(M62) But while many of the great Greek games were celebrated at intervals of four years, others, such as the Nemean and the Isthmian, were celebrated at intervals of two years only; and just as the quadriennial period seems to have been arrived at through a bisection of the octennial period, so we may surmise that the biennial period was produced by a bisection of the quadriennial period. This was the view which the admirable modern chronologer L. Ideler took of the origin of the quadriennial and biennial festivals respectively,(298) and it appears far more probable than the contrary opinion of the ancient chronologer Censorinus, that the quadriennial period was reached by doubling the biennial, and the octennial period by doubling the quadriennial.(299) The theory of Censorinus was that the Greeks started with a biennial cycle of twelve and thirteen lunar months alternately in successive years for the purpose of harmonising solar and lunar time.(300) But as the cycle so produced exceeds the true solar time by seven and a half days,(301) the discrepancy which it leaves between the two great celestial clocks, the sun and moon, was too glaring to escape the observation even of simple farmers, who would soon have been painfully sensible that the times were out of joint, if they had attempted to regulate the various operations of the agricultural year by reference to so very inaccurate an almanac. It is unlikely, therefore, that the Greeks ever made much use of a biennial cycle of this sort.