Period-luminosity (PL) sequences of long period variables (LPVs) are commonly interpreted as different pulsation modes, but there is disagreement on the modal assignment. Here, we re-examine the observed PL sequences in the Large Magellanic Cloud, including the sequence of long secondary periods (LSPs), and their associated pulsation modes. Firstly, we theoretically model the sequences using linear, radial, non-adiabatic pulsation models and a population synthesis model of the LMC red giants. Then, we use a semi-empirical approach to assign modes to the pulsation sequences by exploiting observed multi-mode pulsators. As a result of the combined approaches, we consistently find that sequences B and C$^{prime}$ both correspond to first overtone pulsation, although there are some fundamental mode pulsators at low luminosities on both sequences. The masses of these fundamental mode pulsators are larger at a given luminosity than the mass of the first overtone pulsators. These two sequences B and C$^{prime}$ are separated by a small period interval in which large amplitude pulsation in a long secondary period (sequence D variability) occurs, meaning that the first overtone pulsation is not seen as the primary mode of pulsation. Observationally, this leads to the splitting of the first overtone pulsation sequence into the two observed sequences B and C$^{prime}$. Our two independent examinations also show that sequences A$^{prime}$, A and C correspond to third overtone, second overtone and fundamental mode pulsation, respectively.
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