Context : The central star of the HR 8799 system is a \gamma Doradus-type pulsator .
The system harbours four planetary-mass companions detected by direct imaging , and is a good solar system analogue .
The masses of the companions are not known accurately , because the estimation depends strongly on the age of the system , which is also not known with sufficient accuracy .
Asteroseismic studies of the star might help to better constrain the age of HR 8799 .
We organized an extensive photometric and multi-site spectroscopic observing campaign for studying the pulsations of the central star .

Aims : The aim of the present study is to investigate the pulsation properties of HR 8799 in detail via the ultra-precise 47-d-long nearly continuous photometry obtained with the MOST space telescope , and to find as many independent pulsation modes as possible , which is the prerequisite of an asteroseismic age determination .

Methods : We carried out Fourier analysis of the wide-band photometric time series .

Results : We find that resonance and sudden amplitude changes characterize the pulsation of HR 8799 .
The dominant frequency is always at f _ { 1 } = 1.978 \mathrm { d } ^ { -1 } .
Many multiples of one ninth of the dominant frequency appear in the Fourier spectrum of the MOST data : n / 9 f _ { 1 } , where n = \ { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 13 , 14 , 17 , 18 \ } .
Our analysis also reveals that many of these peaks show strong amplitude decrease and phase variations even on the 47-d time-scale .
The dependencies between the pulsation frequencies of HR 8799 make the planned subsequent asteroseismic analysis rather difficult .
We point out some resemblance between the light curve of HR 8799 and the modulated pulsation light curves of Blazhko RR Lyrae stars .

Conclusions :