Square root two period ratios in Cepheid and RR Lyrae variable stars
  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. 
Michael Hippke, John G. Learned, A. Zee
astro-ph.SR