The power spectral density of the specific activity of radiocarbon variations, using an absolute chronology based on tree ring count, exhibits spectral lines at a number of periods: 2300, 964, 753, 717, 493, 413, 357, 229 and 208 years as well as recording a secular variation over the full 9000-year record. These variations appear in both the La Jolla and Belfast radiocarbon records and some are also detected in the Camp Century 10Be record, though its secular variation appears to lead that of the radiocarbon by about 2100 years. Of the total number of nine prominent radiocarbon features, most are mutually dependent with perhaps only three independent lines. The 208-year period appears modulated by the long 2300-year period. The evidence of modulation of the 208- (and possibly 229-) year period(s) by the 2300-year period suggests a solar source for the latter features, through 200-year spectral features are also detected in the tree ring spectrum, thus tying Sun and climate together. A solar source signalled jointly through correlated radiocarbon and atmospheric temperature variations suggests that solar hydromagnetic and bolometric variations are coupled. Moreover, as evidence is lacking for variations in 10Be or in the geomagnetic field with a period of 2300 years, by a process of elimination together with suggestive global ocean deep water return times of more or less a millennium, a surmise is that chemical resonances may account for the periodicity in radiocarbon with the variation in oceanic carbonate concentration recorded in the radiocarbon record as tracer. The evidence for correlated oscillations in air temperature detected by tree-ring-growth cyclicity in Campito Mt bristlecone pine trees and the radiocarbon variability is consistent with a model of atmosphere-ocean resonances underlying the radiocarbon periodicities.