The Tibetan Ephemeris, Calendar, and Almanac
The Tibetan system of astronomy and astrology is extremely complex. It takes five years to study and master it at the Astro Division of the Tibetan Medical and Astro Institute in Dharamsala, India. Students learn to calculate everything by hand in the traditional manner, on a wooden board covered with soot upon which one writes with a stylus. There is no complete ephemeris compiled in which to look up figures. One of the main aspects of the training is the mathematics involved in all the calculations.
The Kalachakra system, like those of the Hindu traditions, gives formulas for determining "the five planets and five inclusive calendar features." The five planets are Mercury, Venus, Mars, Jupiter, and Saturn. Their positions, as well as those of the sun, moon, and nodes, are calculated for the Tibetan ephemeris according to a mathematical model, as was also the case in the ancient Greek system. Thus, it is unlike Chinese astronomy, which derived the positions and motion of the heavenly bodies based mostly on observation. Chinese mathematics, when sometimes applied, is primarily algebraic.
The ancient Greeks used mainly geometry, namely different geometric proportions, to determine and describe the motion of the planets. The Hindu systems developed the sine function, and thus employ trigonometric rather than solely geometric methods. The calculations in the Tibetan system, on the other hand, involve neither geometric proportions nor trigonometric functions, but are purely arithmetic.
The making of the calendar and almanac entails the five inclusive calendar features: the lunar weekday, the date of the lunar month, the moon's constellation, the combination period, and the action period. The first two are involved in the mechanism through which the lunar and solar calendars are brought into harmony.
Both the Tibetan and Hindu systems present three types of days. A zodiac day is the time it takes for the sun to progress one out of 360 degrees of the zodiac. A solar day, on the other hand, is from dawn to dawn. A lunar date days, correlated with the phases of the moon, is the period the moon takes to travel one-thirtieth the distance between new moon positions in each successive sign in the zodiac. The starting point of lunar date days is calculated by a mathematical process similar to that used for determining the position of the sun and planets. They are counted in a cycle of seven lunar weekdays named for the days of the week, which are also the names of seven of the planets. To correlate the lunar with the solar calendar, these lunar weekdays must be made to fit in with the solar days. This is complicated.
Firstly, the exact new moon does not occur at precisely the same time of day each month. Thus, the moon can start to travel one of these little distances of one-thirtieth of its cycle at any time of the solar day. The period it takes to travel that one-thirtieth the distance of its cycle is called by the day of the week. Thus, the day of the week may start at different times during the solar day.
Furthermore, it takes the moon a different amount of time to cover each of these little one-thirtieth distances, since its speed varies with its own position and with the position of the sun in the zodiac. Consequently, the amount of a lunar weekday that passes between the dawns of two successive solar days varies, because the length of a lunar weekday is likewise variable.
Dates of the lunar month, which constitute the second inclusive calendar feature, are numbered one to thirty and last from dawn to dawn in the manner of solar days. The problem is to determine which date is to be assigned to each day of the week. The solution is not so obvious, because the lunar weekdays – which are what determine the days of the week since they are called Sunday, Monday, and so on – start at and last for different lengths of time.
The rule is that the day of the week is decided by which lunar weekday is occurring at the dawn of the lunar date. For instance, a lunar weekday, such as Monday, may start in the afternoon of the second date of a month and end in the afternoon of the third. Since at the dawn of the third, which here is taken standardly to be at 5 A. M., the lunar weekday is still Monday, the third will be considered a Monday.
A day of the week can never repeat or be skipped. Directly after a Sunday, a Monday must follow, not a second Sunday or a Tuesday. However, sometimes the dawns of two successive dates occur within the same lunar weekday. For instance, the lunar weekday Monday may begin five minutes before the dawn of the third, and the next day, the Tuesday, may begin five minutes after the dawn of the fourth. This would make both the third and the fourth Mondays! There cannot be two Mondays in a row. One of these dates must be omitted. This is why in the Tibetan calendar certain dates of the month are skipped.
On the other hand, sometimes the beginnings of two lunar weekdays occur before the dawn of the next date. For example, if the lunar weekday Monday begins five minutes after the dawn of the third and ends five minutes before the dawn of the fourth, then,by the first rule, the third should be a Sunday and the fourth a Tuesday, and there would be no Monday. Since it is not possible for it to go from a Sunday to a Tuesday without an intervening Monday, one of these dates will have to be doubled in order for one of them to be the Monday. This is why sometimes there are two eighths or two twenty-fifths in a Tibetan month.
To make the lunar calendar further correspond with the solar, a thirteenth month must occasionally be added to the year in the form of an extra doubled or leap-month. The rules for which dates are to be doubled or omitted, and when an extra month is to be added are different in the various Tibetan astro lineages. This is their major difference. The various Hindu calendars also have doubled and omitted dates, and both they and the classical Chinese calendar have doubled months. The rules followed are not the same as those in any of the Tibetan systems.
The third inclusive calendar feature is the moon's constellation. This does not refer to the moon's actual position at the dawn of a lunar date, as calculated by the five planets' techniques, but rather to its successive associated constellation. For any particular lunar date, this is the constellation position the moon would have at the beginning of the lunar weekday occurring at the dawn of that date, according to which that date was assigned its day of the week.
The fourth and fifth features are the combination and the action periods. There are twenty-seven combination periods. Each is the period during which the combined motion of the sun and moon equals one twenty-seventh of a complete zodiac. For any time, then, we derive the combination period by adding the corrected position of the sun to the moon's successive associated constellation position. Thus, each period starts at a different time. They have specific names and interpretations, with some being less auspicious than others are.
Lastly, there are eleven action periods, derived by dividing the thirty lunar dates in a rather unsymmetrical manner. There is no need to give the details here. Each of the eleven action periods has a specific name and likewise some are less favorable than others are for certain activities.