  We have used AAVSO visual and photoelectric V data, and the AAVSO time-series
package VSTAR and the Lomb-Scargle time-series algorithm to determine improved
pulsation periods, "long secondary periods" (LSPs). and their amplitudes in 51
shorter-period pulsating red giants in the AAVSO photoelectric photometry
program, and the AAVSO LPV (long period variable) binocular program. As is well
known, radial pulsation becomes detectable in red giants at about spectral type
M0, with periods of about 20 days. We find that the LSP phenomenon is also
first detectable at about M0. Pulsation and LSP amplitudes increase from near
zero to about 0.1 at pulsation periods of about 100 days. At longer periods,
the pulsation amplitudes continue to increase, but the LSP amplitudes are
generally between 0.1 and 0.2 on average. The ratios of LSP to pulsation period
cluster around 5 and 10, presumably depending on whether the pulsation period
is the fundamental or first overtone. The pulsation and LSP phase curves are
generally close to sinusoidal, except when the amplitude is small, in which
case they may be distorted by observational scatter or, in the case of the LSP
amplitude, by the pulsational variability. As with longer-period stars, the LSP
amplitude increases and decreases by a factor of two or more, for unknown
reasons, on a median time scale of about 20 LSPs. The LSP phenomenon is thus
present and simiklar in radially pulsating red giants of all periods. Its cause
remains unknown.
