  We analyze the distribution of semiregular variables and Mira stars in the
period-luminosity plane. Our sample consists of 6169 oxygen-rich long-period
variables in the Large Magellanic Cloud included in the OGLE-III Catalog of
Variable Stars. There are many stars with periods that lie between the well
known sequences C and C'. Most of these stars are multi-periodic and the period
ratios suggest that these stars oscillate in the same mode as the sequence C
stars. Models suggest that this mode is the fundamental radial pulsation mode.
The stars with primary periods between sequences C and C' preferentially lie on
an additional sequence (named F), and a large fraction of these stars also have
long secondary periods that lie between sequences C and D. There are also a
small number of stars with primary periods lying between sequences C and D. The
origin of this long period variability is unknown, as is the cause of sequence
D variability. In addition, the origin of sequence F is unknown but we
speculate that sequence F variability may be excited by the same phenomenon
that causes the long secondary periods.
