The MACHO data base has been used to examine light curves of all red giant stars brighter than M
bol ∼ −2 in a 0.5° × 0.5° area of the LMC bar. Periods, often multiple, have been searched for in all stars found to be variable. Five distinct period-luminosity sequences have been found on the low mass (M ≲ 2.25M
⊙) giant branch. Comparison of observed periods, luminosities and period ratios with theoretical models identifies Miras unambiguously as radial fundamental mode pulsators, while semi-regular variables can be pulsating in the 1st, 2nd or 3rd overtone, or even the fundamental. All these variables lie on just 3 of the 5 distinct sequences, and they all appear to be on the AGB.
The fourth sequence contains red giants on the first giant branch (FGB) or at the red end of the core-helium burning loops of intermediate mass stars (M ≳ 2.25M
⊙). The light curves of these stars strongly suggest that they are contact binaries, and they make up ∼0.5% of stars within 1 mag. of the FGB tip. Stars on the fifth sequence show semi-regular, eclipse-like light curves. The light curves and periods of these stars suggest that they are in semi-detached binaries, transfering mass to an invisible companion via a stellar wind or Roche lobe overflow. They make up ∼25% of AGB stars. If the existence of these red giant contact and semi-detached binaries is confirmed, then extant theories of binary star evolution will require substantial modification.