How variations in Earth's orbit pace the glacial-interglacial cycles of the Quaternary are probably one of the greatest mysteries of modern climate science. Supposing coevolution of climate, ice sheets, and carbon cycle over the past 3 million years a current theory cannot explain the observations when it is driven by orbital variations as the only external forcing. Taking advantage of the alkenone paleothermometer in sediment cores sampled in the Tasman Sea floor, we show that the transition of glacial-interglacial periods from 41,000- to 100,000-year that happened during the mid-Pleistocene is not singular. A similar transition involving 10 times longer periods occurred at the hinge of Pliocene-Pleistocene. Referring to the recent theory of gyral Rossby waves we put forward the idea that the climate system preferentially responds to certain orbital variations according to subharmonic modes, which is inherited from the resonant forcing of Rossby waves wrapping around the subtropical gyres.