Plate tectonics is driven by Earth-Moon barycentre shifts in the lower mantle. The eastern Canary Islands have geographic and geological conditions derived from the movements of the Central American plates. Some features of these islands are influenced by the rotation of the Earth from west to east in the evolution of the marine currents that surround them and the opening of the North Atlantic to the North Pole with little dependence of the glacial isostatic adjustment (GIA). In addition, their position with respect to the Tropic of Cancer and the African continent affect the north-south and east-west climatic change dynamics and their tectonic stability respectively. Dated lavas contain marine and aeolian deposits and some of the Pleistocene marine deposits indicate higher sea level in cooler circumstances, which is anomalous. Relating those marine deposits produced during the warmest interglacial, the last interglacial and the Holocene with their equivalents in the Southern Hemisphere, they reflect shifts in the barycentre. Thanks to Holocene radiocarbon, topographic and day length data and alkenone temperature, we describe a mechanism by which the oscillation of the Moon's inclination (and declination) reaches extreme values (14˚ and 34˚; about 4.9˚ more than current values) approximately every 1450 years. These values occur when there is a harmonic distortion in surface areas of the Earth's crust as response associated with oscillations in the displacements of the barycentre of the Earth-Moon