Hipparcos period-luminosity relations for Miras and semiregular   variables
  We present period-luminosity diagrams for nearby Miras and semiregulars, selecting stars with parallaxes better than 20 per cent and well-determined periods. Using K-band magnitudes, we find two well-defined P-L sequences, one corresponding to the standard Mira P-L relation and the second shifted to shorter periods by a factor of about 1.9. The second sequence only contains semiregular variables, while the Mira sequence contains both Miras and semiregulars. Several semiregular stars show double periods in agreement with both relations. The Whitelock evolutionary track is shown to fit the data, indicating that the semiregulars are Mira progenitors. The transition between the two sequences may correspond to a change in pulsation mode or to a change in the stellar structure. Large amplitude pulsations leading to classical Mira classification occur mainly near the tip of the local AGB luminosity function. 
T.R. Bedding and A.A. Zijlstra