The maximum inclination of the heliospheric current sheet (the tilt angle)
and the magnitude B of the heliospheric magnetic field are often used to ch
aracterize cosmic ray (CR) modulation. The relevance of B is likely to be t
he coupling of the interplanetary diffusion coefficients K to the field mag
nitude in a relation K proportional toB(-n). In this paper we study the cou
pled influence of tilt angle and magnetic field variations on the modulatio
n of cosmic rays at neutron monitor energies for the 1974 mini-cycle and fo
r the onsets of solar cycles 21, 22, and 23. It is suggested that for A >0
polarity epochs, the sensitivity of the CR response to variations in B is p
artly controlled by the size of the tilt angle, alpha. The onsets of cycles
21 and 23 exhibit differences, related to phase differences in these param
eters. A simple model is used to predict the CR response to variations in B
.