We report evidence for a ca. 40 month signal in air pressure simulated in a general circulation model, together with two further natural signals previously found, the ca. 26 month quasi-biennal oscillation (QBO) and the ca. 14 month atmospheric Chandler tide. These 3 natural signals interact with the annual cycle and its harmonics to create a rich spectrum of summation and difference tones. Theoretically we expect 33 tones to be produced and evidence for 29 of these is found. The three classes of signals combined to contribute 51% of total variance, and range in period from 2 to 68 months. These results indicate that the spectrum of atmospheric variations on these time scales is discrete, unlike that of a chaotic system. ¿ American Geophysical Union 1990