Comte's calendar reform addressed a problem every Gregorian month shares: none of them is the same length, so a given date falls on a different weekday every year and the calendar's grid never repeats cleanly. Thirteen months of exactly twenty-eight days, four weeks each, solved this arithmetically, at the cost of adding a month beyond the familiar twelve and requiring an extra day or two, kept outside the ordinary week entirely, to reach 365.
Comte used the freed structure to turn the calendar into a teaching tool for his new religion: each month commemorated one field of human achievement through its namesake, Moses for early theocracy, Homer for epic poetry, Aristotle for ancient philosophy, and onward through Caesar for statesmanship, Charlemagne for feudal civilisation, Dante and Shakespeare for modern poetry, Gutenberg for the modern industrial arts, and Descartes for modern philosophy, with the physician Bichat closing the year for modern science. Each of the twenty-eight days inside a month carried a further dedication to a lesser figure in that same field, so that a positivist consulting the calendar was, in Comte's design, reminded daily of a specific contributor to human civilisation, a form of veneration meant to replace the saints' days of the Catholic calendar it was structurally descended from.