Orbital forcing has long been the subject of two quite separate communities: the tide community is concerned with the relatively rapid gravitational forces (periods up to 18.6 yr) and the climate community with the long-period Milankovitch insolation terms (exceeding 20 000 yr). The wide gap notwithstanding, the two subjects have much in common. Keeling and Whorf have proposed that the millennial climate variability is associated with high-frequency tidal forcing extending into the 10-octave gap by some nonlinear process. Here, the authors distinguish between two quite distinct processes for generating low frequencies: (i) the `traditional' analogy with eclipse cycles associated with near coincidence of the appropriate orbital alignment of the Sun, the Moon, and Earth, and (ii) sum and differences of tidal frequencies and their harmonics producing low beat frequencies. The first process is associated with long time intervals between extreme tides, but the events are of short duration and only marginally higher than conventional high tides. With proper nonlinearities, (ii) can lead to low-frequency tidal forcing. A few candidate frequencies in the centurial and millennial band are found, which prominently include the Keeling and Whorf forcing at 1795 yr. This is confirmed by a numerical experiment with a computer-generated tidal time series of 275 000 yr. Tidal forcing is very weak and an unlikely candidate for millennial variability; the Keeling and Whorf proposal is considered as the most likely among unlikely candidates.