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To explore the population of variable stars that fall between RR Lyrae stars and classical Cepheids, we have obtained extensive photometric observations for 56 stars with periods between 0.6 and 1.0 days. For these stars and an additional 10, we have examined the form and stability of the light curves to explore the variety of types of stars in this period regime. We conclude that the majority of the sample are Bailey type ab RR Lyrae stars. However, a surprising number that possibly exhibit the Blazhko effect are found. There are a half-dozen other stars that do not appear to be in either of these two groups. One is the well-known multimode pulsator AC And. We suggest that two of the others may be anomalous Cepheids and two may be type II Cepheids.