The spectrum of the sunspot index can be qualitatively accounted for by a very simple time series model which the Hale 22 year cycle dominates; the series is amplitude modulated at the 90 year Gleissberg period with an index of 25%. The square of the modulated Hale cycle reproduces all of the spectral lines of the Zurich sunspot index spectrum, provided that a small offset is included in the Hale carrier. Without this, evidence of the 22 year periodicity disappears. The squaring explains the dominance of the 11 year cycle which is an artifact of the modulation as is the 45 year line. The offset suggests a small relict magnetic field in the Sun's core. Lastly Gilliland (1981) finds a radial eigenmode in the Sun with period of 76¿8 years suggestive of a physical basis for the Gleissberg modulation.