicity, (3) the field star data using averages over the period distributions at given metallicities (the Preston effect), and (4) the field star data at the blue fundamental edge. Because the value of the d log P/d([Fe/H]) slope is the main topic in most recent debates on the Oosterhoff period-metallicity correlation, the purpose of this paper is to establish the slope by methods that are independent of reddening and amplitude. Anticipating the following paper, the high value of the period-metallicity slope at - 0. 122 is shown to reconcile the period-shift observations and the HB models when the observed temperature variation with metallicity at the blue fundamental edge of the instability strip is taken into account. The Oosterhoff-Arp variation of the mean period of cluster variables with metallicity is caused by (1) an increase in luminosity for decreasing metallicity as originally proposed but now enhanced by (2) a decrease in temperature at every place in the strip by DELTA log T(e) = 0.012 for each dex decrease in [Fe/H]. The purpose of this and Sandage [AJ, 106, 703 (1993)] is to calibrate these relations.
