The instrumental cosmic ray data recorded in the interval 1933–1965 by S. E. Forbush and H. V. Neher and cosmogenic 10Be data are merged with the neutron monitor data since 1951 to study the long- and short-term variations in the galactic cosmic radiation intensity for the interval 1428–2005. It is shown that the ionization chamber data published by S. E. Forbush were deliberately detrended to remove long-term changes. The high-altitude ionization chambers used by H. V. Neher during this interval were well calibrated and their data exhibit a substantial decrease between 1933 and 1954 that is consistent with the long-term trends in the cosmogenic 10Be data. Using the specific yield functions appropriate to neutron monitors, ionization chambers, and 10Be, the nonlinear relationships between these data types are determined. It is shown that the nonlinearities are large and will introduce serious errors if ignored. An intercalibrated record (the “pseudo-Climax neutron monitor record”) is developed for the interval 1428–2005. It is used to study several features of the long-term periodicities in the cosmic radiation, after discussion of residual effects due to meteorological effects, and the production of 10Be by solar cosmic rays. It is shown that (1) the average intensity in the neutron monitor energy range for the interval 1954–1996 is ∼16% less than the average for the period 1428–1944 and that it shows a consistency and depth of modulation that had not occurred in the previous 580 years. (2) The residual cosmic ray modulation was low throughout the Gleissberg cycle 1540–1645, considerably higher for the next two Gleissberg Cycles, and highest of all since 1944. (3) The cosmogenic data imply that solar activity was anomalously low throughout the whole interval 1428–1715, the amplitude of the solar activity during the Gleissberg cycle 1540–1645 being ∼50% of that during the following two Gleissberg cycles and ∼25% of that in the post-1954 era. (4) It is proposed that the steadily increasing cosmic ray modulation since 1428 constitutes a quarter cycle of the previously identified 2300 year periodicity in the cosmogenic data. (5) The cosmic ray intensity decreased in two steps between 1889 and 1901 and 1944 and 1954, in broad agreement with the two-step increase in heliomagnetic field strength determined by Schrijver et al. (2002). It is proposed that the “pseudo-Climax neutron record” will be of benefit in the normalization of other cosmogenic records to the neutron monitor record starting in 1951.