The Tibetan calendar, according to the Astrology of the Elements
The Tibetan calendar follows three orientations, the official one, called “of the Tibetan and Mongolian tradition”, one used in the astrology of the constellations, and one explicitly used in the astrology of the elements. For the official calendar, the first month of the year is the month of the Dragon, corresponding in the western calendar approximately to April . The astrology of the constellations and the Kalachakra tradition  always consider the first month as the month of the Dragon but places the New Year at the beginning of the third month, the month of the Horse. For the astrology of the elements, the first month corresponds to the month of the Tiger, coinciding with February. To respect the official order of the calendar, the month of the Tiger is numbered as eleventh, but in the calculations, it is considered the first month of the year, while the month of the Dragon in third place is numbered as first.
The months are associated with the cycle of the twelve animals and each month has a particular name derived from the dominant constellation (table 1). Like the years, the months, depending on the even or odd numbering, match the masculine or feminine gender.
The first-month element is a child of the annual element. For the current year (2022, Water Tiger), for example, the first month will be Wood Tiger, and since each element dominates twice, once per gender, the second month will be Wood Hare. Also, the months follow each other according to the child’s relationship so that the third month will be Fire Dragon, the fourth Fire Snake, the fifth Earth Horse, and so on.
In the Tibetan calendar, the month is a defined lunar month of 30 days, where day 15 is the day of the full moon and day 30 is the day of the new moon; the day is numbered from dawn. Given that a synodic month (the time interval between two new moons) has an average duration of 29.5306 days and that the daily deviation of sidereal time amounts to about 4 minutes, it happens that the days lose the coincidence with the calendar. To overcome this drawback, Tibetan astrologers insert “null” or double days in the month count.
Within astrology of the elements, there are two ways to assign the cycle of the twelve animals to the days of the month.
The first system, of Tibetan origin, assigns the Tiger and the number 1 to every first day of an odd month (masculine), the Monkey and the number 7 to every first day of an even month (feminine). The first day’s element is the child of the month’s element; the other days follow the parenting of the child but are not repeated two by two as happens for the calculation of the year and month. With this method, in the presence of “null” days, the numbering is skipped; for example, if day 1 of the first month is Metal Tiger and day 2 is empty, day 3 will be Wood Dragon and not Water Hare, which is cancelled. Similarly, in the case of “double” days, the animal-element calculation is not repeated, so if we have a Wood Horse, on day 13a, day 13b will also be Wood Horse.
The second system, of Chinese origin, provides that the animal-element succession proceeds regularly following the calendar days without considering null days, double days and the animal-element association assigned to each first day of the month. Each association follows the order of the previous one and serves as the basis for the next one. Also, unlike the last method, each element dominates for two consecutive days. The starting point for establishing the succession of animals is given from the first day of spring (corresponding to the Tiger). To fix the day of departure, you need the annual calendar calculated with the methods of Garzì astrology.
A day is divided into twelve periods of two hours each and is counted from dawn. The first time slot is associated with the Hare; the other time slots follow the order of the animal cycle (pdf here). The element of the first time slot (Hare) is the child of the element of the day; the other elements are associated according to the usual order of filiation without repeating them twice.