  We document the presence of a few Cepheid and RR Lyrae variable stars with
previously unrecognized characteristics. These stars exhibit the property of a
period ratio of main pulsation divided by secondary pulsation P1/P2 very close
to sqrt(2). Other stars of these types have period ratios which do not show
clustering with a close association and a single remarkable non-harmonic
number. Close examination reveals a deviation of multiples of a few times
~0.06% for these stars. This deviation seems to be present in discrete steps on
the order of ~0.000390(4), indicating the possible presence of a sort of fine
structure in this oscillation.
