Article one treats sacred time chiefly as Eliade's theory of festivals re-entering a founding moment. How a tradition actually fixes its calendar is a separate and more concrete story, and the three Abrahamic traditions made three different, doctrinally loaded choices.
Christianity settled the date of its central festival at a council rather than leaving it to local custom. Disagreement over when to keep Easter was serious enough that the Council of Nicaea in 325 addressed it, moving toward a computation independent of the Jewish calendar and tied to the spring equinox and the following full moon; the method was refined for centuries afterward, and the Julian and Gregorian calendars still yield different dates for most Christian bodies today.
Judaism moved the opposite way, from an empirically observed calendar toward a fixed mathematical one. The new month was originally declared on eyewitness testimony of the new moon to a rabbinical court in Jerusalem; the fixed arithmetical calendar now used, traditionally associated with the fourth-century patriarch Hillel II though the precise date of its adoption is debated, removed that dependence once a central court in the land of Israel could no longer reliably convene.
Islam took a third path deliberately. The Quran (9:36-37) rejects the intercalation pre-Islamic Arabs used to keep a lunar calendar aligned with the seasons, fixing a purely lunar year that drifts through the solar year across a roughly thirty-three-year cycle, so Ramadan and the Hajj fall in every season in turn. The drift is not an oversight; it is the doctrinal point, a deliberate rejection of the solar adjustment the other two traditions each made in their own way.